TPTP Problem File: SEV630+1.p
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%------------------------------------------------------------------------------
% File : SEV630+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - HahnTotalExt tot ext trans
% 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 : HahnTotalExt.tot.ext.trans.p [Kal26]
% Status : Theorem
% Rating : 0.83 v9.3.0
% Syntax : Number of formulae : 2560 ( 700 unt; 0 def)
% Number of atoms : 10657 (1515 equ)
% Maximal formula atoms : 82 ( 4 avg)
% Number of connectives : 8168 ( 71 ~; 323 |;1156 &)
% (1017 <=>;5601 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 8 avg)
% Maximal term depth : 21 ( 1 avg)
% Number of predicates : 514 ( 513 usr; 0 prp; 1-18 aty)
% Number of functors : 1107 (1107 usr; 633 con; 0-20 aty)
% Number of variables : 9890 (9400 !; 490 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.list$10308',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2410395___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2410308___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__10312] :
( t(Vvar__1___24Anonymous__10312,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__10313] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__10313)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2410395___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__10312,Vvar__2___24Anonymous__10313)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2410308___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__10312,c_24__fix__10440__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__10313,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$10395',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2410395___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__10399] :
( t(Vvar__1___24Anonymous__10399,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__10400] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__10400)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__10399,Vvar__2___24Anonymous__10400)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2410395___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__10399,c_24__fix__10440__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__10400,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$32099',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__29005___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__32104] :
( t(Vvar__2___24Anonymous__32104,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__32105] :
( t(Vvar__3___24Anonymous__32105,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__32104,Vvar__3___24Anonymous__32105)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2432099___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__32104)),Vvar__3___24Anonymous__32105)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Specif.sumbool$25580',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( c_24__type__24370___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__3 = Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__25592___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__25593___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_2425580___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__let__var__var__7__n__25549__25553__25562___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)) )
| ( Vv__CANONICAL__3 != Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__25594___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__25595___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_2425580___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__let__var__var__7__n__25549__25553__25562___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$36586',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZ0
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2436586___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) )
| ? [Vvar__0___24Anonymous__36587] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36587)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__36587)
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2436586___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__36587) ) )
| ? [Vvar__0___24Anonymous__36588] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36588)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__36588)
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2436586___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__1 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__36588) ) ) ) ) ) ).
fof('$_case_Coq.setoid_ring.Ring_polynom.Pol$27670',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__16)
=> ( ? [Vvar__1___24Anonymous__27673] :
( t(Vvar__1___24Anonymous__27673,Vv__CANONICAL__8)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ( c_24__type__21634___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ( t(Vvar__1___24Anonymous__27673,Vv__CANONICAL__8)
=> ( Vv__CANONICAL__16 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vv__CANONICAL__8,Vvar__1___24Anonymous__27673)
& ( ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__27673),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2427670___24a17(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16) = c_24__let__17__lnum__27437___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15) )
| ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__27673),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2427670___24a17(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16) = happ(happ(Vv__CANONICAL__7,c_24__let__17__lnum__27437___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__16)) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__27676] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__27676)
& ? [Vvar__2___24Anonymous__27677] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__2___24Anonymous__27677)
& Vv__CANONICAL__16 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vv__CANONICAL__8,Vvar__1___24Anonymous__27676,Vvar__2___24Anonymous__27677)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2427670___24a17(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16) = happ(happ(Vv__CANONICAL__7,c_24__let__17__lnum__27437___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__16)) ) )
| ? [Vvar__1___24Anonymous__27680] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__1___24Anonymous__27680)
& ? [Vvar__2___24Anonymous__27681] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__27681)
& ? [Vvar__3___24Anonymous__27682] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__3___24Anonymous__27682)
& Vv__CANONICAL__16 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vv__CANONICAL__8,Vvar__1___24Anonymous__27680,Vvar__2___24Anonymous__27681,Vvar__3___24Anonymous__27682)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2427670___24a17(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16) = happ(happ(Vv__CANONICAL__7,c_24__let__17__lnum__27437___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__16)) ) ) ) ) ) ) ) ).
fof('$_case_Coq.setoid_ring.Ring_polynom.Pol$32643',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( cType___24t(Vv__CANONICAL__13)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__19)
=> ( ? [Vvar__1___24Anonymous__32646] :
( t(Vvar__1___24Anonymous__32646,Vv__CANONICAL__8)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ( c_24__type__32666___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__11)
=> ( cType___24t(Vv__CANONICAL__13)
=> ( t(Vvar__1___24Anonymous__32646,Vv__CANONICAL__8)
=> ( Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vv__CANONICAL__8,Vvar__1___24Anonymous__32646)
& ( ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__32646),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2432643___24a20(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19) = c_24__let__20__lnum__32339___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18) )
| ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__32646),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2432643___24a20(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19) = happ(happ(Vv__CANONICAL__7,c_24__let__20__lnum__32339___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__19)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__32649] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__32649)
& ? [Vvar__2___24Anonymous__32650] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__2___24Anonymous__32650)
& Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vv__CANONICAL__8,Vvar__1___24Anonymous__32649,Vvar__2___24Anonymous__32650)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2432643___24a20(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19) = happ(happ(Vv__CANONICAL__7,c_24__let__20__lnum__32339___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__19)) ) )
| ? [Vvar__1___24Anonymous__32653] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__1___24Anonymous__32653)
& ? [Vvar__2___24Anonymous__32654] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__32654)
& ? [Vvar__3___24Anonymous__32655] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__3___24Anonymous__32655)
& Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vv__CANONICAL__8,Vvar__1___24Anonymous__32653,Vvar__2___24Anonymous__32654,Vvar__3___24Anonymous__32655)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2432643___24a20(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19) = happ(happ(Vv__CANONICAL__7,c_24__let__20__lnum__32339___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__19)) ) ) ) ) ) ) ) ) ).
fof('$_def_$_let_11_subst_l_2928',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__2928___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_30755',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__30758] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30758)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30758)
& c_24__let__16__mkpow__30755___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__30759] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30759)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30759)
& c_24__let__16__mkpow__30755___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__30755___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_lnum_27437',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num] : c_24__let__17__lnum__27437___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num) ).
fof('$_def_$_let_17_mkopp_pow_30756',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__30756___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__30755___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_30757',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__30757___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__30755___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_20_lnum_32339',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num] : c_24__let__20__lnum__32339___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num) ).
fof('$_def_$_let_var_6_p_15957_15960',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15956] : c_24__let__var__6__p__15957__15960___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15956) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15956) ).
fof('$_def_$_let_var_6_p_15959_15961',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15958] : c_24__let__var__6__p__15959__15961___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15958) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15958) ).
fof('$_def_$_let_var_var_7_n_25549_25553_25562',axiom,
! [V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__25546] : c_24__let__var__var__7__n__25549__25553__25562___24a4(V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__25546) = cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,Vvar__2___24Anonymous__25546,V4__x) ).
fof('$_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__4764___24a1(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__955] :
( t(Vvar__1___24Anonymous__955,V0__A)
& ? [Vvar__2___24Anonymous__956] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__956)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__955,Vvar__2___24Anonymous__956)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__955,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__956,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__896] :
( t(Vvar__2___24Anonymous__896,V0__A)
& ? [Vvar__3___24Anonymous__897] :
( t(Vvar__3___24Anonymous__897,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__896,Vvar__3___24Anonymous__897)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__896 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.id',axiom,
! [V0__A,V1__x] : cCoq_2eInit_2eDatatypes_2eid___24a2(V0__A,V1__x) = V1__x ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__945] :
( t(Vvar__1___24Anonymous__945,V0__A)
& ? [Vvar__2___24Anonymous__946] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__946)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__945,Vvar__2___24Anonymous__946)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__946)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.list_rec',axiom,
! [V0__A,V1__P] : cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V0__A,V1__P) = cCoq_2eInit_2eDatatypes_2elist__rect___24a2(V0__A,V1__P) ).
fof('$_def_Coq.Init.Datatypes.list_rect',axiom,
! [V0__A,V1__P,V2__f,V3__f,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__24284___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = V2__f )
| ? [Vvar__1___24Anonymous__24278] :
( t(Vvar__1___24Anonymous__24278,V0__A)
& ? [Vvar__2___24Anonymous__24279] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__24279)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__24278,Vvar__2___24Anonymous__24279)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = happ(happ(happ(V3__f,Vvar__1___24Anonymous__24278),Vvar__2___24Anonymous__24279),cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,Vvar__2___24Anonymous__24279)) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.negb',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_def_Coq.Init.Datatypes.orb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = V1__b2 ) ) ) ).
fof('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__908] :
( t(Vvar__2___24Anonymous__908,V0__A)
& ? [Vvar__3___24Anonymous__909] :
( t(Vvar__3___24Anonymous__909,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__908,Vvar__3___24Anonymous__909)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__909 ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__1927] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1927)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1927)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__1927,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.min',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__1947] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1947)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1947)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__1950] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1950)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1950)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__1947,Vvar__0___24Anonymous__1950)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__1932] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1932)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1932)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__1932,V2__m)) ) ) ) ).
fof('$_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__1925] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1925)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1925)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__1925 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__1935] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1935)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1935)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__1938] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1938)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1938)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__1935,Vvar__0___24Anonymous__1938) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__3407___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__3401] :
( t(Vvar__2__x__3401,V0__A)
& p(happ(V1__P,Vvar__2__x__3401))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__3401)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__3401 ) ) ) ) ).
fof('$_def_Coq.Init.Wf.well_founded',axiom,
! [V0__A,V1__R] :
( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__a) ) ) ).
fof('$_def_Coq.Lists.List.ForallPairs',axiom,
! [V0__A,V1__R,V2__l] :
( cCoq_2eLists_2eList_2eForallPairs___24a3(V0__A,V1__R,V2__l)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__l))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__b,V2__l))
=> p(happ(happ(V1__R,V3__a),V4__b)) ) ) ) ) ) ).
fof('$_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__1890] :
( t(Vvar__1___24Anonymous__1890,V0__A)
& ? [Vvar__2___24Anonymous__1891] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1891)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1890,Vvar__2___24Anonymous__1891)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> ( Vvar__1___24Anonymous__1890 = V2__a
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__1891)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.combine',axiom,
! [V0__A,V1__B,V3__l,V4__l_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__33394] :
( t(Vvar__1___24Anonymous__33394,V0__A)
& ? [Vvar__2___24Anonymous__33395] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33395)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l_27)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33394,Vvar__2___24Anonymous__33395)
& ( ( V4__l_27 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__33406] :
( t(Vvar__1___24Anonymous__33406,V1__B)
& ? [Vvar__2___24Anonymous__33407] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__33407)
& V4__l_27 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__33406,Vvar__2___24Anonymous__33407)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__1___24Anonymous__33394,Vvar__1___24Anonymous__33406),cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,Vvar__2___24Anonymous__33395,Vvar__2___24Anonymous__33407)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.concat',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A))
& cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__1902] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__1___24Anonymous__1902)
& ? [Vvar__2___24Anonymous__1903] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__1903)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__1___24Anonymous__1902,Vvar__2___24Anonymous__1903)
& cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__1___24Anonymous__1902,cCoq_2eLists_2eList_2econcat___24a2(V0__A,Vvar__2___24Anonymous__1903)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.count_occ',axiom,
! [V0__A,V1__eq__dec,V3__l,V4__x] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__25545] :
( t(Vvar__1___24Anonymous__25545,V0__A)
& ? [Vvar__2___24Anonymous__25546] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__25546)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__25545,Vvar__2___24Anonymous__25546)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_2425580___24a5(V0__A,V1__eq__dec,V4__x,Vvar__1___24Anonymous__25545,Vvar__2___24Anonymous__25546) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.existsb',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__33352] :
( t(Vvar__1___24Anonymous__33352,V0__A)
& ? [Vvar__2___24Anonymous__33353] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33353)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33352,Vvar__2___24Anonymous__33353)
& cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(happ(V1__f,Vvar__1___24Anonymous__33352),cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__33353)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.filter',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__28181] :
( t(Vvar__1___24Anonymous__28181,V0__A)
& ? [Vvar__2___24Anonymous__28182] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28182)
& ( cType___24t(V0__A)
=> ( c_24__type__28187___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__28181,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28181,Vvar__2___24Anonymous__28182)
& ( ( happ(V1__f,Vvar__1___24Anonymous__28181) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28181,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__28182)) )
| ( happ(V1__f,Vvar__1___24Anonymous__28181) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__28182) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.find',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__33377] :
( t(Vvar__1___24Anonymous__33377,V0__A)
& ? [Vvar__2___24Anonymous__33378] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33378)
& ( cType___24t(V0__A)
=> ( c_24__type__28187___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__33377,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33377,Vvar__2___24Anonymous__33378)
& ( ( happ(V1__f,Vvar__1___24Anonymous__33377) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__33377) )
| ( happ(V1__f,Vvar__1___24Anonymous__33377) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,Vvar__2___24Anonymous__33378) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.firstn',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__0___24Anonymous__28219] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28219)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28219)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__28226] :
( t(Vvar__1___24Anonymous__28226,V0__A)
& ? [Vvar__2___24Anonymous__28227] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28227)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28226,Vvar__2___24Anonymous__28227)
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28226,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,Vvar__0___24Anonymous__28219,Vvar__2___24Anonymous__28227)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.flat_map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__33232] :
( t(Vvar__1___24Anonymous__33232,V0__A)
& ? [Vvar__2___24Anonymous__33233] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33233)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33232,Vvar__2___24Anonymous__33233)
& cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__33232),cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__33233)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_left',axiom,
! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
| ? [Vvar__1___24Anonymous__33292] :
( t(Vvar__1___24Anonymous__33292,V1__B)
& ? [Vvar__2___24Anonymous__33293] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__33293)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__33292,Vvar__2___24Anonymous__33293)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__33293,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__33292)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_right',axiom,
! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
| ? [Vvar__1___24Anonymous__33321] :
( t(Vvar__1___24Anonymous__33321,V1__B)
& ? [Vvar__2___24Anonymous__33322] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__33322)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__33321,Vvar__2___24Anonymous__33322)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__33321),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__33322)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.forallb',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__1___24Anonymous__33366] :
( t(Vvar__1___24Anonymous__33366,V0__A)
& ? [Vvar__2___24Anonymous__33367] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33367)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33366,Vvar__2___24Anonymous__33367)
& cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eandb___24a2(happ(V1__f,Vvar__1___24Anonymous__33366),cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__33367)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd',axiom,
! [V0__A,V1__default,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = V1__default )
| ? [Vvar__1___24Anonymous__33140] :
( t(Vvar__1___24Anonymous__33140,V0__A)
& ? [Vvar__2___24Anonymous__33141] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33141)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33140,Vvar__2___24Anonymous__33141)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__33140 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd_error',axiom,
! [V0__A,V1__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__33151] :
( t(Vvar__1___24Anonymous__33151,V0__A)
& ? [Vvar__2___24Anonymous__33152] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33152)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33151,Vvar__2___24Anonymous__33152)
& cCoq_2eLists_2eList_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__33151) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.incl',axiom,
! [V0__A,V1__l,V2__m] :
( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m))
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m)) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__24056] :
( t(Vvar__1___24Anonymous__24056,V0__A)
& ? [Vvar__2___24Anonymous__24057] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__24057)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__24057)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__24056,Vvar__2___24Anonymous__24057)
& ( ( Vvar__2___24Anonymous__24057 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__24056 )
| ? [Vvar__1___24Anonymous__24068] :
( t(Vvar__1___24Anonymous__24068,V0__A)
& ? [Vvar__2___24Anonymous__24069] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__24069)
& Vvar__2___24Anonymous__24057 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__24068,Vvar__2___24Anonymous__24069)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__24057,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.lel',axiom,
! [V0__A,V1__l,V2__m] :
( cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V2__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__m)) ) ).
fof('$_def_Coq.Lists.List.map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__25623] :
( t(Vvar__1___24Anonymous__25623,V0__A)
& ? [Vvar__2___24Anonymous__25624] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__25624)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__25623,Vvar__2___24Anonymous__25624)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__25623),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__25624)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__28105] :
( t(Vvar__1___24Anonymous__28105,V0__A)
& ? [Vvar__2___24Anonymous__28106] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28106)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28105,Vvar__2___24Anonymous__28106)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__28105 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__28108] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28108)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28108)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__28115] :
( t(Vvar__1___24Anonymous__28115,V0__A)
& ? [Vvar__2___24Anonymous__28116] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28116)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28115,Vvar__2___24Anonymous__28116)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__28108,Vvar__2___24Anonymous__28116,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_default',axiom,
! [V0__A,V1__default,V2__l,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ? [Vvar__1___24Anonymous__33191] :
( t(Vvar__1___24Anonymous__33191,V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__33191)
& cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V1__default,V2__l,V3__n) = Vvar__1___24Anonymous__33191 )
| ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V1__default,V2__l,V3__n) = V1__default ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_error',axiom,
! [V0__A,V2__l,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__28130] :
( t(Vvar__1___24Anonymous__28130,V0__A)
& ? [Vvar__2___24Anonymous__28131] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28131)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28130,Vvar__2___24Anonymous__28131)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__28130) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__28133] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28133)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28133)
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__28140] :
( t(Vvar__1___24Anonymous__28140,V0__A)
& ? [Vvar__2___24Anonymous__28141] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28141)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28140,Vvar__2___24Anonymous__28141)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,Vvar__2___24Anonymous__28141,Vvar__0___24Anonymous__28133) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_ok',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__33168] :
( t(Vvar__1___24Anonymous__33168,V0__A)
& ? [Vvar__2___24Anonymous__33169] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33169)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33168,Vvar__2___24Anonymous__33169)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__33171] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33171)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33171)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__33178] :
( t(Vvar__1___24Anonymous__33178,V0__A)
& ? [Vvar__2___24Anonymous__33179] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33179)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33178,Vvar__2___24Anonymous__33179)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,Vvar__0___24Anonymous__33171,Vvar__2___24Anonymous__33179,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.removelast',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_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__24080] :
( t(Vvar__1___24Anonymous__24080,V0__A)
& ? [Vvar__2___24Anonymous__24081] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__24081)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__24081)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__24080,Vvar__2___24Anonymous__24081)
& ( ( Vvar__2___24Anonymous__24081 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__24092] :
( t(Vvar__1___24Anonymous__24092,V0__A)
& ? [Vvar__2___24Anonymous__24093] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__24093)
& Vvar__2___24Anonymous__24081 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__24092,Vvar__2___24Anonymous__24093)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__24080,cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,Vvar__2___24Anonymous__24081)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.rev',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__33205] :
( t(Vvar__1___24Anonymous__33205,V0__A)
& ? [Vvar__2___24Anonymous__33206] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33206)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33205,Vvar__2___24Anonymous__33206)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,Vvar__2___24Anonymous__33206),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33205,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.rev\'',axiom,
! [V0__A,V1__l] : cCoq_2eLists_2eList_2erev_27___24a2(V0__A,V1__l) = cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ).
fof('$_def_Coq.Lists.List.rev_append',axiom,
! [V0__A,V2__l,V3__l_27] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V2__l,V3__l_27) = V3__l_27 )
| ? [Vvar__1___24Anonymous__33213] :
( t(Vvar__1___24Anonymous__33213,V0__A)
& ? [Vvar__2___24Anonymous__33214] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33214)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33213,Vvar__2___24Anonymous__33214)
& cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V2__l,V3__l_27) = cCoq_2eLists_2eList_2erev__append___24a3(V0__A,Vvar__2___24Anonymous__33214,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33213,V3__l_27)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.skipn',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = V3__l )
| ? [Vvar__0___24Anonymous__28235] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28235)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28235)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__28242] :
( t(Vvar__1___24Anonymous__28242,V0__A)
& ? [Vvar__2___24Anonymous__28243] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28243)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28242,Vvar__2___24Anonymous__28243)
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = cCoq_2eLists_2eList_2eskipn___24a3(V0__A,Vvar__0___24Anonymous__28235,Vvar__2___24Anonymous__28243) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.tl',axiom,
! [V0__A,V1__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__33160] :
( t(Vvar__1___24Anonymous__33160,V0__A)
& ? [Vvar__2___24Anonymous__33161] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33161)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33160,Vvar__2___24Anonymous__33161)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__33161 ) ) ) ) ) ).
fof('$_def_Coq.Lists.ListDec.decidable_eq',axiom,
! [V0__A] :
( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
<=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__28300___24a3(V0__A,V1__x,V2__y)) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.equivlistA',axiom,
! [V0__A,V1__eqA,V2__l,V3__l_27] :
( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l)
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l_27) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.inclA',axiom,
! [V0__A,V1__eqA,V2__l,V3__l_27] :
( cCoq_2eLists_2eSetoidList_2einclA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l_27) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.removeA',axiom,
! [V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__35853___24t(V0__A,V1__eqA,V1__eqA)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__35829] :
( t(Vvar__1___24Anonymous__35829,V0__A)
& ? [Vvar__2___24Anonymous__35830] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__35830)
& ( cType___24t(V0__A)
=> ( c_24__type__35862___24t(V0__A,V1__eqA,V1__eqA)
=> ( c_24__type__35871___24t(V0__A,V1__eqA,V2__eqA__dec)
=> ( t(V4__x,V0__A)
=> ( t(Vvar__1___24Anonymous__35829,V0__A)
=> ( V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35829,Vvar__2___24Anonymous__35830)
& ( ( p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__35829))
& happ(happ(V2__eqA__dec,V4__x),Vvar__1___24Anonymous__35829) = cCoq_2eInit_2eSpecif_2eleft___24a2(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__35829),c_24__prop__35874___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__35829))
& cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l) = cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,Vvar__2___24Anonymous__35830) )
| ( ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__35829))
& happ(happ(V2__eqA__dec,V4__x),Vvar__1___24Anonymous__35829) = cCoq_2eInit_2eSpecif_2eright___24a2(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__35829),c_24__prop__35875___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__35829))
& cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35829,cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,Vvar__2___24Anonymous__35830)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V6__z)))) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose2',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> ! [V7__z_27] :
( t(V7__z_27,V1__B)
=> ( p(happ(happ(V2__eqB,V6__z),V7__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V7__z_27)))) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V7__z)))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr2',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ! [V8__z_27] :
( t(V8__z_27,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> ( p(happ(happ(V2__eqB,V7__z),V8__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V8__z_27)))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.Logic.FinFun.Full',axiom,
! [V0__A,V1__l] :
( cCoq_2eLogic_2eFinFun_2eFull___24a2(V0__A,V1__l)
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V1__l)) ) ) ).
fof('$_def_Coq.Logic.FinFun.Injective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eInjective___24a3(V0__A,V1__B,V2__f)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( happ(V2__f,V3__x) = happ(V2__f,V4__y)
=> V3__x = V4__y ) ) ) ) ).
fof('$_def_Coq.Logic.FinFun.Listing',axiom,
! [V0__A,V1__l] :
( cCoq_2eLogic_2eFinFun_2eListing___24a2(V0__A,V1__l)
<=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
& cCoq_2eLogic_2eFinFun_2eFull___24a2(V0__A,V1__l) ) ) ).
fof('$_def_Coq.Logic.FinFun.Surjective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eSurjective___24a3(V0__A,V1__B,V2__f)
<=> ! [V3__y] :
( t(V3__y,V1__B)
=> ? [V4__x] :
( t(V4__x,V0__A)
& happ(V2__f,V4__x) = V3__y ) ) ) ).
fof('$_def_Coq.Logic.FinFun.bFun',axiom,
! [V0__n,V1__f] :
( cCoq_2eLogic_2eFinFun_2ebFun___24a2(V0__n,V1__f)
<=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__x,V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(happ(V1__f,V2__x),V0__n) ) ) ) ).
fof('$_def_Coq.Logic.FinFun.bInjective',axiom,
! [V0__n,V1__f] :
( cCoq_2eLogic_2eFinFun_2ebInjective___24a2(V0__n,V1__f)
<=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__x,V0__n)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V3__y,V0__n)
=> ( happ(V1__f,V2__x) = happ(V1__f,V3__y)
=> V2__x = V3__y ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.FinFun.bSurjective',axiom,
! [V0__n,V1__f] :
( cCoq_2eLogic_2eFinFun_2ebSurjective___24a2(V0__n,V1__f)
<=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__y)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__y,V0__n)
=> ? [V4__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__x)
& cCoq_2eInit_2ePeano_2elt___24a2(V4__x,V0__n)
& happ(V1__f,V4__x) = V2__y ) ) ) ) ).
fof('$_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__4662___24a1(V0__A)) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__23463] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23463)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23463)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__23466] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23466)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23466)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__23463,Vvar__0___24Anonymous__23466)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__24109] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24109)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24109)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__24110] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24110)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24110)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__24113] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24113)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24113)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__24110,Vvar__0___24Anonymous__24113) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__23447] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23447)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23447)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__23450] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23450)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23450)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__23447,Vvar__0___24Anonymous__23450)) ) ) ) ) ) ) ) ).
fof('$_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__4585] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4585)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4585)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__4585)) ) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__24127] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24127)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24127)
& ( ? [Vvar__0___24Anonymous__24131] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24131)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24131)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__24126__1__add__carry___24a2(Vvar__0___24Anonymous__24127,Vvar__0___24Anonymous__24131)) )
| ? [Vvar__0___24Anonymous__24132] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24132)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24132)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__24127,Vvar__0___24Anonymous__24132)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__24127)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__24133] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24133)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24133)
& ( ? [Vvar__0___24Anonymous__24137] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24137)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24137)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__24133,Vvar__0___24Anonymous__24137)) )
| ? [Vvar__0___24Anonymous__24138] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24138)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24138)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__24133,Vvar__0___24Anonymous__24138)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24133) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__24139] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24139)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24139)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__24139)) )
| ? [Vvar__0___24Anonymous__24140] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24140)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24140)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24140) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__34269] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34269)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34269)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34269)) )
| ? [Vvar__0___24Anonymous__34270] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34270)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34270)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__34270)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__26015] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26015)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__26015)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__26015 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__26011] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26011)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26011)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__26011)) )
| ? [Vvar__0___24Anonymous__26012] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26012)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26012)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26012) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.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('$_def_Coq.Relations.Relation_Definitions.commut',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2ecommut___24a3(V0__A,V1__R1,V2__R2)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R1,V4__y),V3__x))
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V2__R2,V6__z),V4__y))
=> cCoq_2eInit_2eLogic_2eex2___24a3(V0__A,c_24__lam__2128___24a3(V0__A,V2__R2,V3__x),c_24__lam__2132___24a3(V0__A,V1__R1,V6__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.equiv',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2(V0__A,V1__R)
<=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.inclusion',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__R1,V2__R2)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R1,V3__x),V4__y))
=> p(happ(happ(V2__R2,V3__x),V4__y)) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.reflexive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__83___24a1(V0__A) ).
fof('$_def_Coq.Relations.Relation_Definitions.same_relation',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__R1,V2__R2)
<=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__R1,V2__R2)
& cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__R2,V1__R1) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.symmetric',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> p(happ(happ(V1__R,V3__y),V2__x)) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.transitive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Operators.transp',axiom,
! [V0__A,V1__R,V2__x,V3__y] :
( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4(V0__A,V1__R,V2__x,V3__y)
<=> p(happ(happ(V1__R,V3__y),V2__x)) ) ).
fof('$_def_Coq.Relations.Relation_Operators.union',axiom,
! [V0__A,V1__R1,V2__R2,V3__x,V4__y] :
( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5(V0__A,V1__R1,V2__R2,V3__x,V4__y)
<=> ( p(happ(happ(V1__R1,V3__x),V4__y))
| p(happ(happ(V2__R2,V3__x),V4__y)) ) ) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Sets.Relations_1.Transitive',axiom,
! [V0__U,V1__R] :
( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__U,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ! [V4__z] :
( t(V4__z,V0__U)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.to_list',axiom,
! [V0__A,V1__n,V2__v] : cCoq_2eVectors_2eVectorDef_2eto__list___24a3(V0__A,V1__n,V2__v) = c_24__fix__34226__v__CANONICAL__2___24a5(V0__A,V1__n,V1__n,V2__v,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ).
fof('$_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.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__5016] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5016)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5016)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__5020] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5020)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5020)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__5016,Vvar__0___24Anonymous__5020)) )
| ? [Vvar__0___24Anonymous__5021] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5021)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5021)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__5016,Vvar__0___24Anonymous__5021) ) ) ) ) )
| ? [Vvar__0___24Anonymous__5022] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5022)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5022)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__5026] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5026)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5026)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__5026,Vvar__0___24Anonymous__5022) )
| ? [Vvar__0___24Anonymous__5027] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5027)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5027)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__5022,Vvar__0___24Anonymous__5027)) ) ) ) ) ) ) ) ).
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__26088] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26088)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26088)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__26089] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26089)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26089)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__26090] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26090)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26090)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__26094] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26094)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26094)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__26090,Vvar__0___24Anonymous__26094) )
| ? [Vvar__0___24Anonymous__26095] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26095)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26095)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__26096] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26096)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26096)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__26100] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26100)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26100)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__26101] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26101)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26101)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__26096,Vvar__0___24Anonymous__26101)) ) ) ) ) ) ) ) ).
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__5036] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5036)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5036)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__5040] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5040)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5040)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5036,Vvar__0___24Anonymous__5040)) )
| ? [Vvar__0___24Anonymous__5041] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5041)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5041)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5036,Vvar__0___24Anonymous__5041)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__5042] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5042)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5042)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__5046] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5046)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5046)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5042,Vvar__0___24Anonymous__5046)) )
| ? [Vvar__0___24Anonymous__5047] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5047)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5047)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5042,Vvar__0___24Anonymous__5047)) ) ) ) ) ) ) ) ).
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__24182] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24182)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__24182)
& 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__24182)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__5031] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5031)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5031)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5031) )
| ? [Vvar__0___24Anonymous__5032] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5032)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5032)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5032) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zcomplements.Zlength',axiom,
cCoq_2eZArith_2eZcomplements_2eZlength = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('$_def_Coq.ZArith.Zcomplements.Zlength_aux',axiom,
! [V1__acc,V2__A,V3__l] :
( cType___24t(V2__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V2__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__A)
& cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V1__acc,V2__A,V3__l) = V1__acc )
| ? [Vvar__1___24Anonymous__34257] :
( t(Vvar__1___24Anonymous__34257,V2__A)
& ? [Vvar__2___24Anonymous__34258] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V2__A,Vvar__2___24Anonymous__34258)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__A,Vvar__1___24Anonymous__34257,Vvar__2___24Anonymous__34258)
& cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V1__acc,V2__A,V3__l) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__acc),V2__A,Vvar__2___24Anonymous__34258) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_conj',axiom,
! [V1__A,V2__eval,V3__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__23329] :
( t(Vvar__1___24Anonymous__23329,V1__A)
& ? [Vvar__2___24Anonymous__23330] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__23330)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__23330)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__23329,Vvar__2___24Anonymous__23330)
& ( ( Vvar__2___24Anonymous__23330 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(happ(V2__eval,Vvar__1___24Anonymous__23329)) ) )
| ? [Vvar__1___24Anonymous__23341] :
( t(Vvar__1___24Anonymous__23341,V1__A)
& ? [Vvar__2___24Anonymous__23342] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__23342)
& Vvar__2___24Anonymous__23330 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__23341,Vvar__2___24Anonymous__23342)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__23329))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__23330) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__33573] :
( t(Vvar__1___24Anonymous__33573,V1__A)
& ? [Vvar__2___24Anonymous__33574] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__33574)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__33573,Vvar__2___24Anonymous__33574)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__33573))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__33574,V4__goal) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.NFormula',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C) = cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_def_Coq.micromega.Tauto.clause',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.cnf',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.cons_id',axiom,
! [V0__AF,V1__id,V2__l] :
( cType___24t(V0__AF)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__AF,V1__id)
=> ( ? [Vvar__1___24Anonymous__34121] :
( t(Vvar__1___24Anonymous__34121,V0__AF)
& V1__id = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__AF,Vvar__1___24Anonymous__34121)
& cCoq_2emicromega_2eTauto_2econs__id___24a3(V0__AF,V1__id,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__AF,Vvar__1___24Anonymous__34121,V2__l) )
| ( V1__id = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__AF)
& cCoq_2emicromega_2eTauto_2econs__id___24a3(V0__AF,V1__id,V2__l) = V2__l ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.eval_tt',axiom,
! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__tt] :
( cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__tt)
<=> p(happ(happ(V3__eval_27,V4__env),cCoq_2eInit_2eDatatypes_2efst___24a3(V1__Term_27,V2__Annot,V5__tt))) ) ).
fof('$_def_Coq.micromega.ZMicromega.make_conj',axiom,
cCoq_2emicromega_2eZMicromega_2emake__conj = cCoq_2emicromega_2eRefl_2emake__conj ).
fof('$_def_Coq.micromega.ZMicromega.make_impl',axiom,
cCoq_2emicromega_2eZMicromega_2emake__impl = cCoq_2emicromega_2eRefl_2emake__impl ).
fof('$_def_Coq.setoid_ring.BinList.jump',axiom,
! [V0__A,V2__p,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( ? [Vvar__0___24Anonymous__32277] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32277)
& V2__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32277)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__32277,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__32277,cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l))) )
| ? [Vvar__0___24Anonymous__32278] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32278)
& V2__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32278)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__32278,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__32278,V3__l)) )
| ( V2__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.BinList.nth',axiom,
! [V0__A,V1__default,V3__p,V4__l] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__32285] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32285)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32285)
& cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,V3__p,V4__l) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,Vvar__0___24Anonymous__32285,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__32285,cCoq_2eLists_2eList_2etl___24a2(V0__A,V4__l))) )
| ? [Vvar__0___24Anonymous__32286] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32286)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32286)
& cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,V3__p,V4__l) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,Vvar__0___24Anonymous__32286,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__32286,V4__l)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,V3__p,V4__l) = cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V4__l) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.FEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V9__C)
=> ( cType___24t(V11__Cpow)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,V16__pe)
=> ( ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V1__rO )
| ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__24411] :
( t(Vvar__1___24Anonymous__24411,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__24411)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V10__phi,Vvar__1___24Anonymous__24411) )
| ? [Vvar__1___24Anonymous__24413] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__24413)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__24413)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__24413,V15__l) )
| ? [Vvar__1___24Anonymous__24415] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24415)
& ? [Vvar__2___24Anonymous__24416] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__24416)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__24415,Vvar__2___24Anonymous__24416)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24415)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__24416)) ) )
| ? [Vvar__1___24Anonymous__24419] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24419)
& ? [Vvar__2___24Anonymous__24420] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__24420)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__24419,Vvar__2___24Anonymous__24420)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24419)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__24420)) ) )
| ? [Vvar__1___24Anonymous__24423] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24423)
& ? [Vvar__2___24Anonymous__24424] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__24424)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__24423,Vvar__2___24Anonymous__24424)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24423)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__24424)) ) )
| ? [Vvar__1___24Anonymous__24427] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24427)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__24427)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24427)) )
| ? [Vvar__1___24Anonymous__24429] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24429)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__24429)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V8__rinv,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24429)) )
| ? [Vvar__1___24Anonymous__24431] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24431)
& ? [Vvar__2___24Anonymous__24432] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__24432)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__24431,Vvar__2___24Anonymous__24432)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V7__rdiv,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24431)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__24432)) ) )
| ? [Vvar__1___24Anonymous__24435] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24435)
& ? [Vvar__2___24Anonymous__24436] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__24436)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__24435,Vvar__2___24Anonymous__24436)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V13__rpow,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24435)),happ(V12__Cp__phi,Vvar__2___24Anonymous__24436)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__25198] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__25198)
& ? [Vvar__2___24Anonymous__25199] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__25199)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__25198,Vvar__2___24Anonymous__25199)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__25198),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__25199,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__e,V14__e_27] :
( cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__e,V14__e_27)
<=> ! [V15__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V15__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V15__l,V13__e)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V15__l,V14__e_27))) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.PCond',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__le)
=> ( ( V15__le = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__24738] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__24738)
& ? [Vvar__2___24Anonymous__24739] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__24739)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__24739)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__24738,Vvar__2___24Anonymous__24739)
& ( ( Vvar__2___24Anonymous__24739 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__24738)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__24750] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__24750)
& ? [Vvar__2___24Anonymous__24751] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__24751)
& Vvar__2___24Anonymous__24739 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__24750,Vvar__2___24Anonymous__24751)
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ( ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__24738)),V1__rO))
& cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__24739) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.condition',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__24725] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__24725)
& ? [Vvar__2__denum__24726] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__24726)
& ? [Vvar__3__condition__24727] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__24727)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__24725,Vvar__2__denum__24726,Vvar__3__condition__24727)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__24727 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__24716] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__24716)
& ? [Vvar__2__denum__24717] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__24717)
& ? [Vvar__3__condition__24718] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__24718)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__24716,Vvar__2__denum__24717,Vvar__3__condition__24718)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__24717 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.display_linear',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num,V16__den] : cCoq_2esetoid__ring_2eField__theory_2edisplay__linear___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num,V16__den) = c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2427670___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num,V16__den) ).
fof('$_def_Coq.setoid_ring.Field_theory.display_pow_linear',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den] : cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear___24a20(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den) = c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2432643___24a20(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den) ).
fof('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__24705] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__24705)
& ? [Vvar__2__denum__24706] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__24706)
& ? [Vvar__3__condition__24707] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__24707)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__24705,Vvar__2__denum__24706,Vvar__3__condition__24707)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__24705 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_common',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__27153] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__27153)
& ? [Vvar__2__rsplit__common__27154] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__27154)
& ? [Vvar__3__rsplit__right__27155] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__27155)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__27153,Vvar__2__rsplit__common__27154,Vvar__3__rsplit__right__27155)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,V1__r) = Vvar__2__rsplit__common__27154 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__27142] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__27142)
& ? [Vvar__2__rsplit__common__27143] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__27143)
& ? [Vvar__3__rsplit__right__27144] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__27144)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__27142,Vvar__2__rsplit__common__27143,Vvar__3__rsplit__right__27144)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,V1__r) = Vvar__1__rsplit__left__27142 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__27162] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__27162)
& ? [Vvar__2__rsplit__common__27163] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__27163)
& ? [Vvar__3__rsplit__right__27164] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__27164)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__27162,Vvar__2__rsplit__common__27163,Vvar__3__rsplit__right__27164)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,V1__r) = Vvar__3__rsplit__right__27164 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nopp',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNopp = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nsub',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNsub = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
=> ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
| ? [Vvar__0___24Anonymous__33097] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33097)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__33097)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__33097) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__25362] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25362)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25362)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__25362) )
| ? [Vvar__0___24Anonymous__25363] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25363)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25363)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__25363)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Mphi',axiom,
! [V0__R,V1__rO,V2__rI,V3__rmul,V5__l,V6__M] :
( cType___24t(V0__R)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V6__M)
=> ( ( V6__M = cCoq_2esetoid__ring_2eRing__polynom_2emon0
& cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,V5__l,V6__M) = V2__rI )
| ? [Vvar__0___24Anonymous__28930] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28930)
& ? [Vvar__1___24Anonymous__28931] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__28931)
& V6__M = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__28930,Vvar__1___24Anonymous__28931)
& cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,V5__l,V6__M) = cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__R,Vvar__0___24Anonymous__28930,V5__l),Vvar__1___24Anonymous__28931) ) )
| ? [Vvar__0___24Anonymous__28933] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28933)
& ? [Vvar__1___24Anonymous__28934] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__28934)
& V6__M = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__28933,Vvar__1___24Anonymous__28934)
& cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,V5__l,V6__M) = happ(happ(V3__rmul,cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,cCoq_2eLists_2eList_2etl___24a2(V0__R,V5__l),Vvar__1___24Anonymous__28934)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V3__rmul,cCoq_2eLists_2eList_2ehd___24a3(V0__R,V1__rO,V5__l),Vvar__0___24Anonymous__28933)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.P0',axiom,
! [V0__C,V1__cO] : cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V0__C,V1__cO) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,V1__cO) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.P1',axiom,
! [V0__C,V1__cI] : cCoq_2esetoid__ring_2eRing__polynom_2eP1___24a2(V0__C,V1__cI) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,V1__cI) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V7__C)
=> ( cType___24t(V9__Cpow)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,V14__pe)
=> ( ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V1__rO )
| ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__29210] :
( t(Vvar__1___24Anonymous__29210,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__29210)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V8__phi,Vvar__1___24Anonymous__29210) )
| ? [Vvar__1___24Anonymous__29212] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__29212)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__29212)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__29212,V13__l) )
| ? [Vvar__1___24Anonymous__29214] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__29214)
& ? [Vvar__2___24Anonymous__29215] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__29215)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__29214,Vvar__2___24Anonymous__29215)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__29214)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__29215)) ) )
| ? [Vvar__1___24Anonymous__29218] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__29218)
& ? [Vvar__2___24Anonymous__29219] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__29219)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__29218,Vvar__2___24Anonymous__29219)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__29218)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__29219)) ) )
| ? [Vvar__1___24Anonymous__29222] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__29222)
& ? [Vvar__2___24Anonymous__29223] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__29223)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__29222,Vvar__2___24Anonymous__29223)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__29222)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__29223)) ) )
| ? [Vvar__1___24Anonymous__29226] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__29226)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__29226)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__29226)) )
| ? [Vvar__1___24Anonymous__29228] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__29228)
& ? [Vvar__2___24Anonymous__29229] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__29229)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__29228,Vvar__2___24Anonymous__29229)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V11__rpow,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__29228)),happ(V10__Cp__phi,Vvar__2___24Anonymous__29229)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Peq',axiom,
! [V0__C,V1__ceqb,V3__P,V4__P_27] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V3__P)
=> ( ? [Vvar__1___24Anonymous__2538] :
( t(Vvar__1___24Anonymous__2538,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__2538)
& ( ? [Vvar__1___24Anonymous__2548] :
( t(Vvar__1___24Anonymous__2548,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__2548)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__2538),Vvar__1___24Anonymous__2548) )
| ? [Vvar__1___24Anonymous__2550] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2550)
& ? [Vvar__2___24Anonymous__2551] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__2551)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__2550,Vvar__2___24Anonymous__2551)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__2554] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__2554)
& ? [Vvar__2___24Anonymous__2555] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2555)
& ? [Vvar__3___24Anonymous__2556] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__2556)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__2554,Vvar__2___24Anonymous__2555,Vvar__3___24Anonymous__2556)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__2561] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2561)
& ? [Vvar__2___24Anonymous__2562] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__2562)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__2561,Vvar__2___24Anonymous__2562)
& ( ? [Vvar__1___24Anonymous__2582] :
( t(Vvar__1___24Anonymous__2582,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__2582)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__2584] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2584)
& ? [Vvar__2___24Anonymous__2585] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__2585)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2561)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2584)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__2584,Vvar__2___24Anonymous__2585)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__2561,Vvar__1___24Anonymous__2584) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__2562,Vvar__2___24Anonymous__2585) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__2561,Vvar__1___24Anonymous__2584) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__2561,Vvar__1___24Anonymous__2584) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__2590] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__2590)
& ? [Vvar__2___24Anonymous__2591] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2591)
& ? [Vvar__3___24Anonymous__2592] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__2592)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__2590,Vvar__2___24Anonymous__2591,Vvar__3___24Anonymous__2592)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__2597] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__2597)
& ? [Vvar__2___24Anonymous__2598] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2598)
& ? [Vvar__3___24Anonymous__2599] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__2599)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__2597,Vvar__2___24Anonymous__2598,Vvar__3___24Anonymous__2599)
& ( ? [Vvar__1___24Anonymous__2632] :
( t(Vvar__1___24Anonymous__2632,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__2632)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__2634] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2634)
& ? [Vvar__2___24Anonymous__2635] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__2635)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__2634,Vvar__2___24Anonymous__2635)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__2638] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__2638)
& ? [Vvar__2___24Anonymous__2639] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2639)
& ? [Vvar__3___24Anonymous__2640] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__2640)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2598)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2639)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__2638,Vvar__2___24Anonymous__2639,Vvar__3___24Anonymous__2640)
& ( ( cType___24t(V0__C)
=> ( c_24__type__2653___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__2597)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__2638)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__2598,Vvar__2___24Anonymous__2639) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__2597,Vvar__1___24Anonymous__2638) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__3___24Anonymous__2599,Vvar__3___24Anonymous__2640) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__2597,Vvar__1___24Anonymous__2638) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__2598,Vvar__2___24Anonymous__2639) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__2598,Vvar__2___24Anonymous__2639) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pequiv',axiom,
! [V0__R,V1__rO,V2__radd,V3__rmul,V4__req,V5__C,V6__phi,V7__P,V8__Q] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePequiv___24a9(V0__R,V1__rO,V2__radd,V3__rmul,V4__req,V5__C,V6__phi,V7__P,V8__Q)
<=> ! [V9__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V9__l)
=> p(happ(happ(V4__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V5__C,V6__phi,V9__l,V7__P)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V5__C,V6__phi,V9__l,V8__Q))) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pphi',axiom,
! [V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,V7__l,V8__P] :
( cType___24t(V0__R)
=> ( cType___24t(V4__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,V8__P)
=> ( ? [Vvar__1___24Anonymous__28862] :
( t(Vvar__1___24Anonymous__28862,V4__C)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V4__C,Vvar__1___24Anonymous__28862)
& cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,V7__l,V8__P) = happ(V5__phi,Vvar__1___24Anonymous__28862) )
| ? [Vvar__1___24Anonymous__28864] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__28864)
& ? [Vvar__2___24Anonymous__28865] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__2___24Anonymous__28865)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V4__C,Vvar__1___24Anonymous__28864,Vvar__2___24Anonymous__28865)
& cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,V7__l,V8__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__R,Vvar__1___24Anonymous__28864,V7__l),Vvar__2___24Anonymous__28865) ) )
| ? [Vvar__1___24Anonymous__28868] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__1___24Anonymous__28868)
& ? [Vvar__2___24Anonymous__28869] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__28869)
& ? [Vvar__3___24Anonymous__28870] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__3___24Anonymous__28870)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V4__C,Vvar__1___24Anonymous__28868,Vvar__2___24Anonymous__28869,Vvar__3___24Anonymous__28870)
& cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,V7__l,V8__P) = happ(happ(V2__radd,happ(happ(V3__rmul,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,V7__l,Vvar__1___24Anonymous__28868)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V3__rmul,cCoq_2eLists_2eList_2ehd___24a3(V0__R,V1__rO,V7__l),Vvar__2___24Anonymous__28869))),cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,cCoq_2eLists_2eList_2etl___24a2(V0__R,V7__l),Vvar__3___24Anonymous__28870)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V15__get__sign,c_24__let__16__mkpow__30755___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__30756___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__30757___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),V15__lpe)
=> ( ( V15__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)))
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__30215] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__30215)
& ? [Vvar__2___24Anonymous__30216] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__30216)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__30215)
=> ( V15__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__1___24Anonymous__30215,Vvar__2___24Anonymous__30216)
& ? [Vvar__2___24Anonymous__30234] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__2___24Anonymous__30234)
& ? [Vvar__3___24Anonymous__30235] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__3___24Anonymous__30235)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__30216)
=> ( Vvar__1___24Anonymous__30215 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__30234,Vvar__3___24Anonymous__30235)
& ( ( Vvar__2___24Anonymous__30216 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)))
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__30234)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__3___24Anonymous__30235))) ) )
| ? [Vvar__1___24Anonymous__30246] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__30246)
& ? [Vvar__2___24Anonymous__30247] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__30247)
& Vvar__2___24Anonymous__30216 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__1___24Anonymous__30246,Vvar__2___24Anonymous__30247)
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> ( p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__30234)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__3___24Anonymous__30235)))
& cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__30216) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkZmon',axiom,
! [V0__j,V1__M] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V1__M)
=> ( ( V1__M = cCoq_2esetoid__ring_2eRing__polynom_2emon0
& cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2emon0 )
| ? [Vvar__0___24Anonymous__36389] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36389)
& ? [Vvar__1___24Anonymous__36390] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__36390)
& V1__M = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__36389,Vvar__1___24Anonymous__36390)
& cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V0__j,V1__M) ) )
| ? [Vvar__0___24Anonymous__36392] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36392)
& ? [Vvar__1___24Anonymous__36393] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__36393)
& V1__M = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__36392,Vvar__1___24Anonymous__36393)
& cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V0__j,V1__M) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__15935] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15935)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15935)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(happ(V1__rmul,V3__r),V4__x),V4__x,Vvar__0___24Anonymous__15935),V4__x,Vvar__0___24Anonymous__15935) )
| ? [Vvar__0___24Anonymous__15936] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15936)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15936)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,Vvar__0___24Anonymous__15936),V4__x,Vvar__0___24Anonymous__15936) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__3000___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.r_list_pow',axiom,
! [V0__R,V1__rI,V2__rmul,V4__l] :
( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive))
& cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,V4__l) = V1__rI )
| ? [Vvar__1___24Anonymous__35728] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__35728)
& ? [Vvar__2___24Anonymous__35729] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__2___24Anonymous__35729)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__35728)
=> ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__1___24Anonymous__35728,Vvar__2___24Anonymous__35729)
& ? [Vvar__2___24Anonymous__35741] :
( t(Vvar__2___24Anonymous__35741,V0__R)
& ? [Vvar__3___24Anonymous__35742] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3___24Anonymous__35742)
& Vvar__1___24Anonymous__35728 = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__2___24Anonymous__35741,Vvar__3___24Anonymous__35742)
& cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,V4__l) = happ(happ(V2__rmul,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,Vvar__2___24Anonymous__35741,Vvar__3___24Anonymous__35742)),cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,Vvar__2___24Anonymous__35729)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRopp',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRsub',axiom,
! [V0__R,V1__radd,V2__x,V3__y] : cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V0__R,V1__radd,V2__x,V3__y) = happ(happ(V1__radd,V2__x),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V3__y)) ).
fof('$_def_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
! [V0__C,V1__c] : cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V0__C,V1__c) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__C) ).
fof('$_def_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__3332] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3332)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3332)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__3332) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__15956] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15956)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15956)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__15957__15960___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15956)),c_24__let__var__6__p__15957__15960___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15956))) )
| ? [Vvar__0___24Anonymous__15958] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15958)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15958)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__15959__15961___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15958)),c_24__let__var__6__p__15959__15961___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15958)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_HahnTotalExt.one_ext',axiom,
! [V0__A,V1__elem,V2__r,V3__x,V4__y] :
( cHahnTotalExt_2eone__ext___24a5(V0__A,V1__elem,V2__r,V3__x,V4__y)
<=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V2__r,V3__x,V4__y)
| ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V2__r,V3__x,V1__elem)
& ~ cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V2__r,V4__y,V1__elem) ) ) ) ).
fof('$_def_HahnTotalExt.tot_ext',axiom,
! [V1__A,V2__dom,V3__r] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V2__dom)
=> ( ( V2__dom = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& cHahnTotalExt_2etot__ext___24a3(V1__A,V2__dom,V3__r) = cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V1__A,V3__r) )
| ? [Vvar__1___24Anonymous__32268] :
( t(Vvar__1___24Anonymous__32268,V1__A)
& ? [Vvar__2___24Anonymous__32269] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__32269)
& V2__dom = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__32268,Vvar__2___24Anonymous__32269)
& cHahnTotalExt_2etot__ext___24a3(V1__A,V2__dom,V3__r) = cHahnTotalExt_2eone__ext___24a3(V1__A,Vvar__1___24Anonymous__32268,cHahnTotalExt_2etot__ext___24a3(V1__A,Vvar__2___24Anonymous__32269,V3__r)) ) ) ) ) ) ).
fof('$_def_hahn.HahnBase.NW',axiom,
! [V0__P] :
( chahn_2eHahnBase_2eNW___24a1(V0__P)
<=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2ett)) ) ).
fof('$_def_hahn.HahnBase.is_true',axiom,
! [V0__b] :
( chahn_2eHahnBase_2eis__true___24a1(V0__b)
<=> V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_def_hahn.HahnFuneq.funeq',axiom,
! [V0__A,V1__B,V2__f,V3__r] :
( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
<=> ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(happ(V3__r,V4__a),V5__b))
=> happ(V2__f,V4__a) = happ(V2__f,V5__b) ) ) ) ) ).
fof('$_def_hahn.HahnList.disjoint',axiom,
! [V0__A,V1__l1,V2__l2] :
( chahn_2eHahnList_2edisjoint___24a3(V0__A,V1__l1,V2__l2)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l1))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__l2))
=> p(c_24False) ) ) ) ) ).
fof('$_def_hahn.HahnList.filterP',axiom,
! [V1__A,V2__f,V3__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& chahn_2eHahnList_2efilterP___24a3(V1__A,V2__f,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A) )
| ? [Vvar__1___24Anonymous__1588] :
( t(Vvar__1___24Anonymous__1588,V1__A)
& ? [Vvar__2___24Anonymous__1589] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__1589)
& ( cType___24t(V1__A)
=> ( c_24__type__36___24t(V1__A,V2__f)
=> ( t(Vvar__1___24Anonymous__1588,V1__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__1588,Vvar__2___24Anonymous__1589)
& ( ( p(happ(V2__f,Vvar__1___24Anonymous__1588))
& cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(happ(V2__f,Vvar__1___24Anonymous__1588)) = cCoq_2eInit_2eSpecif_2eleft___24a2(happ(V2__f,Vvar__1___24Anonymous__1588),c_24__prop__1606___24a3(V1__A,V2__f,Vvar__1___24Anonymous__1588))
& chahn_2eHahnList_2efilterP___24a3(V1__A,V2__f,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__1588,chahn_2eHahnList_2efilterP___24a3(V1__A,V2__f,Vvar__2___24Anonymous__1589)) )
| ( ~ p(happ(V2__f,Vvar__1___24Anonymous__1588))
& cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(happ(V2__f,Vvar__1___24Anonymous__1588)) = cCoq_2eInit_2eSpecif_2eright___24a2(happ(V2__f,Vvar__1___24Anonymous__1588),c_24__prop__1607___24a3(V1__A,V2__f,Vvar__1___24Anonymous__1588))
& chahn_2eHahnList_2efilterP___24a3(V1__A,V2__f,V3__l) = chahn_2eHahnList_2efilterP___24a3(V1__A,V2__f,Vvar__2___24Anonymous__1589) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_hahn.HahnList.flatten',axiom,
! [V1__A,V2__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__A),V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__A))
& chahn_2eHahnList_2eflatten___24a2(V1__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A) )
| ? [Vvar__1___24Anonymous__33051] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__1___24Anonymous__33051)
& ? [Vvar__2___24Anonymous__33052] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__A),Vvar__2___24Anonymous__33052)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__A),Vvar__1___24Anonymous__33051,Vvar__2___24Anonymous__33052)
& chahn_2eHahnList_2eflatten___24a2(V1__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__A,Vvar__1___24Anonymous__33051,chahn_2eHahnList_2eflatten___24a2(V1__A,Vvar__2___24Anonymous__33052)) ) ) ) ) ) ).
fof('$_def_hahn.HahnList.map_filter',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& chahn_2eHahnList_2emap__filter___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__33063] :
( t(Vvar__1___24Anonymous__33063,V0__A)
& ? [Vvar__2___24Anonymous__33064] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__33064)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( c_24__type__33076___24t(V0__A,V1__B,V2__f)
=> ( t(Vvar__1___24Anonymous__33063,V0__A)
=> ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__33063,Vvar__2___24Anonymous__33064)
& ( ? [Vvar__1___24Anonymous__33072] :
( t(Vvar__1___24Anonymous__33072,V1__B)
& happ(V2__f,Vvar__1___24Anonymous__33063) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V1__B,Vvar__1___24Anonymous__33072)
& chahn_2eHahnList_2emap__filter___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__33072,chahn_2eHahnList_2emap__filter___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__33064)) )
| ( happ(V2__f,Vvar__1___24Anonymous__33063) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B)
& chahn_2eHahnList_2emap__filter___24a4(V0__A,V1__B,V2__f,V4__l) = chahn_2eHahnList_2emap__filter___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__33064) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__1629] :
( t(Vvar__1___24Anonymous__1629,V1__A)
& ? [Vvar__2___24Anonymous__1630] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__1630)
& ( cType___24t(V1__A)
=> ( t(Vvar__1___24Anonymous__1629,V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__1630)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630)
& ( ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630))
& cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630)) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630),c_24__prop__1646___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630))
& chahn_2eHahnList_2eundup___24a2(V1__A,V2__l) = chahn_2eHahnList_2eundup___24a2(V1__A,Vvar__2___24Anonymous__1630) )
| ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630))
& cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630)) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630),c_24__prop__1658___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630))
& chahn_2eHahnList_2eundup___24a2(V1__A,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__1629,chahn_2eHahnList_2eundup___24a2(V1__A,Vvar__2___24Anonymous__1630)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_hahn.HahnMaxElt.max_elt',axiom,
! [V0__A,V1__r,V2__a] :
( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a)
<=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(happ(happ(V1__r,V2__a),V3__b))
=> p(c_24False) ) ) ) ).
fof('$_def_hahn.HahnMaxElt.wmax_elt',axiom,
! [V0__A,V1__r,V2__a] :
( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
<=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(happ(happ(V1__r,V2__a),V3__b))
=> V2__a = V3__b ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.acyclic',axiom,
! [V0__A,V1__r] :
( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ).
fof('$_def_hahn.HahnRelationsBasic.bunion',axiom,
! [V0__A,V1__B,V2__P,V3__r,V4__x,V5__y] :
( chahn_2eHahnRelationsBasic_2ebunion___24a6(V0__A,V1__B,V2__P,V3__r,V4__x,V5__y)
<=> ? [V6__a] :
( t(V6__a,V0__A)
& p(happ(V2__P,V6__a))
& p(happ(happ(happ(V3__r,V6__a),V4__x),V5__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.clos_refl',axiom,
! [V0__A,V1__r,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ( V2__x = V3__y
| p(happ(happ(V1__r,V2__x),V3__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.clos_refl_sym',axiom,
! [V0__A,V1__r,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ( V2__x = V3__y
| p(happ(happ(V1__r,V2__x),V3__y))
| p(happ(happ(V1__r,V3__y),V2__x)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.clos_sym',axiom,
! [V0__A,V1__r,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eclos__sym___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ( p(happ(happ(V1__r,V2__x),V3__y))
| p(happ(happ(V1__r,V3__y),V2__x)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.codom_rel',axiom,
! [V0__A,V1__r,V2__y] :
( chahn_2eHahnRelationsBasic_2ecodom__rel___24a3(V0__A,V1__r,V2__y)
<=> ? [V3__x] :
( t(V3__x,V0__A)
& p(happ(happ(V1__r,V3__x),V2__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.collect_rel',axiom,
! [V0__A,V1__B,V2__f,V3__r,V4__x,V5__y] :
( chahn_2eHahnRelationsBasic_2ecollect__rel___24a6(V0__A,V1__B,V2__f,V3__r,V4__x,V5__y)
<=> ? [V6__x_27] :
( t(V6__x_27,V0__A)
& ? [V7__y_27] :
( t(V7__y_27,V0__A)
& p(happ(happ(V3__r,V6__x_27),V7__y_27))
& happ(V2__f,V6__x_27) = V4__x
& happ(V2__f,V7__y_27) = V5__y ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.dom_rel',axiom,
! [V0__A,V1__r,V2__x] :
( chahn_2eHahnRelationsBasic_2edom__rel___24a3(V0__A,V1__r,V2__x)
<=> ? [V3__y] :
( t(V3__y,V0__A)
& p(happ(happ(V1__r,V2__x),V3__y)) ) ) ).
fof('$_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('$_def_hahn.HahnRelationsBasic.functional',axiom,
! [V0__A,V1__r] :
( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V3__y))
=> ( p(happ(happ(V1__r,V2__x),V4__z))
=> V3__y = V4__z ) ) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.immediate',axiom,
! [V0__A,V1__r,V2__a,V3__b] :
( chahn_2eHahnRelationsBasic_2eimmediate___24a4(V0__A,V1__r,V2__a,V3__b)
<=> ( p(happ(happ(V1__r,V2__a),V3__b))
& ! [V4__c] :
( t(V4__c,V0__A)
=> ( p(happ(happ(V1__r,V2__a),V4__c))
=> ( p(happ(happ(V1__r,V4__c),V3__b))
=> p(c_24False) ) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.inter_rel',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2einter__rel___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ( p(happ(happ(V1__r,V3__x),V4__y))
& p(happ(happ(V2__r_27,V3__x),V4__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.irreflexive',axiom,
! [V0__A,V1__r] :
( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V2__x))
=> p(c_24False) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.is_total',axiom,
! [V0__A,V1__cond,V2__r] :
( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__cond,V2__r)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(happ(V1__cond,V3__a))
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(V1__cond,V5__b))
=> ( V3__a != V5__b
=> ( p(happ(happ(V2__r,V3__a),V5__b))
| p(happ(happ(V2__r,V5__b),V3__a)) ) ) ) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.map_rel',axiom,
! [V0__A,V1__B,V2__f,V3__r_27_27,V4__x,V5__y] :
( chahn_2eHahnRelationsBasic_2emap__rel___24a6(V0__A,V1__B,V2__f,V3__r_27_27,V4__x,V5__y)
<=> p(happ(happ(V3__r_27_27,happ(V2__f,V4__x)),happ(V2__f,V5__y))) ) ).
fof('$_def_hahn.HahnRelationsBasic.minus_rel',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2eminus__rel___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ( p(happ(happ(V1__r,V3__x),V4__y))
& ~ p(happ(happ(V2__r_27,V3__x),V4__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.pow_rel',axiom,
! [V1__A,V2__r,V3__n] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V3__n) = chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V1__A,c_24__lam__74___24a1(V1__A)) )
| ? [Vvar__0___24Anonymous__72] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__72)
& V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__72)
& 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__72),V2__r) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.restr_eq_rel',axiom,
! [V0__A,V1__B,V2__f,V3__r,V4__x,V5__y] :
( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6(V0__A,V1__B,V2__f,V3__r,V4__x,V5__y)
<=> ( p(happ(happ(V3__r,V4__x),V5__y))
& happ(V2__f,V4__x) = happ(V2__f,V5__y) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.restr_rel',axiom,
! [V0__A,V1__cond,V2__r,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2erestr__rel___24a5(V0__A,V1__cond,V2__r,V3__x,V4__y)
<=> ( p(happ(happ(V2__r,V3__x),V4__y))
& p(happ(V1__cond,V3__x))
& p(happ(V1__cond,V4__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.restr_subset',axiom,
! [V0__A,V1__cond,V2__r,V3__r_27] :
( chahn_2eHahnRelationsBasic_2erestr__subset___24a4(V0__A,V1__cond,V2__r,V3__r_27)
<=> ! [V4__a] :
( t(V4__a,V0__A)
=> ( p(happ(V1__cond,V4__a))
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ( p(happ(V1__cond,V6__b))
=> ( p(happ(happ(V2__r,V4__a),V6__b))
=> p(happ(happ(V3__r_27,V4__a),V6__b)) ) ) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.seq',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2eseq___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ? [V5__z] :
( t(V5__z,V0__A)
& p(happ(happ(V1__r,V3__x),V5__z))
& p(happ(happ(V2__r_27,V5__z),V4__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.singl_rel',axiom,
! [V0__A,V1__a,V2__b,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2esingl__rel___24a5(V0__A,V1__a,V2__b,V3__x,V4__y)
<=> ( V3__x = V1__a
& V4__y = V2__b ) ) ).
fof('$_def_hahn.HahnRelationsBasic.strict_partial_order',axiom,
! [V0__A,V1__r] :
( chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V0__A,V1__r)
<=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.strict_total_order',axiom,
! [V0__A,V1__cond,V2__r] :
( chahn_2eHahnRelationsBasic_2estrict__total__order___24a3(V0__A,V1__cond,V2__r)
<=> ( chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V0__A,V2__r)
& chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__cond,V2__r) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.upward_closed',axiom,
! [V0__A,V1__r,V2__P] :
( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V1__r,V2__P)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__r,V3__x),V4__y))
=> ( p(happ(V2__P,V4__y))
=> p(happ(V2__P,V3__x)) ) ) ) ) ) ).
fof('$_def_hahn.HahnSets.set_compl',axiom,
! [V0__A,V1__s,V2__x] :
( chahn_2eHahnSets_2eset__compl___24a3(V0__A,V1__s,V2__x)
<=> ~ p(happ(V1__s,V2__x)) ) ).
fof('$_def_hahn.HahnSets.set_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_finite',axiom,
! [V0__A,V1__s] :
( chahn_2eHahnSets_2eset__finite___24a2(V0__A,V1__s)
<=> ? [V2__findom] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__findom)
& ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__s,V3__x))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__findom)) ) ) ) ) ).
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('$_def_hahn.Zorn.Private.Equiv',axiom,
! [V0__A] : chahn_2eZorn_2ePrivate_2eEquiv___24a1(V0__A) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) ).
fof('$_def_hahn.Zorn.Private.Le',axiom,
! [V0__A] : chahn_2eZorn_2ePrivate_2eLe___24a1(V0__A) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) ).
fof('$_def_hahn.Zorn.Private.Lt',axiom,
! [V0__A] : chahn_2eZorn_2ePrivate_2eLt___24a1(V0__A) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) ).
fof('$_def_hahn.Zorn.Private.equ',axiom,
! [V0__A,V1__Equiv] : chahn_2eZorn_2ePrivate_2eequ___24a2(V0__A,V1__Equiv) = V1__Equiv ).
fof('$_def_hahn.Zorn.Private.le',axiom,
! [V0__A,V1__Le] : chahn_2eZorn_2ePrivate_2ele___24a2(V0__A,V1__Le) = V1__Le ).
fof('$_def_hahn.Zorn.ZornsLemma',axiom,
! [V0__A,V1__R] :
( chahn_2eZorn_2eZornsLemma___24a2(V0__A,V1__R)
<=> ? [V4__m] :
( t(V4__m,V0__A)
& ! [V5__x] :
( t(V5__x,V0__A)
=> ( p(happ(happ(V1__R,V4__m),V5__x))
=> p(happ(happ(V1__R,V5__x),V4__m)) ) ) ) ) ).
fof('$_def_hahn.Zorn.suspend_R',axiom,
! [V0__A,V1__eqA,V2__S,V3__R,V4__x,V5__y,V6__z] :
( chahn_2eZorn_2esuspend__R___24a7(V0__A,V1__eqA,V2__S,V3__R,V4__x,V5__y,V6__z)
<=> ( p(happ(happ(V3__R,V5__y),V6__z))
| ( p(happ(V2__S,V5__y))
& p(happ(happ(V1__eqA,V4__x),V6__z)) ) ) ) ).
fof('$_def_hahn.Zorn.suspend_S',axiom,
! [V0__A,V1__eqA,V2__S,V3__x,V4__y] :
( chahn_2eZorn_2esuspend__S___24a5(V0__A,V1__eqA,V2__S,V3__x,V4__y)
<=> ( p(happ(V2__S,V4__y))
| p(happ(happ(V1__eqA,V3__x),V4__y)) ) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__5241,Vvar__1___24Anonymous__5242,Vvar__0__P__5243,Vvar__1___24Anonymous__5244] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5241) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5243) ).
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__140] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__140) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__852,Vvar__1___24Anonymous__853,Vvar__0__A__854] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__852,Vvar__1___24Anonymous__853) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__854) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__5426,Vvar__1__B__5427,Vvar__2___24Anonymous__5428,Vvar__0__A__5429,Vvar__1__B__5430,Vvar__2___24Anonymous__5431] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__5426,Vvar__1__B__5427,Vvar__2___24Anonymous__5428) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__5429,Vvar__1__B__5430,Vvar__2___24Anonymous__5431) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__922,Vvar__0__A__923,Vvar__1___24Anonymous__924,Vvar__2___24Anonymous__925] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__922) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__923,Vvar__1___24Anonymous__924,Vvar__2___24Anonymous__925) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__22240,Vvar__1__B__22241,Vvar__2___24Anonymous__22242,Vvar__0__A__22243,Vvar__1__B__22244,Vvar__2___24Anonymous__22245] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__22240,Vvar__1__B__22241,Vvar__2___24Anonymous__22242) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__22243,Vvar__1__B__22244) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__3429,Vvar__1__B__3430,Vvar__2___24Anonymous__3431,Vvar__0__A__3432,Vvar__1__B__3433,Vvar__2___24Anonymous__3434] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3429,Vvar__1__B__3430) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3432,Vvar__1__B__3433) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__807] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__807) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__818] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__818) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__797,Vvar__0___24Anonymous__798] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__797) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__798) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__22762,Vvar__0__A__22763,Vvar__1__h__22764,Vvar__2__n__22765,Vvar__3___24Anonymous__22766] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__22762) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__22763,Vvar__1__h__22764,Vvar__2__n__22765,Vvar__3___24Anonymous__22766) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__22620,Vvar__1__TX__22621,Vvar__2__AA__22622,Vvar__3__AF__22623,Vvar__0__TA__22624,Vvar__1__TX__22625,Vvar__2__AA__22626,Vvar__3__AF__22627] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22620,Vvar__1__TX__22621,Vvar__2__AA__22622,Vvar__3__AF__22623) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22624,Vvar__1__TX__22625,Vvar__2__AA__22626,Vvar__3__AF__22627) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__7031,Vvar__0__C__7032] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__7031) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__7032) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__2870,Vvar__0__C__2871] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2870) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2871) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__2512,Vvar__1___24Anonymous__2513,Vvar__0__C__2514,Vvar__1___24Anonymous__2515,Vvar__2___24Anonymous__2516] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__2512,Vvar__1___24Anonymous__2513) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__2514,Vvar__1___24Anonymous__2515,Vvar__2___24Anonymous__2516) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__2680,Vvar__1___24Anonymous__2681] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__2680,Vvar__1___24Anonymous__2681) ).
fof('$_fix_10440_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__10440__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__10444] :
( t(Vvar__1___24Anonymous__10444,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__10445] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__10445)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__10444,Vvar__2___24Anonymous__10445)
& c_24__fix__10440__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__10444,c_24__fix__10440__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__10445,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_24126_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__24141] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24141)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24141)
& ( ? [Vvar__0___24Anonymous__24145] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24145)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24145)
& c_24__fix__24126__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__24126__1__add__carry___24a2(Vvar__0___24Anonymous__24141,Vvar__0___24Anonymous__24145)) )
| ? [Vvar__0___24Anonymous__24146] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24146)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24146)
& c_24__fix__24126__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__24126__1__add__carry___24a2(Vvar__0___24Anonymous__24141,Vvar__0___24Anonymous__24146)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__24126__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__24141)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__24147] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24147)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24147)
& ( ? [Vvar__0___24Anonymous__24151] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24151)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24151)
& c_24__fix__24126__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__24126__1__add__carry___24a2(Vvar__0___24Anonymous__24147,Vvar__0___24Anonymous__24151)) )
| ? [Vvar__0___24Anonymous__24152] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24152)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24152)
& c_24__fix__24126__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__24147,Vvar__0___24Anonymous__24152)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__24126__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__24147)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__24153] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24153)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24153)
& c_24__fix__24126__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__24153)) )
| ? [Vvar__0___24Anonymous__24154] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24154)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24154)
& c_24__fix__24126__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__24154)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__24126__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_fix_34226_v_CANONICAL_2',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ( ( Vv__CANONICAL__4 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__34226__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__5 )
| ? [Vvar__1__h__34231] :
( t(Vvar__1__h__34231,Vv__CANONICAL__0)
& ? [Vvar__2__n__34232] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__34232)
& ? [Vvar__3___24Anonymous__34233] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vvar__2__n__34232,Vvar__3___24Anonymous__34233)
& Vv__CANONICAL__4 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vvar__1__h__34231,Vvar__2__n__34232,Vvar__3___24Anonymous__34233)
& c_24__fix__34226__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1__h__34231,c_24__fix__34226__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2__n__34232,Vvar__3___24Anonymous__34233,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__5249,Vvar__0__P__5250,Vvar__1___24Anonymous__5251,Vvar__1___24Anonymous__5252] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5249) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5250)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__5249 = Vvar__0__P__5250 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__5245,Vvar__0__P__5246,Vvar__1___24Anonymous__5247,Vvar__1___24Anonymous__5248] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5245) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5246)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__5245 = Vvar__0__P__5246 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__859,Vvar__0__A__860] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__859) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__860)
=> Vvar__0__A__859 = Vvar__0__A__860 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__141,Vvar__0___24Anonymous__142] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__141) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__142)
=> Vvar__0___24Anonymous__141 = Vvar__0___24Anonymous__142 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__855,Vvar__0__A__856,Vvar__1___24Anonymous__857,Vvar__1___24Anonymous__858] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__855,Vvar__1___24Anonymous__857) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__856,Vvar__1___24Anonymous__858)
=> ( Vvar__1___24Anonymous__857 = Vvar__1___24Anonymous__858
& Vvar__0__A__855 = Vvar__0__A__856 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__928,Vvar__0__A__929,Vvar__1___24Anonymous__930,Vvar__1___24Anonymous__931,Vvar__2___24Anonymous__932,Vvar__2___24Anonymous__933] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__928,Vvar__1___24Anonymous__930,Vvar__2___24Anonymous__932) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__929,Vvar__1___24Anonymous__931,Vvar__2___24Anonymous__933)
=> ( Vvar__2___24Anonymous__932 = Vvar__2___24Anonymous__933
& Vvar__1___24Anonymous__930 = Vvar__1___24Anonymous__931
& Vvar__0__A__928 = Vvar__0__A__929 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__5432,Vvar__0__A__5433,Vvar__1__B__5434,Vvar__1__B__5435,Vvar__2___24Anonymous__5436,Vvar__2___24Anonymous__5437] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__5432,Vvar__1__B__5434,Vvar__2___24Anonymous__5436) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__5433,Vvar__1__B__5435,Vvar__2___24Anonymous__5437)
=> ( Vvar__2___24Anonymous__5436 = Vvar__2___24Anonymous__5437
& Vvar__1__B__5434 = Vvar__1__B__5435
& Vvar__0__A__5432 = Vvar__0__A__5433 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__5438,Vvar__0__A__5439,Vvar__1__B__5440,Vvar__1__B__5441,Vvar__2___24Anonymous__5442,Vvar__2___24Anonymous__5443] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__5438,Vvar__1__B__5440,Vvar__2___24Anonymous__5442) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__5439,Vvar__1__B__5441,Vvar__2___24Anonymous__5443)
=> ( Vvar__2___24Anonymous__5442 = Vvar__2___24Anonymous__5443
& Vvar__1__B__5440 = Vvar__1__B__5441
& Vvar__0__A__5438 = Vvar__0__A__5439 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__926,Vvar__0__A__927] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__926) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__927)
=> Vvar__0__A__926 = Vvar__0__A__927 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__876,Vvar__0__A__877,Vvar__1__B__878,Vvar__1__B__879,Vvar__2___24Anonymous__880,Vvar__2___24Anonymous__881,Vvar__3___24Anonymous__882,Vvar__3___24Anonymous__883] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__876,Vvar__1__B__878,Vvar__2___24Anonymous__880,Vvar__3___24Anonymous__882) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__877,Vvar__1__B__879,Vvar__2___24Anonymous__881,Vvar__3___24Anonymous__883)
=> ( Vvar__3___24Anonymous__882 = Vvar__3___24Anonymous__883
& Vvar__2___24Anonymous__880 = Vvar__2___24Anonymous__881
& Vvar__1__B__878 = Vvar__1__B__879
& Vvar__0__A__876 = Vvar__0__A__877 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__3375,Vvar__0__A__3376,Vvar__1__P__3377,Vvar__1__P__3378,Vvar__2__x__3379,Vvar__2__x__3380,Vvar__3___24Anonymous__3381,Vvar__3___24Anonymous__3382] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__3375,Vvar__1__P__3377,Vvar__2__x__3379) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__3376,Vvar__1__P__3378,Vvar__2__x__3380)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__3379 = Vvar__2__x__3380
& Vvar__1__P__3377 = Vvar__1__P__3378
& Vvar__0__A__3375 = Vvar__0__A__3376 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__22164,Vvar__0__A__22165,Vvar__1__P__22166,Vvar__1__P__22167,Vvar__2__x__22168,Vvar__2__x__22169,Vvar__3___24Anonymous__22170,Vvar__3___24Anonymous__22171] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__22164,Vvar__1__P__22166,Vvar__2__x__22168,Vvar__3___24Anonymous__22170) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__22165,Vvar__1__P__22167,Vvar__2__x__22169,Vvar__3___24Anonymous__22171)
=> ( Vvar__3___24Anonymous__22170 = Vvar__3___24Anonymous__22171
& Vvar__2__x__22168 = Vvar__2__x__22169
& Vvar__1__P__22166 = Vvar__1__P__22167
& Vvar__0__A__22164 = Vvar__0__A__22165 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__22246,Vvar__0__A__22247,Vvar__1__B__22248,Vvar__1__B__22249,Vvar__2___24Anonymous__22250,Vvar__2___24Anonymous__22251] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__22246,Vvar__1__B__22248,Vvar__2___24Anonymous__22250) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__22247,Vvar__1__B__22249,Vvar__2___24Anonymous__22251)
=> ( Vvar__2___24Anonymous__22250 = Vvar__2___24Anonymous__22251
& Vvar__1__B__22248 = Vvar__1__B__22249
& Vvar__0__A__22246 = Vvar__0__A__22247 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__22252,Vvar__0__A__22253,Vvar__1__B__22254,Vvar__1__B__22255,Vvar__2___24Anonymous__22256,Vvar__2___24Anonymous__22257] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__22252,Vvar__1__B__22254) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__22253,Vvar__1__B__22255)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__22254 = Vvar__1__B__22255
& Vvar__0__A__22252 = Vvar__0__A__22253 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__3435,Vvar__0__A__3436,Vvar__1__B__3437,Vvar__1__B__3438,Vvar__2___24Anonymous__3439,Vvar__2___24Anonymous__3440] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3435,Vvar__1__B__3437) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3436,Vvar__1__B__3438)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__3437 = Vvar__1__B__3438
& Vvar__0__A__3435 = Vvar__0__A__3436 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__3441,Vvar__0__A__3442,Vvar__1__B__3443,Vvar__1__B__3444,Vvar__2___24Anonymous__3445,Vvar__2___24Anonymous__3446] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3441,Vvar__1__B__3443) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3442,Vvar__1__B__3444)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__3443 = Vvar__1__B__3444
& Vvar__0__A__3441 = Vvar__0__A__3442 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__808,Vvar__0___24Anonymous__809] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__808) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__809)
=> Vvar__0___24Anonymous__808 = Vvar__0___24Anonymous__809 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__821,Vvar__0___24Anonymous__822] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__821) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__822)
=> Vvar__0___24Anonymous__821 = Vvar__0___24Anonymous__822 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__819,Vvar__0___24Anonymous__820] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__819) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__820)
=> Vvar__0___24Anonymous__819 = Vvar__0___24Anonymous__820 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__799,Vvar__0___24Anonymous__800] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__799) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__800)
=> Vvar__0___24Anonymous__799 = Vvar__0___24Anonymous__800 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__801,Vvar__0___24Anonymous__802] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__801) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__802)
=> Vvar__0___24Anonymous__801 = Vvar__0___24Anonymous__802 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__2042,Vvar__0__Qnum__2043,Vvar__1__Qden__2044,Vvar__1__Qden__2045] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__2042,Vvar__1__Qden__2044) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__2043,Vvar__1__Qden__2045)
=> ( Vvar__1__Qden__2044 = Vvar__1__Qden__2045
& Vvar__0__Qnum__2042 = Vvar__0__Qnum__2043 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__22769,Vvar__0__A__22770,Vvar__1__h__22771,Vvar__1__h__22772,Vvar__2__n__22773,Vvar__2__n__22774,Vvar__3___24Anonymous__22775,Vvar__3___24Anonymous__22776] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__22769,Vvar__1__h__22771,Vvar__2__n__22773,Vvar__3___24Anonymous__22775) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__22770,Vvar__1__h__22772,Vvar__2__n__22774,Vvar__3___24Anonymous__22776)
=> ( Vvar__3___24Anonymous__22775 = Vvar__3___24Anonymous__22776
& Vvar__2__n__22773 = Vvar__2__n__22774
& Vvar__1__h__22771 = Vvar__1__h__22772
& Vvar__0__A__22769 = Vvar__0__A__22770 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__22767,Vvar__0__A__22768] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__22767) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__22768)
=> Vvar__0__A__22767 = Vvar__0__A__22768 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__15926,Vvar__0__T__15927,Vvar__1__Flhs__15928,Vvar__1__Flhs__15929,Vvar__2__Fop__15930,Vvar__2__Fop__15931,Vvar__3__Frhs__15932,Vvar__3__Frhs__15933] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__15926,Vvar__1__Flhs__15928,Vvar__2__Fop__15930,Vvar__3__Frhs__15932) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__15927,Vvar__1__Flhs__15929,Vvar__2__Fop__15931,Vvar__3__Frhs__15933)
=> ( Vvar__3__Frhs__15932 = Vvar__3__Frhs__15933
& Vvar__2__Fop__15930 = Vvar__2__Fop__15931
& Vvar__1__Flhs__15928 = Vvar__1__Flhs__15929
& Vvar__0__T__15926 = Vvar__0__T__15927 ) ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__22654,Vvar__0__TA__22655,Vvar__1__TX__22656,Vvar__1__TX__22657,Vvar__2__AA__22658,Vvar__2__AA__22659,Vvar__3__AF__22660,Vvar__3__AF__22661,Vvar__4___24Anonymous__22662,Vvar__4___24Anonymous__22663,Vvar__5___24Anonymous__22664,Vvar__5___24Anonymous__22665] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__22654,Vvar__1__TX__22656,Vvar__2__AA__22658,Vvar__3__AF__22660,Vvar__4___24Anonymous__22662,Vvar__5___24Anonymous__22664) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__22655,Vvar__1__TX__22657,Vvar__2__AA__22659,Vvar__3__AF__22661,Vvar__4___24Anonymous__22663,Vvar__5___24Anonymous__22665)
=> ( Vvar__5___24Anonymous__22664 = Vvar__5___24Anonymous__22665
& Vvar__4___24Anonymous__22662 = Vvar__4___24Anonymous__22663
& Vvar__3__AF__22660 = Vvar__3__AF__22661
& Vvar__2__AA__22658 = Vvar__2__AA__22659
& Vvar__1__TX__22656 = Vvar__1__TX__22657
& Vvar__0__TA__22654 = Vvar__0__TA__22655 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__22666,Vvar__0__TA__22667,Vvar__1__TX__22668,Vvar__1__TX__22669,Vvar__2__AA__22670,Vvar__2__AA__22671,Vvar__3__AF__22672,Vvar__3__AF__22673,Vvar__4___24Anonymous__22674,Vvar__4___24Anonymous__22675,Vvar__5___24Anonymous__22676,Vvar__5___24Anonymous__22677] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__22666,Vvar__1__TX__22668,Vvar__2__AA__22670,Vvar__3__AF__22672,Vvar__4___24Anonymous__22674,Vvar__5___24Anonymous__22676) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__22667,Vvar__1__TX__22669,Vvar__2__AA__22671,Vvar__3__AF__22673,Vvar__4___24Anonymous__22675,Vvar__5___24Anonymous__22677)
=> ( Vvar__5___24Anonymous__22676 = Vvar__5___24Anonymous__22677
& Vvar__4___24Anonymous__22674 = Vvar__4___24Anonymous__22675
& Vvar__3__AF__22672 = Vvar__3__AF__22673
& Vvar__2__AA__22670 = Vvar__2__AA__22671
& Vvar__1__TX__22668 = Vvar__1__TX__22669
& Vvar__0__TA__22666 = Vvar__0__TA__22667 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__22678,Vvar__0__TA__22679,Vvar__1__TX__22680,Vvar__1__TX__22681,Vvar__2__AA__22682,Vvar__2__AA__22683,Vvar__3__AF__22684,Vvar__3__AF__22685,Vvar__4___24Anonymous__22686,Vvar__4___24Anonymous__22687,Vvar__5___24Anonymous__22688,Vvar__5___24Anonymous__22689] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__22678,Vvar__1__TX__22680,Vvar__2__AA__22682,Vvar__3__AF__22684,Vvar__4___24Anonymous__22686,Vvar__5___24Anonymous__22688) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__22679,Vvar__1__TX__22681,Vvar__2__AA__22683,Vvar__3__AF__22685,Vvar__4___24Anonymous__22687,Vvar__5___24Anonymous__22689)
=> ( Vvar__5___24Anonymous__22688 = Vvar__5___24Anonymous__22689
& Vvar__4___24Anonymous__22686 = Vvar__4___24Anonymous__22687
& Vvar__3__AF__22684 = Vvar__3__AF__22685
& Vvar__2__AA__22682 = Vvar__2__AA__22683
& Vvar__1__TX__22680 = Vvar__1__TX__22681
& Vvar__0__TA__22678 = Vvar__0__TA__22679 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__22636,Vvar__0__TA__22637,Vvar__1__TX__22638,Vvar__1__TX__22639,Vvar__2__AA__22640,Vvar__2__AA__22641,Vvar__3__AF__22642,Vvar__3__AF__22643] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22636,Vvar__1__TX__22638,Vvar__2__AA__22640,Vvar__3__AF__22642) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22637,Vvar__1__TX__22639,Vvar__2__AA__22641,Vvar__3__AF__22643)
=> ( Vvar__3__AF__22642 = Vvar__3__AF__22643
& Vvar__2__AA__22640 = Vvar__2__AA__22641
& Vvar__1__TX__22638 = Vvar__1__TX__22639
& Vvar__0__TA__22636 = Vvar__0__TA__22637 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__22700,Vvar__0__TA__22701,Vvar__1__TX__22702,Vvar__1__TX__22703,Vvar__2__AA__22704,Vvar__2__AA__22705,Vvar__3__AF__22706,Vvar__3__AF__22707,Vvar__4___24Anonymous__22708,Vvar__4___24Anonymous__22709,Vvar__5___24Anonymous__22710,Vvar__5___24Anonymous__22711,Vvar__6___24Anonymous__22712,Vvar__6___24Anonymous__22713] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__22700,Vvar__1__TX__22702,Vvar__2__AA__22704,Vvar__3__AF__22706,Vvar__4___24Anonymous__22708,Vvar__5___24Anonymous__22710,Vvar__6___24Anonymous__22712) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__22701,Vvar__1__TX__22703,Vvar__2__AA__22705,Vvar__3__AF__22707,Vvar__4___24Anonymous__22709,Vvar__5___24Anonymous__22711,Vvar__6___24Anonymous__22713)
=> ( Vvar__6___24Anonymous__22712 = Vvar__6___24Anonymous__22713
& Vvar__5___24Anonymous__22710 = Vvar__5___24Anonymous__22711
& Vvar__4___24Anonymous__22708 = Vvar__4___24Anonymous__22709
& Vvar__3__AF__22706 = Vvar__3__AF__22707
& Vvar__2__AA__22704 = Vvar__2__AA__22705
& Vvar__1__TX__22702 = Vvar__1__TX__22703
& Vvar__0__TA__22700 = Vvar__0__TA__22701 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__22690,Vvar__0__TA__22691,Vvar__1__TX__22692,Vvar__1__TX__22693,Vvar__2__AA__22694,Vvar__2__AA__22695,Vvar__3__AF__22696,Vvar__3__AF__22697,Vvar__4___24Anonymous__22698,Vvar__4___24Anonymous__22699] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__22690,Vvar__1__TX__22692,Vvar__2__AA__22694,Vvar__3__AF__22696,Vvar__4___24Anonymous__22698) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__22691,Vvar__1__TX__22693,Vvar__2__AA__22695,Vvar__3__AF__22697,Vvar__4___24Anonymous__22699)
=> ( Vvar__4___24Anonymous__22698 = Vvar__4___24Anonymous__22699
& Vvar__3__AF__22696 = Vvar__3__AF__22697
& Vvar__2__AA__22694 = Vvar__2__AA__22695
& Vvar__1__TX__22692 = Vvar__1__TX__22693
& Vvar__0__TA__22690 = Vvar__0__TA__22691 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__22628,Vvar__0__TA__22629,Vvar__1__TX__22630,Vvar__1__TX__22631,Vvar__2__AA__22632,Vvar__2__AA__22633,Vvar__3__AF__22634,Vvar__3__AF__22635] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22628,Vvar__1__TX__22630,Vvar__2__AA__22632,Vvar__3__AF__22634) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22629,Vvar__1__TX__22631,Vvar__2__AA__22633,Vvar__3__AF__22635)
=> ( Vvar__3__AF__22634 = Vvar__3__AF__22635
& Vvar__2__AA__22632 = Vvar__2__AA__22633
& Vvar__1__TX__22630 = Vvar__1__TX__22631
& Vvar__0__TA__22628 = Vvar__0__TA__22629 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__22644,Vvar__0__TA__22645,Vvar__1__TX__22646,Vvar__1__TX__22647,Vvar__2__AA__22648,Vvar__2__AA__22649,Vvar__3__AF__22650,Vvar__3__AF__22651,Vvar__4___24Anonymous__22652,Vvar__4___24Anonymous__22653] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__22644,Vvar__1__TX__22646,Vvar__2__AA__22648,Vvar__3__AF__22650,Vvar__4___24Anonymous__22652) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__22645,Vvar__1__TX__22647,Vvar__2__AA__22649,Vvar__3__AF__22651,Vvar__4___24Anonymous__22653)
=> ( Vvar__4___24Anonymous__22652 = Vvar__4___24Anonymous__22653
& Vvar__3__AF__22650 = Vvar__3__AF__22651
& Vvar__2__AA__22648 = Vvar__2__AA__22649
& Vvar__1__TX__22646 = Vvar__1__TX__22647
& Vvar__0__TA__22644 = Vvar__0__TA__22645 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__7035,Vvar__0__C__7036] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__7035) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__7036)
=> Vvar__0__C__7035 = Vvar__0__C__7036 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__7033,Vvar__0__C__7034] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__7033) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__7034)
=> Vvar__0__C__7033 = Vvar__0__C__7034 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__7041,Vvar__0__C__7042,Vvar__1___24Anonymous__7043,Vvar__1___24Anonymous__7044] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__7041,Vvar__1___24Anonymous__7043) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__7042,Vvar__1___24Anonymous__7044)
=> ( Vvar__1___24Anonymous__7043 = Vvar__1___24Anonymous__7044
& Vvar__0__C__7041 = Vvar__0__C__7042 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__7045,Vvar__0__C__7046,Vvar__1___24Anonymous__7047,Vvar__1___24Anonymous__7048,Vvar__2___24Anonymous__7049,Vvar__2___24Anonymous__7050] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__7045,Vvar__1___24Anonymous__7047,Vvar__2___24Anonymous__7049) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__7046,Vvar__1___24Anonymous__7048,Vvar__2___24Anonymous__7050)
=> ( Vvar__2___24Anonymous__7049 = Vvar__2___24Anonymous__7050
& Vvar__1___24Anonymous__7047 = Vvar__1___24Anonymous__7048
& Vvar__0__C__7045 = Vvar__0__C__7046 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__7037,Vvar__0__C__7038,Vvar__1___24Anonymous__7039,Vvar__1___24Anonymous__7040] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__7037,Vvar__1___24Anonymous__7039) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__7038,Vvar__1___24Anonymous__7040)
=> ( Vvar__1___24Anonymous__7039 = Vvar__1___24Anonymous__7040
& Vvar__0__C__7037 = Vvar__0__C__7038 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__7071,Vvar__0__C__7072,Vvar__1___24Anonymous__7073,Vvar__1___24Anonymous__7074,Vvar__2___24Anonymous__7075,Vvar__2___24Anonymous__7076] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__7071,Vvar__1___24Anonymous__7073,Vvar__2___24Anonymous__7075) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__7072,Vvar__1___24Anonymous__7074,Vvar__2___24Anonymous__7076)
=> ( Vvar__2___24Anonymous__7075 = Vvar__2___24Anonymous__7076
& Vvar__1___24Anonymous__7073 = Vvar__1___24Anonymous__7074
& Vvar__0__C__7071 = Vvar__0__C__7072 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__7067,Vvar__0__C__7068,Vvar__1___24Anonymous__7069,Vvar__1___24Anonymous__7070] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__7067,Vvar__1___24Anonymous__7069) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__7068,Vvar__1___24Anonymous__7070)
=> ( Vvar__1___24Anonymous__7069 = Vvar__1___24Anonymous__7070
& Vvar__0__C__7067 = Vvar__0__C__7068 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__7057,Vvar__0__C__7058,Vvar__1___24Anonymous__7059,Vvar__1___24Anonymous__7060,Vvar__2___24Anonymous__7061,Vvar__2___24Anonymous__7062] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__7057,Vvar__1___24Anonymous__7059,Vvar__2___24Anonymous__7061) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__7058,Vvar__1___24Anonymous__7060,Vvar__2___24Anonymous__7062)
=> ( Vvar__2___24Anonymous__7061 = Vvar__2___24Anonymous__7062
& Vvar__1___24Anonymous__7059 = Vvar__1___24Anonymous__7060
& Vvar__0__C__7057 = Vvar__0__C__7058 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__7063,Vvar__0__C__7064,Vvar__1___24Anonymous__7065,Vvar__1___24Anonymous__7066] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__7063,Vvar__1___24Anonymous__7065) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__7064,Vvar__1___24Anonymous__7066)
=> ( Vvar__1___24Anonymous__7065 = Vvar__1___24Anonymous__7066
& Vvar__0__C__7063 = Vvar__0__C__7064 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__7077,Vvar__0__C__7078,Vvar__1___24Anonymous__7079,Vvar__1___24Anonymous__7080,Vvar__2___24Anonymous__7081,Vvar__2___24Anonymous__7082] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__7077,Vvar__1___24Anonymous__7079,Vvar__2___24Anonymous__7081) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__7078,Vvar__1___24Anonymous__7080,Vvar__2___24Anonymous__7082)
=> ( Vvar__2___24Anonymous__7081 = Vvar__2___24Anonymous__7082
& Vvar__1___24Anonymous__7079 = Vvar__1___24Anonymous__7080
& Vvar__0__C__7077 = Vvar__0__C__7078 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__7051,Vvar__0__C__7052,Vvar__1___24Anonymous__7053,Vvar__1___24Anonymous__7054,Vvar__2___24Anonymous__7055,Vvar__2___24Anonymous__7056] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__7051,Vvar__1___24Anonymous__7053,Vvar__2___24Anonymous__7055) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__7052,Vvar__1___24Anonymous__7054,Vvar__2___24Anonymous__7056)
=> ( Vvar__2___24Anonymous__7055 = Vvar__2___24Anonymous__7056
& Vvar__1___24Anonymous__7053 = Vvar__1___24Anonymous__7054
& Vvar__0__C__7051 = Vvar__0__C__7052 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__7089,Vvar__0__C__7090,Vvar__1__num__7091,Vvar__1__num__7092,Vvar__2__denum__7093,Vvar__2__denum__7094,Vvar__3__condition__7095,Vvar__3__condition__7096] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__7089,Vvar__1__num__7091,Vvar__2__denum__7093,Vvar__3__condition__7095) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__7090,Vvar__1__num__7092,Vvar__2__denum__7094,Vvar__3__condition__7096)
=> ( Vvar__3__condition__7095 = Vvar__3__condition__7096
& Vvar__2__denum__7093 = Vvar__2__denum__7094
& Vvar__1__num__7091 = Vvar__1__num__7092
& Vvar__0__C__7089 = Vvar__0__C__7090 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__7103,Vvar__0__C__7104,Vvar__1__rsplit__left__7105,Vvar__1__rsplit__left__7106,Vvar__2__rsplit__common__7107,Vvar__2__rsplit__common__7108,Vvar__3__rsplit__right__7109,Vvar__3__rsplit__right__7110] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__7103,Vvar__1__rsplit__left__7105,Vvar__2__rsplit__common__7107,Vvar__3__rsplit__right__7109) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__7104,Vvar__1__rsplit__left__7106,Vvar__2__rsplit__common__7108,Vvar__3__rsplit__right__7110)
=> ( Vvar__3__rsplit__right__7109 = Vvar__3__rsplit__right__7110
& Vvar__2__rsplit__common__7107 = Vvar__2__rsplit__common__7108
& Vvar__1__rsplit__left__7105 = Vvar__1__rsplit__left__7106
& Vvar__0__C__7103 = Vvar__0__C__7104 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__2874,Vvar__0__C__2875] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2874) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2875)
=> Vvar__0__C__2874 = Vvar__0__C__2875 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__2872,Vvar__0__C__2873] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2872) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2873)
=> Vvar__0__C__2872 = Vvar__0__C__2873 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__2880,Vvar__0__C__2881,Vvar__1___24Anonymous__2882,Vvar__1___24Anonymous__2883] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2880,Vvar__1___24Anonymous__2882) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2881,Vvar__1___24Anonymous__2883)
=> ( Vvar__1___24Anonymous__2882 = Vvar__1___24Anonymous__2883
& Vvar__0__C__2880 = Vvar__0__C__2881 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__2884,Vvar__0__C__2885,Vvar__1___24Anonymous__2886,Vvar__1___24Anonymous__2887,Vvar__2___24Anonymous__2888,Vvar__2___24Anonymous__2889] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2884,Vvar__1___24Anonymous__2886,Vvar__2___24Anonymous__2888) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2885,Vvar__1___24Anonymous__2887,Vvar__2___24Anonymous__2889)
=> ( Vvar__2___24Anonymous__2888 = Vvar__2___24Anonymous__2889
& Vvar__1___24Anonymous__2886 = Vvar__1___24Anonymous__2887
& Vvar__0__C__2884 = Vvar__0__C__2885 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__2876,Vvar__0__C__2877,Vvar__1___24Anonymous__2878,Vvar__1___24Anonymous__2879] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2876,Vvar__1___24Anonymous__2878) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2877,Vvar__1___24Anonymous__2879)
=> ( Vvar__1___24Anonymous__2878 = Vvar__1___24Anonymous__2879
& Vvar__0__C__2876 = Vvar__0__C__2877 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__2896,Vvar__0__C__2897,Vvar__1___24Anonymous__2898,Vvar__1___24Anonymous__2899,Vvar__2___24Anonymous__2900,Vvar__2___24Anonymous__2901] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2896,Vvar__1___24Anonymous__2898,Vvar__2___24Anonymous__2900) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2897,Vvar__1___24Anonymous__2899,Vvar__2___24Anonymous__2901)
=> ( Vvar__2___24Anonymous__2900 = Vvar__2___24Anonymous__2901
& Vvar__1___24Anonymous__2898 = Vvar__1___24Anonymous__2899
& Vvar__0__C__2896 = Vvar__0__C__2897 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__2902,Vvar__0__C__2903,Vvar__1___24Anonymous__2904,Vvar__1___24Anonymous__2905] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2902,Vvar__1___24Anonymous__2904) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2903,Vvar__1___24Anonymous__2905)
=> ( Vvar__1___24Anonymous__2904 = Vvar__1___24Anonymous__2905
& Vvar__0__C__2902 = Vvar__0__C__2903 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__2906,Vvar__0__C__2907,Vvar__1___24Anonymous__2908,Vvar__1___24Anonymous__2909,Vvar__2___24Anonymous__2910,Vvar__2___24Anonymous__2911] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2906,Vvar__1___24Anonymous__2908,Vvar__2___24Anonymous__2910) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2907,Vvar__1___24Anonymous__2909,Vvar__2___24Anonymous__2911)
=> ( Vvar__2___24Anonymous__2910 = Vvar__2___24Anonymous__2911
& Vvar__1___24Anonymous__2908 = Vvar__1___24Anonymous__2909
& Vvar__0__C__2906 = Vvar__0__C__2907 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__2890,Vvar__0__C__2891,Vvar__1___24Anonymous__2892,Vvar__1___24Anonymous__2893,Vvar__2___24Anonymous__2894,Vvar__2___24Anonymous__2895] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2890,Vvar__1___24Anonymous__2892,Vvar__2___24Anonymous__2894) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2891,Vvar__1___24Anonymous__2893,Vvar__2___24Anonymous__2895)
=> ( Vvar__2___24Anonymous__2894 = Vvar__2___24Anonymous__2895
& Vvar__1___24Anonymous__2892 = Vvar__1___24Anonymous__2893
& Vvar__0__C__2890 = Vvar__0__C__2891 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__2527,Vvar__0__C__2528,Vvar__1___24Anonymous__2529,Vvar__1___24Anonymous__2530,Vvar__2___24Anonymous__2531,Vvar__2___24Anonymous__2532,Vvar__3___24Anonymous__2533,Vvar__3___24Anonymous__2534] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__2527,Vvar__1___24Anonymous__2529,Vvar__2___24Anonymous__2531,Vvar__3___24Anonymous__2533) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__2528,Vvar__1___24Anonymous__2530,Vvar__2___24Anonymous__2532,Vvar__3___24Anonymous__2534)
=> ( Vvar__3___24Anonymous__2533 = Vvar__3___24Anonymous__2534
& Vvar__2___24Anonymous__2531 = Vvar__2___24Anonymous__2532
& Vvar__1___24Anonymous__2529 = Vvar__1___24Anonymous__2530
& Vvar__0__C__2527 = Vvar__0__C__2528 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__2517,Vvar__0__C__2518,Vvar__1___24Anonymous__2519,Vvar__1___24Anonymous__2520] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__2517,Vvar__1___24Anonymous__2519) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__2518,Vvar__1___24Anonymous__2520)
=> ( Vvar__1___24Anonymous__2519 = Vvar__1___24Anonymous__2520
& Vvar__0__C__2517 = Vvar__0__C__2518 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__2521,Vvar__0__C__2522,Vvar__1___24Anonymous__2523,Vvar__1___24Anonymous__2524,Vvar__2___24Anonymous__2525,Vvar__2___24Anonymous__2526] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__2521,Vvar__1___24Anonymous__2523,Vvar__2___24Anonymous__2525) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__2522,Vvar__1___24Anonymous__2524,Vvar__2___24Anonymous__2526)
=> ( Vvar__2___24Anonymous__2525 = Vvar__2___24Anonymous__2526
& Vvar__1___24Anonymous__2523 = Vvar__1___24Anonymous__2524
& Vvar__0__C__2521 = Vvar__0__C__2522 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__2686,Vvar__0___24Anonymous__2687,Vvar__1___24Anonymous__2688,Vvar__1___24Anonymous__2689] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__2686,Vvar__1___24Anonymous__2688) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__2687,Vvar__1___24Anonymous__2689)
=> ( Vvar__1___24Anonymous__2688 = Vvar__1___24Anonymous__2689
& Vvar__0___24Anonymous__2686 = Vvar__0___24Anonymous__2687 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__2682,Vvar__0___24Anonymous__2683,Vvar__1___24Anonymous__2684,Vvar__1___24Anonymous__2685] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__2682,Vvar__1___24Anonymous__2684) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__2683,Vvar__1___24Anonymous__2685)
=> ( Vvar__1___24Anonymous__2684 = Vvar__1___24Anonymous__2685
& Vvar__0___24Anonymous__2682 = Vvar__0___24Anonymous__2683 ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__5231,Vvar__1___24Anonymous__5232,VX5233] :
( cProp___24t(Vvar__0__P__5231)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__5232)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__5231,Vvar__1___24Anonymous__5232,VX5233)
=> ( ( p(Vvar__0__P__5231)
& Vvar__1___24Anonymous__5232 = cCoq_2eInit_2eDatatypes_2etrue
& VX5233 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5231) )
| ( ~ p(Vvar__0__P__5231)
& Vvar__1___24Anonymous__5232 = cCoq_2eInit_2eDatatypes_2efalse
& VX5233 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5231) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__5406,Vvar__1__Q__5407,Vvar__2___24Anonymous__5408] :
( cProp___24t(Vvar__0__P__5406)
=> ( cProp___24t(Vvar__1__Q__5407)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__5408)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__5406,Vvar__1__Q__5407,Vvar__2___24Anonymous__5408)
=> ( ( p(Vvar__0__P__5406)
& Vvar__2___24Anonymous__5408 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__5407)
& Vvar__2___24Anonymous__5408 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__5445,Vvar__1__Plt__5446,Vvar__2__Pgt__5447,Vvar__3___24Anonymous__5448] :
( cProp___24t(Vvar__0__Peq__5445)
=> ( cProp___24t(Vvar__1__Plt__5446)
=> ( cProp___24t(Vvar__2__Pgt__5447)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__5448)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__5445,Vvar__1__Plt__5446,Vvar__2__Pgt__5447,Vvar__3___24Anonymous__5448)
=> ( ( p(Vvar__0__Peq__5445)
& Vvar__3___24Anonymous__5448 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__5446)
& Vvar__3___24Anonymous__5448 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__5447)
& Vvar__3___24Anonymous__5448 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX846] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX846)
=> ( VX846 = cCoq_2eInit_2eDatatypes_2etrue
| VX846 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX5444] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX5444)
=> ( VX5444 = cCoq_2eInit_2eDatatypes_2eEq
| VX5444 = cCoq_2eInit_2eDatatypes_2eLt
| VX5444 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__916,VX917] :
( cType___24t(Vvar__0__A__916)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__916,VX917)
=> ( VX917 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__916)
| ? [Vvar__1___24Anonymous__920] :
( t(Vvar__1___24Anonymous__920,Vvar__0__A__916)
& ? [Vvar__2___24Anonymous__921] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__916,Vvar__2___24Anonymous__921)
& VX917 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__916,Vvar__1___24Anonymous__920,Vvar__2___24Anonymous__921) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX138] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX138)
=> ( VX138 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__139] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__139)
& VX138 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__139) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__847,VX848] :
( cType___24t(Vvar__0__A__847)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__847,VX848)
=> ( ? [Vvar__1___24Anonymous__850] :
( t(Vvar__1___24Anonymous__850,Vvar__0__A__847)
& VX848 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__847,Vvar__1___24Anonymous__850) )
| VX848 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__847) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__866,Vvar__1__B__867,VX868] :
( cType___24t(Vvar__0__A__866)
=> ( cType___24t(Vvar__1__B__867)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__866,Vvar__1__B__867,VX868)
=> ? [Vvar__2___24Anonymous__871] :
( t(Vvar__2___24Anonymous__871,Vvar__0__A__866)
& ? [Vvar__3___24Anonymous__872] :
( t(Vvar__3___24Anonymous__872,Vvar__1__B__867)
& VX868 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__866,Vvar__1__B__867,Vvar__2___24Anonymous__871,Vvar__3___24Anonymous__872) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__5416,Vvar__1__B__5417,VX5418] :
( cType___24t(Vvar__0__A__5416)
=> ( cType___24t(Vvar__1__B__5417)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__5416,Vvar__1__B__5417,VX5418)
=> ( ? [Vvar__2___24Anonymous__5421] :
( t(Vvar__2___24Anonymous__5421,Vvar__0__A__5416)
& VX5418 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__5416,Vvar__1__B__5417,Vvar__2___24Anonymous__5421) )
| ? [Vvar__2___24Anonymous__5424] :
( t(Vvar__2___24Anonymous__5424,Vvar__1__B__5417)
& VX5418 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__5416,Vvar__1__B__5417,Vvar__2___24Anonymous__5424) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX137] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX137)
=> VX137 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__2003,Vvar__1___24Anonymous__2004] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__2003)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__2004)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__2003,Vvar__1___24Anonymous__2004)
=> ( Vvar__1___24Anonymous__2004 = Vvar__0__n__2003
| ? [Vvar__1__m__2008] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__2008)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__2003,Vvar__1__m__2008)
& Vvar__1___24Anonymous__2004 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__2008) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__3354,Vvar__1__P__3355,VX3358] :
( cType___24t(Vvar__0__A__3354)
=> ( c_24__type__3368___24t(Vvar__0__A__3354,Vvar__1__P__3355,Vvar__1__P__3355)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__3354,Vvar__1__P__3355,VX3358)
=> ? [Vvar__2__x__3363] :
( t(Vvar__2__x__3363,Vvar__0__A__3354)
& p(happ(Vvar__1__P__3355,Vvar__2__x__3363))
& VX3358 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__3354,Vvar__1__P__3355,Vvar__2__x__3363) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__22143,Vvar__1__P__22144,VX22147] :
( cType___24t(Vvar__0__A__22143)
=> ( c_24__type__22157___24t(Vvar__0__A__22143,Vvar__1__P__22144,Vvar__1__P__22144)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__22143,Vvar__1__P__22144,VX22147)
=> ? [Vvar__2__x__22152] :
( t(Vvar__2__x__22152,Vvar__0__A__22143)
& ? [Vvar__3___24Anonymous__22153] :
( t(Vvar__3___24Anonymous__22153,happ(Vvar__1__P__22144,Vvar__2__x__22152))
& VX22147 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__22143,Vvar__1__P__22144,Vvar__2__x__22152,Vvar__3___24Anonymous__22153) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__3417,Vvar__1__B__3418,VX3419] :
( cProp___24t(Vvar__0__A__3417)
=> ( cProp___24t(Vvar__1__B__3418)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__3417,Vvar__1__B__3418,VX3419)
=> ( ( p(Vvar__0__A__3417)
& VX3419 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3417,Vvar__1__B__3418) )
| ( p(Vvar__1__B__3418)
& VX3419 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3417,Vvar__1__B__3418) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__22228,Vvar__1__B__22229,VX22230] :
( cType___24t(Vvar__0__A__22228)
=> ( cProp___24t(Vvar__1__B__22229)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__22228,Vvar__1__B__22229,VX22230)
=> ( ? [Vvar__2___24Anonymous__22233] :
( t(Vvar__2___24Anonymous__22233,Vvar__0__A__22228)
& VX22230 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__22228,Vvar__1__B__22229,Vvar__2___24Anonymous__22233) )
| ( p(Vvar__1__B__22229)
& VX22230 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__22228,Vvar__1__B__22229) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__3447,Vvar__1__R__3448,Vvar__2__x__3453] :
( cType___24t(Vvar__0__A__3447)
=> ( c_24__type__3482___24t(Vvar__0__A__3447,Vvar__1__R__3448,Vvar__2__x__3453,Vvar__1__R__3448)
=> ( t(Vvar__2__x__3453,Vvar__0__A__3447)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__3447,Vvar__1__R__3448,Vvar__2__x__3453)
=> ( ! [Vvar__var__var__var__var__3__y__3463__3465__3467__3469__3471] :
( t(Vvar__var__var__var__var__3__y__3463__3465__3467__3469__3471,Vvar__0__A__3447)
=> ( p(happ(happ(Vvar__1__R__3448,Vvar__var__var__var__var__3__y__3463__3465__3467__3469__3471),Vvar__2__x__3453))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__3447,Vvar__1__R__3448,Vvar__var__var__var__var__3__y__3463__3465__3467__3469__3471) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__28248,Vvar__1__a__28249,Vvar__2___24Anonymous__28250,Vvar__3___24Anonymous__28251] :
( cType___24t(Vvar__0__A__28248)
=> ( t(Vvar__1__a__28249,Vvar__0__A__28248)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28248,Vvar__2___24Anonymous__28250)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28248,Vvar__3___24Anonymous__28251)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__28248,Vvar__1__a__28249,Vvar__2___24Anonymous__28250,Vvar__3___24Anonymous__28251)
=> ( ? [Vvar__2__l__28255] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28248,Vvar__2__l__28255)
& Vvar__3___24Anonymous__28251 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28248,Vvar__1__a__28249,Vvar__2__l__28255)
& Vvar__2___24Anonymous__28250 = Vvar__2__l__28255 )
| ? [Vvar__2__x__28258] :
( t(Vvar__2__x__28258,Vvar__0__A__28248)
& ? [Vvar__3__l__28259] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28248,Vvar__3__l__28259)
& ? [Vvar__4__l_27__28260] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28248,Vvar__4__l_27__28260)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__28248,Vvar__1__a__28249,Vvar__3__l__28259,Vvar__4__l_27__28260)
& Vvar__3___24Anonymous__28251 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28248,Vvar__2__x__28258,Vvar__4__l_27__28260)
& Vvar__2___24Anonymous__28250 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28248,Vvar__2__x__28258,Vvar__3__l__28259) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__8475,Vvar__1__P__8476,Vvar__2___24Anonymous__8479] :
( cType___24t(Vvar__0__A__8475)
=> ( c_24__type__8499___24t(Vvar__0__A__8475,Vvar__1__P__8476,Vvar__2___24Anonymous__8479,Vvar__1__P__8476)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8475,Vvar__2___24Anonymous__8479)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__8475,Vvar__1__P__8476,Vvar__2___24Anonymous__8479)
=> ( ? [Vvar__2__x__8485] :
( t(Vvar__2__x__8485,Vvar__0__A__8475)
& ? [Vvar__3__l__8486] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8475,Vvar__3__l__8486)
& p(happ(Vvar__1__P__8476,Vvar__2__x__8485))
& Vvar__2___24Anonymous__8479 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8475,Vvar__2__x__8485,Vvar__3__l__8486) ) )
| ? [Vvar__2__x__8492] :
( t(Vvar__2__x__8492,Vvar__0__A__8475)
& ? [Vvar__3__l__8493] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8475,Vvar__3__l__8493)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__8475,Vvar__1__P__8476,Vvar__3__l__8493)
& Vvar__2___24Anonymous__8479 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8475,Vvar__2__x__8492,Vvar__3__l__8493) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__23266,Vvar__1__P__23267,Vvar__2___24Anonymous__23270] :
( cType___24t(Vvar__0__A__23266)
=> ( c_24__type__23288___24t(Vvar__0__A__23266,Vvar__1__P__23267,Vvar__2___24Anonymous__23270,Vvar__1__P__23267)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23266,Vvar__2___24Anonymous__23270)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__23266,Vvar__1__P__23267,Vvar__2___24Anonymous__23270)
=> ( Vvar__2___24Anonymous__23270 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23266)
| ? [Vvar__2__x__23280] :
( t(Vvar__2__x__23280,Vvar__0__A__23266)
& ? [Vvar__3__l__23281] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23266,Vvar__3__l__23281)
& p(happ(Vvar__1__P__23267,Vvar__2__x__23280))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__23266,Vvar__1__P__23267,Vvar__3__l__23281)
& Vvar__2___24Anonymous__23270 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23266,Vvar__2__x__23280,Vvar__3__l__23281) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__8501,Vvar__1__B__8502,Vvar__2__R__8503,Vvar__3___24Anonymous__8508,Vvar__4___24Anonymous__8509] :
( cType___24t(Vvar__0__A__8501)
=> ( cType___24t(Vvar__1__B__8502)
=> ( c_24__type__8546___24t(Vvar__0__A__8501,Vvar__1__B__8502,Vvar__2__R__8503,Vvar__3___24Anonymous__8508,Vvar__4___24Anonymous__8509,Vvar__2__R__8503)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8501,Vvar__3___24Anonymous__8508)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__8502,Vvar__4___24Anonymous__8509)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__8501,Vvar__1__B__8502,Vvar__2__R__8503,Vvar__3___24Anonymous__8508,Vvar__4___24Anonymous__8509)
=> ( ( Vvar__4___24Anonymous__8509 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__8502)
& Vvar__3___24Anonymous__8508 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__8501) )
| ? [Vvar__3__x__8525] :
( t(Vvar__3__x__8525,Vvar__0__A__8501)
& ? [Vvar__4__y__8526] :
( t(Vvar__4__y__8526,Vvar__1__B__8502)
& ? [Vvar__5__l__8527] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8501,Vvar__5__l__8527)
& ? [Vvar__6__l_27__8528] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__8502,Vvar__6__l_27__8528)
& p(happ(happ(Vvar__2__R__8503,Vvar__3__x__8525),Vvar__4__y__8526))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__8501,Vvar__1__B__8502,Vvar__2__R__8503,Vvar__5__l__8527,Vvar__6__l_27__8528)
& Vvar__4___24Anonymous__8509 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__8502,Vvar__4__y__8526,Vvar__6__l_27__8528)
& Vvar__3___24Anonymous__8508 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8501,Vvar__3__x__8525,Vvar__5__l__8527) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__23290,Vvar__1__R__23291,Vvar__2___24Anonymous__23296] :
( cType___24t(Vvar__0__A__23290)
=> ( c_24__type__23323___24t(Vvar__0__A__23290,Vvar__1__R__23291,Vvar__2___24Anonymous__23296,Vvar__1__R__23291)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23290,Vvar__2___24Anonymous__23296)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__23290,Vvar__1__R__23291,Vvar__2___24Anonymous__23296)
=> ( Vvar__2___24Anonymous__23296 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23290)
| ? [Vvar__2__a__23310] :
( t(Vvar__2__a__23310,Vvar__0__A__23290)
& ? [Vvar__3__l__23311] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23290,Vvar__3__l__23311)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__23290,happ(Vvar__1__R__23291,Vvar__2__a__23310),Vvar__3__l__23311)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__23290,Vvar__1__R__23291,Vvar__3__l__23311)
& Vvar__2___24Anonymous__23296 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23290,Vvar__2__a__23310,Vvar__3__l__23311) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__1908,Vvar__1___24Anonymous__1909] :
( cType___24t(Vvar__0__A__1908)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1908,Vvar__1___24Anonymous__1909)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__1908,Vvar__1___24Anonymous__1909))
=> ( Vvar__1___24Anonymous__1909 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1908)
| ? [Vvar__1__x__1913] :
( t(Vvar__1__x__1913,Vvar__0__A__1908)
& ? [Vvar__2__l__1914] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1908,Vvar__2__l__1914)
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__1908,Vvar__1__x__1913,Vvar__2__l__1914))
& p(cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__1908,Vvar__2__l__1914))
& Vvar__1___24Anonymous__1909 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1908,Vvar__1__x__1913,Vvar__2__l__1914) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__21726,Vvar__1__eqA__21727,Vvar__2__x__21732,Vvar__3___24Anonymous__21733] :
( cType___24t(Vvar__0__A__21726)
=> ( c_24__type__21766___24t(Vvar__0__A__21726,Vvar__1__eqA__21727,Vvar__2__x__21732,Vvar__3___24Anonymous__21733,Vvar__1__eqA__21727)
=> ( t(Vvar__2__x__21732,Vvar__0__A__21726)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21726,Vvar__3___24Anonymous__21733)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__21726,Vvar__1__eqA__21727,Vvar__2__x__21732,Vvar__3___24Anonymous__21733)
=> ( ? [Vvar__3__y__21742] :
( t(Vvar__3__y__21742,Vvar__0__A__21726)
& ? [Vvar__4__l__21743] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21726,Vvar__4__l__21743)
& p(happ(happ(Vvar__1__eqA__21727,Vvar__2__x__21732),Vvar__3__y__21742))
& Vvar__3___24Anonymous__21733 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21726,Vvar__3__y__21742,Vvar__4__l__21743) ) )
| ? [Vvar__3__y__21752] :
( t(Vvar__3__y__21752,Vvar__0__A__21726)
& ? [Vvar__4__l__21753] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21726,Vvar__4__l__21753)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__21726,Vvar__1__eqA__21727,Vvar__2__x__21732,Vvar__4__l__21753)
& Vvar__3___24Anonymous__21733 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21726,Vvar__3__y__21752,Vvar__4__l__21753) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__21768,Vvar__1__eqA__21769,Vvar__2___24Anonymous__21774] :
( cType___24t(Vvar__0__A__21768)
=> ( c_24__type__21801___24t(Vvar__0__A__21768,Vvar__1__eqA__21769,Vvar__2___24Anonymous__21774,Vvar__1__eqA__21769)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21768,Vvar__2___24Anonymous__21774)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__21768,Vvar__1__eqA__21769,Vvar__2___24Anonymous__21774)
=> ( Vvar__2___24Anonymous__21774 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__21768)
| ? [Vvar__2__x__21788] :
( t(Vvar__2__x__21788,Vvar__0__A__21768)
& ? [Vvar__3__l__21789] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21768,Vvar__3__l__21789)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__21768,Vvar__1__eqA__21769,Vvar__2__x__21788,Vvar__3__l__21789)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__21768,Vvar__1__eqA__21769,Vvar__3__l__21789)
& Vvar__2___24Anonymous__21774 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21768,Vvar__2__x__21788,Vvar__3__l__21789) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__21803,Vvar__1__eqA__21804,Vvar__2___24Anonymous__21809,Vvar__3___24Anonymous__21810] :
( cType___24t(Vvar__0__A__21803)
=> ( c_24__type__21841___24t(Vvar__0__A__21803,Vvar__1__eqA__21804,Vvar__2___24Anonymous__21809,Vvar__3___24Anonymous__21810,Vvar__1__eqA__21804)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21803,Vvar__2___24Anonymous__21809)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21803,Vvar__3___24Anonymous__21810)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__21803,Vvar__1__eqA__21804,Vvar__2___24Anonymous__21809,Vvar__3___24Anonymous__21810)
=> ( ( Vvar__3___24Anonymous__21810 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__21803)
& Vvar__2___24Anonymous__21809 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__21803) )
| ? [Vvar__2__x__21824] :
( t(Vvar__2__x__21824,Vvar__0__A__21803)
& ? [Vvar__3__x_27__21825] :
( t(Vvar__3__x_27__21825,Vvar__0__A__21803)
& ? [Vvar__4__l__21826] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21803,Vvar__4__l__21826)
& ? [Vvar__5__l_27__21827] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21803,Vvar__5__l_27__21827)
& p(happ(happ(Vvar__1__eqA__21804,Vvar__2__x__21824),Vvar__3__x_27__21825))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__21803,Vvar__1__eqA__21804,Vvar__4__l__21826,Vvar__5__l_27__21827)
& Vvar__3___24Anonymous__21810 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21803,Vvar__3__x_27__21825,Vvar__5__l_27__21827)
& Vvar__2___24Anonymous__21809 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21803,Vvar__2__x__21824,Vvar__4__l__21826) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX805] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX805)
=> ( VX805 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__806] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__806)
& VX805 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__806) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX812] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX812)
=> ( VX812 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__813] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__813)
& VX812 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__813) )
| ? [Vvar__0___24Anonymous__814] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__814)
& VX812 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__814) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX792] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX792)
=> ( ? [Vvar__0___24Anonymous__793] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__793)
& VX792 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__793) )
| ? [Vvar__0___24Anonymous__794] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__794)
& VX792 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__794) )
| VX792 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX2039] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX2039)
=> ? [Vvar__0__Qnum__2040] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__2040)
& ? [Vvar__1__Qden__2041] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__2041)
& VX2039 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__2040,Vvar__1__Qden__2041) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
! [Vvar__0__A__2118,Vvar__1__R__2119] :
( cType___24t(Vvar__0__A__2118)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2118,Vvar__1__R__2119)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__2118,Vvar__1__R__2119)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__2118,Vvar__1__R__2119)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__2118,Vvar__1__R__2119)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
! [Vvar__0__A__2110,Vvar__1__R__2111] :
( cType___24t(Vvar__0__A__2110)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2110,Vvar__1__R__2111)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__2110,Vvar__1__R__2111)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__2110,Vvar__1__R__2111)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__2110,Vvar__1__R__2111)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__2110,Vvar__1__R__2111)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
! [Vvar__0__A__2102,Vvar__1__R__2103] :
( cType___24t(Vvar__0__A__2102)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2102,Vvar__1__R__2103)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__2102,Vvar__1__R__2103)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__2102,Vvar__1__R__2103)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__2102,Vvar__1__R__2103)
& cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__2102,Vvar__1__R__2103)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__2095,Vvar__1__R__2096] :
( cType___24t(Vvar__0__A__2095)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2095,Vvar__1__R__2096)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__2095,Vvar__1__R__2096)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__2095,Vvar__1__R__2096)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__2095,Vvar__1__R__2096)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__10014,Vvar__1__leA__10015,Vvar__2___24Anonymous__10020] :
( cType___24t(Vvar__0__A__10014)
=> ( c_24__type__10110___24t(Vvar__0__A__10014,Vvar__1__leA__10015,Vvar__2___24Anonymous__10020,Vvar__1__leA__10015)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10014,Vvar__2___24Anonymous__10020)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__10014,Vvar__1__leA__10015,Vvar__2___24Anonymous__10020)
=> ( Vvar__2___24Anonymous__10020 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__10014)
| ? [Vvar__2__x__10034] :
( t(Vvar__2__x__10034,Vvar__0__A__10014)
& Vvar__2___24Anonymous__10020 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__10014,Vvar__2__x__10034,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__10014)) )
| ? [Vvar__2__x__10041] :
( t(Vvar__2__x__10041,Vvar__0__A__10014)
& ? [Vvar__3__y__10042] :
( t(Vvar__3__y__10042,Vvar__0__A__10014)
& ? [Vvar__4__l__10043] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10014,Vvar__4__l__10043)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__10014,Vvar__1__leA__10015,Vvar__2__x__10041,Vvar__3__y__10042)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__10014,Vvar__1__leA__10015,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__10014,Vvar__4__l__10043,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__10014,Vvar__3__y__10042,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__10014))))
& Vvar__2___24Anonymous__10020 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2410308___24a6(Vvar__0__A__10014,Vvar__1__leA__10015,Vvar__2___24Anonymous__10020,Vvar__2__x__10041,Vvar__3__y__10042,Vvar__4__l__10043) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__23351,Vvar__1__leA__23352,Vvar__2___24Anonymous__23357,Vvar__3___24Anonymous__23358] :
( cType___24t(Vvar__0__A__23351)
=> ( c_24__type__23400___24t(Vvar__0__A__23351,Vvar__1__leA__23352,Vvar__2___24Anonymous__23357,Vvar__3___24Anonymous__23358,Vvar__1__leA__23352)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23351,Vvar__2___24Anonymous__23357)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23351,Vvar__3___24Anonymous__23358)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__23351,Vvar__1__leA__23352,Vvar__2___24Anonymous__23357,Vvar__3___24Anonymous__23358)
=> ( ? [Vvar__2__a__23366] :
( t(Vvar__2__a__23366,Vvar__0__A__23351)
& ? [Vvar__3__x__23367] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23351,Vvar__3__x__23367)
& Vvar__3___24Anonymous__23358 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23351,Vvar__2__a__23366,Vvar__3__x__23367)
& Vvar__2___24Anonymous__23357 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23351) ) )
| ? [Vvar__2__a__23374] :
( t(Vvar__2__a__23374,Vvar__0__A__23351)
& ? [Vvar__3__b__23375] :
( t(Vvar__3__b__23375,Vvar__0__A__23351)
& p(happ(happ(Vvar__1__leA__23352,Vvar__2__a__23374),Vvar__3__b__23375))
& ? [Vvar__5__x__23377] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23351,Vvar__5__x__23377)
& ? [Vvar__6__y__23378] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23351,Vvar__6__y__23378)
& Vvar__3___24Anonymous__23358 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23351,Vvar__3__b__23375,Vvar__6__y__23378)
& Vvar__2___24Anonymous__23357 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23351,Vvar__2__a__23374,Vvar__5__x__23377) ) ) ) )
| ? [Vvar__2__a__23385] :
( t(Vvar__2__a__23385,Vvar__0__A__23351)
& ? [Vvar__3__x__23386] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23351,Vvar__3__x__23386)
& ? [Vvar__4__y__23387] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23351,Vvar__4__y__23387)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__23351,Vvar__1__leA__23352,Vvar__3__x__23386,Vvar__4__y__23387)
& Vvar__3___24Anonymous__23358 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23351,Vvar__2__a__23385,Vvar__4__y__23387)
& Vvar__2___24Anonymous__23357 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23351,Vvar__2__a__23385,Vvar__3__x__23386) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__710,Vvar__1__R__711,Vvar__2__x__712,Vvar__3___24Anonymous__713] :
( cType___24t(Vvar__0__A__710)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__710,Vvar__1__R__711)
=> ( t(Vvar__2__x__712,Vvar__0__A__710)
=> ( t(Vvar__3___24Anonymous__713,Vvar__0__A__710)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__710,Vvar__1__R__711,Vvar__2__x__712,Vvar__3___24Anonymous__713)
=> ( ? [Vvar__3__y__718] :
( t(Vvar__3__y__718,Vvar__0__A__710)
& p(happ(happ(Vvar__1__R__711,Vvar__2__x__712),Vvar__3__y__718))
& Vvar__3___24Anonymous__713 = Vvar__3__y__718 )
| Vvar__3___24Anonymous__713 = Vvar__2__x__712 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans',axiom,
! [Vvar__0__A__740,Vvar__1__R__741,Vvar__1___24Anonymous__742,Vvar__2___24Anonymous__743] :
( cType___24t(Vvar__0__A__740)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__740,Vvar__1__R__741)
=> ( t(Vvar__1___24Anonymous__742,Vvar__0__A__740)
=> ( t(Vvar__2___24Anonymous__743,Vvar__0__A__740)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__740,Vvar__1__R__741,Vvar__1___24Anonymous__742,Vvar__2___24Anonymous__743)
=> ( ? [Vvar__2__x__747] :
( t(Vvar__2__x__747,Vvar__0__A__740)
& ? [Vvar__3__y__748] :
( t(Vvar__3__y__748,Vvar__0__A__740)
& p(happ(happ(Vvar__1__R__741,Vvar__2__x__747),Vvar__3__y__748))
& Vvar__2___24Anonymous__743 = Vvar__3__y__748
& Vvar__1___24Anonymous__742 = Vvar__2__x__747 ) )
| ? [Vvar__2__x__752] :
( t(Vvar__2__x__752,Vvar__0__A__740)
& Vvar__2___24Anonymous__743 = Vvar__2__x__752
& Vvar__1___24Anonymous__742 = Vvar__2__x__752 )
| ? [Vvar__2__x__755] :
( t(Vvar__2__x__755,Vvar__0__A__740)
& ? [Vvar__3__y__756] :
( t(Vvar__3__y__756,Vvar__0__A__740)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__740,Vvar__1__R__741,Vvar__2__x__755,Vvar__3__y__756)
& Vvar__2___24Anonymous__743 = Vvar__2__x__755
& Vvar__1___24Anonymous__742 = Vvar__3__y__756 ) )
| ? [Vvar__2__x__760] :
( t(Vvar__2__x__760,Vvar__0__A__740)
& ? [Vvar__3__y__761] :
( t(Vvar__3__y__761,Vvar__0__A__740)
& ? [Vvar__4__z__762] :
( t(Vvar__4__z__762,Vvar__0__A__740)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__740,Vvar__1__R__741,Vvar__2__x__760,Vvar__3__y__761)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__740,Vvar__1__R__741,Vvar__3__y__761,Vvar__4__z__762)
& Vvar__2___24Anonymous__743 = Vvar__4__z__762
& Vvar__1___24Anonymous__742 = Vvar__2__x__760 ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
! [Vvar__0__A__2266,Vvar__1__R__2267,Vvar__2__x__2268,Vvar__3___24Anonymous__2269] :
( cType___24t(Vvar__0__A__2266)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2266,Vvar__1__R__2267)
=> ( t(Vvar__2__x__2268,Vvar__0__A__2266)
=> ( t(Vvar__3___24Anonymous__2269,Vvar__0__A__2266)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__2266,Vvar__1__R__2267,Vvar__2__x__2268,Vvar__3___24Anonymous__2269)
=> ( Vvar__3___24Anonymous__2269 = Vvar__2__x__2268
| ? [Vvar__3__y__2277] :
( t(Vvar__3__y__2277,Vvar__0__A__2266)
& ? [Vvar__4__z__2278] :
( t(Vvar__4__z__2278,Vvar__0__A__2266)
& ( p(happ(happ(Vvar__1__R__2267,Vvar__2__x__2268),Vvar__3__y__2277))
| p(happ(happ(Vvar__1__R__2267,Vvar__3__y__2277),Vvar__2__x__2268)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__2266,Vvar__1__R__2267,Vvar__3__y__2277,Vvar__4__z__2278)
& Vvar__3___24Anonymous__2269 = Vvar__4__z__2278 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
! [Vvar__0__A__2301,Vvar__1__R__2302,Vvar__2__x__2303,Vvar__3___24Anonymous__2304] :
( cType___24t(Vvar__0__A__2301)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2301,Vvar__1__R__2302)
=> ( t(Vvar__2__x__2303,Vvar__0__A__2301)
=> ( t(Vvar__3___24Anonymous__2304,Vvar__0__A__2301)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__2301,Vvar__1__R__2302,Vvar__2__x__2303,Vvar__3___24Anonymous__2304)
=> ( Vvar__3___24Anonymous__2304 = Vvar__2__x__2303
| ? [Vvar__3__y__2312] :
( t(Vvar__3__y__2312,Vvar__0__A__2301)
& ? [Vvar__4__z__2313] :
( t(Vvar__4__z__2313,Vvar__0__A__2301)
& ( p(happ(happ(Vvar__1__R__2302,Vvar__3__y__2312),Vvar__4__z__2313))
| p(happ(happ(Vvar__1__R__2302,Vvar__4__z__2313),Vvar__3__y__2312)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__2301,Vvar__1__R__2302,Vvar__2__x__2303,Vvar__3__y__2312)
& Vvar__3___24Anonymous__2304 = Vvar__4__z__2313 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
! [Vvar__0__A__229,Vvar__1__R__230,Vvar__2__x__231,Vvar__3___24Anonymous__232] :
( cType___24t(Vvar__0__A__229)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__229,Vvar__1__R__230)
=> ( t(Vvar__2__x__231,Vvar__0__A__229)
=> ( t(Vvar__3___24Anonymous__232,Vvar__0__A__229)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__229,Vvar__1__R__230,Vvar__2__x__231,Vvar__3___24Anonymous__232)
=> ( ? [Vvar__3__y__237] :
( t(Vvar__3__y__237,Vvar__0__A__229)
& p(happ(happ(Vvar__1__R__230,Vvar__2__x__231),Vvar__3__y__237))
& Vvar__3___24Anonymous__232 = Vvar__3__y__237 )
| Vvar__3___24Anonymous__232 = Vvar__2__x__231
| ? [Vvar__3__y__245] :
( t(Vvar__3__y__245,Vvar__0__A__229)
& ? [Vvar__4__z__246] :
( t(Vvar__4__z__246,Vvar__0__A__229)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__229,Vvar__1__R__230,Vvar__2__x__231,Vvar__3__y__245)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__229,Vvar__1__R__230,Vvar__3__y__245,Vvar__4__z__246)
& Vvar__3___24Anonymous__232 = Vvar__4__z__246 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
! [Vvar__0__A__2186,Vvar__1__R__2187,Vvar__2__x__2188,Vvar__3___24Anonymous__2189] :
( cType___24t(Vvar__0__A__2186)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2186,Vvar__1__R__2187)
=> ( t(Vvar__2__x__2188,Vvar__0__A__2186)
=> ( t(Vvar__3___24Anonymous__2189,Vvar__0__A__2186)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__2186,Vvar__1__R__2187,Vvar__2__x__2188,Vvar__3___24Anonymous__2189)
=> ( Vvar__3___24Anonymous__2189 = Vvar__2__x__2188
| ? [Vvar__3__y__2197] :
( t(Vvar__3__y__2197,Vvar__0__A__2186)
& ? [Vvar__4__z__2198] :
( t(Vvar__4__z__2198,Vvar__0__A__2186)
& p(happ(happ(Vvar__1__R__2187,Vvar__2__x__2188),Vvar__3__y__2197))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__2186,Vvar__1__R__2187,Vvar__3__y__2197,Vvar__4__z__2198)
& Vvar__3___24Anonymous__2189 = Vvar__4__z__2198 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
! [Vvar__0__A__2221,Vvar__1__R__2222,Vvar__2__x__2223,Vvar__3___24Anonymous__2224] :
( cType___24t(Vvar__0__A__2221)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2221,Vvar__1__R__2222)
=> ( t(Vvar__2__x__2223,Vvar__0__A__2221)
=> ( t(Vvar__3___24Anonymous__2224,Vvar__0__A__2221)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__2221,Vvar__1__R__2222,Vvar__2__x__2223,Vvar__3___24Anonymous__2224)
=> ( Vvar__3___24Anonymous__2224 = Vvar__2__x__2223
| ? [Vvar__3__y__2232] :
( t(Vvar__3__y__2232,Vvar__0__A__2221)
& ? [Vvar__4__z__2233] :
( t(Vvar__4__z__2233,Vvar__0__A__2221)
& p(happ(happ(Vvar__1__R__2222,Vvar__3__y__2232),Vvar__4__z__2233))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__2221,Vvar__1__R__2222,Vvar__2__x__2223,Vvar__3__y__2232)
& Vvar__3___24Anonymous__2224 = Vvar__4__z__2233 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
! [Vvar__0__A__95,Vvar__1__R__96,Vvar__2__x__97,Vvar__3___24Anonymous__98] :
( cType___24t(Vvar__0__A__95)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__95,Vvar__1__R__96)
=> ( t(Vvar__2__x__97,Vvar__0__A__95)
=> ( t(Vvar__3___24Anonymous__98,Vvar__0__A__95)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__95,Vvar__1__R__96,Vvar__2__x__97,Vvar__3___24Anonymous__98)
=> ( ? [Vvar__3__y__103] :
( t(Vvar__3__y__103,Vvar__0__A__95)
& p(happ(happ(Vvar__1__R__96,Vvar__2__x__97),Vvar__3__y__103))
& Vvar__3___24Anonymous__98 = Vvar__3__y__103 )
| ? [Vvar__3__y__108] :
( t(Vvar__3__y__108,Vvar__0__A__95)
& ? [Vvar__4__z__109] :
( t(Vvar__4__z__109,Vvar__0__A__95)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__95,Vvar__1__R__96,Vvar__2__x__97,Vvar__3__y__108)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__95,Vvar__1__R__96,Vvar__3__y__108,Vvar__4__z__109)
& Vvar__3___24Anonymous__98 = Vvar__4__z__109 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
! [Vvar__0__A__516,Vvar__1__R__517,Vvar__2__x__518,Vvar__3___24Anonymous__519] :
( cType___24t(Vvar__0__A__516)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__516,Vvar__1__R__517)
=> ( t(Vvar__2__x__518,Vvar__0__A__516)
=> ( t(Vvar__3___24Anonymous__519,Vvar__0__A__516)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__516,Vvar__1__R__517,Vvar__2__x__518,Vvar__3___24Anonymous__519)
=> ( ? [Vvar__3__y__524] :
( t(Vvar__3__y__524,Vvar__0__A__516)
& p(happ(happ(Vvar__1__R__517,Vvar__2__x__518),Vvar__3__y__524))
& Vvar__3___24Anonymous__519 = Vvar__3__y__524 )
| ? [Vvar__3__y__529] :
( t(Vvar__3__y__529,Vvar__0__A__516)
& ? [Vvar__4__z__530] :
( t(Vvar__4__z__530,Vvar__0__A__516)
& p(happ(happ(Vvar__1__R__517,Vvar__2__x__518),Vvar__3__y__529))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__516,Vvar__1__R__517,Vvar__3__y__529,Vvar__4__z__530)
& Vvar__3___24Anonymous__519 = Vvar__4__z__530 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
! [Vvar__0__A__685,Vvar__1__R__686,Vvar__2__x__687,Vvar__3___24Anonymous__688] :
( cType___24t(Vvar__0__A__685)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__685,Vvar__1__R__686)
=> ( t(Vvar__2__x__687,Vvar__0__A__685)
=> ( t(Vvar__3___24Anonymous__688,Vvar__0__A__685)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__685,Vvar__1__R__686,Vvar__2__x__687,Vvar__3___24Anonymous__688)
=> ( ? [Vvar__3__y__693] :
( t(Vvar__3__y__693,Vvar__0__A__685)
& p(happ(happ(Vvar__1__R__686,Vvar__2__x__687),Vvar__3__y__693))
& Vvar__3___24Anonymous__688 = Vvar__3__y__693 )
| ? [Vvar__3__y__698] :
( t(Vvar__3__y__698,Vvar__0__A__685)
& ? [Vvar__4__z__699] :
( t(Vvar__4__z__699,Vvar__0__A__685)
& p(happ(happ(Vvar__1__R__686,Vvar__3__y__698),Vvar__4__z__699))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__685,Vvar__1__R__686,Vvar__2__x__687,Vvar__3__y__698)
& Vvar__3___24Anonymous__688 = Vvar__4__z__699 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Permutation.Permutation',axiom,
! [Vvar__0__A__2013,Vvar__1___24Anonymous__2014,Vvar__2___24Anonymous__2015] :
( cType___24t(Vvar__0__A__2013)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2013,Vvar__1___24Anonymous__2014)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2013,Vvar__2___24Anonymous__2015)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__2013,Vvar__1___24Anonymous__2014,Vvar__2___24Anonymous__2015)
=> ( ( Vvar__2___24Anonymous__2015 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2013)
& Vvar__1___24Anonymous__2014 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2013) )
| ? [Vvar__1__x__2019] :
( t(Vvar__1__x__2019,Vvar__0__A__2013)
& ? [Vvar__2__l__2020] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2013,Vvar__2__l__2020)
& ? [Vvar__3__l_27__2021] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2013,Vvar__3__l_27__2021)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__2013,Vvar__2__l__2020,Vvar__3__l_27__2021)
& Vvar__2___24Anonymous__2015 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2013,Vvar__1__x__2019,Vvar__3__l_27__2021)
& Vvar__1___24Anonymous__2014 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2013,Vvar__1__x__2019,Vvar__2__l__2020) ) ) )
| ? [Vvar__1__x__2024] :
( t(Vvar__1__x__2024,Vvar__0__A__2013)
& ? [Vvar__2__y__2025] :
( t(Vvar__2__y__2025,Vvar__0__A__2013)
& ? [Vvar__3__l__2026] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2013,Vvar__3__l__2026)
& Vvar__2___24Anonymous__2015 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2013,Vvar__1__x__2024,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2013,Vvar__2__y__2025,Vvar__3__l__2026))
& Vvar__1___24Anonymous__2014 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2013,Vvar__2__y__2025,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2013,Vvar__1__x__2024,Vvar__3__l__2026)) ) ) )
| ? [Vvar__1__l__2028] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2013,Vvar__1__l__2028)
& ? [Vvar__2__l_27__2029] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2013,Vvar__2__l_27__2029)
& ? [Vvar__3__l_27_27__2030] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2013,Vvar__3__l_27_27__2030)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__2013,Vvar__1__l__2028,Vvar__2__l_27__2029)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__2013,Vvar__2__l_27__2029,Vvar__3__l_27_27__2030)
& Vvar__2___24Anonymous__2015 = Vvar__3__l_27_27__2030
& Vvar__1___24Anonymous__2014 = Vvar__1__l__2028 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__22013,Vvar__1__R__22014,Vvar__2__a__22019,Vvar__3___24Anonymous__22020] :
( cType___24t(Vvar__0__A__22013)
=> ( c_24__type__22050___24t(Vvar__0__A__22013,Vvar__1__R__22014,Vvar__2__a__22019,Vvar__3___24Anonymous__22020,Vvar__1__R__22014)
=> ( t(Vvar__2__a__22019,Vvar__0__A__22013)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22013,Vvar__3___24Anonymous__22020)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__22013,Vvar__1__R__22014,Vvar__2__a__22019,Vvar__3___24Anonymous__22020)
=> ( Vvar__3___24Anonymous__22020 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22013)
| ? [Vvar__3__b__22036] :
( t(Vvar__3__b__22036,Vvar__0__A__22013)
& ? [Vvar__4__l__22037] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22013,Vvar__4__l__22037)
& p(happ(happ(Vvar__1__R__22014,Vvar__2__a__22019),Vvar__3__b__22036))
& Vvar__3___24Anonymous__22020 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22013,Vvar__3__b__22036,Vvar__4__l__22037) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__21970,Vvar__1__R__21971,Vvar__2___24Anonymous__21976] :
( cType___24t(Vvar__0__A__21970)
=> ( c_24__type__22011___24t(Vvar__0__A__21970,Vvar__1__R__21971,Vvar__2___24Anonymous__21976,Vvar__1__R__21971)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21970,Vvar__2___24Anonymous__21976)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__21970,Vvar__1__R__21971,Vvar__2___24Anonymous__21976)
=> ( Vvar__2___24Anonymous__21976 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__21970)
| ? [Vvar__2__a__21990] :
( t(Vvar__2__a__21990,Vvar__0__A__21970)
& Vvar__2___24Anonymous__21976 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21970,Vvar__2__a__21990,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__21970)) )
| ? [Vvar__2__a__21997] :
( t(Vvar__2__a__21997,Vvar__0__A__21970)
& ? [Vvar__3__b__21998] :
( t(Vvar__3__b__21998,Vvar__0__A__21970)
& ? [Vvar__4__l__21999] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21970,Vvar__4__l__21999)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__21970,Vvar__1__R__21971,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21970,Vvar__3__b__21998,Vvar__4__l__21999))
& p(happ(happ(Vvar__1__R__21971,Vvar__2__a__21997),Vvar__3__b__21998))
& Vvar__2___24Anonymous__21976 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21970,Vvar__2__a__21997,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21970,Vvar__3__b__21998,Vvar__4__l__21999)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__22052,Vvar__1__R__22053,Vvar__2___24Anonymous__22058] :
( cType___24t(Vvar__0__A__22052)
=> ( c_24__type__22085___24t(Vvar__0__A__22052,Vvar__1__R__22053,Vvar__2___24Anonymous__22058,Vvar__1__R__22053)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22052,Vvar__2___24Anonymous__22058)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__22052,Vvar__1__R__22053,Vvar__2___24Anonymous__22058)
=> ( Vvar__2___24Anonymous__22058 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22052)
| ? [Vvar__2__a__22072] :
( t(Vvar__2__a__22072,Vvar__0__A__22052)
& ? [Vvar__3__l__22073] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22052,Vvar__3__l__22073)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__22052,Vvar__1__R__22053,Vvar__3__l__22073)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__22052,Vvar__1__R__22053,Vvar__2__a__22072,Vvar__3__l__22073)
& Vvar__2___24Anonymous__22058 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22052,Vvar__2__a__22072,Vvar__3__l__22073) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__23405,Vvar__1__R__23406,Vvar__2___24Anonymous__23411] :
( cType___24t(Vvar__0__A__23405)
=> ( c_24__type__23438___24t(Vvar__0__A__23405,Vvar__1__R__23406,Vvar__2___24Anonymous__23411,Vvar__1__R__23406)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23405,Vvar__2___24Anonymous__23411)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__23405,Vvar__1__R__23406,Vvar__2___24Anonymous__23411)
=> ( Vvar__2___24Anonymous__23411 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23405)
| ? [Vvar__2__a__23425] :
( t(Vvar__2__a__23425,Vvar__0__A__23405)
& ? [Vvar__3__l__23426] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23405,Vvar__3__l__23426)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__23405,Vvar__1__R__23406,Vvar__3__l__23426)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__23405,happ(Vvar__1__R__23406,Vvar__2__a__23425),Vvar__3__l__23426)
& Vvar__2___24Anonymous__23411 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23405,Vvar__2__a__23425,Vvar__3__l__23426) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__22751,Vvar__1___24Anonymous__22752,VX22753] :
( cType___24t(Vvar__0__A__22751)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__22752)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__22751,Vvar__1___24Anonymous__22752,VX22753)
=> ( ( Vvar__1___24Anonymous__22752 = cCoq_2eInit_2eDatatypes_2eO
& VX22753 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__22751) )
| ? [Vvar__1__h__22756] :
( t(Vvar__1__h__22756,Vvar__0__A__22751)
& ? [Vvar__2__n__22757] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__22757)
& ? [Vvar__3___24Anonymous__22758] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__22751,Vvar__2__n__22757,Vvar__3___24Anonymous__22758)
& Vvar__1___24Anonymous__22752 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__22757)
& VX22753 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__22751,Vvar__1__h__22756,Vvar__2__n__22757,Vvar__3___24Anonymous__22758) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__8549,Vvar__1__rO__8550,Vvar__2__rI__8551,Vvar__3__rplus__8552,Vvar__4__rtimes__8557,Vvar__5__rminus__8562,Vvar__6__ropp__8567,Vvar__7__req__8570,Vvar__8__rle__8575,Vvar__9__rlt__8580] :
( cType___24t(Vvar__0__R__8549)
=> ( t(Vvar__1__rO__8550,Vvar__0__R__8549)
=> ( t(Vvar__2__rI__8551,Vvar__0__R__8549)
=> ( c_24__type__8981___24t(Vvar__0__R__8549,Vvar__1__rO__8550,Vvar__2__rI__8551,Vvar__3__rplus__8552,Vvar__4__rtimes__8557,Vvar__5__rminus__8562,Vvar__6__ropp__8567,Vvar__7__req__8570,Vvar__8__rle__8575,Vvar__9__rlt__8580,Vvar__3__rplus__8552)
=> ( c_24__type__9082___24t(Vvar__0__R__8549,Vvar__1__rO__8550,Vvar__2__rI__8551,Vvar__3__rplus__8552,Vvar__4__rtimes__8557,Vvar__5__rminus__8562,Vvar__6__ropp__8567,Vvar__7__req__8570,Vvar__8__rle__8575,Vvar__9__rlt__8580,Vvar__4__rtimes__8557)
=> ( c_24__type__9183___24t(Vvar__0__R__8549,Vvar__1__rO__8550,Vvar__2__rI__8551,Vvar__3__rplus__8552,Vvar__4__rtimes__8557,Vvar__5__rminus__8562,Vvar__6__ropp__8567,Vvar__7__req__8570,Vvar__8__rle__8575,Vvar__9__rlt__8580,Vvar__5__rminus__8562)
=> ( c_24__type__9273___24t(Vvar__0__R__8549,Vvar__1__rO__8550,Vvar__2__rI__8551,Vvar__3__rplus__8552,Vvar__4__rtimes__8557,Vvar__5__rminus__8562,Vvar__6__ropp__8567,Vvar__7__req__8570,Vvar__8__rle__8575,Vvar__9__rlt__8580,Vvar__6__ropp__8567)
=> ( c_24__type__9374___24t(Vvar__0__R__8549,Vvar__1__rO__8550,Vvar__2__rI__8551,Vvar__3__rplus__8552,Vvar__4__rtimes__8557,Vvar__5__rminus__8562,Vvar__6__ropp__8567,Vvar__7__req__8570,Vvar__8__rle__8575,Vvar__9__rlt__8580,Vvar__7__req__8570)
=> ( c_24__type__9475___24t(Vvar__0__R__8549,Vvar__1__rO__8550,Vvar__2__rI__8551,Vvar__3__rplus__8552,Vvar__4__rtimes__8557,Vvar__5__rminus__8562,Vvar__6__ropp__8567,Vvar__7__req__8570,Vvar__8__rle__8575,Vvar__9__rlt__8580,Vvar__8__rle__8575)
=> ( c_24__type__9576___24t(Vvar__0__R__8549,Vvar__1__rO__8550,Vvar__2__rI__8551,Vvar__3__rplus__8552,Vvar__4__rtimes__8557,Vvar__5__rminus__8562,Vvar__6__ropp__8567,Vvar__7__req__8570,Vvar__8__rle__8575,Vvar__9__rlt__8580,Vvar__9__rlt__8580)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__8549,Vvar__1__rO__8550,Vvar__2__rI__8551,Vvar__3__rplus__8552,Vvar__4__rtimes__8557,Vvar__5__rminus__8562,Vvar__6__ropp__8567,Vvar__7__req__8570,Vvar__8__rle__8575,Vvar__9__rlt__8580)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__8549,Vvar__7__req__8570)
& ! [Vvar__var__var__var__var__11__x1__8624__8630__8735__8741__8747] :
( t(Vvar__var__var__var__var__11__x1__8624__8630__8735__8741__8747,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__12__x2__8625__8631__8736__8742__8748] :
( t(Vvar__var__var__var__var__12__x2__8625__8631__8736__8742__8748,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__7__req__8570,Vvar__var__var__var__var__11__x1__8624__8630__8735__8741__8747),Vvar__var__var__var__var__12__x2__8625__8631__8736__8742__8748))
=> ! [Vvar__var__var__var__var__14__y1__8626__8632__8737__8743__8749] :
( t(Vvar__var__var__var__var__14__y1__8626__8632__8737__8743__8749,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__15__y2__8627__8633__8738__8744__8750] :
( t(Vvar__var__var__var__var__15__y2__8627__8633__8738__8744__8750,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__7__req__8570,Vvar__var__var__var__var__14__y1__8626__8632__8737__8743__8749),Vvar__var__var__var__var__15__y2__8627__8633__8738__8744__8750))
=> p(happ(happ(Vvar__7__req__8570,happ(happ(Vvar__3__rplus__8552,Vvar__var__var__var__var__11__x1__8624__8630__8735__8741__8747),Vvar__var__var__var__var__14__y1__8626__8632__8737__8743__8749)),happ(happ(Vvar__3__rplus__8552,Vvar__var__var__var__var__12__x2__8625__8631__8736__8742__8748),Vvar__var__var__var__var__15__y2__8627__8633__8738__8744__8750))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__8637__8643__8753__8759__8765] :
( t(Vvar__var__var__var__var__12__x1__8637__8643__8753__8759__8765,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__13__x2__8638__8644__8754__8760__8766] :
( t(Vvar__var__var__var__var__13__x2__8638__8644__8754__8760__8766,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__7__req__8570,Vvar__var__var__var__var__12__x1__8637__8643__8753__8759__8765),Vvar__var__var__var__var__13__x2__8638__8644__8754__8760__8766))
=> ! [Vvar__var__var__var__var__15__y1__8639__8645__8755__8761__8767] :
( t(Vvar__var__var__var__var__15__y1__8639__8645__8755__8761__8767,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__16__y2__8640__8646__8756__8762__8768] :
( t(Vvar__var__var__var__var__16__y2__8640__8646__8756__8762__8768,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__7__req__8570,Vvar__var__var__var__var__15__y1__8639__8645__8755__8761__8767),Vvar__var__var__var__var__16__y2__8640__8646__8756__8762__8768))
=> p(happ(happ(Vvar__7__req__8570,happ(happ(Vvar__4__rtimes__8557,Vvar__var__var__var__var__12__x1__8637__8643__8753__8759__8765),Vvar__var__var__var__var__15__y1__8639__8645__8755__8761__8767)),happ(happ(Vvar__4__rtimes__8557,Vvar__var__var__var__var__13__x2__8638__8644__8754__8760__8766),Vvar__var__var__var__var__16__y2__8640__8646__8756__8762__8768))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__8650__8653__8771__8774__8777] :
( t(Vvar__var__var__var__var__13__x1__8650__8653__8771__8774__8777,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__14__x2__8651__8654__8772__8775__8778] :
( t(Vvar__var__var__var__var__14__x2__8651__8654__8772__8775__8778,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__7__req__8570,Vvar__var__var__var__var__13__x1__8650__8653__8771__8774__8777),Vvar__var__var__var__var__14__x2__8651__8654__8772__8775__8778))
=> p(happ(happ(Vvar__7__req__8570,happ(Vvar__6__ropp__8567,Vvar__var__var__var__var__13__x1__8650__8653__8771__8774__8777)),happ(Vvar__6__ropp__8567,Vvar__var__var__var__var__14__x2__8651__8654__8772__8775__8778))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__8657__8663__8780__8786__8792] :
( t(Vvar__var__var__var__var__14__x1__8657__8663__8780__8786__8792,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__15__x2__8658__8664__8781__8787__8793] :
( t(Vvar__var__var__var__var__15__x2__8658__8664__8781__8787__8793,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__7__req__8570,Vvar__var__var__var__var__14__x1__8657__8663__8780__8786__8792),Vvar__var__var__var__var__15__x2__8658__8664__8781__8787__8793))
=> ! [Vvar__var__var__var__var__17__y1__8659__8665__8782__8788__8794] :
( t(Vvar__var__var__var__var__17__y1__8659__8665__8782__8788__8794,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__18__y2__8660__8666__8783__8789__8795] :
( t(Vvar__var__var__var__var__18__y2__8660__8666__8783__8789__8795,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__7__req__8570,Vvar__var__var__var__var__17__y1__8659__8665__8782__8788__8794),Vvar__var__var__var__var__18__y2__8660__8666__8783__8789__8795))
=> ( p(happ(happ(Vvar__8__rle__8575,Vvar__var__var__var__var__14__x1__8657__8663__8780__8786__8792),Vvar__var__var__var__var__17__y1__8659__8665__8782__8788__8794))
<=> p(happ(happ(Vvar__8__rle__8575,Vvar__var__var__var__var__15__x2__8658__8664__8781__8787__8793),Vvar__var__var__var__var__18__y2__8660__8666__8783__8789__8795)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__8670__8676__8798__8804__8810] :
( t(Vvar__var__var__var__var__15__x1__8670__8676__8798__8804__8810,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__16__x2__8671__8677__8799__8805__8811] :
( t(Vvar__var__var__var__var__16__x2__8671__8677__8799__8805__8811,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__7__req__8570,Vvar__var__var__var__var__15__x1__8670__8676__8798__8804__8810),Vvar__var__var__var__var__16__x2__8671__8677__8799__8805__8811))
=> ! [Vvar__var__var__var__var__18__y1__8672__8678__8800__8806__8812] :
( t(Vvar__var__var__var__var__18__y1__8672__8678__8800__8806__8812,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__19__y2__8673__8679__8801__8807__8813] :
( t(Vvar__var__var__var__var__19__y2__8673__8679__8801__8807__8813,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__7__req__8570,Vvar__var__var__var__var__18__y1__8672__8678__8800__8806__8812),Vvar__var__var__var__var__19__y2__8673__8679__8801__8807__8813))
=> ( p(happ(happ(Vvar__9__rlt__8580,Vvar__var__var__var__var__15__x1__8670__8676__8798__8804__8810),Vvar__var__var__var__var__18__y1__8672__8678__8800__8806__8812))
<=> p(happ(happ(Vvar__9__rlt__8580,Vvar__var__var__var__var__16__x2__8671__8677__8799__8805__8811),Vvar__var__var__var__var__19__y2__8673__8679__8801__8807__8813)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__8549,Vvar__1__rO__8550,Vvar__2__rI__8551,Vvar__3__rplus__8552,Vvar__4__rtimes__8557,Vvar__5__rminus__8562,Vvar__6__ropp__8567,Vvar__7__req__8570)
& ! [Vvar__var__var__var__17__n__8684__8685__8816__8817] :
( t(Vvar__var__var__var__17__n__8684__8685__8816__8817,Vvar__0__R__8549)
=> p(happ(happ(Vvar__8__rle__8575,Vvar__var__var__var__17__n__8684__8685__8816__8817),Vvar__var__var__var__17__n__8684__8685__8816__8817)) )
& ! [Vvar__var__var__var__var__18__n__8687__8691__8818__8822__8826] :
( t(Vvar__var__var__var__var__18__n__8687__8691__8818__8822__8826,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__19__m__8688__8692__8819__8823__8827] :
( t(Vvar__var__var__var__var__19__m__8688__8692__8819__8823__8827,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__8__rle__8575,Vvar__var__var__var__var__18__n__8687__8691__8818__8822__8826),Vvar__var__var__var__var__19__m__8688__8692__8819__8823__8827))
=> ( p(happ(happ(Vvar__8__rle__8575,Vvar__var__var__var__var__19__m__8688__8692__8819__8823__8827),Vvar__var__var__var__var__18__n__8687__8691__8818__8822__8826))
=> p(happ(happ(Vvar__7__req__8570,Vvar__var__var__var__var__18__n__8687__8691__8818__8822__8826),Vvar__var__var__var__var__19__m__8688__8692__8819__8823__8827)) ) ) ) )
& ! [Vvar__var__var__var__19__n__8696__8701__8830__8835] :
( t(Vvar__var__var__var__19__n__8696__8701__8830__8835,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__20__m__8697__8702__8831__8836] :
( t(Vvar__var__var__var__20__m__8697__8702__8831__8836,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__21__p__8698__8703__8832__8837] :
( t(Vvar__var__var__var__21__p__8698__8703__8832__8837,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__8__rle__8575,Vvar__var__var__var__19__n__8696__8701__8830__8835),Vvar__var__var__var__20__m__8697__8702__8831__8836))
=> ( p(happ(happ(Vvar__8__rle__8575,Vvar__var__var__var__20__m__8697__8702__8831__8836),Vvar__var__var__var__21__p__8698__8703__8832__8837))
=> p(happ(happ(Vvar__8__rle__8575,Vvar__var__var__var__19__n__8696__8701__8830__8835),Vvar__var__var__var__21__p__8698__8703__8832__8837)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__8707__8709__8840__8842__8844__8846] :
( t(Vvar__var__var__var__var__var__20__n__8707__8709__8840__8842__8844__8846,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__var__21__m__8708__8710__8841__8843__8845__8847] :
( t(Vvar__var__var__var__var__var__21__m__8708__8710__8841__8843__8845__8847,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__9__rlt__8580,Vvar__var__var__var__var__var__20__n__8707__8709__8840__8842__8844__8846),Vvar__var__var__var__var__var__21__m__8708__8710__8841__8843__8845__8847))
<=> ( p(happ(happ(Vvar__8__rle__8575,Vvar__var__var__var__var__var__20__n__8707__8709__8840__8842__8844__8846),Vvar__var__var__var__var__var__21__m__8708__8710__8841__8843__8845__8847))
& ~ p(happ(happ(Vvar__7__req__8570,Vvar__var__var__var__var__var__20__n__8707__8709__8840__8842__8844__8846),Vvar__var__var__var__var__var__21__m__8708__8710__8841__8843__8845__8847)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__8712__8714__8848__8850__8852] :
( t(Vvar__var__var__var__var__21__n__8712__8714__8848__8850__8852,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__22__m__8713__8715__8849__8851__8853] :
( t(Vvar__var__var__var__var__22__m__8713__8715__8849__8851__8853,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__9__rlt__8580,Vvar__var__var__var__var__21__n__8712__8714__8848__8850__8852),Vvar__var__var__var__var__22__m__8713__8715__8849__8851__8853))
| p(happ(happ(Vvar__7__req__8570,Vvar__var__var__var__var__21__n__8712__8714__8848__8850__8852),Vvar__var__var__var__var__22__m__8713__8715__8849__8851__8853))
| p(happ(happ(Vvar__9__rlt__8580,Vvar__var__var__var__var__22__m__8713__8715__8849__8851__8853),Vvar__var__var__var__var__21__n__8712__8714__8848__8850__8852)) ) ) )
& ! [Vvar__var__var__var__var__22__n__8717__8721__8854__8858__8862] :
( t(Vvar__var__var__var__var__22__n__8717__8721__8854__8858__8862,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__23__m__8718__8722__8855__8859__8863] :
( t(Vvar__var__var__var__var__23__m__8718__8722__8855__8859__8863,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__24__p__8719__8723__8856__8860__8864] :
( t(Vvar__var__var__var__var__24__p__8719__8723__8856__8860__8864,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__8__rle__8575,Vvar__var__var__var__var__22__n__8717__8721__8854__8858__8862),Vvar__var__var__var__var__23__m__8718__8722__8855__8859__8863))
=> p(happ(happ(Vvar__8__rle__8575,happ(happ(Vvar__3__rplus__8552,Vvar__var__var__var__var__24__p__8719__8723__8856__8860__8864),Vvar__var__var__var__var__22__n__8717__8721__8854__8858__8862)),happ(happ(Vvar__3__rplus__8552,Vvar__var__var__var__var__24__p__8719__8723__8856__8860__8864),Vvar__var__var__var__var__23__m__8718__8722__8855__8859__8863))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__8726__8730__8866__8870__8874__8878] :
( t(Vvar__var__var__var__var__var__23__n__8726__8730__8866__8870__8874__8878,Vvar__0__R__8549)
=> ! [Vvar__var__var__var__var__var__24__m__8727__8731__8867__8871__8875__8879] :
( t(Vvar__var__var__var__var__var__24__m__8727__8731__8867__8871__8875__8879,Vvar__0__R__8549)
=> ( p(happ(happ(Vvar__9__rlt__8580,Vvar__1__rO__8550),Vvar__var__var__var__var__var__23__n__8726__8730__8866__8870__8874__8878))
=> ( p(happ(happ(Vvar__9__rlt__8580,Vvar__1__rO__8550),Vvar__var__var__var__var__var__24__m__8727__8731__8867__8871__8875__8879))
=> p(happ(happ(Vvar__9__rlt__8580,Vvar__1__rO__8550),happ(happ(Vvar__4__rtimes__8557,Vvar__var__var__var__var__var__23__n__8726__8730__8866__8870__8874__8878),Vvar__var__var__var__var__var__24__m__8727__8731__8867__8871__8875__8879))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__8570,Vvar__1__rO__8550),Vvar__2__rI__8551))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__15920,VX15921] :
( cType___24t(Vvar__0__T__15920)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__15920,VX15921)
=> ? [Vvar__1__Flhs__15923] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__15920,Vvar__1__Flhs__15923)
& ? [Vvar__2__Fop__15924] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__15924)
& ? [Vvar__3__Frhs__15925] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__15920,Vvar__3__Frhs__15925)
& VX15921 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__15920,Vvar__1__Flhs__15923,Vvar__2__Fop__15924,Vvar__3__Frhs__15925) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,VX22275] :
( cType___24t(Vvar__0__TA__22271)
=> ( cType___24t(Vvar__1__TX__22272)
=> ( cType___24t(Vvar__2__AA__22273)
=> ( cType___24t(Vvar__3__AF__22274)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,VX22275)
=> ( VX22275 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274)
| VX22275 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274)
| ? [Vvar__4___24Anonymous__22288] :
( t(Vvar__4___24Anonymous__22288,Vvar__1__TX__22272)
& VX22275 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__4___24Anonymous__22288) )
| ? [Vvar__4___24Anonymous__22293] :
( t(Vvar__4___24Anonymous__22293,Vvar__0__TA__22271)
& ? [Vvar__5___24Anonymous__22294] :
( t(Vvar__5___24Anonymous__22294,Vvar__2__AA__22273)
& VX22275 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__4___24Anonymous__22293,Vvar__5___24Anonymous__22294) ) )
| ? [Vvar__4___24Anonymous__22299] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__4___24Anonymous__22299)
& ? [Vvar__5___24Anonymous__22300] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__5___24Anonymous__22300)
& VX22275 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__4___24Anonymous__22299,Vvar__5___24Anonymous__22300) ) )
| ? [Vvar__4___24Anonymous__22305] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__4___24Anonymous__22305)
& ? [Vvar__5___24Anonymous__22306] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__5___24Anonymous__22306)
& VX22275 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__4___24Anonymous__22305,Vvar__5___24Anonymous__22306) ) )
| ? [Vvar__4___24Anonymous__22311] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__4___24Anonymous__22311)
& VX22275 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__4___24Anonymous__22311) )
| ? [Vvar__4___24Anonymous__22316] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__4___24Anonymous__22316)
& ? [Vvar__5___24Anonymous__22317] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__22274,Vvar__5___24Anonymous__22317)
& ? [Vvar__6___24Anonymous__22318] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__6___24Anonymous__22318)
& VX22275 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__22271,Vvar__1__TX__22272,Vvar__2__AA__22273,Vvar__3__AF__22274,Vvar__4___24Anonymous__22316,Vvar__5___24Anonymous__22317,Vvar__6___24Anonymous__22318) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__6756,VX6757] :
( cType___24t(Vvar__0__C__6756)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6756,VX6757)
=> ( VX6757 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__6756)
| VX6757 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__6756)
| ? [Vvar__1___24Anonymous__6761] :
( t(Vvar__1___24Anonymous__6761,Vvar__0__C__6756)
& VX6757 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__6756,Vvar__1___24Anonymous__6761) )
| ? [Vvar__1___24Anonymous__6763] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6763)
& VX6757 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__6756,Vvar__1___24Anonymous__6763) )
| ? [Vvar__1___24Anonymous__6765] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6756,Vvar__1___24Anonymous__6765)
& ? [Vvar__2___24Anonymous__6766] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6756,Vvar__2___24Anonymous__6766)
& VX6757 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__6756,Vvar__1___24Anonymous__6765,Vvar__2___24Anonymous__6766) ) )
| ? [Vvar__1___24Anonymous__6768] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6756,Vvar__1___24Anonymous__6768)
& ? [Vvar__2___24Anonymous__6769] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6756,Vvar__2___24Anonymous__6769)
& VX6757 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__6756,Vvar__1___24Anonymous__6768,Vvar__2___24Anonymous__6769) ) )
| ? [Vvar__1___24Anonymous__6771] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6756,Vvar__1___24Anonymous__6771)
& ? [Vvar__2___24Anonymous__6772] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6756,Vvar__2___24Anonymous__6772)
& VX6757 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__6756,Vvar__1___24Anonymous__6771,Vvar__2___24Anonymous__6772) ) )
| ? [Vvar__1___24Anonymous__6774] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6756,Vvar__1___24Anonymous__6774)
& VX6757 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__6756,Vvar__1___24Anonymous__6774) )
| ? [Vvar__1___24Anonymous__6776] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6756,Vvar__1___24Anonymous__6776)
& VX6757 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__6756,Vvar__1___24Anonymous__6776) )
| ? [Vvar__1___24Anonymous__6778] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6756,Vvar__1___24Anonymous__6778)
& ? [Vvar__2___24Anonymous__6779] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6756,Vvar__2___24Anonymous__6779)
& VX6757 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__6756,Vvar__1___24Anonymous__6778,Vvar__2___24Anonymous__6779) ) )
| ? [Vvar__1___24Anonymous__6781] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6756,Vvar__1___24Anonymous__6781)
& ? [Vvar__2___24Anonymous__6782] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6782)
& VX6757 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__6756,Vvar__1___24Anonymous__6781,Vvar__2___24Anonymous__6782) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__6020,Vvar__1__rO__6021,Vvar__2__rI__6022,Vvar__3__radd__6023,Vvar__4__rmul__6028,Vvar__5__rsub__6033,Vvar__6__ropp__6038,Vvar__7__rdiv__6041,Vvar__8__rinv__6046,Vvar__9__req__6049] :
( cType___24t(Vvar__0__R__6020)
=> ( t(Vvar__1__rO__6021,Vvar__0__R__6020)
=> ( t(Vvar__2__rI__6022,Vvar__0__R__6020)
=> ( c_24__type__6214___24t(Vvar__0__R__6020,Vvar__1__rO__6021,Vvar__2__rI__6022,Vvar__3__radd__6023,Vvar__4__rmul__6028,Vvar__5__rsub__6033,Vvar__6__ropp__6038,Vvar__7__rdiv__6041,Vvar__8__rinv__6046,Vvar__9__req__6049,Vvar__3__radd__6023)
=> ( c_24__type__6307___24t(Vvar__0__R__6020,Vvar__1__rO__6021,Vvar__2__rI__6022,Vvar__3__radd__6023,Vvar__4__rmul__6028,Vvar__5__rsub__6033,Vvar__6__ropp__6038,Vvar__7__rdiv__6041,Vvar__8__rinv__6046,Vvar__9__req__6049,Vvar__4__rmul__6028)
=> ( c_24__type__6400___24t(Vvar__0__R__6020,Vvar__1__rO__6021,Vvar__2__rI__6022,Vvar__3__radd__6023,Vvar__4__rmul__6028,Vvar__5__rsub__6033,Vvar__6__ropp__6038,Vvar__7__rdiv__6041,Vvar__8__rinv__6046,Vvar__9__req__6049,Vvar__5__rsub__6033)
=> ( c_24__type__6482___24t(Vvar__0__R__6020,Vvar__1__rO__6021,Vvar__2__rI__6022,Vvar__3__radd__6023,Vvar__4__rmul__6028,Vvar__5__rsub__6033,Vvar__6__ropp__6038,Vvar__7__rdiv__6041,Vvar__8__rinv__6046,Vvar__9__req__6049,Vvar__6__ropp__6038)
=> ( c_24__type__6575___24t(Vvar__0__R__6020,Vvar__1__rO__6021,Vvar__2__rI__6022,Vvar__3__radd__6023,Vvar__4__rmul__6028,Vvar__5__rsub__6033,Vvar__6__ropp__6038,Vvar__7__rdiv__6041,Vvar__8__rinv__6046,Vvar__9__req__6049,Vvar__7__rdiv__6041)
=> ( c_24__type__6657___24t(Vvar__0__R__6020,Vvar__1__rO__6021,Vvar__2__rI__6022,Vvar__3__radd__6023,Vvar__4__rmul__6028,Vvar__5__rsub__6033,Vvar__6__ropp__6038,Vvar__7__rdiv__6041,Vvar__8__rinv__6046,Vvar__9__req__6049,Vvar__8__rinv__6046)
=> ( c_24__type__6750___24t(Vvar__0__R__6020,Vvar__1__rO__6021,Vvar__2__rI__6022,Vvar__3__radd__6023,Vvar__4__rmul__6028,Vvar__5__rsub__6033,Vvar__6__ropp__6038,Vvar__7__rdiv__6041,Vvar__8__rinv__6046,Vvar__9__req__6049,Vvar__9__req__6049)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__6020,Vvar__1__rO__6021,Vvar__2__rI__6022,Vvar__3__radd__6023,Vvar__4__rmul__6028,Vvar__5__rsub__6033,Vvar__6__ropp__6038,Vvar__7__rdiv__6041,Vvar__8__rinv__6046,Vvar__9__req__6049)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__6020,Vvar__1__rO__6021,Vvar__2__rI__6022,Vvar__3__radd__6023,Vvar__4__rmul__6028,Vvar__5__rsub__6033,Vvar__6__ropp__6038,Vvar__9__req__6049)
& ~ p(happ(happ(Vvar__9__req__6049,Vvar__2__rI__6022),Vvar__1__rO__6021))
& ! [Vvar__var__var__var__var__var__var__12__p__6092__6094__6101__6103__6105__6107__6109] :
( t(Vvar__var__var__var__var__var__var__12__p__6092__6094__6101__6103__6105__6107__6109,Vvar__0__R__6020)
=> ! [Vvar__var__var__var__var__var__var__13__q__6093__6095__6102__6104__6106__6108__6110] :
( t(Vvar__var__var__var__var__var__var__13__q__6093__6095__6102__6104__6106__6108__6110,Vvar__0__R__6020)
=> p(happ(happ(Vvar__9__req__6049,happ(happ(Vvar__7__rdiv__6041,Vvar__var__var__var__var__var__var__12__p__6092__6094__6101__6103__6105__6107__6109),Vvar__var__var__var__var__var__var__13__q__6093__6095__6102__6104__6106__6108__6110)),happ(happ(Vvar__4__rmul__6028,Vvar__var__var__var__var__var__var__12__p__6092__6094__6101__6103__6105__6107__6109),happ(Vvar__8__rinv__6046,Vvar__var__var__var__var__var__var__13__q__6093__6095__6102__6104__6106__6108__6110)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__6097__6099__6111__6113__6115__6117__6119__6121] :
( t(Vvar__var__var__var__var__var__var__var__13__p__6097__6099__6111__6113__6115__6117__6119__6121,Vvar__0__R__6020)
=> ( ~ p(happ(happ(Vvar__9__req__6049,Vvar__var__var__var__var__var__var__var__13__p__6097__6099__6111__6113__6115__6117__6119__6121),Vvar__1__rO__6021))
=> p(happ(happ(Vvar__9__req__6049,happ(happ(Vvar__4__rmul__6028,happ(Vvar__8__rinv__6046,Vvar__var__var__var__var__var__var__var__13__p__6097__6099__6111__6113__6115__6117__6119__6121)),Vvar__var__var__var__var__var__var__var__13__p__6097__6099__6111__6113__6115__6117__6119__6121)),Vvar__2__rI__6022)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__7083,VX7084] :
( cType___24t(Vvar__0__C__7083)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__7083,VX7084)
=> ? [Vvar__1__num__7086] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7083,Vvar__1__num__7086)
& ? [Vvar__2__denum__7087] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7083,Vvar__2__denum__7087)
& ? [Vvar__3__condition__7088] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__7083),Vvar__3__condition__7088)
& VX7084 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__7083,Vvar__1__num__7086,Vvar__2__denum__7087,Vvar__3__condition__7088) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__7097,VX7098] :
( cType___24t(Vvar__0__C__7097)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__7097,VX7098)
=> ? [Vvar__1__rsplit__left__7100] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7097,Vvar__1__rsplit__left__7100)
& ? [Vvar__2__rsplit__common__7101] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7097,Vvar__2__rsplit__common__7101)
& ? [Vvar__3__rsplit__right__7102] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7097,Vvar__3__rsplit__right__7102)
& VX7098 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__7097,Vvar__1__rsplit__left__7100,Vvar__2__rsplit__common__7101,Vvar__3__rsplit__right__7102) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX2669] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX2669)
=> ( VX2669 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__2670] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2670)
& ? [Vvar__1___24Anonymous__2671] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__2671)
& VX2669 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__2670,Vvar__1___24Anonymous__2671) ) )
| ? [Vvar__0___24Anonymous__2672] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2672)
& ? [Vvar__1___24Anonymous__2673] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__2673)
& VX2669 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__2672,Vvar__1___24Anonymous__2673) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__2690,VX2691] :
( cType___24t(Vvar__0__C__2690)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2690,VX2691)
=> ( VX2691 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2690)
| VX2691 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2690)
| ? [Vvar__1___24Anonymous__2695] :
( t(Vvar__1___24Anonymous__2695,Vvar__0__C__2690)
& VX2691 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2690,Vvar__1___24Anonymous__2695) )
| ? [Vvar__1___24Anonymous__2697] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2697)
& VX2691 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2690,Vvar__1___24Anonymous__2697) )
| ? [Vvar__1___24Anonymous__2699] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2690,Vvar__1___24Anonymous__2699)
& ? [Vvar__2___24Anonymous__2700] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2690,Vvar__2___24Anonymous__2700)
& VX2691 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2690,Vvar__1___24Anonymous__2699,Vvar__2___24Anonymous__2700) ) )
| ? [Vvar__1___24Anonymous__2702] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2690,Vvar__1___24Anonymous__2702)
& ? [Vvar__2___24Anonymous__2703] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2690,Vvar__2___24Anonymous__2703)
& VX2691 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2690,Vvar__1___24Anonymous__2702,Vvar__2___24Anonymous__2703) ) )
| ? [Vvar__1___24Anonymous__2705] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2690,Vvar__1___24Anonymous__2705)
& ? [Vvar__2___24Anonymous__2706] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2690,Vvar__2___24Anonymous__2706)
& VX2691 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2690,Vvar__1___24Anonymous__2705,Vvar__2___24Anonymous__2706) ) )
| ? [Vvar__1___24Anonymous__2708] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2690,Vvar__1___24Anonymous__2708)
& VX2691 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2690,Vvar__1___24Anonymous__2708) )
| ? [Vvar__1___24Anonymous__2710] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2690,Vvar__1___24Anonymous__2710)
& ? [Vvar__2___24Anonymous__2711] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2711)
& VX2691 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2690,Vvar__1___24Anonymous__2710,Vvar__2___24Anonymous__2711) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__2488,VX2489] :
( cType___24t(Vvar__0__C__2488)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__2488,VX2489)
=> ( ? [Vvar__1___24Anonymous__2491] :
( t(Vvar__1___24Anonymous__2491,Vvar__0__C__2488)
& VX2489 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__2488,Vvar__1___24Anonymous__2491) )
| ? [Vvar__1___24Anonymous__2493] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2493)
& ? [Vvar__2___24Anonymous__2494] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__2488,Vvar__2___24Anonymous__2494)
& VX2489 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__2488,Vvar__1___24Anonymous__2493,Vvar__2___24Anonymous__2494) ) )
| ? [Vvar__1___24Anonymous__2496] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__2488,Vvar__1___24Anonymous__2496)
& ? [Vvar__2___24Anonymous__2497] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2497)
& ? [Vvar__3___24Anonymous__2498] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__2488,Vvar__3___24Anonymous__2498)
& VX2489 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__2488,Vvar__1___24Anonymous__2496,Vvar__2___24Anonymous__2497,Vvar__3___24Anonymous__2498) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__16240,Vvar__1__rO__16241,Vvar__2__rI__16242,Vvar__3__radd__16243,Vvar__4__rmul__16248,Vvar__5__rsub__16253,Vvar__6__ropp__16258,Vvar__7__req__16261] :
( cType___24t(Vvar__0__R__16240)
=> ( t(Vvar__1__rO__16241,Vvar__0__R__16240)
=> ( t(Vvar__2__rI__16242,Vvar__0__R__16240)
=> ( c_24__type__16489___24t(Vvar__0__R__16240,Vvar__1__rO__16241,Vvar__2__rI__16242,Vvar__3__radd__16243,Vvar__4__rmul__16248,Vvar__5__rsub__16253,Vvar__6__ropp__16258,Vvar__7__req__16261,Vvar__3__radd__16243)
=> ( c_24__type__16552___24t(Vvar__0__R__16240,Vvar__1__rO__16241,Vvar__2__rI__16242,Vvar__3__radd__16243,Vvar__4__rmul__16248,Vvar__5__rsub__16253,Vvar__6__ropp__16258,Vvar__7__req__16261,Vvar__4__rmul__16248)
=> ( c_24__type__16615___24t(Vvar__0__R__16240,Vvar__1__rO__16241,Vvar__2__rI__16242,Vvar__3__radd__16243,Vvar__4__rmul__16248,Vvar__5__rsub__16253,Vvar__6__ropp__16258,Vvar__7__req__16261,Vvar__5__rsub__16253)
=> ( c_24__type__16669___24t(Vvar__0__R__16240,Vvar__1__rO__16241,Vvar__2__rI__16242,Vvar__3__radd__16243,Vvar__4__rmul__16248,Vvar__5__rsub__16253,Vvar__6__ropp__16258,Vvar__7__req__16261,Vvar__6__ropp__16258)
=> ( c_24__type__16732___24t(Vvar__0__R__16240,Vvar__1__rO__16241,Vvar__2__rI__16242,Vvar__3__radd__16243,Vvar__4__rmul__16248,Vvar__5__rsub__16253,Vvar__6__ropp__16258,Vvar__7__req__16261,Vvar__7__req__16261)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__16240,Vvar__1__rO__16241,Vvar__2__rI__16242,Vvar__3__radd__16243,Vvar__4__rmul__16248,Vvar__5__rsub__16253,Vvar__6__ropp__16258,Vvar__7__req__16261)
=> ( ! [Vvar__var__var__var__var__var__8__x__16294__16295__16348__16349__16350__16351] :
( t(Vvar__var__var__var__var__var__8__x__16294__16295__16348__16349__16350__16351,Vvar__0__R__16240)
=> p(happ(happ(Vvar__7__req__16261,happ(happ(Vvar__3__radd__16243,Vvar__1__rO__16241),Vvar__var__var__var__var__var__8__x__16294__16295__16348__16349__16350__16351)),Vvar__var__var__var__var__var__8__x__16294__16295__16348__16349__16350__16351)) )
& ! [Vvar__var__var__var__var__9__x__16297__16299__16352__16354__16356] :
( t(Vvar__var__var__var__var__9__x__16297__16299__16352__16354__16356,Vvar__0__R__16240)
=> ! [Vvar__var__var__var__var__10__y__16298__16300__16353__16355__16357] :
( t(Vvar__var__var__var__var__10__y__16298__16300__16353__16355__16357,Vvar__0__R__16240)
=> p(happ(happ(Vvar__7__req__16261,happ(happ(Vvar__3__radd__16243,Vvar__var__var__var__var__9__x__16297__16299__16352__16354__16356),Vvar__var__var__var__var__10__y__16298__16300__16353__16355__16357)),happ(happ(Vvar__3__radd__16243,Vvar__var__var__var__var__10__y__16298__16300__16353__16355__16357),Vvar__var__var__var__var__9__x__16297__16299__16352__16354__16356))) ) )
& ! [Vvar__var__var__var__var__10__x__16302__16305__16358__16361__16364] :
( t(Vvar__var__var__var__var__10__x__16302__16305__16358__16361__16364,Vvar__0__R__16240)
=> ! [Vvar__var__var__var__var__11__y__16303__16306__16359__16362__16365] :
( t(Vvar__var__var__var__var__11__y__16303__16306__16359__16362__16365,Vvar__0__R__16240)
=> ! [Vvar__var__var__var__var__12__z__16304__16307__16360__16363__16366] :
( t(Vvar__var__var__var__var__12__z__16304__16307__16360__16363__16366,Vvar__0__R__16240)
=> p(happ(happ(Vvar__7__req__16261,happ(happ(Vvar__3__radd__16243,Vvar__var__var__var__var__10__x__16302__16305__16358__16361__16364),happ(happ(Vvar__3__radd__16243,Vvar__var__var__var__var__11__y__16303__16306__16359__16362__16365),Vvar__var__var__var__var__12__z__16304__16307__16360__16363__16366))),happ(happ(Vvar__3__radd__16243,happ(happ(Vvar__3__radd__16243,Vvar__var__var__var__var__10__x__16302__16305__16358__16361__16364),Vvar__var__var__var__var__11__y__16303__16306__16359__16362__16365)),Vvar__var__var__var__var__12__z__16304__16307__16360__16363__16366))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__16309__16310__16367__16368__16369__16370] :
( t(Vvar__var__var__var__var__var__11__x__16309__16310__16367__16368__16369__16370,Vvar__0__R__16240)
=> p(happ(happ(Vvar__7__req__16261,happ(happ(Vvar__4__rmul__16248,Vvar__2__rI__16242),Vvar__var__var__var__var__var__11__x__16309__16310__16367__16368__16369__16370)),Vvar__var__var__var__var__var__11__x__16309__16310__16367__16368__16369__16370)) )
& ! [Vvar__var__var__var__var__var__12__x__16312__16313__16371__16372__16373__16374] :
( t(Vvar__var__var__var__var__var__12__x__16312__16313__16371__16372__16373__16374,Vvar__0__R__16240)
=> p(happ(happ(Vvar__7__req__16261,happ(happ(Vvar__4__rmul__16248,Vvar__1__rO__16241),Vvar__var__var__var__var__var__12__x__16312__16313__16371__16372__16373__16374)),Vvar__1__rO__16241)) )
& ! [Vvar__var__var__var__var__13__x__16315__16317__16375__16377__16379] :
( t(Vvar__var__var__var__var__13__x__16315__16317__16375__16377__16379,Vvar__0__R__16240)
=> ! [Vvar__var__var__var__var__14__y__16316__16318__16376__16378__16380] :
( t(Vvar__var__var__var__var__14__y__16316__16318__16376__16378__16380,Vvar__0__R__16240)
=> p(happ(happ(Vvar__7__req__16261,happ(happ(Vvar__4__rmul__16248,Vvar__var__var__var__var__13__x__16315__16317__16375__16377__16379),Vvar__var__var__var__var__14__y__16316__16318__16376__16378__16380)),happ(happ(Vvar__4__rmul__16248,Vvar__var__var__var__var__14__y__16316__16318__16376__16378__16380),Vvar__var__var__var__var__13__x__16315__16317__16375__16377__16379))) ) )
& ! [Vvar__var__var__var__var__14__x__16320__16323__16381__16384__16387] :
( t(Vvar__var__var__var__var__14__x__16320__16323__16381__16384__16387,Vvar__0__R__16240)
=> ! [Vvar__var__var__var__var__15__y__16321__16324__16382__16385__16388] :
( t(Vvar__var__var__var__var__15__y__16321__16324__16382__16385__16388,Vvar__0__R__16240)
=> ! [Vvar__var__var__var__var__16__z__16322__16325__16383__16386__16389] :
( t(Vvar__var__var__var__var__16__z__16322__16325__16383__16386__16389,Vvar__0__R__16240)
=> p(happ(happ(Vvar__7__req__16261,happ(happ(Vvar__4__rmul__16248,Vvar__var__var__var__var__14__x__16320__16323__16381__16384__16387),happ(happ(Vvar__4__rmul__16248,Vvar__var__var__var__var__15__y__16321__16324__16382__16385__16388),Vvar__var__var__var__var__16__z__16322__16325__16383__16386__16389))),happ(happ(Vvar__4__rmul__16248,happ(happ(Vvar__4__rmul__16248,Vvar__var__var__var__var__14__x__16320__16323__16381__16384__16387),Vvar__var__var__var__var__15__y__16321__16324__16382__16385__16388)),Vvar__var__var__var__var__16__z__16322__16325__16383__16386__16389))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__16327__16330__16390__16393__16396__16399] :
( t(Vvar__var__var__var__var__var__15__x__16327__16330__16390__16393__16396__16399,Vvar__0__R__16240)
=> ! [Vvar__var__var__var__var__var__16__y__16328__16331__16391__16394__16397__16400] :
( t(Vvar__var__var__var__var__var__16__y__16328__16331__16391__16394__16397__16400,Vvar__0__R__16240)
=> ! [Vvar__var__var__var__var__var__17__z__16329__16332__16392__16395__16398__16401] :
( t(Vvar__var__var__var__var__var__17__z__16329__16332__16392__16395__16398__16401,Vvar__0__R__16240)
=> p(happ(happ(Vvar__7__req__16261,happ(happ(Vvar__4__rmul__16248,happ(happ(Vvar__3__radd__16243,Vvar__var__var__var__var__var__15__x__16327__16330__16390__16393__16396__16399),Vvar__var__var__var__var__var__16__y__16328__16331__16391__16394__16397__16400)),Vvar__var__var__var__var__var__17__z__16329__16332__16392__16395__16398__16401)),happ(happ(Vvar__3__radd__16243,happ(happ(Vvar__4__rmul__16248,Vvar__var__var__var__var__var__15__x__16327__16330__16390__16393__16396__16399),Vvar__var__var__var__var__var__17__z__16329__16332__16392__16395__16398__16401)),happ(happ(Vvar__4__rmul__16248,Vvar__var__var__var__var__var__16__y__16328__16331__16391__16394__16397__16400),Vvar__var__var__var__var__var__17__z__16329__16332__16392__16395__16398__16401)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__16334__16336__16402__16404__16406__16408] :
( t(Vvar__var__var__var__var__var__16__x__16334__16336__16402__16404__16406__16408,Vvar__0__R__16240)
=> ! [Vvar__var__var__var__var__var__17__y__16335__16337__16403__16405__16407__16409] :
( t(Vvar__var__var__var__var__var__17__y__16335__16337__16403__16405__16407__16409,Vvar__0__R__16240)
=> p(happ(happ(Vvar__7__req__16261,happ(Vvar__6__ropp__16258,happ(happ(Vvar__4__rmul__16248,Vvar__var__var__var__var__var__16__x__16334__16336__16402__16404__16406__16408),Vvar__var__var__var__var__var__17__y__16335__16337__16403__16405__16407__16409))),happ(happ(Vvar__4__rmul__16248,happ(Vvar__6__ropp__16258,Vvar__var__var__var__var__var__16__x__16334__16336__16402__16404__16406__16408)),Vvar__var__var__var__var__var__17__y__16335__16337__16403__16405__16407__16409))) ) )
& ! [Vvar__var__var__var__var__var__17__x__16339__16341__16410__16412__16414__16416] :
( t(Vvar__var__var__var__var__var__17__x__16339__16341__16410__16412__16414__16416,Vvar__0__R__16240)
=> ! [Vvar__var__var__var__var__var__18__y__16340__16342__16411__16413__16415__16417] :
( t(Vvar__var__var__var__var__var__18__y__16340__16342__16411__16413__16415__16417,Vvar__0__R__16240)
=> p(happ(happ(Vvar__7__req__16261,happ(Vvar__6__ropp__16258,happ(happ(Vvar__3__radd__16243,Vvar__var__var__var__var__var__17__x__16339__16341__16410__16412__16414__16416),Vvar__var__var__var__var__var__18__y__16340__16342__16411__16413__16415__16417))),happ(happ(Vvar__3__radd__16243,happ(Vvar__6__ropp__16258,Vvar__var__var__var__var__var__17__x__16339__16341__16410__16412__16414__16416)),happ(Vvar__6__ropp__16258,Vvar__var__var__var__var__var__18__y__16340__16342__16411__16413__16415__16417)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__16344__16346__16418__16420__16422__16424__16426] :
( t(Vvar__var__var__var__var__var__var__18__x__16344__16346__16418__16420__16422__16424__16426,Vvar__0__R__16240)
=> ! [Vvar__var__var__var__var__var__var__19__y__16345__16347__16419__16421__16423__16425__16427] :
( t(Vvar__var__var__var__var__var__var__19__y__16345__16347__16419__16421__16423__16425__16427,Vvar__0__R__16240)
=> p(happ(happ(Vvar__7__req__16261,happ(happ(Vvar__5__rsub__16253,Vvar__var__var__var__var__var__var__18__x__16344__16346__16418__16420__16422__16424__16426),Vvar__var__var__var__var__var__var__19__y__16345__16347__16419__16421__16423__16425__16427)),happ(happ(Vvar__3__radd__16243,Vvar__var__var__var__var__var__var__18__x__16344__16346__16418__16420__16422__16424__16426),happ(Vvar__6__ropp__16258,Vvar__var__var__var__var__var__var__19__y__16345__16347__16419__16421__16423__16425__16427)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__31704,Vvar__1__req__31705,Vvar__2__C__31710,Vvar__3__cadd__31711,Vvar__4__cmul__31716,Vvar__5__phi__31721,Vvar__6__cdiv__31724] :
( cType___24t(Vvar__0__R__31704)
=> ( c_24__type__31844___24t(Vvar__0__R__31704,Vvar__1__req__31705,Vvar__2__C__31710,Vvar__3__cadd__31711,Vvar__4__cmul__31716,Vvar__5__phi__31721,Vvar__6__cdiv__31724,Vvar__1__req__31705)
=> ( cType___24t(Vvar__2__C__31710)
=> ( c_24__type__31894___24t(Vvar__0__R__31704,Vvar__1__req__31705,Vvar__2__C__31710,Vvar__3__cadd__31711,Vvar__4__cmul__31716,Vvar__5__phi__31721,Vvar__6__cdiv__31724,Vvar__3__cadd__31711)
=> ( c_24__type__31944___24t(Vvar__0__R__31704,Vvar__1__req__31705,Vvar__2__C__31710,Vvar__3__cadd__31711,Vvar__4__cmul__31716,Vvar__5__phi__31721,Vvar__6__cdiv__31724,Vvar__4__cmul__31716)
=> ( c_24__type__31986___24t(Vvar__0__R__31704,Vvar__1__req__31705,Vvar__2__C__31710,Vvar__3__cadd__31711,Vvar__4__cmul__31716,Vvar__5__phi__31721,Vvar__6__cdiv__31724,Vvar__5__phi__31721)
=> ( c_24__type__32036___24t(Vvar__0__R__31704,Vvar__1__req__31705,Vvar__2__C__31710,Vvar__3__cadd__31711,Vvar__4__cmul__31716,Vvar__5__phi__31721,Vvar__6__cdiv__31724,Vvar__6__cdiv__31724)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__31704,Vvar__1__req__31705,Vvar__2__C__31710,Vvar__3__cadd__31711,Vvar__4__cmul__31716,Vvar__5__phi__31721,Vvar__6__cdiv__31724)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__31756__31761__31766__31771__31776__31781__31786__31791] :
( t(Vvar__var__var__var__var__var__var__var__7__a__31756__31761__31766__31771__31776__31781__31786__31791,Vvar__2__C__31710)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__31757__31762__31767__31772__31777__31782__31787__31792] :
( t(Vvar__var__var__var__var__var__var__var__8__b__31757__31762__31767__31772__31777__31782__31787__31792,Vvar__2__C__31710)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2432099___24a9(Vvar__0__R__31704,Vvar__1__req__31705,Vvar__2__C__31710,Vvar__3__cadd__31711,Vvar__4__cmul__31716,Vvar__5__phi__31721,Vvar__6__cdiv__31724,Vvar__var__var__var__var__var__var__var__7__a__31756__31761__31766__31771__31776__31781__31786__31791,Vvar__var__var__var__var__var__var__var__8__b__31757__31762__31767__31772__31777__31782__31787__31792) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__21280,Vvar__1__rI__21281,Vvar__2__rmul__21282,Vvar__3__req__21287,Vvar__4__Cpow__21292,Vvar__5__Cp__phi__21293,Vvar__6__rpow__21296] :
( cType___24t(Vvar__0__R__21280)
=> ( t(Vvar__1__rI__21281,Vvar__0__R__21280)
=> ( c_24__type__21382___24t(Vvar__0__R__21280,Vvar__1__rI__21281,Vvar__2__rmul__21282,Vvar__3__req__21287,Vvar__4__Cpow__21292,Vvar__5__Cp__phi__21293,Vvar__6__rpow__21296,Vvar__2__rmul__21282)
=> ( c_24__type__21426___24t(Vvar__0__R__21280,Vvar__1__rI__21281,Vvar__2__rmul__21282,Vvar__3__req__21287,Vvar__4__Cpow__21292,Vvar__5__Cp__phi__21293,Vvar__6__rpow__21296,Vvar__3__req__21287)
=> ( cType___24t(Vvar__4__Cpow__21292)
=> ( c_24__type__21462___24t(Vvar__0__R__21280,Vvar__1__rI__21281,Vvar__2__rmul__21282,Vvar__3__req__21287,Vvar__4__Cpow__21292,Vvar__5__Cp__phi__21293,Vvar__6__rpow__21296,Vvar__5__Cp__phi__21293)
=> ( c_24__type__21506___24t(Vvar__0__R__21280,Vvar__1__rI__21281,Vvar__2__rmul__21282,Vvar__3__req__21287,Vvar__4__Cpow__21292,Vvar__5__Cp__phi__21293,Vvar__6__rpow__21296,Vvar__6__rpow__21296)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__21280,Vvar__1__rI__21281,Vvar__2__rmul__21282,Vvar__3__req__21287,Vvar__4__Cpow__21292,Vvar__5__Cp__phi__21293,Vvar__6__rpow__21296)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__21324__21326__21328__21330__21332__21334__21336__21338] :
( t(Vvar__var__var__var__var__var__var__var__7__r__21324__21326__21328__21330__21332__21334__21336__21338,Vvar__0__R__21280)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__21325__21327__21329__21331__21333__21335__21337__21339] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__21325__21327__21329__21331__21333__21335__21337__21339)
=> p(happ(happ(Vvar__3__req__21287,happ(happ(Vvar__6__rpow__21296,Vvar__var__var__var__var__var__var__var__7__r__21324__21326__21328__21330__21332__21334__21336__21338),happ(Vvar__5__Cp__phi__21293,Vvar__var__var__var__var__var__var__var__8__n__21325__21327__21329__21331__21333__21335__21337__21339))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__21280,Vvar__1__rI__21281,Vvar__2__rmul__21282,Vvar__var__var__var__var__var__var__var__7__r__21324__21326__21328__21330__21332__21334__21336__21338,Vvar__var__var__var__var__var__var__var__8__n__21325__21327__21329__21331__21333__21335__21337__21339))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__17465,Vvar__1__radd__17466,Vvar__2__rmul__17471,Vvar__3__ropp__17476,Vvar__4__req__17479] :
( cType___24t(Vvar__0__R__17465)
=> ( c_24__type__17570___24t(Vvar__0__R__17465,Vvar__1__radd__17466,Vvar__2__rmul__17471,Vvar__3__ropp__17476,Vvar__4__req__17479,Vvar__1__radd__17466)
=> ( c_24__type__17600___24t(Vvar__0__R__17465,Vvar__1__radd__17466,Vvar__2__rmul__17471,Vvar__3__ropp__17476,Vvar__4__req__17479,Vvar__2__rmul__17471)
=> ( c_24__type__17624___24t(Vvar__0__R__17465,Vvar__1__radd__17466,Vvar__2__rmul__17471,Vvar__3__ropp__17476,Vvar__4__req__17479,Vvar__3__ropp__17476)
=> ( c_24__type__17654___24t(Vvar__0__R__17465,Vvar__1__radd__17466,Vvar__2__rmul__17471,Vvar__3__ropp__17476,Vvar__4__req__17479,Vvar__4__req__17479)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__17465,Vvar__1__radd__17466,Vvar__2__rmul__17471,Vvar__3__ropp__17476,Vvar__4__req__17479)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17684___24a5(Vvar__0__R__17465,Vvar__1__radd__17466,Vvar__2__rmul__17471,Vvar__3__ropp__17476,Vvar__4__req__17479),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17465,c_24__type__17708___24a5(Vvar__0__R__17465,Vvar__1__radd__17466,Vvar__2__rmul__17471,Vvar__3__ropp__17476,Vvar__4__req__17479),Vvar__4__req__17479,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17465,Vvar__0__R__17465,Vvar__4__req__17479,Vvar__4__req__17479)),Vvar__1__radd__17466)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17741___24a5(Vvar__0__R__17465,Vvar__1__radd__17466,Vvar__2__rmul__17471,Vvar__3__ropp__17476,Vvar__4__req__17479),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17465,c_24__type__17765___24a5(Vvar__0__R__17465,Vvar__1__radd__17466,Vvar__2__rmul__17471,Vvar__3__ropp__17476,Vvar__4__req__17479),Vvar__4__req__17479,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17465,Vvar__0__R__17465,Vvar__4__req__17479,Vvar__4__req__17479)),Vvar__2__rmul__17471)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17792___24a5(Vvar__0__R__17465,Vvar__1__radd__17466,Vvar__2__rmul__17471,Vvar__3__ropp__17476,Vvar__4__req__17479),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17465,Vvar__0__R__17465,Vvar__4__req__17479,Vvar__4__req__17479),Vvar__3__ropp__17476)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845] :
( cType___24t(Vvar__0__R__18793)
=> ( t(Vvar__1__rO__18794,Vvar__0__R__18793)
=> ( t(Vvar__2__rI__18795,Vvar__0__R__18793)
=> ( c_24__type__19189___24t(Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845,Vvar__3__radd__18796)
=> ( c_24__type__19402___24t(Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845,Vvar__4__rmul__18801)
=> ( c_24__type__19615___24t(Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845,Vvar__5__rsub__18806)
=> ( c_24__type__19810___24t(Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845,Vvar__6__ropp__18811)
=> ( c_24__type__20023___24t(Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845,Vvar__7__req__18814)
=> ( cType___24t(Vvar__8__C__18819)
=> ( t(Vvar__9__cO__18820,Vvar__8__C__18819)
=> ( t(Vvar__10__cI__18821,Vvar__8__C__18819)
=> ( c_24__type__20236___24t(Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845,Vvar__11__cadd__18822)
=> ( c_24__type__20449___24t(Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845,Vvar__12__cmul__18827)
=> ( c_24__type__20662___24t(Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845,Vvar__13__csub__18832)
=> ( c_24__type__20857___24t(Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845,Vvar__14__copp__18837)
=> ( c_24__type__21070___24t(Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845,Vvar__15__ceqb__18840)
=> ( c_24__type__21265___24t(Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845,Vvar__16__phi__18845)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__18793,Vvar__1__rO__18794,Vvar__2__rI__18795,Vvar__3__radd__18796,Vvar__4__rmul__18801,Vvar__5__rsub__18806,Vvar__6__ropp__18811,Vvar__7__req__18814,Vvar__8__C__18819,Vvar__9__cO__18820,Vvar__10__cI__18821,Vvar__11__cadd__18822,Vvar__12__cmul__18827,Vvar__13__csub__18832,Vvar__14__copp__18837,Vvar__15__ceqb__18840,Vvar__16__phi__18845)
=> ( p(happ(happ(Vvar__7__req__18814,happ(Vvar__16__phi__18845,Vvar__9__cO__18820)),Vvar__1__rO__18794))
& p(happ(happ(Vvar__7__req__18814,happ(Vvar__16__phi__18845,Vvar__10__cI__18821)),Vvar__2__rI__18795))
& ! [Vvar__var__var__var__var__var__var__19__x__18907__18909__18931__18933__18935__18937__18939] :
( t(Vvar__var__var__var__var__var__var__19__x__18907__18909__18931__18933__18935__18937__18939,Vvar__8__C__18819)
=> ! [Vvar__var__var__var__var__var__var__20__y__18908__18910__18932__18934__18936__18938__18940] :
( t(Vvar__var__var__var__var__var__var__20__y__18908__18910__18932__18934__18936__18938__18940,Vvar__8__C__18819)
=> p(happ(happ(Vvar__7__req__18814,happ(Vvar__16__phi__18845,happ(happ(Vvar__11__cadd__18822,Vvar__var__var__var__var__var__var__19__x__18907__18909__18931__18933__18935__18937__18939),Vvar__var__var__var__var__var__var__20__y__18908__18910__18932__18934__18936__18938__18940))),happ(happ(Vvar__3__radd__18796,happ(Vvar__16__phi__18845,Vvar__var__var__var__var__var__var__19__x__18907__18909__18931__18933__18935__18937__18939)),happ(Vvar__16__phi__18845,Vvar__var__var__var__var__var__var__20__y__18908__18910__18932__18934__18936__18938__18940)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__18912__18914__18941__18943__18945__18947__18949] :
( t(Vvar__var__var__var__var__var__var__20__x__18912__18914__18941__18943__18945__18947__18949,Vvar__8__C__18819)
=> ! [Vvar__var__var__var__var__var__var__21__y__18913__18915__18942__18944__18946__18948__18950] :
( t(Vvar__var__var__var__var__var__var__21__y__18913__18915__18942__18944__18946__18948__18950,Vvar__8__C__18819)
=> p(happ(happ(Vvar__7__req__18814,happ(Vvar__16__phi__18845,happ(happ(Vvar__13__csub__18832,Vvar__var__var__var__var__var__var__20__x__18912__18914__18941__18943__18945__18947__18949),Vvar__var__var__var__var__var__var__21__y__18913__18915__18942__18944__18946__18948__18950))),happ(happ(Vvar__5__rsub__18806,happ(Vvar__16__phi__18845,Vvar__var__var__var__var__var__var__20__x__18912__18914__18941__18943__18945__18947__18949)),happ(Vvar__16__phi__18845,Vvar__var__var__var__var__var__var__21__y__18913__18915__18942__18944__18946__18948__18950)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__18917__18919__18951__18953__18955__18957__18959] :
( t(Vvar__var__var__var__var__var__var__21__x__18917__18919__18951__18953__18955__18957__18959,Vvar__8__C__18819)
=> ! [Vvar__var__var__var__var__var__var__22__y__18918__18920__18952__18954__18956__18958__18960] :
( t(Vvar__var__var__var__var__var__var__22__y__18918__18920__18952__18954__18956__18958__18960,Vvar__8__C__18819)
=> p(happ(happ(Vvar__7__req__18814,happ(Vvar__16__phi__18845,happ(happ(Vvar__12__cmul__18827,Vvar__var__var__var__var__var__var__21__x__18917__18919__18951__18953__18955__18957__18959),Vvar__var__var__var__var__var__var__22__y__18918__18920__18952__18954__18956__18958__18960))),happ(happ(Vvar__4__rmul__18801,happ(Vvar__16__phi__18845,Vvar__var__var__var__var__var__var__21__x__18917__18919__18951__18953__18955__18957__18959)),happ(Vvar__16__phi__18845,Vvar__var__var__var__var__var__var__22__y__18918__18920__18952__18954__18956__18958__18960)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__18922__18923__18961__18962__18963__18964__18965] :
( t(Vvar__var__var__var__var__var__var__22__x__18922__18923__18961__18962__18963__18964__18965,Vvar__8__C__18819)
=> p(happ(happ(Vvar__7__req__18814,happ(Vvar__16__phi__18845,happ(Vvar__14__copp__18837,Vvar__var__var__var__var__var__var__22__x__18922__18923__18961__18962__18963__18964__18965))),happ(Vvar__6__ropp__18811,happ(Vvar__16__phi__18845,Vvar__var__var__var__var__var__var__22__x__18922__18923__18961__18962__18963__18964__18965)))) )
& ! [Vvar__var__var__var__var__var__23__x__18925__18928__18966__18969__18972__18975] :
( t(Vvar__var__var__var__var__var__23__x__18925__18928__18966__18969__18972__18975,Vvar__8__C__18819)
=> ! [Vvar__var__var__var__var__var__24__y__18926__18929__18967__18970__18973__18976] :
( t(Vvar__var__var__var__var__var__24__y__18926__18929__18967__18970__18973__18976,Vvar__8__C__18819)
=> ( happ(happ(Vvar__15__ceqb__18840,Vvar__var__var__var__var__var__23__x__18925__18928__18966__18969__18972__18975),Vvar__var__var__var__var__var__24__y__18926__18929__18967__18970__18973__18976) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__18814,happ(Vvar__16__phi__18845,Vvar__var__var__var__var__var__23__x__18925__18928__18966__18969__18972__18975)),happ(Vvar__16__phi__18845,Vvar__var__var__var__var__var__24__y__18926__18929__18967__18970__18973__18976))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__31610,Vvar__1__copp__31611,Vvar__2__ceqb__31614,Vvar__3__get__sign__31619] :
( cType___24t(Vvar__0__C__31610)
=> ( c_24__type__31666___24t(Vvar__0__C__31610,Vvar__1__copp__31611,Vvar__2__ceqb__31614,Vvar__3__get__sign__31619,Vvar__1__copp__31611)
=> ( c_24__type__31685___24t(Vvar__0__C__31610,Vvar__1__copp__31611,Vvar__2__ceqb__31614,Vvar__3__get__sign__31619,Vvar__2__ceqb__31614)
=> ( c_24__type__31699___24t(Vvar__0__C__31610,Vvar__1__copp__31611,Vvar__2__ceqb__31614,Vvar__3__get__sign__31619,Vvar__3__get__sign__31619)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__31610,Vvar__1__copp__31611,Vvar__2__ceqb__31614,Vvar__3__get__sign__31619)
=> ( ! [Vvar__var__var__var__var__var__4__c__31636__31639__31642__31645__31648__31651] :
( t(Vvar__var__var__var__var__var__4__c__31636__31639__31642__31645__31648__31651,Vvar__0__C__31610)
=> ! [Vvar__var__var__var__var__var__5__c_27__31637__31640__31643__31646__31649__31652] :
( t(Vvar__var__var__var__var__var__5__c_27__31637__31640__31643__31646__31649__31652,Vvar__0__C__31610)
=> ( happ(Vvar__3__get__sign__31619,Vvar__var__var__var__var__var__4__c__31636__31639__31642__31645__31648__31651) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__31610,Vvar__var__var__var__var__var__5__c_27__31637__31640__31643__31646__31649__31652)
=> happ(happ(Vvar__2__ceqb__31614,Vvar__var__var__var__var__var__4__c__31636__31639__31642__31645__31648__31651),happ(Vvar__1__copp__31611,Vvar__var__var__var__var__var__5__c_27__31637__31640__31643__31646__31649__31652)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__17243,Vvar__1__radd__17244,Vvar__2__rmul__17249,Vvar__3__req__17254] :
( cType___24t(Vvar__0__R__17243)
=> ( c_24__type__17329___24t(Vvar__0__R__17243,Vvar__1__radd__17244,Vvar__2__rmul__17249,Vvar__3__req__17254,Vvar__1__radd__17244)
=> ( c_24__type__17352___24t(Vvar__0__R__17243,Vvar__1__radd__17244,Vvar__2__rmul__17249,Vvar__3__req__17254,Vvar__2__rmul__17249)
=> ( c_24__type__17375___24t(Vvar__0__R__17243,Vvar__1__radd__17244,Vvar__2__rmul__17249,Vvar__3__req__17254,Vvar__3__req__17254)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__17243,Vvar__1__radd__17244,Vvar__2__rmul__17249,Vvar__3__req__17254)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17398___24a4(Vvar__0__R__17243,Vvar__1__radd__17244,Vvar__2__rmul__17249,Vvar__3__req__17254),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17243,c_24__type__17416___24a4(Vvar__0__R__17243,Vvar__1__radd__17244,Vvar__2__rmul__17249,Vvar__3__req__17254),Vvar__3__req__17254,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17243,Vvar__0__R__17243,Vvar__3__req__17254,Vvar__3__req__17254)),Vvar__1__radd__17244)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17442___24a4(Vvar__0__R__17243,Vvar__1__radd__17244,Vvar__2__rmul__17249,Vvar__3__req__17254),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17243,c_24__type__17460___24a4(Vvar__0__R__17243,Vvar__1__radd__17244,Vvar__2__rmul__17249,Vvar__3__req__17254),Vvar__3__req__17254,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17243,Vvar__0__R__17243,Vvar__3__req__17254,Vvar__3__req__17254)),Vvar__2__rmul__17249)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_hahn.Zorn.continues_raw',axiom,
! [Vvar__0__A__3840,Vvar__1__S__3841,Vvar__2__S_27__3844,Vvar__3__R__3847,Vvar__4__R_27__3848] :
( cType___24t(Vvar__0__A__3840)
=> ( c_24__type__3934___24t(Vvar__0__A__3840,Vvar__1__S__3841,Vvar__2__S_27__3844,Vvar__3__R__3847,Vvar__4__R_27__3848,Vvar__1__S__3841)
=> ( c_24__type__3944___24t(Vvar__0__A__3840,Vvar__1__S__3841,Vvar__2__S_27__3844,Vvar__3__R__3847,Vvar__4__R_27__3848,Vvar__2__S_27__3844)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3840,Vvar__3__R__3847)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3840,Vvar__4__R_27__3848)
=> ( chahn_2eZorn_2econtinues__raw___24a5(Vvar__0__A__3840,Vvar__1__S__3841,Vvar__2__S_27__3844,Vvar__3__R__3847,Vvar__4__R_27__3848)
=> ( ! [Vvar__var__var__var__var__5__x__3860__3862__3884__3886__3888] :
( t(Vvar__var__var__var__var__5__x__3860__3862__3884__3886__3888,Vvar__0__A__3840)
=> ( p(happ(Vvar__1__S__3841,Vvar__var__var__var__var__5__x__3860__3862__3884__3886__3888))
=> p(happ(Vvar__2__S_27__3844,Vvar__var__var__var__var__5__x__3860__3862__3884__3886__3888)) ) )
& ! [Vvar__var__var__var__var__var__6__x__3865__3870__3890__3895__3900__3905] :
( t(Vvar__var__var__var__var__var__6__x__3865__3870__3890__3895__3900__3905,Vvar__0__A__3840)
=> ! [Vvar__var__var__var__var__var__7__y__3866__3871__3891__3896__3901__3906] :
( t(Vvar__var__var__var__var__var__7__y__3866__3871__3891__3896__3901__3906,Vvar__0__A__3840)
=> ( p(happ(Vvar__2__S_27__3844,Vvar__var__var__var__var__var__6__x__3865__3870__3890__3895__3900__3905))
=> ( p(happ(Vvar__1__S__3841,Vvar__var__var__var__var__var__7__y__3866__3871__3891__3896__3901__3906))
=> ( p(happ(happ(Vvar__4__R_27__3848,Vvar__var__var__var__var__var__6__x__3865__3870__3890__3895__3900__3905),Vvar__var__var__var__var__var__7__y__3866__3871__3891__3896__3901__3906))
=> p(happ(Vvar__1__S__3841,Vvar__var__var__var__var__var__6__x__3865__3870__3890__3895__3900__3905)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__7__x__3876__3880__3910__3914__3918__3922] :
( t(Vvar__var__var__var__var__var__7__x__3876__3880__3910__3914__3918__3922,Vvar__0__A__3840)
=> ! [Vvar__var__var__var__var__var__8__y__3877__3881__3911__3915__3919__3923] :
( t(Vvar__var__var__var__var__var__8__y__3877__3881__3911__3915__3919__3923,Vvar__0__A__3840)
=> ( p(happ(Vvar__1__S__3841,Vvar__var__var__var__var__var__7__x__3876__3880__3910__3914__3918__3922))
=> ( p(happ(Vvar__1__S__3841,Vvar__var__var__var__var__var__8__y__3877__3881__3911__3915__3919__3923))
=> ( p(happ(happ(Vvar__3__R__3847,Vvar__var__var__var__var__var__7__x__3876__3880__3910__3914__3918__3922),Vvar__var__var__var__var__var__8__y__3877__3881__3911__3915__3919__3923))
<=> p(happ(happ(Vvar__4__R_27__3848,Vvar__var__var__var__var__var__7__x__3876__3880__3910__3914__3918__3922),Vvar__var__var__var__var__var__8__y__3877__3881__3911__3915__3919__3923)) ) ) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_hahn.Zorn.ordered_subset',axiom,
! [Vvar__0__A__3686,Vvar__1__eqA__3687,Vvar__2__S__3688,Vvar__3__R__3691] :
( cType___24t(Vvar__0__A__3686)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3686,Vvar__1__eqA__3687)
=> ( c_24__type__3770___24t(Vvar__0__A__3686,Vvar__1__eqA__3687,Vvar__2__S__3688,Vvar__3__R__3691,Vvar__2__S__3688)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3686,Vvar__3__R__3691)
=> ( chahn_2eZorn_2eordered__subset___24a4(Vvar__0__A__3686,Vvar__1__eqA__3687,Vvar__2__S__3688,Vvar__3__R__3691)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3778___24a4(Vvar__0__A__3686,Vvar__1__eqA__3687,Vvar__2__S__3688,Vvar__3__R__3691),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__A__3686,cProp,Vvar__1__eqA__3687,c_3c_3d_3e),Vvar__2__S__3688)
& cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(Vvar__0__A__3686,Vvar__3__R__3691)
& cCoq_2eInit_2eWf_2ewell__founded___24a2(Vvar__0__A__3686,Vvar__3__R__3691)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3792___24a4(Vvar__0__A__3686,Vvar__1__eqA__3687,Vvar__2__S__3688,Vvar__3__R__3691),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__A__3686,c_24__type__3800___24a4(Vvar__0__A__3686,Vvar__1__eqA__3687,Vvar__2__S__3688,Vvar__3__R__3691),Vvar__1__eqA__3687,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__A__3686,cProp,Vvar__1__eqA__3687,c_3c_3d_3e)),Vvar__3__R__3691)
& ! [Vvar__var__var__var__var__8__x__3712__3715__3739__3742__3745] :
( t(Vvar__var__var__var__var__8__x__3712__3715__3739__3742__3745,Vvar__0__A__3686)
=> ! [Vvar__var__var__var__var__9__y__3713__3716__3740__3743__3746] :
( t(Vvar__var__var__var__var__9__y__3713__3716__3740__3743__3746,Vvar__0__A__3686)
=> ( p(happ(happ(Vvar__3__R__3691,Vvar__var__var__var__var__8__x__3712__3715__3739__3742__3745),Vvar__var__var__var__var__9__y__3713__3716__3740__3743__3746))
=> ( p(happ(Vvar__2__S__3688,Vvar__var__var__var__var__8__x__3712__3715__3739__3742__3745))
& p(happ(Vvar__2__S__3688,Vvar__var__var__var__var__9__y__3713__3716__3740__3743__3746)) ) ) ) )
& ! [Vvar__var__var__var__var__var__9__x__3719__3723__3748__3752__3756__3760] :
( t(Vvar__var__var__var__var__var__9__x__3719__3723__3748__3752__3756__3760,Vvar__0__A__3686)
=> ! [Vvar__var__var__var__var__var__10__y__3720__3724__3749__3753__3757__3761] :
( t(Vvar__var__var__var__var__var__10__y__3720__3724__3749__3753__3757__3761,Vvar__0__A__3686)
=> ( p(happ(Vvar__2__S__3688,Vvar__var__var__var__var__var__9__x__3719__3723__3748__3752__3756__3760))
=> ( p(happ(Vvar__2__S__3688,Vvar__var__var__var__var__var__10__y__3720__3724__3749__3753__3757__3761))
=> ( p(happ(happ(Vvar__1__eqA__3687,Vvar__var__var__var__var__var__9__x__3719__3723__3748__3752__3756__3760),Vvar__var__var__var__var__var__10__y__3720__3724__3749__3753__3757__3761))
| p(happ(happ(Vvar__3__R__3691,Vvar__var__var__var__var__var__9__x__3719__3723__3748__3752__3756__3760),Vvar__var__var__var__var__var__10__y__3720__3724__3749__3753__3757__3761))
| p(happ(happ(Vvar__3__R__3691,Vvar__var__var__var__var__var__10__y__3720__3724__3749__3753__3757__3761),Vvar__var__var__var__var__var__9__x__3719__3723__3748__3752__3756__3760)) ) ) ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_hahn.Zorn.well_order',axiom,
! [Vvar__0__A__3602,Vvar__1__eqA__3603,Vvar__2__ltA__3604] :
( cType___24t(Vvar__0__A__3602)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3602,Vvar__1__eqA__3603)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3602,Vvar__2__ltA__3604)
=> ( chahn_2eZorn_2ewell__order___24a3(Vvar__0__A__3602,Vvar__1__eqA__3603,Vvar__2__ltA__3604)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(Vvar__0__A__3602,Vvar__1__eqA__3603)
& cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(Vvar__0__A__3602,Vvar__2__ltA__3604)
& cCoq_2eInit_2eWf_2ewell__founded___24a2(Vvar__0__A__3602,Vvar__2__ltA__3604)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3646___24a3(Vvar__0__A__3602,Vvar__1__eqA__3603,Vvar__2__ltA__3604),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__A__3602,c_24__type__3651___24a3(Vvar__0__A__3602,Vvar__1__eqA__3603,Vvar__2__ltA__3604),Vvar__1__eqA__3603,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__A__3602,cProp,Vvar__1__eqA__3603,c_3c_3d_3e)),Vvar__2__ltA__3604)
& ! [Vvar__var__var__var__var__7__x__3620__3622__3633__3635__3637] :
( t(Vvar__var__var__var__var__7__x__3620__3622__3633__3635__3637,Vvar__0__A__3602)
=> ! [Vvar__var__var__var__var__8__y__3621__3623__3634__3636__3638] :
( t(Vvar__var__var__var__var__8__y__3621__3623__3634__3636__3638,Vvar__0__A__3602)
=> ( p(happ(happ(Vvar__1__eqA__3603,Vvar__var__var__var__var__7__x__3620__3622__3633__3635__3637),Vvar__var__var__var__var__8__y__3621__3623__3634__3636__3638))
| p(happ(happ(Vvar__2__ltA__3604,Vvar__var__var__var__var__7__x__3620__3622__3633__3635__3637),Vvar__var__var__var__var__8__y__3621__3623__3634__3636__3638))
| p(happ(happ(Vvar__2__ltA__3604,Vvar__var__var__var__var__8__y__3621__3623__3634__3636__3638),Vvar__var__var__var__var__7__x__3620__3622__3633__3635__3637)) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_lam_1125',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__1125___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(c_24False) ) ).
fof('$_lam_1150',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__1150___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__4),Vv__CANONICAL__3) ).
fof('$_lam_1164',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__1164___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('$_lam_1172',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__1172___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(c_24False) ) ).
fof('$_lam_1268',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1268___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 ).
fof('$_lam_1274',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1274___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(Vv__CANONICAL__1,Vv__CANONICAL__3)) ).
fof('$_lam_1283',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1283___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('$_lam_1308',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__1308___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
& p(happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ).
fof('$_lam_1319',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__1319___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ).
fof('$_lam_1336',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__1336___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__4))
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5))
& p(happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ) ) ).
fof('$_lam_1523',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__1523___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('$_lam_1817',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__1817___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
| p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ).
fof('$_lam_1825',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__1825___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('$_lam_2128',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__2128___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_2132',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__2132___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('$_lam_2341',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__2341___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> p(happ(happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4)),happ(Vv__CANONICAL__2,Vv__CANONICAL__5))) ) ).
fof('$_lam_3000',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11] : c_24__lam__3000___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11) = c_24__let__11__subst__l__2928___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__11)) ).
fof('$_lam_33250',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__33250___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_33268',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__33268___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__4,happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_lam_4662',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__4662___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_4764',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__4764___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_613',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__613___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_619',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__619___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('$_lam_628',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__628___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_74',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__74___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(c_24True) ) ).
fof('$_prop_1606',axiom,
! [V1__A,V2__f,Vvar__1___24Anonymous__1588] :
( p(c_24__prop__1606___24a3(V1__A,V2__f,Vvar__1___24Anonymous__1588))
<=> ~ p(happ(V2__f,Vvar__1___24Anonymous__1588)) ) ).
fof('$_prop_1607',axiom,
! [V1__A,V2__f,Vvar__1___24Anonymous__1588] :
( p(c_24__prop__1607___24a3(V1__A,V2__f,Vvar__1___24Anonymous__1588))
<=> ~ p(happ(V2__f,Vvar__1___24Anonymous__1588)) ) ).
fof('$_prop_1646',axiom,
! [V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630] :
( p(c_24__prop__1646___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630)) ) ).
fof('$_prop_1658',axiom,
! [V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630] :
( p(c_24__prop__1658___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630)) ) ).
fof('$_prop_24190',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__24190___24a1(Vv__CANONICAL__0))
<=> ~ p(Vv__CANONICAL__0) ) ).
fof('$_prop_24372',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__24372___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__2 ) ).
fof('$_prop_24373',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__24373___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__2 ) ).
fof('$_prop_25592',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__25592___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_25593',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__25593___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_25594',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__25594___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_25595',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__25595___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_26270',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__26270___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_28300',axiom,
! [V0__A,V1__x,V2__y] :
( p(c_24__prop__28300___24a3(V0__A,V1__x,V2__y))
<=> V1__x = V2__y ) ).
fof('$_prop_35873',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__35873___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_35874',axiom,
! [V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__35829] :
( p(c_24__prop__35874___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__35829))
<=> ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__35829)) ) ).
fof('$_prop_35875',axiom,
! [V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__35829] :
( p(c_24__prop__35875___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__35829))
<=> ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__35829)) ) ).
fof('$_prop_35908',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__35908___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_type_1',axiom,
! [Vvar__2] :
( c_24__type__1___24t(Vvar__2)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__2,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10',axiom,
! [Vv__CANONICAL__0,Vvar__11] :
( c_24__type__10___24t(Vv__CANONICAL__0,Vvar__11)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__11,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_10110',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10111] :
( c_24__type__10110___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10111)
<=> ! [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__10111,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_1012',axiom,
! [Vv__CANONICAL__0,Vvar__1013] :
( c_24__type__1012___24t(Vv__CANONICAL__0,Vvar__1013)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__1013,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1153',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1154] :
( c_24__type__1153___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1154)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1154,Vv__CANONICAL__2)) ) ) ).
fof('$_type_13',axiom,
! [Vv__CANONICAL__0,Vvar__14] :
( c_24__type__13___24t(Vv__CANONICAL__0,Vvar__14)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__14,Vv__CANONICAL__1)) ) ) ).
fof('$_type_135',axiom,
! [Vvar__136] :
( c_24__type__135___24t(Vvar__136)
<=> ! [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__136,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_1405',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1406] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1406)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__1406,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_1568',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1569] :
( c_24__type__1568___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1569)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(Vvar__1569,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_158',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__159] :
( c_24__type__158___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__159)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(Vvar__159,Vv__CANONICAL__2)) ) ) ).
fof('$_type_15950',axiom,
! [Vvar__15951] :
( c_24__type__15950___24t(Vvar__15951)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__15951,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_15971',axiom,
! [Vvar__15972] :
( c_24__type__15971___24t(Vvar__15972)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__15972,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_1612',axiom,
! [Vvar__1613] :
( c_24__type__1612___24t(Vvar__1613)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1613,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1623',axiom,
! [Vvar__1624] :
( c_24__type__1623___24t(Vvar__1624)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__1624,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_16489',axiom,
! [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__16490] :
( c_24__type__16489___24t(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__16490)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16490,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16552',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__16553] :
( c_24__type__16552___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__16553)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16553,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1660',axiom,
! [Vvar__1661] :
( c_24__type__1660___24t(Vvar__1661)
<=> ! [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__1661,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16615',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__16616] :
( c_24__type__16615___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__16616)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16616,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16669',axiom,
! [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__16670] :
( c_24__type__16669___24t(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__16670)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__16670,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_16732',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__16733] :
( c_24__type__16732___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__16733)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__16733,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_17329',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17330] :
( c_24__type__17329___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17330)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17330,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1735',axiom,
! [Vvar__1736] :
( c_24__type__1735___24t(Vvar__1736)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1736,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17352',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17353] :
( c_24__type__17352___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17353)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17353,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17375',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17376] :
( c_24__type__17375___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17376)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__17376,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_17398',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17399] :
( c_24__type__17398___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17399)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17399,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1740',axiom,
! [Vvar__1741] :
( c_24__type__1740___24t(Vvar__1741)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__1741,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17416',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17417] :
( c_24__type__17416___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17417)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__17417,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_17442',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17443] :
( c_24__type__17442___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17443)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17443,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17460',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17461] :
( c_24__type__17460___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17461)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__17461,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_1750',axiom,
! [Vvar__1751] :
( c_24__type__1750___24t(Vvar__1751)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__1751,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_17570',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17571] :
( c_24__type__17570___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17571)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17571,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1758',axiom,
! [Vvar__1759] :
( c_24__type__1758___24t(Vvar__1759)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__1759,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17600',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17601] :
( c_24__type__17600___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17601)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17601,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17624',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17625] :
( c_24__type__17624___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17625)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__17625,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_17654',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17655] :
( c_24__type__17654___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17655)
<=> ! [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__17655,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_17684',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17685] :
( c_24__type__17684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17685)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17685,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17708',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17709] :
( c_24__type__17708___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17709)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__17709,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_17741',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17742] :
( c_24__type__17741___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17742)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17742,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17765',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17766] :
( c_24__type__17765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17766)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__17766,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_17792',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17793] :
( c_24__type__17792___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17793)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__17793,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_1827',axiom,
! [Vvar__1828] :
( c_24__type__1827___24t(Vvar__1828)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1828,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1833',axiom,
! [Vvar__1834] :
( c_24__type__1833___24t(Vvar__1834)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__1834,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1845',axiom,
! [Vvar__1846] :
( c_24__type__1845___24t(Vvar__1846)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__1846,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_187',axiom,
! [Vvar__188] :
( c_24__type__187___24t(Vvar__188)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__188,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1879',axiom,
! [Vvar__1880] :
( c_24__type__1879___24t(Vvar__1880)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__505___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__1880,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_1896',axiom,
! [Vvar__1897] :
( c_24__type__1896___24t(Vvar__1897)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__1897,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1906',axiom,
! [Vvar__1907] :
( c_24__type__1906___24t(Vvar__1907)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__1907,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1918',axiom,
! [Vv__CANONICAL__0,Vvar__1919] :
( c_24__type__1918___24t(Vv__CANONICAL__0,Vvar__1919)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__1919,Vv__CANONICAL__1)) ) ) ).
fof('$_type_19189',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19190] :
( c_24__type__19189___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19190)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19190,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1929',axiom,
! [Vvar__1930] :
( c_24__type__1929___24t(Vvar__1930)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__1930,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19402',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19403] :
( c_24__type__19402___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19403)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19403,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19615',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19616] :
( c_24__type__19615___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19616)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19616,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19810',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19811] :
( c_24__type__19810___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19811)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__19811,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_20023',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20024] :
( c_24__type__20023___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20024)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__20024,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_2011',axiom,
! [Vvar__2012] :
( c_24__type__2011___24t(Vvar__2012)
<=> ! [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__2012,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20236',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20237] :
( c_24__type__20236___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20237)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__20237,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_2036',axiom,
! [Vv__CANONICAL__0,Vvar__2037] :
( c_24__type__2036___24t(Vv__CANONICAL__0,Vvar__2037)
<=> ! [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(Vvar__2037,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_20449',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20450] :
( c_24__type__20449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20450)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__20450,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_20662',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20663] :
( c_24__type__20662___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20663)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__20663,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_20857',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20858] :
( c_24__type__20857___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20858)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__20858,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_209',axiom,
! [Vvar__210] :
( c_24__type__209___24t(Vvar__210)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__158___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__210,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_21070',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__21071] :
( c_24__type__21070___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__21071)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__21071,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_21265',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__21266] :
( c_24__type__21265___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__21266)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__21266,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_21278',axiom,
! [Vvar__21279] :
( c_24__type__21278___24t(Vvar__21279)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21279,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21382',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21383] :
( c_24__type__21382___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21383)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21383,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21426',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21427] :
( c_24__type__21426___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21427)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21427,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_21462',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21463] :
( c_24__type__21462___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21463)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__21463,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_21506',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21507] :
( c_24__type__21506___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21507)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__21507,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21613',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21614] :
( c_24__type__21613___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21614)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__21614,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_21627',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21628] :
( c_24__type__21627___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21628)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__21628,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_21634',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21635] :
( c_24__type__21634___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21635)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__21635,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_21766',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__21767] :
( c_24__type__21766___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__21767)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21767,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_21801',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__21802] :
( c_24__type__21801___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__21802)
<=> ! [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__21802,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_21841',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__21842] :
( c_24__type__21841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__21842)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21842,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_21861',axiom,
! [Vvar__21862] :
( c_24__type__21861___24t(Vvar__21862)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__83___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__21871___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__21862,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_21871',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21872] :
( c_24__type__21871___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21872)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__21872,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_21904',axiom,
! [Vvar__21905] :
( c_24__type__21904___24t(Vvar__21905)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__83___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__21914___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__21871___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__21905,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_21914',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21915] :
( c_24__type__21914___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21915)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21915,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_220',axiom,
! [Vvar__221] :
( c_24__type__220___24t(Vvar__221)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__221,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22011',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22012] :
( c_24__type__22011___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22012)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22012,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_22050',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22051] :
( c_24__type__22050___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22051)
<=> ! [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__22051,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_22085',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22086] :
( c_24__type__22085___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22086)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22086,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_22157',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22158] :
( c_24__type__22157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22158)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__22158,Vv__CANONICAL__2)) ) ) ).
fof('$_type_22161',axiom,
! [Vvar__22162] :
( c_24__type__22161___24t(Vvar__22162)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5304___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__22162,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22238',axiom,
! [Vvar__22239] :
( c_24__type__22238___24t(Vvar__22239)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__22239,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22325',axiom,
! [Vvar__22326] :
( c_24__type__22325___24t(Vvar__22326)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__22326,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_225',axiom,
! [Vvar__226] :
( c_24__type__225___24t(Vvar__226)
<=> ! [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__226,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22760',axiom,
! [Vvar__22761] :
( c_24__type__22760___24t(Vvar__22761)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__22761,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22871',axiom,
! [Vvar__22872] :
( c_24__type__22871___24t(Vvar__22872)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22872,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22888',axiom,
! [Vvar__22889] :
( c_24__type__22888___24t(Vvar__22889)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22889,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23006',axiom,
! [Vvar__23007] :
( c_24__type__23006___24t(Vvar__23007)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__23007,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23255',axiom,
! [Vvar__23256] :
( c_24__type__23255___24t(Vvar__23256)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__23256,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23288',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23289] :
( c_24__type__23288___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23289)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__23289,Vv__CANONICAL__3)) ) ) ).
fof('$_type_23323',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23324] :
( c_24__type__23323___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23324)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23324,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_23348',axiom,
! [Vvar__23349] :
( c_24__type__23348___24t(Vvar__23349)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__23349,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23400',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23401] :
( c_24__type__23400___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23401)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23401,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_23438',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23439] :
( c_24__type__23438___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23439)
<=> ! [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__23439,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_23452',axiom,
! [Vvar__23453] :
( c_24__type__23452___24t(Vvar__23453)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__23453,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23493',axiom,
! [Vvar__23494] :
( c_24__type__23493___24t(Vvar__23494)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__23494,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24074',axiom,
! [Vvar__24075] :
( c_24__type__24074___24t(Vvar__24075)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__24075,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_24115',axiom,
! [Vvar__24116] :
( c_24__type__24115___24t(Vvar__24116)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__24116,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24183',axiom,
! [Vvar__24184] :
( c_24__type__24183___24t(Vvar__24184)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__24184,Vv__CANONICAL__0)) ) ) ).
fof('$_type_24188',axiom,
! [Vvar__24189] :
( c_24__type__24188___24t(Vvar__24189)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,c_24__prop__24190___24a1(Vv__CANONICAL__0),happ(Vvar__24189,Vv__CANONICAL__0)) ) ) ).
fof('$_type_24284',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24285] :
( c_24__type__24284___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24285)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__24285,Vv__CANONICAL__2)) ) ) ).
fof('$_type_24309',axiom,
! [Vvar__24310] :
( c_24__type__24309___24t(Vvar__24310)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__24312___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__3] :
( c_24__type__24324___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__24310,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_24312',axiom,
! [Vv__CANONICAL__0,Vvar__24313] :
( c_24__type__24312___24t(Vv__CANONICAL__0,Vvar__24313)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__24313,Vv__CANONICAL__1)) ) ) ).
fof('$_type_24324',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24325] :
( c_24__type__24324___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24325)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(happ(Vvar__24325,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))) ) ) ) ) ).
fof('$_type_24370',axiom,
! [Vv__CANONICAL__0,Vvar__24371] :
( c_24__type__24370___24t(Vv__CANONICAL__0,Vvar__24371)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__24372___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__24373___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(Vvar__24371,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_24392',axiom,
! [Vvar__24393] :
( c_24__type__24392___24t(Vvar__24393)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__24393,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24395',axiom,
! [Vvar__24396] :
( c_24__type__24395___24t(Vvar__24396)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__24396,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24400',axiom,
! [Vvar__24401] :
( c_24__type__24400___24t(Vvar__24401)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__24401,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_24403',axiom,
! [Vvar__24404] :
( c_24__type__24403___24t(Vvar__24404)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__24404,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24663',axiom,
! [Vvar__24664] :
( c_24__type__24663___24t(Vvar__24664)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__8276___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__24684___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__24693___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__9,Vv__CANONICAL__15)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__24664,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_24684',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24685] :
( c_24__type__24684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24685)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__24685,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_24693',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24694] :
( c_24__type__24693___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24694)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__24694,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24712',axiom,
! [Vvar__24713] :
( c_24__type__24712___24t(Vvar__24713)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__24713,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24732',axiom,
! [Vvar__24733] :
( c_24__type__24732___24t(Vvar__24733)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__24733,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24951',axiom,
! [Vvar__24952] :
( c_24__type__24951___24t(Vvar__24952)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__83___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__8276___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__24684___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__24693___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__24952,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_25210',axiom,
! [Vvar__25211] :
( c_24__type__25210___24t(Vvar__25211)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__25215___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__25211,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_25215',axiom,
! [Vv__CANONICAL__0,Vvar__25216] :
( c_24__type__25215___24t(Vv__CANONICAL__0,Vvar__25216)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__25216,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_25406',axiom,
! [Vvar__25407] :
( c_24__type__25406___24t(Vvar__25407)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__25407,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_255',axiom,
! [Vvar__256] :
( c_24__type__255___24t(Vvar__256)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__256,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_25605',axiom,
! [Vvar__25606] :
( c_24__type__25605___24t(Vvar__25606)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__24370___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__25606,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_25634',axiom,
! [Vvar__25635] :
( c_24__type__25634___24t(Vvar__25635)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__25635,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_257',axiom,
! [Vvar__258] :
( c_24__type__257___24t(Vvar__258)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__259___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__258,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25773',axiom,
! [Vvar__25774] :
( c_24__type__25773___24t(Vvar__25774)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__25774,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25782',axiom,
! [Vvar__25783] :
( c_24__type__25782___24t(Vvar__25783)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5304___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__25783,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_25788',axiom,
! [Vvar__25789] :
( c_24__type__25788___24t(Vvar__25789)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__25789,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_25793',axiom,
! [Vvar__25794] :
( c_24__type__25793___24t(Vvar__25794)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__25794,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_259',axiom,
! [Vvar__260] :
( c_24__type__259___24t(Vvar__260)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__260,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26103',axiom,
! [Vvar__26104] :
( c_24__type__26103___24t(Vvar__26104)
<=> ! [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__26104,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2653',axiom,
! [Vv__CANONICAL__0,Vvar__2654] :
( c_24__type__2653___24t(Vv__CANONICAL__0,Vvar__2654)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__2654,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_2664',axiom,
! [Vvar__2665] :
( c_24__type__2664___24t(Vvar__2665)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2653___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__2665,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_26647',axiom,
! [Vvar__26648] :
( c_24__type__26647___24t(Vvar__26648)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__26648,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_26929',axiom,
! [Vvar__26930] :
( c_24__type__26929___24t(Vvar__26930)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__83___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__8276___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__24684___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__24693___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__26930,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_27149',axiom,
! [Vvar__27150] :
( c_24__type__27149___24t(Vvar__27150)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__27150,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27923',axiom,
! [Vvar__27924] :
( c_24__type__27923___24t(Vvar__27924)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__11] :
( c_24__type__21634___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__8276___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__27947___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__16)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__27924,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__16),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_27947',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27948] :
( c_24__type__27947___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27948)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__27948,Vv__CANONICAL__2)) ) ) ).
fof('$_type_28060',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28061] :
( c_24__type__28060___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28061)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__28061,Vv__CANONICAL__3)) ) ) ).
fof('$_type_28072',axiom,
! [Vvar__28073] :
( c_24__type__28072___24t(Vvar__28073)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__28073,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28124',axiom,
! [Vvar__28125] :
( c_24__type__28124___24t(Vvar__28125)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__28125,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_28146',axiom,
! [Vvar__28147] :
( c_24__type__28146___24t(Vvar__28147)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__28147,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_28187',axiom,
! [Vv__CANONICAL__0,Vvar__28188] :
( c_24__type__28187___24t(Vv__CANONICAL__0,Vvar__28188)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__28188,Vv__CANONICAL__1)) ) ) ).
fof('$_type_28193',axiom,
! [Vvar__28194] :
( c_24__type__28193___24t(Vvar__28194)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__28187___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__28194,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_28216',axiom,
! [Vvar__28217] :
( c_24__type__28216___24t(Vvar__28217)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__28217,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_28232',axiom,
! [Vvar__28233] :
( c_24__type__28232___24t(Vvar__28233)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__28233,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_28265',axiom,
! [Vv__CANONICAL__0,Vvar__28266] :
( c_24__type__28265___24t(Vv__CANONICAL__0,Vvar__28266)
<=> ! [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)
=> cProp___24t(happ(happ(Vvar__28266,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_28919',axiom,
! [Vvar__28920] :
( c_24__type__28919___24t(Vvar__28920)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__8276___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__4,Vv__CANONICAL__7)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__28920,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ).
fof('$_type_28958',axiom,
! [Vvar__28959] :
( c_24__type__28958___24t(Vvar__28959)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__28959,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_29005',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29006] :
( c_24__type__29005___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29006)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__29006,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_2913',axiom,
! [Vvar__2914] :
( c_24__type__2913___24t(Vvar__2914)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__2914,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2916',axiom,
! [Vvar__2917] :
( c_24__type__2916___24t(Vvar__2917)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__2917,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_292',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__293] :
( c_24__type__292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__293)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__293,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_29203',axiom,
! [Vvar__29204] :
( c_24__type__29203___24t(Vvar__29204)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__29204,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2921',axiom,
! [Vvar__2922] :
( c_24__type__2921___24t(Vvar__2922)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2922,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_29396',axiom,
! [Vvar__29397] :
( c_24__type__29396___24t(Vvar__29397)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__8276___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__24684___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__24693___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__29397,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_3',axiom,
! [Vvar__4] :
( c_24__type__3___24t(Vvar__4)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30',axiom,
! [Vv__CANONICAL__0,Vvar__31] :
( c_24__type__30___24t(Vv__CANONICAL__0,Vvar__31)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__31,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_30447',axiom,
! [Vvar__30448] :
( c_24__type__30447___24t(Vvar__30448)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__83___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__8276___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__24684___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__24693___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8)),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__30448,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_31035',axiom,
! [Vvar__31036] :
( c_24__type__31035___24t(Vvar__31036)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__10] :
( c_24__type__21634___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__8276___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__24684___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__24693___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__28060___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__16)
=> ! [Vv__CANONICAL__17] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__7,Vv__CANONICAL__17)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__31036,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__16),Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_3132',axiom,
! [Vvar__3133] :
( c_24__type__3132___24t(Vvar__3133)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__2653___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__3154___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__3133,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_3137',axiom,
! [Vv__CANONICAL__0,Vvar__3138] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vvar__3138)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3138,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3146',axiom,
! [Vv__CANONICAL__0,Vvar__3147] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vvar__3147)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__3147,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_3154',axiom,
! [Vv__CANONICAL__0,Vvar__3155] :
( c_24__type__3154___24t(Vv__CANONICAL__0,Vvar__3155)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__3155,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_31666',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31667] :
( c_24__type__31666___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31667)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__31667,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_31685',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31686] :
( c_24__type__31685___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31686)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__31686,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_31699',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31700] :
( c_24__type__31699___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31700)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__31700,Vv__CANONICAL__4)) ) ) ).
fof('$_type_31844',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31845] :
( c_24__type__31844___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31845)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31845,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_31894',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31895] :
( c_24__type__31894___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31895)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__31895,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_31944',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31945] :
( c_24__type__31944___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31945)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__31945,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_31986',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31987] :
( c_24__type__31986___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31987)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__31987,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_32036',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32037] :
( c_24__type__32036___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32037)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__32037,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_32125',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32126] :
( c_24__type__32125___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32126)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__32126,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_32132',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32133] :
( c_24__type__32132___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32133)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__32133,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32226',axiom,
! [Vvar__32227] :
( c_24__type__32226___24t(Vvar__32227)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__83___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__32227,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_32274',axiom,
! [Vvar__32275] :
( c_24__type__32274___24t(Vvar__32275)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__32275,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_32282',axiom,
! [Vvar__32283] :
( c_24__type__32282___24t(Vvar__32283)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(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__32283,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_32293',axiom,
! [Vvar__32294] :
( c_24__type__32293___24t(Vvar__32294)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__32294,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_32307',axiom,
! [Vvar__32308] :
( c_24__type__32307___24t(Vvar__32308)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(Vvar__32308,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32321',axiom,
! [Vvar__32322] :
( c_24__type__32321___24t(Vvar__32322)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__32322,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_32666',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32667] :
( c_24__type__32666___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32667)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__32667,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_33',axiom,
! [Vv__CANONICAL__0,Vvar__34] :
( c_24__type__33___24t(Vv__CANONICAL__0,Vvar__34)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__34,Vv__CANONICAL__1)) ) ) ).
fof('$_type_33002',axiom,
! [Vvar__33003] :
( c_24__type__33002___24t(Vvar__33003)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__11] :
( c_24__type__21634___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__8276___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cType___24t(Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__24684___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__24693___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( c_24__type__28060___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__16)
=> ! [Vv__CANONICAL__17] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__17)
=> ! [Vv__CANONICAL__18] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__18)
=> ! [Vv__CANONICAL__19] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__19)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__33003,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__16),Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__19),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_33039',axiom,
! [Vvar__33040] :
( c_24__type__33039___24t(Vvar__33040)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__33040,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33076',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33077] :
( c_24__type__33076___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33077)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__33077,Vv__CANONICAL__2)) ) ) ).
fof('$_type_33086',axiom,
! [Vvar__33087] :
( c_24__type__33086___24t(Vvar__33087)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__33076___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__33087,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33129',axiom,
! [Vvar__33130] :
( c_24__type__33129___24t(Vvar__33130)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__33130,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_33146',axiom,
! [Vvar__33147] :
( c_24__type__33146___24t(Vvar__33147)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__33147,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_33155',axiom,
! [Vvar__33156] :
( c_24__type__33155___24t(Vvar__33156)
<=> ! [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_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__33156,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33187',axiom,
! [Vvar__33188] :
( c_24__type__33187___24t(Vvar__33188)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__33188,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33199',axiom,
! [Vvar__33200] :
( c_24__type__33199___24t(Vvar__33200)
<=> ! [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)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__33200,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_33243',axiom,
! [Vvar__33244] :
( c_24__type__33243___24t(Vvar__33244)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__33247___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__33244,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33247',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33248] :
( c_24__type__33247___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33248)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(Vvar__33248,Vv__CANONICAL__2)) ) ) ).
fof('$_type_33310',axiom,
! [Vvar__33311] :
( c_24__type__33310___24t(Vvar__33311)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32132___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(happ(Vvar__33311,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_33339',axiom,
! [Vvar__33340] :
( c_24__type__33339___24t(Vvar__33340)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__33346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__33340,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_33346',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33347] :
( c_24__type__33346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33347)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__33347,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_33359',axiom,
! [Vvar__33360] :
( c_24__type__33359___24t(Vvar__33360)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__28187___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__33360,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_33387',axiom,
! [Vvar__33388] :
( c_24__type__33387___24t(Vvar__33388)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__28187___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__33388,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3348',axiom,
! [Vvar__3349] :
( c_24__type__3348___24t(Vvar__3349)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__3349,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_33481',axiom,
! [Vvar__33482] :
( c_24__type__33481___24t(Vvar__33482)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__24312___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__4] :
( c_24__type__33500___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__33482,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ) ).
fof('$_type_33500',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33501] :
( c_24__type__33500___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33501)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(Vvar__33501,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ) ).
fof('$_type_33523',axiom,
! [Vvar__33524] :
( c_24__type__33523___24t(Vvar__33524)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__83___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__33524,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_33585',axiom,
! [Vvar__33586] :
( c_24__type__33585___24t(Vvar__33586)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__33586,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33600',axiom,
! [Vvar__33601] :
( c_24__type__33600___24t(Vvar__33601)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__33601,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33642',axiom,
! [Vvar__33643] :
( c_24__type__33642___24t(Vvar__33643)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__33643,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33647',axiom,
! [Vvar__33648] :
( c_24__type__33647___24t(Vvar__33648)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__33648,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_33655',axiom,
! [Vvar__33656] :
( c_24__type__33655___24t(Vvar__33656)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__33656,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33660',axiom,
! [Vvar__33661] :
( c_24__type__33660___24t(Vvar__33661)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(happ(happ(Vvar__33661,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3368',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3369] :
( c_24__type__3368___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3369)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3369,Vv__CANONICAL__2)) ) ) ).
fof('$_type_3372',axiom,
! [Vvar__3373] :
( c_24__type__3372___24t(Vvar__3373)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__3373,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33726',axiom,
! [Vvar__33727] :
( c_24__type__33726___24t(Vvar__33727)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__83___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__8276___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__5,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__5,Vv__CANONICAL__8)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__33727,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_33779',axiom,
! [Vvar__33780] :
( c_24__type__33779___24t(Vvar__33780)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__33780,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_33884',axiom,
! [Vvar__33885] :
( c_24__type__33884___24t(Vvar__33885)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__33885,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_3390',axiom,
! [Vvar__3391] :
( c_24__type__3390___24t(Vvar__3391)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__3391,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_3407',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3408] :
( c_24__type__3407___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3408)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3408,Vv__CANONICAL__2)) ) ) ).
fof('$_type_34112',axiom,
! [Vvar__34113] :
( c_24__type__34112___24t(Vvar__34113)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__34113,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34117',axiom,
! [Vvar__34118] :
( c_24__type__34117___24t(Vvar__34118)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__34118,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_34126',axiom,
! [Vvar__34127] :
( c_24__type__34126___24t(Vvar__34127)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__34127,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3413',axiom,
! [Vvar__3414] :
( c_24__type__3413___24t(Vvar__3414)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__3414,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_34152',axiom,
! [Vvar__34153] :
( c_24__type__34152___24t(Vvar__34153)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__831___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__34153,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_34159',axiom,
! [Vvar__34160] :
( c_24__type__34159___24t(Vvar__34160)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__34160,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34167',axiom,
! [Vvar__34168] :
( c_24__type__34167___24t(Vvar__34168)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),happ(happ(happ(happ(Vvar__34168,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_34240',axiom,
! [Vvar__34241] :
( c_24__type__34240___24t(Vvar__34241)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__34241,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34263',axiom,
! [Vvar__34264] :
( c_24__type__34263___24t(Vvar__34264)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(happ(Vvar__34264,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34266',axiom,
! [Vvar__34267] :
( c_24__type__34266___24t(Vvar__34267)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__34267,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3427',axiom,
! [Vvar__3428] :
( c_24__type__3427___24t(Vvar__3428)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__3428,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3482',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3483] :
( c_24__type__3482___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3483)
<=> ! [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__3483,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_3517',axiom,
! [Vvar__3518] :
( c_24__type__3517___24t(Vvar__3518)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__3518,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35755',axiom,
! [Vvar__35756] :
( c_24__type__35755___24t(Vvar__35756)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3137___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__35756,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_3585',axiom,
! [Vvar__3586] :
( c_24__type__3585___24t(Vvar__3586)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__3] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__3,Vv__CANONICAL__4))
=> ( p(happ(Vv__CANONICAL__3,Vv__CANONICAL__5))
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5))
| p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__5),Vv__CANONICAL__4)) ) ) ) ) )
=> ? [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
& ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__3,Vv__CANONICAL__6))
=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__6),Vv__CANONICAL__5)) ) ) ) ) )
=> cProp___24t(happ(happ(Vvar__3586,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ).
fof('$_type_35853',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35854] :
( c_24__type__35853___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35854)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__35854,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_35862',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35863] :
( c_24__type__35862___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35863)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__35863,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_35871',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35872] :
( c_24__type__35871___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35872)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__35873___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__35872,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_35894',axiom,
! [Vvar__35895] :
( c_24__type__35894___24t(Vvar__35895)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__83___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__35906___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(Vvar__35895,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_35906',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35907] :
( c_24__type__35906___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35907)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__35908___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__35907,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_36',axiom,
! [Vv__CANONICAL__0,Vvar__37] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vvar__37)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__37,Vv__CANONICAL__1)) ) ) ).
fof('$_type_36217',axiom,
! [Vvar__36218] :
( c_24__type__36217___24t(Vvar__36218)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__36218,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_36222',axiom,
! [Vvar__36223] :
( c_24__type__36222___24t(Vvar__36223)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__36223,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_36268',axiom,
! [Vvar__36269] :
( c_24__type__36268___24t(Vvar__36269)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__36269,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36311',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__36312] :
( c_24__type__36311___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__36312)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(Vvar__36312,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_3646',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3647] :
( c_24__type__3646___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3647)
<=> ! [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__3647,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_3651',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3652] :
( c_24__type__3651___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3652)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3652,Vv__CANONICAL__3)) ) ) ).
fof('$_type_36555',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__36556] :
( c_24__type__36555___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__36556)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__36556,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_3770',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__3771] :
( c_24__type__3770___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__3771)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3771,Vv__CANONICAL__4)) ) ) ).
fof('$_type_3778',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__3779] :
( c_24__type__3778___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__3779)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3779,Vv__CANONICAL__4)) ) ) ).
fof('$_type_3792',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__3793] :
( c_24__type__3792___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__3793)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__3793,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_3800',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__3801] :
( c_24__type__3800___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__3801)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3801,Vv__CANONICAL__4)) ) ) ).
fof('$_type_3934',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3935] :
( c_24__type__3934___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3935)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3935,Vv__CANONICAL__5)) ) ) ).
fof('$_type_3944',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3945] :
( c_24__type__3944___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3945)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3945,Vv__CANONICAL__5)) ) ) ).
fof('$_type_41',axiom,
! [Vvar__42] :
( c_24__type__41___24t(Vvar__42)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__42,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4124',axiom,
! [Vvar__4125] :
( c_24__type__4124___24t(Vvar__4125)
<=> ! [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__36___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__4125,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_4150',axiom,
! [Vvar__4151] :
( c_24__type__4150___24t(Vvar__4151)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__4151,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_436',axiom,
! [Vvar__437] :
( c_24__type__436___24t(Vvar__437)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__292___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__437,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4586',axiom,
! [Vvar__4587] :
( c_24__type__4586___24t(Vvar__4587)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__4587,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4593',axiom,
! [Vvar__4594] :
( c_24__type__4593___24t(Vvar__4594)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4594,Vv__CANONICAL__0)) ) ) ).
fof('$_type_467',axiom,
! [Vvar__468] :
( c_24__type__467___24t(Vvar__468)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__468,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4674',axiom,
! [Vvar__4675] :
( c_24__type__4674___24t(Vvar__4675)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4679___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__4675,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_4679',axiom,
! [Vv__CANONICAL__0,Vvar__4680] :
( c_24__type__4679___24t(Vv__CANONICAL__0,Vvar__4680)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4680,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4776',axiom,
! [Vvar__4777] :
( c_24__type__4776___24t(Vvar__4777)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4781___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__4777,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_4781',axiom,
! [Vv__CANONICAL__0,Vvar__4782] :
( c_24__type__4781___24t(Vv__CANONICAL__0,Vvar__4782)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4782,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_479',axiom,
! [Vvar__480] :
( c_24__type__479___24t(Vvar__480)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__292___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__480,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4814',axiom,
! [Vv__CANONICAL__0,Vvar__4815] :
( c_24__type__4814___24t(Vv__CANONICAL__0,Vvar__4815)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__4815,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_4867',axiom,
! [Vvar__4868] :
( c_24__type__4867___24t(Vvar__4868)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( chahn_2eZorn_2ePrivate_2eLe___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__4868,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4873',axiom,
! [Vvar__4874] :
( c_24__type__4873___24t(Vvar__4874)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( chahn_2eZorn_2ePrivate_2eEquiv___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__4874,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_492',axiom,
! [Vvar__493] :
( c_24__type__492___24t(Vvar__493)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__292___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__493,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_500',axiom,
! [Vvar__501] :
( c_24__type__500___24t(Vvar__501)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__501,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5029',axiom,
! [Vvar__5030] :
( c_24__type__5029___24t(Vvar__5030)
<=> ! [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__5030,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5033',axiom,
! [Vvar__5034] :
( c_24__type__5033___24t(Vvar__5034)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__5034,Vv__CANONICAL__0)) ) ) ).
fof('$_type_505',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__506] :
( c_24__type__505___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__506)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__506,Vv__CANONICAL__2)) ) ) ).
fof('$_type_509',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__510] :
( c_24__type__509___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__510)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__510,Vv__CANONICAL__2)) ) ) ).
fof('$_type_52',axiom,
! [Vvar__53] :
( c_24__type__52___24t(Vvar__53)
<=> ! [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__53,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5224',axiom,
! [Vvar__5225] :
( c_24__type__5224___24t(Vvar__5225)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5225,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5239',axiom,
! [Vvar__5240] :
( c_24__type__5239___24t(Vvar__5240)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__5240,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5304',axiom,
! [Vv__CANONICAL__0,Vvar__5305] :
( c_24__type__5304___24t(Vv__CANONICAL__0,Vvar__5305)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__5305,Vv__CANONICAL__1)) ) ) ).
fof('$_type_5314',axiom,
! [Vvar__5315] :
( c_24__type__5314___24t(Vvar__5315)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5315,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5398',axiom,
! [Vvar__5399] :
( c_24__type__5398___24t(Vvar__5399)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__5399,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5402',axiom,
! [Vvar__5403] :
( c_24__type__5402___24t(Vvar__5403)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__5403,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5542',axiom,
! [Vvar__5543] :
( c_24__type__5542___24t(Vvar__5543)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5543,Vv__CANONICAL__0)) ) ) ).
fof('$_type_56',axiom,
! [Vvar__57] :
( c_24__type__56___24t(Vvar__57)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__57,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6214',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6215] :
( c_24__type__6214___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6215)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6215,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_63',axiom,
! [Vvar__64] :
( c_24__type__63___24t(Vvar__64)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__64,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6307',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6308] :
( c_24__type__6307___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6308)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6308,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6400',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6401] :
( c_24__type__6400___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6401)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6401,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6482',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6483] :
( c_24__type__6482___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6483)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__6483,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_6575',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6576] :
( c_24__type__6575___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6576)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6576,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6657',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6658] :
( c_24__type__6657___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6658)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__6658,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_6750',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6751] :
( c_24__type__6750___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6751)
<=> ! [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__6751,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_69',axiom,
! [Vvar__70] :
( c_24__type__69___24t(Vvar__70)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__70,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_78',axiom,
! [Vvar__79] :
( c_24__type__78___24t(Vvar__79)
<=> ! [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__79,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_787',axiom,
! [Vvar__788] :
( c_24__type__787___24t(Vvar__788)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__83___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__788,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_803',axiom,
! [Vvar__804] :
( c_24__type__803___24t(Vvar__804)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__804,Vv__CANONICAL__0)) ) ) ).
fof('$_type_810',axiom,
! [Vvar__811] :
( c_24__type__810___24t(Vvar__811)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__811,Vv__CANONICAL__0)) ) ) ).
fof('$_type_823',axiom,
! [Vvar__824] :
( c_24__type__823___24t(Vvar__824)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__824,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8265',axiom,
! [Vvar__8266] :
( c_24__type__8265___24t(Vvar__8266)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__8266,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8276',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8277] :
( c_24__type__8276___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8277)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__8277,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_83',axiom,
! [Vv__CANONICAL__0,Vvar__84] :
( c_24__type__83___24t(Vv__CANONICAL__0,Vvar__84)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__84,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_831',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__832] :
( c_24__type__831___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__832)
<=> ! [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__832,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_8499',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8500] :
( c_24__type__8499___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8500)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__8500,Vv__CANONICAL__3)) ) ) ).
fof('$_type_85',axiom,
! [Vvar__86] :
( c_24__type__85___24t(Vvar__86)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__86,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8546',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8547] :
( c_24__type__8546___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8547)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__8547,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_862',axiom,
! [Vvar__863] :
( c_24__type__862___24t(Vvar__863)
<=> ! [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__863,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_864',axiom,
! [Vvar__865] :
( c_24__type__864___24t(Vvar__865)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__865,Vv__CANONICAL__0)) ) ) ).
fof('$_type_874',axiom,
! [Vvar__875] :
( c_24__type__874___24t(Vvar__875)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__875,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_890',axiom,
! [Vvar__891] :
( c_24__type__890___24t(Vvar__891)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__891,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8981',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__8982] :
( c_24__type__8981___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__8982)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8982,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_90',axiom,
! [Vvar__91] :
( c_24__type__90___24t(Vvar__91)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__91,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_902',axiom,
! [Vvar__903] :
( c_24__type__902___24t(Vvar__903)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__903,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_9082',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9083] :
( c_24__type__9082___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9083)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9083,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_914',axiom,
! [Vvar__915] :
( c_24__type__914___24t(Vvar__915)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__915,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_9183',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9184] :
( c_24__type__9183___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9184)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9184,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9273',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__9274] :
( c_24__type__9273___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__9274)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__9274,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_934',axiom,
! [Vvar__935] :
( c_24__type__934___24t(Vvar__935)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__935,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9374',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__9375] :
( c_24__type__9374___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__9375)
<=> ! [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__9375,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_939',axiom,
! [Vvar__940] :
( c_24__type__939___24t(Vvar__940)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__940,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9475',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__9476] :
( c_24__type__9475___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__9476)
<=> ! [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__9476,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_949',axiom,
! [Vvar__950] :
( c_24__type__949___24t(Vvar__950)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__950,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9576',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__9577] :
( c_24__type__9576___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__9577)
<=> ! [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__9577,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_961',axiom,
! [Vvar__962] :
( c_24__type__961___24t(Vvar__962)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__962,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_typeof_A',axiom,
cType___24t(cA) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__4776___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__5239___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__864___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__1___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__862___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__5398___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__961___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_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__939___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__902___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.id',axiom,
cCoq_2eInit_2eDatatypes_2eID___24t(cCoq_2eInit_2eDatatypes_2eid) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__36217___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__36222___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__949___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__85___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.list_rec',axiom,
c_24__type__24309___24t(cCoq_2eInit_2eDatatypes_2elist__rec) ).
fof('$_typeof_Coq.Init.Datatypes.list_rect',axiom,
c_24__type__24309___24t(cCoq_2eInit_2eDatatypes_2elist__rect) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__5402___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__934___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__85___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__5398___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__890___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__874___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__914___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__874___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.Nat.add',axiom,
c_24__type__1929___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__1929___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__1929___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__1___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__1929___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__2011___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__2011___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__2011___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__3390___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__25782___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__34112___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__34117___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__25788___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__3413___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__25793___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__3372___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__22161___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__3427___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__22238___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__787___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.ForallPairs',axiom,
c_24__type__33523___24t(cCoq_2eLists_2eList_2eForallPairs) ).
fof('$_typeof_Coq.Lists.List.Forall_rect',axiom,
c_24__type__33481___24t(cCoq_2eLists_2eList_2eForall__rect) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__1896___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.combine',axiom,
c_24__type__28216___24t(cCoq_2eLists_2eList_2ecombine) ).
fof('$_typeof_Coq.Lists.List.concat',axiom,
c_24__type__1906___24t(cCoq_2eLists_2eList_2econcat) ).
fof('$_typeof_Coq.Lists.List.count_occ',axiom,
c_24__type__25605___24t(cCoq_2eLists_2eList_2ecount__occ) ).
fof('$_typeof_Coq.Lists.List.existsb',axiom,
c_24__type__33359___24t(cCoq_2eLists_2eList_2eexistsb) ).
fof('$_typeof_Coq.Lists.List.filter',axiom,
c_24__type__28193___24t(cCoq_2eLists_2eList_2efilter) ).
fof('$_typeof_Coq.Lists.List.find',axiom,
c_24__type__33387___24t(cCoq_2eLists_2eList_2efind) ).
fof('$_typeof_Coq.Lists.List.firstn',axiom,
c_24__type__28232___24t(cCoq_2eLists_2eList_2efirstn) ).
fof('$_typeof_Coq.Lists.List.flat_map',axiom,
c_24__type__33243___24t(cCoq_2eLists_2eList_2eflat__map) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__33310___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__33339___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.forallb',axiom,
c_24__type__33359___24t(cCoq_2eLists_2eList_2eforallb) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__33146___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.hd_error',axiom,
c_24__type__33155___24t(cCoq_2eLists_2eList_2ehd__error) ).
fof('$_typeof_Coq.Lists.List.incl',axiom,
c_24__type__1623___24t(cCoq_2eLists_2eList_2eincl) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__24074___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.lel',axiom,
c_24__type__1623___24t(cCoq_2eLists_2eList_2elel) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__25634___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__28124___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.nth_default',axiom,
c_24__type__33199___24t(cCoq_2eLists_2eList_2enth__default) ).
fof('$_typeof_Coq.Lists.List.nth_error',axiom,
c_24__type__28146___24t(cCoq_2eLists_2eList_2enth__error) ).
fof('$_typeof_Coq.Lists.List.nth_ok',axiom,
c_24__type__33187___24t(cCoq_2eLists_2eList_2enth__ok) ).
fof('$_typeof_Coq.Lists.List.removelast',axiom,
c_24__type__1660___24t(cCoq_2eLists_2eList_2eremovelast) ).
fof('$_typeof_Coq.Lists.List.rev',axiom,
c_24__type__1660___24t(cCoq_2eLists_2eList_2erev) ).
fof('$_typeof_Coq.Lists.List.rev\'',axiom,
c_24__type__1660___24t(cCoq_2eLists_2eList_2erev_27) ).
fof('$_typeof_Coq.Lists.List.rev_append',axiom,
c_24__type__961___24t(cCoq_2eLists_2eList_2erev__append) ).
fof('$_typeof_Coq.Lists.List.skipn',axiom,
c_24__type__28232___24t(cCoq_2eLists_2eList_2eskipn) ).
fof('$_typeof_Coq.Lists.List.tl',axiom,
c_24__type__1660___24t(cCoq_2eLists_2eList_2etl) ).
fof('$_typeof_Coq.Lists.ListDec.decidable_eq',axiom,
c_24__type__5314___24t(cCoq_2eLists_2eListDec_2edecidable__eq) ).
fof('$_typeof_Coq.Lists.SetoidList.equivlistA',axiom,
c_24__type__32226___24t(cCoq_2eLists_2eSetoidList_2eequivlistA) ).
fof('$_typeof_Coq.Lists.SetoidList.inclA',axiom,
c_24__type__32226___24t(cCoq_2eLists_2eSetoidList_2einclA) ).
fof('$_typeof_Coq.Lists.SetoidList.removeA',axiom,
c_24__type__35894___24t(cCoq_2eLists_2eSetoidList_2eremoveA) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__21861___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__21861___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__21904___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__21904___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.ClassicalDescription.excluded_middle_informative',axiom,
c_24__type__24188___24t(cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__5542___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.FinFun.Full',axiom,
c_24__type__28072___24t(cCoq_2eLogic_2eFinFun_2eFull) ).
fof('$_typeof_Coq.Logic.FinFun.Injective',axiom,
c_24__type__8265___24t(cCoq_2eLogic_2eFinFun_2eInjective) ).
fof('$_typeof_Coq.Logic.FinFun.Listing',axiom,
c_24__type__28072___24t(cCoq_2eLogic_2eFinFun_2eListing) ).
fof('$_typeof_Coq.Logic.FinFun.Surjective',axiom,
c_24__type__8265___24t(cCoq_2eLogic_2eFinFun_2eSurjective) ).
fof('$_typeof_Coq.Logic.FinFun.bFun',axiom,
c_24__type__33039___24t(cCoq_2eLogic_2eFinFun_2ebFun) ).
fof('$_typeof_Coq.Logic.FinFun.bInjective',axiom,
c_24__type__33039___24t(cCoq_2eLogic_2eFinFun_2ebInjective) ).
fof('$_typeof_Coq.Logic.FinFun.bSurjective',axiom,
c_24__type__33039___24t(cCoq_2eLogic_2eFinFun_2ebSurjective) ).
fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
c_24__type__4674___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__23452___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__24115___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__23452___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__4586___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_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__810___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('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__823___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__823___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('$_typeof_Coq.Numbers.BinNums.xI',axiom,
c_24__type__803___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__803___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__23006___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__23493___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
c_24__type__803___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__23493___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__803___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_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.Relations.Relation_Definitions.antisymmetric',axiom,
c_24__type__225___24t(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.commut',axiom,
c_24__type__90___24t(cCoq_2eRelations_2eRelation__Definitions_2ecommut) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.equiv',axiom,
c_24__type__225___24t(cCoq_2eRelations_2eRelation__Definitions_2eequiv) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.inclusion',axiom,
c_24__type__90___24t(cCoq_2eRelations_2eRelation__Definitions_2einclusion) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__225___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__85___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.same_relation',axiom,
c_24__type__90___24t(cCoq_2eRelations_2eRelation__Definitions_2esame__relation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.symmetric',axiom,
c_24__type__225___24t(cCoq_2eRelations_2eRelation__Definitions_2esymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__225___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Relations.Relation_Operators.transp',axiom,
c_24__type__255___24t(cCoq_2eRelations_2eRelation__Operators_2etransp) ).
fof('$_typeof_Coq.Relations.Relation_Operators.union',axiom,
c_24__type__135___24t(cCoq_2eRelations_2eRelation__Operators_2eunion) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__225___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Transitive',axiom,
c_24__type__33600___24t(cCoq_2eSets_2eRelations__1_2eTransitive) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__34167___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__34159___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__22760___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.to_list',axiom,
c_24__type__34240___24t(cCoq_2eVectors_2eVectorDef_2eto__list) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__23255___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__23255___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__23255___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__5029___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__26103___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__5029___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__24183___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__5033___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__5029___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__5033___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__3517___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength',axiom,
c_24__type__34266___24t(cCoq_2eZArith_2eZcomplements_2eZlength) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength_aux',axiom,
c_24__type__34263___24t(cCoq_2eZArith_2eZcomplements_2eZlength__aux) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__23348___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__33585___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__85___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__85___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__22325___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__874___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.Tauto.cnf',axiom,
c_24__type__874___24t(cCoq_2emicromega_2eTauto_2ecnf) ).
fof('$_typeof_Coq.micromega.Tauto.cons_id',axiom,
c_24__type__34126___24t(cCoq_2emicromega_2eTauto_2econs__id) ).
fof('$_typeof_Coq.micromega.Tauto.eval_tt',axiom,
c_24__type__34152___24t(cCoq_2emicromega_2eTauto_2eeval__tt) ).
fof('$_typeof_Coq.micromega.ZMicromega.make_conj',axiom,
c_24__type__23348___24t(cCoq_2emicromega_2eZMicromega_2emake__conj) ).
fof('$_typeof_Coq.micromega.ZMicromega.make_impl',axiom,
c_24__type__33585___24t(cCoq_2emicromega_2eZMicromega_2emake__impl) ).
fof('$_typeof_Coq.setoid_ring.BinList.jump',axiom,
c_24__type__32282___24t(cCoq_2esetoid__ring_2eBinList_2ejump) ).
fof('$_typeof_Coq.setoid_ring.BinList.nth',axiom,
c_24__type__32293___24t(cCoq_2esetoid__ring_2eBinList_2enth) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEI',axiom,
c_24__type__32307___24t(cCoq_2esetoid__ring_2eField__theory_2eFEI) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEO',axiom,
c_24__type__32307___24t(cCoq_2esetoid__ring_2eField__theory_2eFEO) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__24395___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__24400___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__24392___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEdiv',axiom,
c_24__type__24400___24t(cCoq_2esetoid__ring_2eField__theory_2eFEdiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__24663___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__24403___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__24400___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEopp',axiom,
c_24__type__24403___24t(cCoq_2esetoid__ring_2eField__theory_2eFEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEpow',axiom,
c_24__type__32321___24t(cCoq_2esetoid__ring_2eField__theory_2eFEpow) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEsub',axiom,
c_24__type__24400___24t(cCoq_2esetoid__ring_2eField__theory_2eFEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__85___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__25210___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
c_24__type__26929___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__24951___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__24732___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__24712___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.display_linear',axiom,
c_24__type__27923___24t(cCoq_2esetoid__ring_2eField__theory_2edisplay__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.display_pow_linear',axiom,
c_24__type__33002___24t(cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__85___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__24712___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__85___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_common',axiom,
c_24__type__27149___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__common) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
c_24__type__27149___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__left) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
c_24__type__27149___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__right) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__4586___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nsub',axiom,
c_24__type__23452___24t(cCoq_2esetoid__ring_2eInitialRing_2eNsub) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__33129___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__25406___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mphi',axiom,
c_24__type__28958___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.P0',axiom,
c_24__type__33642___24t(cCoq_2esetoid__ring_2eRing__polynom_2eP0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.P1',axiom,
c_24__type__33642___24t(cCoq_2esetoid__ring_2eRing__polynom_2eP1) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__29203___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__29203___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__2916___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__2921___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__2913___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__29396___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__2921___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__25773___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__33779___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__2921___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__85___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__33655___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__33642___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__2664___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pequiv',axiom,
c_24__type__33726___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePequiv) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__33647___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__85___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi',axiom,
c_24__type__28919___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__31035___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
c_24__type__30447___24t(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkZmon',axiom,
c_24__type__33660___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkZmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__15950___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__3132___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.r_list_pow',axiom,
c_24__type__35755___24t(cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.vmon',axiom,
c_24__type__33660___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
c_24__type__33660___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__21278___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__33884___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
c_24__type__862___24t(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__4586___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__3348___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__15971___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_HahnTotalExt.one_ext',axiom,
c_24__type__26647___24t(cHahnTotalExt_2eone__ext) ).
fof('$_typeof_HahnTotalExt.tot_ext',axiom,
c_24__type__32274___24t(cHahnTotalExt_2etot__ext) ).
fof('$_typeof_dom',axiom,
cCoq_2eInit_2eDatatypes_2elist___24t(cA,cdom) ).
fof('$_typeof_hahn.HahnBase.NW',axiom,
c_24__type__257___24t(chahn_2eHahnBase_2eNW) ).
fof('$_typeof_hahn.HahnBase.is_true',axiom,
c_24__type__5224___24t(chahn_2eHahnBase_2eis__true) ).
fof('$_typeof_hahn.HahnFuneq.funeq',axiom,
c_24__type__436___24t(chahn_2eHahnFuneq_2efuneq) ).
fof('$_typeof_hahn.HahnList.disjoint',axiom,
c_24__type__1623___24t(chahn_2eHahnList_2edisjoint) ).
fof('$_typeof_hahn.HahnList.filterP',axiom,
c_24__type__1612___24t(chahn_2eHahnList_2efilterP) ).
fof('$_typeof_hahn.HahnList.flatten',axiom,
c_24__type__1906___24t(chahn_2eHahnList_2eflatten) ).
fof('$_typeof_hahn.HahnList.map_filter',axiom,
c_24__type__33086___24t(chahn_2eHahnList_2emap__filter) ).
fof('$_typeof_hahn.HahnList.undup',axiom,
c_24__type__1660___24t(chahn_2eHahnList_2eundup) ).
fof('$_typeof_hahn.HahnMaxElt.max_elt',axiom,
c_24__type__41___24t(chahn_2eHahnMaxElt_2emax__elt) ).
fof('$_typeof_hahn.HahnMaxElt.wmax_elt',axiom,
c_24__type__41___24t(chahn_2eHahnMaxElt_2ewmax__elt) ).
fof('$_typeof_hahn.HahnRelationsBasic.acyclic',axiom,
c_24__type__225___24t(chahn_2eHahnRelationsBasic_2eacyclic) ).
fof('$_typeof_hahn.HahnRelationsBasic.bunion',axiom,
c_24__type__209___24t(chahn_2eHahnRelationsBasic_2ebunion) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_refl',axiom,
c_24__type__187___24t(chahn_2eHahnRelationsBasic_2eclos__refl) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_refl_sym',axiom,
c_24__type__187___24t(chahn_2eHahnRelationsBasic_2eclos__refl__sym) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_sym',axiom,
c_24__type__187___24t(chahn_2eHahnRelationsBasic_2eclos__sym) ).
fof('$_typeof_hahn.HahnRelationsBasic.codom_rel',axiom,
c_24__type__41___24t(chahn_2eHahnRelationsBasic_2ecodom__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.collect_rel',axiom,
c_24__type__492___24t(chahn_2eHahnRelationsBasic_2ecollect__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.dom_rel',axiom,
c_24__type__41___24t(chahn_2eHahnRelationsBasic_2edom__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eq_rel',axiom,
c_24__type__1735___24t(chahn_2eHahnRelationsBasic_2eeq__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eqv_dom_rel',axiom,
c_24__type__1740___24t(chahn_2eHahnRelationsBasic_2eeqv__dom__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eqv_rel',axiom,
c_24__type__56___24t(chahn_2eHahnRelationsBasic_2eeqv__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.functional',axiom,
c_24__type__225___24t(chahn_2eHahnRelationsBasic_2efunctional) ).
fof('$_typeof_hahn.HahnRelationsBasic.immediate',axiom,
c_24__type__187___24t(chahn_2eHahnRelationsBasic_2eimmediate) ).
fof('$_typeof_hahn.HahnRelationsBasic.inter_rel',axiom,
c_24__type__69___24t(chahn_2eHahnRelationsBasic_2einter__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.irreflexive',axiom,
c_24__type__225___24t(chahn_2eHahnRelationsBasic_2eirreflexive) ).
fof('$_typeof_hahn.HahnRelationsBasic.is_total',axiom,
c_24__type__500___24t(chahn_2eHahnRelationsBasic_2eis__total) ).
fof('$_typeof_hahn.HahnRelationsBasic.map_rel',axiom,
c_24__type__479___24t(chahn_2eHahnRelationsBasic_2emap__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.minus_rel',axiom,
c_24__type__69___24t(chahn_2eHahnRelationsBasic_2eminus__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.pow_rel',axiom,
c_24__type__78___24t(chahn_2eHahnRelationsBasic_2epow__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_eq_rel',axiom,
c_24__type__467___24t(chahn_2eHahnRelationsBasic_2erestr__eq__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_rel',axiom,
c_24__type__63___24t(chahn_2eHahnRelationsBasic_2erestr__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_subset',axiom,
c_24__type__1750___24t(chahn_2eHahnRelationsBasic_2erestr__subset) ).
fof('$_typeof_hahn.HahnRelationsBasic.seq',axiom,
c_24__type__69___24t(chahn_2eHahnRelationsBasic_2eseq) ).
fof('$_typeof_hahn.HahnRelationsBasic.singl_rel',axiom,
c_24__type__52___24t(chahn_2eHahnRelationsBasic_2esingl__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.strict_partial_order',axiom,
c_24__type__225___24t(chahn_2eHahnRelationsBasic_2estrict__partial__order) ).
fof('$_typeof_hahn.HahnRelationsBasic.strict_total_order',axiom,
c_24__type__500___24t(chahn_2eHahnRelationsBasic_2estrict__total__order) ).
fof('$_typeof_hahn.HahnRelationsBasic.upward_closed',axiom,
c_24__type__1758___24t(chahn_2eHahnRelationsBasic_2eupward__closed) ).
fof('$_typeof_hahn.HahnSets.set_compl',axiom,
c_24__type__1833___24t(chahn_2eHahnSets_2eset__compl) ).
fof('$_typeof_hahn.HahnSets.set_empty',axiom,
c_24__type__1827___24t(chahn_2eHahnSets_2eset__empty) ).
fof('$_typeof_hahn.HahnSets.set_equiv',axiom,
c_24__type__220___24t(chahn_2eHahnSets_2eset__equiv) ).
fof('$_typeof_hahn.HahnSets.set_finite',axiom,
c_24__type__36268___24t(chahn_2eHahnSets_2eset__finite) ).
fof('$_typeof_hahn.HahnSets.set_inter',axiom,
c_24__type__1845___24t(chahn_2eHahnSets_2eset__inter) ).
fof('$_typeof_hahn.HahnSets.set_map',axiom,
c_24__type__1879___24t(chahn_2eHahnSets_2eset__map) ).
fof('$_typeof_hahn.HahnSets.set_subset',axiom,
c_24__type__220___24t(chahn_2eHahnSets_2eset__subset) ).
fof('$_typeof_hahn.HahnSets.set_union',axiom,
c_24__type__1845___24t(chahn_2eHahnSets_2eset__union) ).
fof('$_typeof_hahn.Zorn.Private.Equiv',axiom,
c_24__type__85___24t(chahn_2eZorn_2ePrivate_2eEquiv) ).
fof('$_typeof_hahn.Zorn.Private.Le',axiom,
c_24__type__85___24t(chahn_2eZorn_2ePrivate_2eLe) ).
fof('$_typeof_hahn.Zorn.Private.Lt',axiom,
c_24__type__85___24t(chahn_2eZorn_2ePrivate_2eLt) ).
fof('$_typeof_hahn.Zorn.Private.equ',axiom,
c_24__type__4873___24t(chahn_2eZorn_2ePrivate_2eequ) ).
fof('$_typeof_hahn.Zorn.Private.le',axiom,
c_24__type__4867___24t(chahn_2eZorn_2ePrivate_2ele) ).
fof('$_typeof_hahn.Zorn.ZornsLemma',axiom,
c_24__type__3585___24t(chahn_2eZorn_2eZornsLemma) ).
fof('$_typeof_hahn.Zorn.suspend_R',axiom,
c_24__type__4150___24t(chahn_2eZorn_2esuspend__R) ).
fof('$_typeof_hahn.Zorn.suspend_S',axiom,
c_24__type__4124___24t(chahn_2eZorn_2esuspend__S) ).
fof('$_typeof_r',axiom,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,cr) ).
fof('Coq.Arith.Gt.gt_S_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Gt.gt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Le.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Le.le_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_or_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.Lt.lt_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Lt.lt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Lt.lt_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.Minus.minus_diag_reverse',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eO = cCoq_2eInit_2eNat_2esub___24a2(V0__n,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_diag',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,V0__n) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.Plus.le_plus_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Plus.le_plus_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1918___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__l))) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ).
fof('Coq.Init.Datatypes.list_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1918___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__l))) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__3___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Peano.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__4814___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Init.Peano.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.Init.Peano.le_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
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.proj2_sig',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__e] :
( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> p(happ(V1__P,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e))) ) ) ) ).
fof('Coq.Init.Wf.Acc_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__36___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__83___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.Init.Wf.well_founded_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
=> ! [V3__P] :
( c_24__type__36___24t(V0__A,V3__P)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V4__x))
=> p(happ(V3__P,V5__y)) ) )
=> p(happ(V3__P,V4__x)) ) )
=> ! [V5__a] :
( t(V5__a,V0__A)
=> p(happ(V3__P,V5__a)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l2))) ) ) ) ) ).
fof('Coq.Lists.List.Add_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V3__l,V4__l_27)
=> cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V4__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l)) ) ) ) ).
fof('Coq.Lists.List.Add_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V3__l_27))
<=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l))) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__P] :
( c_24__type__28265___24t(V0__A,V2__P)
=> ( ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> p(happ(happ(V2__P,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l))) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l_27)
=> ( p(happ(happ(V2__P,V5__l),V6__l_27))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l_27))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l)
=> p(happ(happ(V2__P,V5__l),V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V2__l))
=> ? [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
& cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V4__l_27,V2__l) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l_27) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__P] :
( c_24__type__28265___24t(V0__A,V2__P)
=> ( ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> p(happ(happ(V2__P,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l))) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l_27)
=> ( p(happ(happ(V2__P,V5__l),V6__l_27))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l_27))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l)
=> p(happ(happ(V2__P,V5__l),V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l))
<=> ( p(happ(V1__P,V2__x))
| cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V3__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(happ(V1__P,V2__x))
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V3__l)
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_exists',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V2__l)
<=> ? [V3__x] :
( t(V3__x,V0__A)
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
& p(happ(V1__P,V3__x)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_impl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__36___24t(V0__A,V2__Q)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
=> p(happ(V2__Q,V3__x)) ) )
=> ! [V4__xs] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__xs)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V4__xs)
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V2__Q,V4__xs) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__1918___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V3__x))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V5__l)
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l))) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__1918___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V3__x))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V5__l)
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l))) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.FOP_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,happ(V1__R,V2__a),V3__l)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V3__l)
=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall2_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__831___24t(V0__A,V1__B,V2__R)
=> ! [V3__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l1)
=> ! [V4__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l2)
=> ! [V5__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l1_27)
=> ! [V6__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V6__l2_27)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V3__l1,V5__l1_27)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V4__l2,V6__l2_27)
=> cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l1,V4__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,V5__l1_27,V6__l2_27)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall2_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__831___24t(V0__A,V1__B,V2__R)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V6__l_27)
=> ( p(happ(happ(V2__R,V3__x),V4__y))
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V5__l,V6__l_27)
=> cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V5__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,V4__y,V6__l_27)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall2_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__831___24t(V0__A,V1__B,V2__R)
=> ! [V3__P] :
( c_24__type__36311___24t(V0__A,V1__B,V3__P)
=> ( p(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V1__B)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ! [V8__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V8__l_27)
=> ( p(happ(happ(V2__R,V5__x),V6__y))
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V7__l,V8__l_27)
=> ( p(happ(happ(V3__P,V7__l),V8__l_27))
=> p(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x,V7__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,V6__y,V8__l_27))) ) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V7__l)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V6__l,V7__l)
=> p(happ(happ(V3__P,V6__l),V7__l)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.ForallOrdPairs_ForallPairs',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ( ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) )
=> ( ! [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(V1__R,V4__y),V3__x)) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V4__l)
=> cCoq_2eLists_2eList_2eForallPairs___24a3(V0__A,V1__R,V4__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.ForallOrdPairs_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V2__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V2__l))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__y,V2__l))
=> ( V4__x = V5__y
| p(happ(happ(V1__R,V4__x),V5__y))
| p(happ(happ(V1__R,V5__y),V4__x)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.ForallPairs_ForallOrdPairs',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForallPairs___24a3(V0__A,V1__R,V2__l)
=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V2__l) ) ) ) ) ).
fof('Coq.Lists.List.Forall_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(happ(V1__P,V2__x))
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_dec_subproof',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( ~ p(happ(V1__P,V2__a))
=> ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_dec_subproof0',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l_27)
=> ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_forall',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
=> p(happ(V1__P,V3__x)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_impl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__36___24t(V0__A,V2__Q)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(happ(V1__P,V3__a))
=> p(happ(V2__Q,V3__a)) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V4__l)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V2__Q,V4__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__1918___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(happ(V1__P,V4__x))
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V5__l)
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l))
=> p(happ(V1__P,V2__a)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_inv_tail',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__x0] :
( t(V2__x0,V0__A)
=> ! [V3__xs] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__xs)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x0,V3__xs))
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__xs) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.Forall_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__1918___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(happ(V1__P,V4__x))
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V5__l)
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_cons',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))
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l))) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_incl_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)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__l_27))
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1918___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))
=> ( p(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)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l))
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_length_incl',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)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__l_27))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l_27,V1__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_map_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ).
fof('Coq.Lists.List.app_assoc',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__m,V3__n)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m),V3__n) ) ) ) ) ).
fof('Coq.Lists.List.app_assoc_reverse',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m),V3__n) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__m,V3__n)) ) ) ) ) ).
fof('Coq.Lists.List.app_comm_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__y)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,V2__y)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V1__x),V2__y) ) ) ) ) ).
fof('Coq.Lists.List.app_inv_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l1) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V3__l2)
=> V2__l1 = V3__l2 ) ) ) ) ) ).
fof('Coq.Lists.List.app_inv_tail',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V1__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l2,V1__l)
=> V2__l1 = V3__l2 ) ) ) ) ) ).
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.app_nil_end',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> V1__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.app_nil_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),V1__l) = V1__l ) ) ).
fof('Coq.Lists.List.app_nil_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) = V1__l ) ) ).
fof('Coq.Lists.List.ext_in_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__292___24t(V0__A,V1__B,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V4__l)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V6__a,V4__l))
=> happ(V2__f,V6__a) = happ(V3__g,V6__a) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.firstn_all',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V1__l) = V1__l ) ) ).
fof('Coq.Lists.List.firstn_le_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l)),V1__n) ) ) ) ).
fof('Coq.Lists.List.fold_right_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__21871___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ! [V5__i] :
( t(V5__i,V1__B)
=> cCoq_2eLists_2eList_2efold__right___24a5(V1__B,V0__A,V2__f,V5__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27)) = cCoq_2eLists_2eList_2efold__right___24a5(V1__B,V0__A,V2__f,cCoq_2eLists_2eList_2efold__right___24a5(V1__B,V0__A,V2__f,V5__i,V4__l_27),V3__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.fold_symmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__3137___24t(V0__A,V1__f)
=> ( ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> happ(happ(V1__f,V2__x),happ(happ(V1__f,V3__y),V4__z)) = happ(happ(V1__f,happ(happ(V1__f,V2__x),V3__y)),V4__z) ) ) )
=> ! [V3__a0] :
( t(V3__a0,V0__A)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> happ(happ(V1__f,V3__a0),V4__y) = happ(happ(V1__f,V4__y),V3__a0) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V0__A,V1__f,V5__l,V3__a0) = cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V0__A,V1__f,V3__a0,V5__l) ) ) ) ) ) ) ).
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_app_or',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [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__m)))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,V3__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l))) ) ) ) ) ) ).
fof('Coq.Lists.List.in_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l))) ) ) ) ).
fof('Coq.Lists.List.in_flat_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__33247___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V4__y,cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,V3__l)))
<=> ? [V5__x] :
( t(V5__x,V0__A)
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V3__l))
& p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V4__y,happ(V2__f,V5__x))) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l)))
=> ( V1__a = V2__b
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,happ(V2__f,V4__x),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l))) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_map_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V4__y,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)))
<=> ? [V5__x] :
( t(V5__x,V0__A)
& happ(V2__f,V5__x) = V4__y
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V3__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_or_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m)) )
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m))) ) ) ) ) ) ).
fof('Coq.Lists.List.in_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V1__l))
<=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l))) ) ) ) ) ).
fof('Coq.Lists.List.in_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V2__l))
=> ? [V4__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
& ? [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
& V2__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V5__l2)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n))
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__m,V3__n))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m),V3__n)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_appl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__n,V2__m))) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_appr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__m,V3__n))) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V3__m))
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__m))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l),V3__m)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V1__l)) ) ) ).
fof('Coq.Lists.List.incl_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__m))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__m))) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_tran',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m))
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__m,V3__n))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__b] :
( t(V1__b,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V2__l,V3__m)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__b,V3__m)) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_cons_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V3__l,V4__m)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__b,V4__m)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V1__l) ) ) ).
fof('Coq.Lists.List.lel_tail',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__b,V4__m))
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,V3__l,V4__m) ) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V2__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V2__m,V3__n)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V3__n) ) ) ) ) ) ) ).
fof('Coq.Lists.List.map_ext',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__292___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> happ(V2__f,V4__a) = happ(V3__g,V4__a) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V5__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V5__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.map_ext_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__292___24t(V0__A,V1__B,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__a,V4__l))
=> happ(V2__f,V5__a) = happ(V3__g,V5__a) ) )
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V4__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.map_ext_in_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__292___24t(V0__A,V1__B,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V4__l)
<=> ! [V5__a] :
( t(V5__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__a,V4__l))
=> happ(V2__f,V5__a) = happ(V3__g,V5__a) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.map_id',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V0__A,c_24__lam__33250___24a1(V0__A),V1__l) = V1__l ) ) ).
fof('Coq.Lists.List.map_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l) ) ) ) ) ).
fof('Coq.Lists.List.map_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__292___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__1405___24t(V0__A,V1__B,V2__C,V4__g)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2emap___24a4(V1__B,V2__C,V4__g,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__f,V5__l)) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V2__C,c_24__lam__33268___24a5(V0__A,V1__B,V2__C,V3__f,V4__g),V5__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.map_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__d] :
( t(V4__d,V0__A)
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> cCoq_2eLists_2eList_2enth___24a4(V1__B,V5__n,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l),happ(V2__f,V4__d)) = happ(V2__f,cCoq_2eLists_2eList_2enth___24a4(V0__A,V5__n,V3__l,V4__d)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nil_cons',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)
=> cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) != cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l) ) ) ) ).
fof('Coq.Lists.List.nth_default_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V3__d,V2__l,V1__n) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V1__n,V2__l,V3__d) ) ) ) ) ).
fof('Coq.Lists.List.nth_indep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ! [V4__d_27] :
( t(V4__d_27,V0__A)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V4__d_27) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_overflow',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V2__n)
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V3__d) = V3__d ) ) ) ) ) ).
fof('Coq.Lists.List.rev_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1918___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(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))))) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.rev_involutive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2erev___24a2(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l)) = V1__l ) ) ).
fof('Coq.Lists.List.rev_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l)) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) ) ) ).
fof('Coq.Lists.List.skipn_O',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2eskipn___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eO,V1__l) = V1__l ) ) ).
fof('Coq.Lists.ListDec.In_decidable',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ).
fof('Coq.Lists.ListDec.NoDup_decidable',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l)) ) ) ) ).
fof('Coq.Lists.ListDec.incl_decidable',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__l_27)) ) ) ) ) ).
fof('Coq.Lists.ListDec.uniquify',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ? [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
& p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l_27))
& p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__l_27)) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_InfA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__ltA] :
( c_24__type__83___24t(V0__A,V3__ltA)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ( ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V6__y,V4__l)
=> p(happ(happ(V3__ltA,V5__x),V6__y)) ) )
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V3__ltA,V5__x,V4__l) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_alt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V3__l)
<=> ? [V4__y] :
( t(V4__y,V0__A)
& p(happ(happ(V1__eqA,V2__x),V4__y))
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__y,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_altdef',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V3__l)
<=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,happ(V1__eqA,V2__x),V3__l) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2))
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l1)
| cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l2) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_app_idem',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V3__l))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V3__l) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_app_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2))
<=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l1)
| cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l2) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l))
<=> ( p(happ(happ(V1__eqA,V2__x),V3__y))
| cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V4__l) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(happ(V1__eqA,V2__x),V3__y))
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V4__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_double_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_eqA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__eqA,V4__x),V5__y))
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V5__y,V3__l) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__1918___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(happ(happ(V1__eqA,V2__x),V4__y))
=> p(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__y,V5__l))) ) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V6__l)
=> ( p(happ(V3__P,V6__l))
=> p(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,V6__l))) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V6__l)
=> p(happ(V3__P,V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_permute_heads',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__z,V5__l)))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__z,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V5__l))) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__p] :
( t(V2__p,V0__A)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__p,cCoq_2eLists_2eList_2erev___24a2(V0__A,V3__m))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__p,V3__m) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__1918___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(happ(happ(V1__eqA,V2__x),V4__y))
=> p(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__y,V5__l))) ) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V6__l)
=> ( p(happ(V3__P,V6__l))
=> p(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,V6__l))) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V6__l)
=> p(happ(V3__P,V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V3__x,V2__l)
=> ? [V5__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l1)
& ? [V6__y] :
( t(V6__y,V0__A)
& ? [V7__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l2)
& p(happ(happ(V1__eqA,V3__x),V6__y))
& V2__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V5__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,V7__l2)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.In_InA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l))
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.In_InfA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__ltA] :
( c_24__type__83___24t(V0__A,V1__ltA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__y,V2__l))
=> p(happ(happ(V1__ltA,V3__x),V4__y)) ) )
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V3__x,V2__l) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InfA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__ltA] :
( c_24__type__83___24t(V0__A,V1__ltA)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ! [V4__a] :
( t(V4__a,V0__A)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V4__a,V2__l1)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V4__a,V3__l2)
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V4__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InfA_ltA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__ltA] :
( c_24__type__83___24t(V0__A,V1__ltA)
=> ( cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(V0__A,V1__ltA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__ltA,V4__x),V5__y))
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V5__y,V3__l)
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V4__x,V3__l) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V3__l)
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V3__l)
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eLists_2eList_2erev___24a2(V0__A,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqarefl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__A,V1__eqA) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_altdef',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
<=> cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V0__A,V1__eqA,V2__l,V3__l_27) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l1)
=> ! [V4__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1_27)
=> ! [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
=> ! [V6__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V3__l1,V4__l1_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V5__l2,V6__l2_27)
=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l1,V5__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1_27,V6__l2_27)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__x_27] :
( t(V3__x_27,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l_27)
=> ( p(happ(happ(V1__eqA,V2__x),V3__x_27))
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V4__l,V5__l_27)
=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V4__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x_27,V5__l_27)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_equiv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA)) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__P] :
( c_24__type__28265___24t(V0__A,V2__P)
=> ( p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__x_27] :
( t(V5__x_27,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27)
=> ( p(happ(happ(V1__eqA,V4__x),V5__x_27))
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V6__l,V7__l_27)
=> ( p(happ(happ(V2__P,V6__l),V7__l_27))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x_27,V7__l_27))) ) ) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V5__l,V6__l)
=> p(happ(happ(V2__P,V5__l),V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l_27) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l1_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V2__l1,V3__l1_27)
=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l1),cCoq_2eLists_2eList_2erev___24a2(V0__A,V3__l1_27)) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_app_idem',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V2__l),V2__l) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_double_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_permute_heads',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V4__l))) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_eqlistA2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__eqB] :
( c_24__type__36555___24t(V0__A,V2__B,V3__eqB)
=> ! [V4__f] :
( c_24__type__21871___24t(V0__A,V2__B,V4__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__21871___24a2(V0__A,V2__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__21627___24a2(V0__A,V2__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V2__B,V2__B,V3__eqB,V3__eqB)),V4__f)
=> ! [V6__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__s)
=> ! [V7__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__s_27)
=> ! [V8__i] :
( t(V8__i,V2__B)
=> ! [V9__j] :
( t(V9__j,V2__B)
=> ( p(happ(happ(V3__eqB,V8__i),V9__j))
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V6__s,V7__s_27)
=> p(happ(happ(V3__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V2__B,V0__A,V4__f,V8__i,V6__s)),cCoq_2eLists_2eList_2efold__right___24a5(V2__B,V0__A,V4__f,V9__j,V7__s_27))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.incl_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__83___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eSetoidList_2einclA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),V2__l) ) ) ) ).
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_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.FinFun.Injective_map_NoDup',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLogic_2eFinFun_2eInjective___24a3(V0__A,V1__B,V2__f)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l))) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.peano_ind',axiom,
! [V0__P] :
( c_24__type__4593___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.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__22888___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.add_comm',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V1__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V0__p) ) ) ).
fof('Coq.PArith.BinPos.Pos.peano_ind',axiom,
! [V0__P] :
( c_24__type__22888___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V2__p))) ) )
=> ! [V3__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> p(happ(V0__P,V3__p)) ) ) ) ) ).
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)
=> 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__36___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__36___24t(V0__A,V2__P)
=> ! [V3__z] :
( t(V3__z,V0__A)
=> ( p(happ(V2__P,V3__z))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__R,V5__x),V6__y))
=> ( p(happ(V2__P,V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V3__z)
=> p(happ(V2__P,V5__x)) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V3__z)
=> p(happ(V2__P,V6__x)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_idempotent',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_is_equiv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rst1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_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)
=> 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)
=> 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.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__36___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.Lt_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__83___24t(V0__A,V1__leA)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(happ(happ(V1__leA,V2__a),V3__b))
=> ! [V5__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__x)
=> ! [V6__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__y)
=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V5__x),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__b,V6__y)) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.Lt_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__83___24t(V0__A,V1__leA)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__x)
=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__x)) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.Lt_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__83___24t(V0__A,V1__leA)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__x)
=> ! [V4__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,V3__x,V4__y)
=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__x),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V4__y)) ) ) ) ) ) ) ).
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__36___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__36___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__83___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__83___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__83___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__36___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__36___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__83___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__83___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__83___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__83___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__36___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__36___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__83___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__83___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__83___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__83___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__36___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__36___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__83___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__292___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__2341___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.Sorting.Permutation.NoDup_Permutation',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)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l_27))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V1__l))
<=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V2__l_27)) ) )
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_Add',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l),V3__l_27) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_Add_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l1,V3__l2)
=> ! [V5__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l1_27)
=> ! [V6__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l1_27,V2__l1)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V6__l2_27,V3__l2)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V5__l1_27,V6__l2_27) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_NoDup',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_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l_27)) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_add_inside',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ! [V4__tl] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__tl)
=> ! [V5__tl_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__tl_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l,V3__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V4__tl,V5__tl_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V4__tl)),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l_27,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V5__tl_27))) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ! [V4__m_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__m_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V3__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__m,V4__m_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l_27,V4__m_27)) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app_comm',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_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l_27,V1__l)) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__tl] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__tl)
=> ! [V3__tl_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__tl_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__tl,V3__tl_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__tl),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V3__tl_27)) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app_inv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l1),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V3__l2))
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l1,V3__l2) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app_inv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V1__l),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l2,V1__l))
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l1,V3__l2) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app_tail',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__tl] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__tl)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V3__tl),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l_27,V3__tl)) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_cons_inv',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)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V1__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V2__l_27))
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_in',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__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V1__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l_27)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_in\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2036___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__1918___24a1(V0__A),c_3d___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cProp,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),c_3c_3d_3e)),cCoq_2eLists_2eList_2eIn___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.Permutation_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__28265___24t(V0__A,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),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)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V4__l,V5__l_27)
=> ( p(happ(happ(V1__P,V4__l),V5__l_27))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V5__l_27))) ) ) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,V6__l)))) ) ) )
=> ( ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ! [V7__l_27_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V5__l,V6__l_27)
=> ( p(happ(happ(V1__P,V5__l),V6__l_27))
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l_27,V7__l_27_27)
=> ( p(happ(happ(V1__P,V6__l_27),V7__l_27_27))
=> p(happ(happ(V1__P,V5__l),V7__l_27_27)) ) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l,V7__l)
=> p(happ(happ(V1__P,V6__l),V7__l)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_ind_bis',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__28265___24t(V0__A,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),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)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V4__l,V5__l_27)
=> ( p(happ(happ(V1__P,V4__l),V5__l_27))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V5__l_27))) ) ) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l,V7__l_27)
=> ( p(happ(happ(V1__P,V6__l),V7__l_27))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,V7__l_27)))) ) ) ) ) ) )
=> ( ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ! [V7__l_27_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V5__l,V6__l_27)
=> ( p(happ(happ(V1__P,V5__l),V6__l_27))
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l_27,V7__l_27_27)
=> ( p(happ(happ(V1__P,V6__l_27),V7__l_27_27))
=> p(happ(happ(V1__P,V5__l),V7__l_27_27)) ) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l,V7__l_27)
=> p(happ(happ(V1__P,V6__l),V7__l_27)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_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_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V3__l,V4__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l_27)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_middle',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l1)
=> ! [V2__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l2)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l1,V2__l2)),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V2__l2))) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),V1__l)
=> V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V1__l) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l)) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_sym',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_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l_27,V1__l) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_trans',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__l_27_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l_27,V3__l_27_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V3__l_27_27) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.perm_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.perm_skip',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)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l,V3__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V3__l_27)) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.perm_swap',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V3__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__y,V3__l))) ) ) ) ) ).
fof('Coq.Sorting.Permutation.perm_trans',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__l_27_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l_27,V3__l_27_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V3__l_27_27) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.HdRel_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(happ(V1__R,V2__a),V3__b))
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V2__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__b,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.HdRel_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V2__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__b,V4__l))
=> p(happ(happ(V1__R,V2__a),V3__b)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.HdRel_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V2__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ) ).
fof('Coq.Sorting.Sorted.SSorted_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V3__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,happ(V1__R,V2__a),V3__l)
=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_StronglySorted',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__A,V1__R)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V3__l)
=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V3__l) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V3__l)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V2__a,V3__l)
=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.StronglySorted_Sorted',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__83___24t(V0__A,V1__R)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V2__l)
=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V2__l) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__26270___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.pos_sub_discr',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2436586___24a2(V0__p,V1__q) ) ) ).
fof('Coq.micromega.OrderedRing.ropp_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__3137___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__3137___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__3137___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__83___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__83___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3146___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req),V6__ropp) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.rplus_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__3137___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__3137___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__3137___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__83___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__83___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3137___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3146___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V3__rplus) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.rtimes_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__3137___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__3137___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__3137___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__83___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__83___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3137___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3146___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V4__rtimes) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_conj_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__36___24t(V0__A,V1__eval)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2))
<=> ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V2__l1)
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V3__l2) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_conj_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__36___24t(V0__A,V1__eval)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l))
<=> ( p(happ(V1__eval,V2__a))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V3__l) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_conj_impl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__36___24t(V0__A,V1__eval)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__g] :
( cProp___24t(V3__g)
=> ( ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V2__l)
=> p(V3__g) )
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V0__A,V1__eval,V2__l,V3__g) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_conj_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__36___24t(V0__A,V1__eval)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V2__l)
=> ! [V4__p] :
( t(V4__p,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__p,V2__l))
=> p(happ(V1__eval,V4__p)) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_impl_true',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__36___24t(V0__A,V1__eval)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V0__A,V1__eval,V2__l,c_24True) ) ) ) ).
fof('Coq.micromega.RingMicromega.ropp_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__3137___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__3137___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__3137___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__83___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__83___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3146___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req),V6__ropp) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.rplus_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__3137___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__3137___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__3137___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__83___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__83___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3137___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3146___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V3__rplus) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.rtimes_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__3137___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__3137___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__3137___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__83___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__83___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3137___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3146___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V4__rtimes) ) ) ) ) ) ) ) ) ) ) ) ).
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__22871___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.setoid_ring.Field_theory.AF_1_neq_0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__3137___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3146___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__83___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ~ p(happ(happ(V9__req,V2__rI),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AF_AR',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__3137___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3146___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__83___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AFdiv_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__3137___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3146___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__83___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ! [V12__q] :
( t(V12__q,V0__R)
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V11__p),V12__q)),happ(happ(V4__rmul,V11__p),happ(V8__rinv,V12__q)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AFinv_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__3137___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3146___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__83___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V11__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V11__p)),V11__p)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.radd_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3137___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3137___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3146___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__83___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3137___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3146___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__3137___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3146___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__83___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__r] :
( t(V13__r,V0__R)
=> p(happ(happ(V9__req,V13__r),happ(happ(V7__rdiv,V13__r),V2__rI))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rinv_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rinv] :
( c_24__type__3146___24t(V0__R,V1__rinv)
=> ! [V2__req] :
( c_24__type__83___24t(V0__R,V2__req)
=> ( ! [V3__p] :
( t(V3__p,V0__R)
=> ! [V4__q] :
( t(V4__q,V0__R)
=> ( p(happ(happ(V2__req,V3__p),V4__q))
=> p(happ(happ(V2__req,happ(V1__rinv,V3__p)),happ(V1__rinv,V4__q))) ) ) )
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3146___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V2__req,V2__req),V1__rinv) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3137___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3137___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3146___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__83___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3137___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3146___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ropp_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3137___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3137___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3146___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__83___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3146___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.Pphi0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__21613___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__21613___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__21613___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__21627___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__21634___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__8276___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V18__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V8__C,V16__phi,V18__l,cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V8__C,V9__cO))),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.Pphi1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__21613___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__21613___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__21613___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__21627___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__21634___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__8276___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V18__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V8__C,V16__phi,V18__l,cCoq_2esetoid__ring_2eRing__polynom_2eP1___24a2(V8__C,V10__cI))),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.jump_add\'',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__i] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__i)
=> ! [V2__j] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__j)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V3__l)
=> cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__R,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__i,V2__j),V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__R,V2__j,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__R,V1__i,V3__l)) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.radd_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3137___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3137___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3146___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__83___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3137___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3146___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3137___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3137___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3146___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__83___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3137___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3146___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.ropp_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3137___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3137___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3146___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__83___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3146___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_0_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),V1__rO)),V10__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_assoc',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),happ(happ(V3__radd,V10__y),V11__z))),happ(happ(V3__radd,happ(happ(V3__radd,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_assoc1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ! [V12__z] :
( t(V12__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z)),happ(happ(V3__radd,happ(happ(V3__radd,V11__y),V12__z)),V10__x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_assoc2',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> ! [V12__y] :
( t(V12__y,V0__R)
=> ! [V13__z] :
( t(V13__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,happ(happ(V3__radd,V12__y),V11__x)),V13__z)),happ(happ(V3__radd,happ(happ(V3__radd,V12__y),V13__z)),V11__x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARdistr_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V9__x),V10__y)),V11__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V9__x),V11__z)),happ(happ(V4__rmul,V10__y),V11__z)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARdistr_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> ! [V12__y] :
( t(V12__y,V0__R)
=> ! [V13__z] :
( t(V13__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V13__z),happ(happ(V3__radd,V11__x),V12__y))),happ(happ(V3__radd,happ(happ(V4__rmul,V13__z),V11__x)),happ(happ(V4__rmul,V13__z),V12__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V1__rO),V9__x)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_1_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_1_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V2__rI)),V10__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_assoc',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),happ(happ(V4__rmul,V10__y),V11__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_assoc1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ! [V12__z] :
( t(V12__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V4__rmul,V10__x),V11__y)),V12__z)),happ(happ(V4__rmul,happ(happ(V4__rmul,V11__y),V12__z)),V10__x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_assoc2',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> ! [V12__y] :
( t(V12__y,V0__R)
=> ! [V13__z] :
( t(V13__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V4__rmul,V12__y),V11__x)),V13__z)),happ(happ(V4__rmul,happ(happ(V4__rmul,V12__y),V13__z)),V11__x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_add',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V3__radd,V9__x),V10__y))),happ(happ(V3__radd,happ(V6__ropp,V9__x)),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V9__x),V10__y))),happ(happ(V4__rmul,happ(V6__ropp,V9__x)),V10__y))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_zero',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> p(happ(happ(V7__req,happ(V6__ropp,V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARsub_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARth_SRth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V7__req) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Radd_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3137___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3137___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3146___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__83___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3137___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3146___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Rmul_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3137___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3137___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3146___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__83___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3137___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3146___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Rth_ARth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_reqe',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3137___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3137___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3146___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__83___24t(V0__R,V4__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3137___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3146___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3137___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3146___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3146___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__21613___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__21613___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__21613___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__21627___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__21634___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__8276___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V9__cO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__21613___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__21613___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__21613___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__21627___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__21634___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__8276___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_add',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__21613___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__21613___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__21613___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__21627___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__21634___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__8276___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V11__cadd,V18__x),V19__y))),happ(happ(V3__radd,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_eq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__21613___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__21613___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__21613___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__21627___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__21634___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__8276___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> ( happ(happ(V15__ceqb,V18__x),V19__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V7__req,happ(V16__phi,V18__x)),happ(V16__phi,V19__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_mul',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3137___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3137___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3137___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3146___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__83___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__21613___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__21613___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__21613___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__21627___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__21634___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__8276___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V12__cmul,V18__x),V19__y))),happ(happ(V4__rmul,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.rpow_pow_N',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__3137___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__83___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__32125___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__32132___24t(V0__R,V4__Cpow,V6__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V1__rI,V2__rmul,V3__req,V4__Cpow,V5__Cp__phi,V6__rpow)
=> ! [V8__r] :
( t(V8__r,V0__R)
=> ! [V9__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V9__n)
=> p(happ(happ(V3__req,happ(happ(V6__rpow,V8__r),happ(V5__Cp__phi,V9__n))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V8__r,V9__n))) ) ) ) ) ) ) ) ) ) ) ).
fof('HahnTotalExt.one_ext_extends',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__elem] :
( t(V1__elem,V0__A)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,cHahnTotalExt_2eone__ext___24a3(V0__A,V1__elem,V2__r)) ) ) ) ).
fof('HahnTotalExt.one_ext_total_elem',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__elem] :
( t(V1__elem,V0__A)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( V3__x != V1__elem
=> ( cHahnTotalExt_2eone__ext___24a5(V0__A,V1__elem,V2__r,V1__elem,V3__x)
| cHahnTotalExt_2eone__ext___24a5(V0__A,V1__elem,V2__r,V3__x,V1__elem) ) ) ) ) ) ) ).
fof('HahnTotalExt.one_ext_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__elem] :
( t(V1__elem,V0__A)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,cHahnTotalExt_2eone__ext___24a3(V0__A,V1__elem,V2__r)) ) ) ) ).
fof('HahnTotalExt.tot_ext_extends',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,cHahnTotalExt_2etot__ext___24a3(V0__A,V1__dom,V2__r)) ) ) ) ).
fof('hahn.HahnBase.hahn__true_is_true',axiom,
chahn_2eHahnBase_2eis__true___24a1(cCoq_2eInit_2eDatatypes_2etrue) ).
fof('hahn.HahnEquational.acyclic_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V1__r)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnEquational.acyclic_seqC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27))
<=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)) ) ) ) ) ).
fof('hahn.HahnEquational.bunion_empty',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__rr] :
( c_24__type__158___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__1172___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__158___24t(V0__B,V1__A,V3__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,c_3d___24a2(V0__B,V2__a),V3__rr),happ(V3__rr,V2__a)) ) ) ) ) ).
fof('hahn.HahnEquational.clos_refl_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eclos__refl___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_refl_trans_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_refl_trans_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13___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__13___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eclos__refl___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_trans_imm',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V4__L] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__L)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__L))
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ! [V7__b] :
( t(V7__b,V0__A)
=> ( ! [V8__c] :
( t(V8__c,V0__A)
=> ( p(happ(happ(V1__r,V6__a),V8__c))
=> ( p(happ(happ(V1__r,V8__c),V7__b))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V8__c,V4__L)) ) ) )
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V6__a,V7__b) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_imm2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V4__L] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__L)
=> ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ( ! [V7__c] :
( t(V7__c,V0__A)
=> ( p(happ(happ(V1__r,V5__a),V7__c))
=> ( p(happ(happ(V1__r,V7__c),V6__b))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V7__c,V4__L)) ) ) )
=> ( p(happ(happ(V1__r,V5__a),V6__b))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V5__a,V6__b) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_immediate1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V3__a,V4__b)
=> p(happ(happ(V1__r,V3__a),V4__b)) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_immediate2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ! [V4__dom] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__dom)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ( p(happ(happ(V1__r,V5__a),V6__b))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V6__b,V4__dom)) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ! [V7__b] :
( t(V7__b,V0__A)
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V6__a,V7__b) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13___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_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13___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.collect_rel_acyclic',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r))
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V3__r) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_irr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r))
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V3__r) ) ) ) ) ) ).
fof('hahn.HahnEquational.crE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__74___24a1(V0__A)),V1__r)) ) ) ).
fof('hahn.HahnEquational.cr_of_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.cr_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnEquational.crs_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.cs_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.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_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.ct_end',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V1__r)) ) ) ).
fof('hahn.HahnEquational.ct_imm1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V4__acts] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__acts)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r),c_24__lam__1523___24a2(V0__A,V4__acts))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r))) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.ct_imm2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V4__acts] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__acts)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V1__r),c_24__lam__1523___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__13___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V3__r),V4__r_27)
=> ( ! [V6__k] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__k)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V6__k),V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V6__k)),V4__r_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r)),V4__r_27) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.ct_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__13___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V3__r),V4__r_27)
=> ( ! [V6__k] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__k)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V6__k),V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__k,V3__r)),V4__r_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r)),V4__r_27) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.ct_of_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_seq_swap',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)))) ) ) ) ).
fof('hahn.HahnEquational.ct_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.ct_unit',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.eqv_dom_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1012___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.good_ctx_compose',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__13___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__Q] :
( c_24__type__13___24t(V0__A,V3__Q)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V3__Q)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__628___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__1268___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__613___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.good_ctx_seq_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__13___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__619___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__13___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__1274___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__13___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__Q] :
( c_24__type__13___24t(V0__A,V3__Q)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V3__Q)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__1283___24a3(V0__A,V1__P,V3__Q)) ) ) ) ) ) ).
fof('hahn.HahnEquational.immediate_clos_trans_elim',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnRelationsBasic_2eimmediate___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__a,V3__b)
=> ( p(happ(happ(V1__r,V2__a),V3__b))
& ! [V5__c] :
( t(V5__c,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V5__c)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V5__c,V3__b)
=> p(c_24False) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.inclusion_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__33___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_rel_Reflexive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.inclusion_rel_Transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.inclusion_seq_eqv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__36___24t(V0__A,V2__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom),V1__r),V1__r) ) ) ) ).
fof('hahn.HahnEquational.inclusion_seq_eqv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__36___24t(V0__A,V2__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom)),V1__r) ) ) ) ).
fof('hahn.HahnEquational.inclusion_step2_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.inclusion_transpE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27) ) ) ) ) ).
fof('hahn.HahnEquational.interA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r1,V2__r2),V3__r3),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r2,V3__r3))) ) ) ) ) ).
fof('hahn.HahnEquational.interAC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V3__r_27_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V3__r_27_27))) ) ) ) ) ).
fof('hahn.HahnEquational.interC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r1,V2__r2),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r2,V1__r1)) ) ) ) ).
fof('hahn.HahnEquational.interK',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V1__r),V1__r) ) ) ).
fof('hahn.HahnEquational.inter_absorb_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V1__r),V1__r) ) ) ) ) ).
fof('hahn.HahnEquational.inter_absorb_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V1__r) ) ) ) ) ).
fof('hahn.HahnEquational.inter_false_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,c_24__lam__1125___24a1(V0__A),V1__r),c_24__lam__1125___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__1125___24a1(V0__A)),c_24__lam__1125___24a1(V0__A)) ) ) ).
fof('hahn.HahnEquational.inter_inclusion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__i] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__i)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__i),V1__r) ) ) ) ).
fof('hahn.HahnEquational.inter_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__10___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__13___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_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnEquational.inter_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__i] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__i)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V3__i)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V3__i),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V3__i)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__i)) ) ) ) ) ) ).
fof('hahn.HahnEquational.irreflexive_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33___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.map_rel_acyclic',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V1__B,V3__r)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_irr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V1__B,V3__r)
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnEquational.minusK',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V1__r),c_24__lam__1125___24a1(V0__A)) ) ) ).
fof('hahn.HahnEquational.minus_absorb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),c_24__lam__1125___24a1(V0__A)) ) ) ) ) ).
fof('hahn.HahnEquational.minus_false_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,c_24__lam__1125___24a1(V0__A),V1__r),c_24__lam__1125___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__1125___24a1(V0__A)),V1__r) ) ) ).
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.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_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)
=> 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_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V2__r,V1__n)),V2__r) ) ) ) ) ).
fof('hahn.HahnEquational.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__36___24t(V0__A,V1__d)
=> ! [V2__d_27] :
( c_24__type__36___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_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__292___24t(V0__A,V2__B,V3__f)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__r,V4__x),V5__y))
=> happ(V3__f,V4__x) = happ(V3__f,V5__y) ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V2__B,V3__f,V1__r),V1__r) ) ) ) ) ) ).
fof('hahn.HahnEquational.restr_full',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,c_24__lam__74___24a1(V0__A),V1__r),V1__r) ) ) ).
fof('hahn.HahnEquational.restr_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__36___24t(V0__A,V1__s)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__s,V2__r)) ) ) ) ) ).
fof('hahn.HahnEquational.rtE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__74___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnEquational.rt_of_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.rt_of_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.rt_of_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.rt_of_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnEquational.rt_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.rt_seq_swap',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)))) ) ) ) ).
fof('hahn.HahnEquational.rt_unit',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.same_rel',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.same_rel_Reflexive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.same_rel_Symmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.same_rel_Transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.same_relation_exp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__r,V4__x),V5__y))
<=> p(happ(happ(V2__r_27,V4__x),V5__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.same_relation_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__36___24t(V0__B,V2__P)
=> ! [V3__rr] :
( c_24__type__158___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__1150___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__1153___24t(V0__B,V1__A,V3__P)
=> ! [V4__rr] :
( c_24__type__158___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__1164___24a4(V0__B,V1__A,V2__r,V4__rr))) ) ) ) ) ) ).
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__36___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__1319___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__36___24t(V0__A,V2__dom1)
=> ! [V3__dom2] :
( c_24__type__36___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__1336___24a4(V0__A,V1__r,V2__dom1,V3__dom2)) ) ) ) ) ).
fof('hahn.HahnEquational.seq_eqv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__36___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__1308___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__1125___24a1(V0__A),V1__r),c_24__lam__1125___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__1125___24a1(V0__A)),c_24__lam__1125___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__74___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__74___24a1(V0__A))),V1__r) ) ) ).
fof('hahn.HahnEquational.seq_minus_transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r1)
=> ! [V3__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r2)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r1,V3__r2),V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r1,V1__r),V3__r2),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r1,V1__r),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V3__r2,V1__r)))) ) ) ) ) ) ).
fof('hahn.HahnEquational.seq_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__10___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__13___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),chahn_2eHahnRelationsBasic_2eseq___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.seq_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__10___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__13___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_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.symmetric_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33___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__36___24t(V0__X,V2__dom)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__X,V2__dom,V1__mo)
=> ! [V4__a] :
( t(V4__a,V0__X)
=> ! [V5__b] :
( t(V5__b,V0__X)
=> ( p(happ(V2__dom,V4__a))
=> ( p(happ(V2__dom,V5__b))
=> ( ~ p(happ(happ(V1__mo,V4__a),V5__b))
=> ( V4__a != V5__b
=> p(happ(happ(V1__mo,V5__b),V4__a)) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.trailing_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__e] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__e)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V3__e))) ) ) ) ) ) ).
fof('hahn.HahnEquational.transitive_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__x)
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__y) ) ) ) ) ) ).
fof('hahn.HahnEquational.transitive_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33___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_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_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13___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_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnEquational.unionA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,V2__r2),V3__r3),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r2,V3__r3))) ) ) ) ) ).
fof('hahn.HahnEquational.unionAC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__r_27_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V3__r_27_27))) ) ) ) ) ).
fof('hahn.HahnEquational.unionC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,V2__r2),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r2,V1__r1)) ) ) ) ).
fof('hahn.HahnEquational.unionK',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V1__r),V1__r) ) ) ).
fof('hahn.HahnEquational.union_absorb_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V2__r_27) ) ) ) ) ).
fof('hahn.HahnEquational.union_absorb_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V1__r),V2__r_27) ) ) ) ) ).
fof('hahn.HahnEquational.union_false_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,c_24__lam__1125___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__1125___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__10___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__13___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),cCoq_2eRelations_2eRelation__Operators_2eunion___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.union_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__10___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__13___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A))),cCoq_2eRelations_2eRelation__Operators_2eunion___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.union_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_inter_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_inter_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__t)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ! [V5__dom] :
( c_24__type__1153___24t(V0__A,V1__B,V5__dom)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V5__dom,V3__r)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ! [V5__C] :
( cType___24t(V5__C)
=> ! [V6__dom] :
( c_24__type__1568___24t(V0__A,V1__B,V5__C,V6__dom)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V5__C,V6__dom,V3__r)) ) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_restr_eq_rel',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__t)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_transp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__t)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ) ).
fof('hahn.HahnList.ForallE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
=> p(happ(V1__P,V3__x)) ) ) ) ) ) ) ).
fof('hahn.HahnList.Forall_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2))
<=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l1)
& cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l2) ) ) ) ) ) ) ).
fof('hahn.HahnList.Forall_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l))
<=> ( p(happ(V1__P,V2__a))
& cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l) ) ) ) ) ) ) ).
fof('hahn.HahnList.Forall_filter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__f] :
( c_24__type__28187___24t(V0__A,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V2__f,V3__l)) ) ) ) ) ) ).
fof('hahn.HahnList.Forall_filterP',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__f] :
( c_24__type__36___24t(V0__A,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,chahn_2eHahnList_2efilterP___24a3(V0__A,V2__f,V3__l)) ) ) ) ) ) ).
fof('hahn.HahnList.Permutation_filter',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_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ! [V4__f] :
( c_24__type__28187___24t(V0__A,V4__f)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V4__f,V1__l),cCoq_2eLists_2eList_2efilter___24a3(V0__A,V4__f,V2__l_27)) ) ) ) ) ) ).
fof('hahn.HahnList.Permutation_filterP',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_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ! [V4__f] :
( c_24__type__36___24t(V0__A,V4__f)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,chahn_2eHahnList_2efilterP___24a3(V0__A,V4__f,V1__l),chahn_2eHahnList_2efilterP___24a3(V0__A,V4__f,V2__l_27)) ) ) ) ) ) ).
fof('hahn.HahnList.Permutation_filterP2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__36___24t(V0__A,V1__f)
=> ! [V2__f_27] :
( c_24__type__36___24t(V0__A,V2__f_27)
=> ( chahn_2eHahnSets_2eset__equiv___24a3(V0__A,V1__f,V2__f_27)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V4__l,V5__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,chahn_2eHahnList_2efilterP___24a3(V0__A,V1__f,V4__l),chahn_2eHahnList_2efilterP___24a3(V0__A,V2__f_27,V5__l_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnList.Permutation_nodup',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_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l_27)) ) ) ) ) ) ).
fof('hahn.HahnList.Permutation_undup',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_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,chahn_2eHahnList_2eundup___24a2(V0__A,V1__l),chahn_2eHahnList_2eundup___24a2(V0__A,V2__l_27)) ) ) ) ) ).
fof('hahn.HahnList.appA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m),V3__n) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__m,V3__n)) ) ) ) ) ).
fof('hahn.HahnList.filterP_set_equiv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__36___24t(V0__A,V1__f)
=> ! [V2__f_27] :
( c_24__type__36___24t(V0__A,V2__f_27)
=> ( chahn_2eHahnSets_2eset__equiv___24a3(V0__A,V1__f,V2__f_27)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> chahn_2eHahnList_2efilterP___24a3(V0__A,V1__f,V4__l) = chahn_2eHahnList_2efilterP___24a3(V0__A,V2__f_27,V4__l) ) ) ) ) ) ).
fof('hahn.HahnList.in_app_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V2__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__l_27))) ) ) ) ) ) ).
fof('hahn.HahnList.in_app_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V3__l_27))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__l_27))) ) ) ) ) ) ).
fof('hahn.HahnList.in_cons_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l)))
<=> ( V1__a = V2__b
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,V3__l)) ) ) ) ) ) ) ).
fof('hahn.HahnList.in_filterP_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__f] :
( c_24__type__36___24t(V0__A,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,chahn_2eHahnList_2efilterP___24a3(V0__A,V2__f,V3__l)))
<=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V3__l))
& p(happ(V2__f,V1__x)) ) ) ) ) ) ) ).
fof('hahn.HahnList.in_split_perm',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__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V4__l_27)) ) ) ) ) ) ).
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_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l1)
=> ! [V2__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l2)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l1,V2__l2)))
<=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l1))
& p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l2))
& chahn_2eHahnList_2edisjoint___24a3(V0__A,V1__l1,V2__l2) ) ) ) ) ) ).
fof('hahn.HahnList.nodup_append_commut',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__a)
=> ! [V2__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__b)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__a,V2__b)))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__b,V1__a))) ) ) ) ) ).
fof('hahn.HahnList.nodup_append_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l1)
=> ! [V2__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l2)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l1,V2__l2)))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l1)) ) ) ) ) ).
fof('hahn.HahnList.nodup_append_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l1)
=> ! [V2__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l2)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l1,V2__l2)))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l2)) ) ) ) ) ).
fof('hahn.HahnList.nodup_cons',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_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l)))
<=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V2__l))
& p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l)) ) ) ) ) ) ).
fof('hahn.HahnList.nodup_consD',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_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l)))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l)) ) ) ) ) ).
fof('hahn.HahnList.nodup_filter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> ! [V3__f] :
( c_24__type__28187___24t(V0__A,V3__f)
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V3__f,V1__l))) ) ) ) ) ).
fof('hahn.HahnList.nodup_filterP',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> ! [V3__f] :
( c_24__type__36___24t(V0__A,V3__f)
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,chahn_2eHahnList_2efilterP___24a3(V0__A,V3__f,V1__l))) ) ) ) ) ).
fof('hahn.HahnList.nodup_mapD',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l)) ) ) ) ) ) ).
fof('hahn.HahnList.nodup_undup',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,chahn_2eHahnList_2eundup___24a2(V0__A,V1__l))) ) ) ).
fof('hahn.HahnList.undup_nodup',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> chahn_2eHahnList_2eundup___24a2(V0__A,V1__l) = V1__l ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__f] :
( c_24__type__292___24t(V0__A,V3__B,V4__f)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V3__B,V4__f,V1__r),V2__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_seq1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_seq2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__a)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__a)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_weaken',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_max',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),c_24__lam__1125___24a1(V0__A)) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_wmax',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.set_equiv_max_elt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r),chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnMaxElt.set_equiv_wmax_elt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnMaxElt_2ewmax__elt___24a2(V0__A,V1__r),chahn_2eHahnMaxElt_2ewmax__elt___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnMaxElt.set_subset_max_elt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V1__r)
=> chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r),chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnMaxElt.set_subset_wmax_elt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V1__r)
=> chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnMaxElt_2ewmax__elt___24a2(V0__A,V1__r),chahn_2eHahnMaxElt_2ewmax__elt___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__f] :
( c_24__type__292___24t(V0__A,V3__B,V4__f)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V3__B,V4__f,V1__r),V2__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_seq1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_seq2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__a)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__a)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.acyclic_antisymmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_refl_transE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V2__a,V3__b)
<=> ( V2__a = V3__b
| cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V3__b) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_refl_trans_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V3__a,V4__b)
=> ( ! [V6__a] :
( t(V6__a,V0__A)
=> ! [V7__b] :
( t(V7__b,V0__A)
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> p(happ(happ(V2__r_27,V6__a),V7__b)) ) ) )
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V2__r_27,V3__a,V4__b) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_refl_trans_of_transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V3__x,V4__y)
<=> chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V3__x,V4__y) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__f] :
( c_24__type__292___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__1817___24a3(V0__A,V1__r,V2__r_27),V3__x,V4__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,c_24__lam__1825___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__36___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__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r),V4__x,V5__y)
=> happ(V2__f,V4__x) = happ(V2__f,V5__y) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.eq_in_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.eq_in_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V1__r) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_inter_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_inter_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__36___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.immediateE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r))) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_acyclic',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_bunion_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__P] :
( c_24__type__505___24t(V0__A,V1__B,V3__P)
=> ! [V4__rr] :
( c_24__type__509___24t(V0__A,V1__B,V4__rr)
=> ( ! [V5__x] :
( t(V5__x,V1__B)
=> ( p(happ(V3__P,V5__x))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V4__rr,V5__x),V2__r_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V1__B,V0__A,V3__P,V4__rr),V2__r_27) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_bunion_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__x] :
( t(V3__x,V1__B)
=> ! [V4__P] :
( c_24__type__505___24t(V0__A,V1__B,V4__P)
=> ! [V5__rr] :
( c_24__type__509___24t(V0__A,V1__B,V5__rr)
=> ( p(happ(V4__P,V3__x))
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,happ(V5__rr,V3__x))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2ebunion___24a4(V1__B,V0__A,V4__P,V5__rr)) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_cr_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_eqv_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__36___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_eqv_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__36___24t(V0__A,V1__dom)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_id_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__74___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_id_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__74___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r_27)) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_l1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V1__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_l1_search',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V3__r_27_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_l2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V2__r_27) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_l2_search',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V3__r_27_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__s)
=> ! [V4__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__s,V4__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V3__s),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V4__s_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_minus_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__s)
=> ! [V4__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V4__s_27,V3__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V3__s),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r_27,V4__s_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_minus_rel',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V1__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_r_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_r_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_refl2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V1__r) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__36___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r),V2__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r),V3__r) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_restr_eq_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__r,V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r),V4__r_27) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_restr_rel_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__36___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r),V3__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_rt_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_rt_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_rt_rt2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__s)
=> ! [V4__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__s,V4__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V3__s),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V4__s_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)),V3__r_27_27) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__t)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V3__t)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__t)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__t)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__t) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_step_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_step_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_step_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r),V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_t2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V3__r_27_27) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V2__r_27)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__s)
=> ! [V4__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__s,V4__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V3__s),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V4__s_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
| cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r1_search',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r2_search',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_inclusion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__36___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r)
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r))
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V3__r) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_seqC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27))
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27))
<=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
& chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.is_total_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__36___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__dom,V2__r)
=> chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__dom,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.r_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V2__x,V2__x) ) ) ) ).
fof('hahn.HahnRelationsBasic.r_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V3__y))
=> chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V2__x,V3__y) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_union_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_union_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.restr_eq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__292___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.rt_t_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__c] :
( t(V4__c,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V2__a,V3__b)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V3__b,V4__c)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V4__c) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.same_relation_refl2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V1__r) ) ) ).
fof('hahn.HahnRelationsBasic.strict_partial_order_antisymmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.t_rt_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ? [V4__z] :
( t(V4__z,V0__A)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V2__x,V4__z)
& p(happ(happ(V1__r,V4__z),V3__y)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.t_rt_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__c] :
( t(V4__c,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V3__b)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V3__b,V4__c)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V4__c) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.t_step_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ? [V4__z] :
( t(V4__z,V0__A)
& p(happ(happ(V1__r,V2__x),V4__z))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V4__z,V3__y) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.trans_irr_acyclic',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.trans_irr_antisymmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__r) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.transitive_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnRelationsBasic.transitive_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.transitive_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__36___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__36___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__36___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__36___24t(V0__A,V3__P)
=> ( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V1__r,V3__P)
=> ( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V2__r_27,V3__P)
=> chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__P) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.hahn_inclusion_exp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__r,V4__x),V5__y))
=> p(happ(happ(V2__r_27,V4__x),V5__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.rewrite_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r),V1__r) ) ) ) ).
fof('hahn.HahnRewrite.rewrite_trans_seq_cr_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnRewrite.rewrite_trans_seq_cr_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),V1__r),V1__r) ) ) ) ).
fof('hahn.HahnRewrite.rewrite_trans_seq_cr_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),V1__r) ) ) ) ).
fof('hahn.HahnRewrite.seq2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,V2__r2),V3__r)
=> ! [V5__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V5__s)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V5__s)) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.seq3',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V3__r3)),V4__r)
=> ! [V6__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,V6__s))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r,V6__s)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.seq4',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,V4__r4))),V5__r)
=> ! [V7__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,V7__s)))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r,V7__s)) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.seq5',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r5] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r5)
=> ! [V6__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,V5__r5)))),V6__r)
=> ! [V8__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V8__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,V8__s))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__r,V8__s)) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.seq6',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r5] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r5)
=> ! [V6__r6] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r6)
=> ! [V7__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,V6__r6))))),V7__r)
=> ! [V9__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V9__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__r6,V9__s)))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V7__r,V9__s)) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,V2__r2),V3__r)
=> ! [V5__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V5__s)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V5__s)) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin3',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V3__r3)),V4__r)
=> ! [V6__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,V6__s))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r,V6__s)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin4',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,V4__r4))),V5__r)
=> ! [V7__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,V7__s)))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r,V7__s)) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin5',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r5] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r5)
=> ! [V6__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,V5__r5)))),V6__r)
=> ! [V8__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V8__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,V8__s))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__r,V8__s)) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin6',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r5] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r5)
=> ! [V6__r6] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r6)
=> ! [V7__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,V6__r6))))),V7__r)
=> ! [V9__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V9__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__r6,V9__s)))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V7__r,V9__s)) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.transitiveI',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r),V1__r)
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r) ) ) ) ).
fof('hahn.HahnSets.set_equiv_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(c_24__type__36___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___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__36___24a1(V0__A),chahn_2eHahnSets_2eset__subset___24a1(V0__A)) ) ).
fof('hahn.Zorn.Build_continues_raw',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__S] :
( c_24__type__36___24t(V0__A,V1__S)
=> ! [V2__S_27] :
( c_24__type__36___24t(V0__A,V2__S_27)
=> ! [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)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ( p(happ(V1__S,V5__x))
=> p(happ(V2__S_27,V5__x)) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ( p(happ(V2__S_27,V6__x))
=> ( p(happ(V1__S,V7__y))
=> ( p(happ(happ(V4__R_27,V6__x),V7__y))
=> p(happ(V1__S,V6__x)) ) ) ) ) )
=> ( ! [V7__x] :
( t(V7__x,V0__A)
=> ! [V8__y] :
( t(V8__y,V0__A)
=> ( p(happ(V1__S,V7__x))
=> ( p(happ(V1__S,V8__y))
=> ( p(happ(happ(V3__R,V7__x),V8__y))
<=> p(happ(happ(V4__R_27,V7__x),V8__y)) ) ) ) ) )
=> chahn_2eZorn_2econtinues__raw___24a5(V0__A,V1__S,V2__S_27,V3__R,V4__R_27) ) ) ) ) ) ) ) ) ).
fof('hahn.Zorn.R_coincides',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__S] :
( c_24__type__36___24t(V0__A,V1__S)
=> ! [V2__S_27] :
( c_24__type__36___24t(V0__A,V2__S_27)
=> ! [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)
=> ( chahn_2eZorn_2econtinues__raw___24a5(V0__A,V1__S,V2__S_27,V3__R,V4__R_27)
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ( p(happ(V1__S,V6__x))
=> ( p(happ(V1__S,V7__y))
=> ( p(happ(happ(V3__R,V6__x),V7__y))
<=> p(happ(happ(V4__R_27,V6__x),V7__y)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.Zorn.S_closed',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__S] :
( c_24__type__36___24t(V0__A,V1__S)
=> ! [V2__S_27] :
( c_24__type__36___24t(V0__A,V2__S_27)
=> ! [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)
=> ( chahn_2eZorn_2econtinues__raw___24a5(V0__A,V1__S,V2__S_27,V3__R,V4__R_27)
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ( p(happ(V2__S_27,V6__x))
=> ( p(happ(V1__S,V7__y))
=> ( p(happ(happ(V4__R_27,V6__x),V7__y))
=> p(happ(V1__S,V6__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.Zorn.S_sub',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__S] :
( c_24__type__36___24t(V0__A,V1__S)
=> ! [V2__S_27] :
( c_24__type__36___24t(V0__A,V2__S_27)
=> ! [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)
=> ( chahn_2eZorn_2econtinues__raw___24a5(V0__A,V1__S,V2__S_27,V3__R,V4__R_27)
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ( p(happ(V1__S,V6__x))
=> p(happ(V2__S_27,V6__x)) ) ) ) ) ) ) ) ) ).
fof('hahn.Zorn.well_ordering_theorem',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ? [V3__ltA] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__ltA)
& chahn_2eZorn_2ewell__order___24a3(V0__A,V1__eqA,V3__ltA) ) ) ) ) ).
fof('hahn.Zorn.zorns_lemma',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(V0__A,V1__R)
=> ( ! [V3__C] :
( c_24__type__36___24t(V0__A,V3__C)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(V3__C,V4__x))
=> ( p(happ(V3__C,V5__y))
=> ( p(happ(happ(V1__R,V4__x),V5__y))
| p(happ(happ(V1__R,V5__y),V4__x)) ) ) ) ) )
=> ? [V5__m] :
( t(V5__m,V0__A)
& ! [V6__x] :
( t(V6__x,V0__A)
=> ( p(happ(V3__C,V6__x))
=> p(happ(happ(V1__R,V6__x),V5__m)) ) ) ) ) )
=> ? [V4__m] :
( t(V4__m,V0__A)
& ! [V5__x] :
( t(V5__x,V0__A)
=> ( p(happ(happ(V1__R,V4__m),V5__x))
=> p(happ(happ(V1__R,V5__x),V4__m)) ) ) ) ) ) ) ) ).
fof('$adef_hahn.Zorn.suspend_S_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eZorn_2esuspend__S,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eZorn_2esuspend__S___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_hahn.HahnSets.set_equiv_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnSets_2eset__equiv,V_24X1) = chahn_2eHahnSets_2eset__equiv___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_16_mkpow_30755_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__let__16__mkpow__30755,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__30755___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.Zorn.ZornsLemma_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eZorn_2eZornsLemma,V_24X1),V_24X2))
<=> chahn_2eZorn_2eZornsLemma___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Logic.FinFun.Injective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eInjective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eInjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$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('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_$_let_17_mkopp_pow_30756_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__30756,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__30756___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_Coq.Relations.Relation_Definitions.PER_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ePER,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_2132_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__2132,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__2132___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
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('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pequiv_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePequiv,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9))
<=> cCoq_2esetoid__ring_2eRing__polynom_2ePequiv___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_hahn.Zorn.Private.equ_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eZorn_2ePrivate_2eequ,V_24X1),V_24X2) = chahn_2eZorn_2ePrivate_2eequ___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.Exists_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eExists,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eExists___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.cons_id_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eTauto_2econs__id,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eTauto_2econs__id___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEequiv_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.Logic.FinFun.Full_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2eFull,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2eFull___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_dev_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$36586_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2436586,V_24X1),V_24X2))
<=> c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2436586___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.acyclic_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnRelationsBasic_2eacyclic,V_24X1),V_24X2))
<=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.get_sign_None_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1336_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__1336,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__1336___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$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_Coq.Lists.List.count_occ_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2ecount__occ,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2ecount__occ___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnRelationsBasic.restr_eq_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2erestr__eq__rel,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnRelationsBasic.immediate_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eimmediate,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eimmediate___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_628_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__628,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__628___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.List.nth_error_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2enth__error,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2enth__error___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.lel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2elel,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2elel___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnSets.set_subset_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnSets_2eset__subset,V_24X1) = chahn_2eHahnSets_2eset__subset___24a1(V_24X1) ).
fof('$adef_Coq.Sorting.Sorted.LocallySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eLocallySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.eq_rel_$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('$adef_Coq.Lists.SetoidList.inclA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2einclA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2einclA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Operators.Desc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eDesc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.inclusion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2einclusion,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V_24X1) ).
fof('$adef_$_lam_33268_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__33268,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__33268___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.BinList.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_25592_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__25592,V_24X1),V_24X2),V_24X3) = c_24__prop__25592___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_hahn.HahnMaxElt.max_elt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnMaxElt_2emax__elt,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnMaxElt_2emax__elt___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_HahnTotalExt.one_ext_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cHahnTotalExt_2eone__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cHahnTotalExt_2eone__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_1308_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__1308,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__1308___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_HahnTotalExt.tot_ext_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHahnTotalExt_2etot__ext,V_24X1),V_24X2),V_24X3) = cHahnTotalExt_2etot__ext___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.FinFun.bSurjective_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2ebSurjective,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2ebSurjective___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.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_$_lam_33250_$a1',axiom,
! [V_24X1] : happ(c_24__lam__33250,V_24X1) = c_24__lam__33250___24a1(V_24X1) ).
fof('$adef_$_prop_28300_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__28300,V_24X1),V_24X2),V_24X3) = c_24__prop__28300___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.rev_append_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2erev__append,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2erev__append___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_1646_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__1646,V_24X1),V_24X2),V_24X3) = c_24__prop__1646___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.strict_partial_order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnRelationsBasic_2estrict__partial__order,V_24X1),V_24X2))
<=> chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnRelationsBasic.eqv_dom_rel_$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('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.existT_$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('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Tauto.eval_tt_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__tt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$10395_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2410395,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2410395___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Lists.List.concat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2econcat,V_24X1),V_24X2) = cCoq_2eLists_2eList_2econcat___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('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnList.undup_$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('$adef_hahn.HahnSets.set_finite_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnSets_2eset__finite,V_24X1),V_24X2))
<=> chahn_2eHahnSets_2eset__finite___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_1125_$a1',axiom,
! [V_24X1] : happ(c_24__lam__1125,V_24X1) = c_24__lam__1125___24a1(V_24X1) ).
fof('$adef_$_let_var_var_7_n_25549_25553_25562_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__var__7__n__25549__25553__25562,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__var__7__n__25549__25553__25562___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_hahn.HahnBase.is_true_$a1',axiom,
! [V_24X1] :
( p(happ(chahn_2eHahnBase_2eis__true,V_24X1))
<=> chahn_2eHahnBase_2eis__true___24a1(V_24X1) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$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('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_pow_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_2341_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2341,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2341___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_prop_1607_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__1607,V_24X1),V_24X2),V_24X3) = c_24__prop__1607___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_17_lnum_27437_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__lnum__27437,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = c_24__let__17__lnum__27437___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_Coq.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_$_let_17_mkopp_pow_30756_$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(c_24__let__17__mkopp__pow__30756,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__30756___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.Classes.RelationClasses.StrictOrder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eStrictOrder,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_$_lam_3000_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__3000,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__3000___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_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_Coq.setoid_ring.Ring_polynom.r_list_pow_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1172_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1172,V_24X1),V_24X2) = c_24__lam__1172___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.codom_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2ecodom__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_lam_613_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__613,V_24X1),V_24X2) = c_24__lam__613___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_hahn.Zorn.ordered_subset_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eZorn_2eordered__subset,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eZorn_2eordered__subset___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_hahn.Zorn.Private.Le_$a1',axiom,
! [V_24X1] : happ(chahn_2eZorn_2ePrivate_2eLe,V_24X1) = chahn_2eZorn_2ePrivate_2eLe___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.existsb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eexistsb,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eexistsb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_Coq.Sets.Relations_1.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_35873_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__35873,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__35873___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('$adef_$_prop_1606_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__1606,V_24X1),V_24X2),V_24X3) = c_24__prop__1606___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_25593_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__25593,V_24X1),V_24X2),V_24X3) = c_24__prop__25593___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.hd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2ehd,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2ehd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1523_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__1523,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__1523___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_let_var_6_p_15957_15960_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__15957__15960,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__15957__15960___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('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1274_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1274,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1274___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_lam_74_$a1',axiom,
! [V_24X1] : happ(c_24__lam__74,V_24X1) = c_24__lam__74___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_$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_2esetoid__ring_2eRing__polynom_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_hahn.HahnBase.NW_$a1',axiom,
! [V_24X1] :
( p(happ(chahn_2eHahnBase_2eNW,V_24X1))
<=> chahn_2eHahnBase_2eNW___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.Zcomplements.Zlength_aux_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eZArith_2eZcomplements_2eZlength__aux,V_24X1),V_24X2),V_24X3) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_25595_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__25595,V_24X1),V_24X2),V_24X3) = c_24__prop__25595___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_hahn.Zorn.Private.Lt_$a1',axiom,
! [V_24X1] : happ(chahn_2eZorn_2ePrivate_2eLt,V_24X1) = chahn_2eZorn_2ePrivate_2eLt___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.forallb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eforallb,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eforallb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.Zorn.suspend_R_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(chahn_2eZorn_2esuspend__R,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> chahn_2eZorn_2esuspend__R___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$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_Coq.ZArith.Zcomplements.Zlength_aux_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZcomplements_2eZlength__aux,V_24X1) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a1(V_24X1) ).
fof('$adef_hahn.HahnSets.set_subset_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnSets_2eset__subset,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnSets_2eset__subset___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.irreflexive_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eirreflexive,V_24X1) = chahn_2eHahnRelationsBasic_2eirreflexive___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.skipn_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eskipn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eskipn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.eqlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.irreflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnRelationsBasic_2eirreflexive,V_24X1),V_24X2))
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.In_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLists_2eList_2eIn,V_24X1) = cCoq_2eLists_2eList_2eIn___24a1(V_24X1) ).
fof('$adef_$_lam_628_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__628,V_24X1),V_24X2),V_24X3) = c_24__lam__628___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_35875_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__35875,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__35875___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequivalence,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_2128_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__2128,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__2128___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.bunion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ebunion,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnRelationsBasic_2ebunion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$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_1319_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__1319,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__1319___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_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_$_lam_1268_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1268,V_24X1),V_24X2) = c_24__lam__1268___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_24190_$a1',axiom,
! [V_24X1] : happ(c_24__prop__24190,V_24X1) = c_24__prop__24190___24a1(V_24X1) ).
fof('$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.id_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eid,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eid___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.list_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rect,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_case_Coq.setoid_ring.Ring_polynom.Pol$32643_$a20',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2432643,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20) = c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2432643___24a20(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20) ).
fof('$adef_hahn.HahnList.map_filter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnList_2emap__filter,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnList_2emap__filter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_pow_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Coq.Logic.FinFun.Surjective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eSurjective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eSurjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_1658_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__1658,V_24X1),V_24X2),V_24X3) = c_24__prop__1658___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.interp_PElist_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).
fof('$adef_$_fix_24126_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__24126__1__add__carry,V_24X1),V_24X2) = c_24__fix__24126__1__add__carry___24a2(V_24X1,V_24X2) ).
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('$adef_hahn.HahnRelationsBasic.map_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2emap__rel,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnRelationsBasic_2emap__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_sym_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eclos__refl__sym,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_$_lam_1319_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1319,V_24X1),V_24X2),V_24X3) = c_24__lam__1319___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.restr_eq_rel_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2erestr__eq__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__right,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.BinList.jump_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2ejump,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_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.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_Coq.setoid_ring.Field_theory.display_pow_linear_$a20',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20) = cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear___24a20(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkZmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkZmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1336_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1336,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1336___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Lists.SetoidList.transpose2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose2,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.list_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2elist__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_1308_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1308,V_24X1),V_24X2),V_24X3) = c_24__lam__1308___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Vectors.VectorDef.to_list_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eto__list,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2eto__list___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1125_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__1125,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__1125___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_$_lam_1825_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__1825,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__1825___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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_$_lam_2128_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2128,V_24X1),V_24X2),V_24X3) = c_24__lam__2128___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_4764_$a1',axiom,
! [V_24X1] : happ(c_24__lam__4764,V_24X1) = c_24__lam__4764___24a1(V_24X1) ).
fof('$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_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.Lists.List.Forall2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eList_2eForall2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_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_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnMaxElt_2ewmax__elt,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Operators.union_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eunion,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eRelations_2eRelation__Operators_2eunion___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_$_prop_35908_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__35908,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__35908___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Sorting.Sorted.Sorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eSorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.eqv_dom_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eeqv__dom__rel,V_24X1) = chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a1(V_24X1) ).
fof('$adef_Coq.Logic.FinFun.bFun_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2ebFun,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2ebFun___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__left,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.FinFun.Listing_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2eListing,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2eListing___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnRelationsBasic.inter_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2einter__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2einter__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_35874_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__35874,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__35874___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnRelationsBasic_2eis__total,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnRelationsBasic_2eis__total___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_HahnTotalExt.one_ext_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHahnTotalExt_2eone__ext,V_24X1),V_24X2),V_24X3) = cHahnTotalExt_2eone__ext___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.list_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rec,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_24372_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__24372,V_24X1),V_24X2),V_24X3) = c_24__prop__24372___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('$adef_$_let_16_mkpow_30755_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__30755,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__30755___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.cnf_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_34226_v_CANONICAL_2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__fix__34226__v__CANONICAL__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__fix__34226__v__CANONICAL__2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_lam_1274_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1274,V_24X1),V_24X2),V_24X3) = c_24__lam__1274___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.P0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eP0,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_sym_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eclos__refl__sym,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnList.filterP_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnList_2efilterP,V_24X1),V_24X2),V_24X3) = chahn_2eHahnList_2efilterP___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$32099_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2432099,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2432099___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnSets.set_empty_$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('$adef_Coq.setoid_ring.Ring_polynom.Mphi_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eMphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_hahn.HahnRelationsBasic.eqv_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eeqv__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_4764_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__4764,V_24X1),V_24X2) = c_24__lam__4764___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
<=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_18_mkmult_pow_30757_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__30757,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__30757___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
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('$adef_Coq.setoid_ring.Field_theory.condition_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2econdition,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.cons_$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('$adef_Coq.Lists.List.rev\'_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2erev_27,V_24X1),V_24X2) = cCoq_2eLists_2eList_2erev_27___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('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___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('$adef_hahn.Zorn.well_order_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eZorn_2ewell__order,V_24X1),V_24X2),V_24X3))
<=> chahn_2eZorn_2ewell__order___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ClassicalDescription.excluded_middle_informative_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative,V_24X1) = cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.inter_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2einter__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2einter__rel___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.Lists.List.nth_ok_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth__ok,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth__ok___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Lists.List.combine_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2ecombine,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2ecombine___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.Zorn.Private.Equiv_$a1',axiom,
! [V_24X1] : happ(chahn_2eZorn_2ePrivate_2eEquiv,V_24X1) = chahn_2eZorn_2ePrivate_2eEquiv___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.P1_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eP1,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2eP1___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.find_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2efind,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2efind___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_1817_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1817,V_24X1),V_24X2),V_24X3) = c_24__lam__1817___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Lists.List.ForallOrdPairs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallOrdPairs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_$_lam_1283_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1283,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1283___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1817_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__1817,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__1817___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.display_linear_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2edisplay__linear,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eField__theory_2edisplay__linear___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).
fof('$adef_Coq.Init.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.Lists.SetoidList.eqlistA_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2) = cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.clause_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2eclause,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2341_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__2341,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__2341___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_lam_1150_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1150,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1150___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_hahn.Zorn.continues_raw_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eZorn_2econtinues__raw,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eZorn_2econtinues__raw___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.removelast_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2eremovelast,V_24X1),V_24X2) = cCoq_2eLists_2eList_2eremovelast___24a2(V_24X1,V_24X2) ).
fof('$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.setoid_ring.Ring_polynom.norm_subst_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_hahn.HahnList.disjoint_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnList_2edisjoint,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnList_2edisjoint___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_Coq.setoid_ring.Ring_polynom.Pphi_pow_$a18',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18) ).
fof('$adef_Coq.Init.Specif.right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_1283_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1283,V_24X1),V_24X2),V_24X3) = c_24__lam__1283___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_20_lnum_32339_$a18',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__20__lnum__32339,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18) = c_24__let__20__lnum__32339___24a18(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18) ).
fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Lists.List.ForallPairs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallPairs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForallPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_1164_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1164,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1164___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Sorting.Permutation.Permutation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1) = cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V_24X1) ).
fof('$adef_$_lam_619_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__619,V_24X1),V_24X2),V_24X3) = c_24__lam__619___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_18_mkmult_pow_30757_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__30757,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__30757___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Lists.SetoidList.removeA_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eremoveA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.List.Add_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eList_2eAdd,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eList_2eAdd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_2132_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2132,V_24X1),V_24X2),V_24X3) = c_24__lam__2132___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.rev_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2erev,V_24X1),V_24X2) = cCoq_2eLists_2eList_2erev___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$10308_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2410308,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2410308___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_1825_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1825,V_24X1),V_24X2),V_24X3) = c_24__lam__1825___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_4662_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__4662,V_24X1),V_24X2) = c_24__lam__4662___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.ListDec.decidable_eq_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLists_2eListDec_2edecidable__eq,V_24X1))
<=> cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V_24X1) ) ).
fof('$adef_Coq.Lists.List.hd_error_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2ehd__error,V_24X1),V_24X2) = cCoq_2eLists_2eList_2ehd__error___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_$_lam_1523_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1523,V_24X1),V_24X2) = c_24__lam__1523___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_1164_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1164,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1164___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_33268_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__33268,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__33268___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.same_relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2esame__relation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V_24X1) ).
fof('$adef_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_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_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_$_prop_24373_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__24373,V_24X1),V_24X2),V_24X3) = c_24__prop__24373___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_4662_$a1',axiom,
! [V_24X1] : happ(c_24__lam__4662,V_24X1) = c_24__lam__4662___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiN_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Relations.Relation_Definitions.inclusion_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2einclusion,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_hahn.HahnRelationsBasic.bunion_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ebunion,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> chahn_2eHahnRelationsBasic_2ebunion___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.equivlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eequivlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Nat.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.union_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eunion,V_24X1),V_24X2),V_24X3) = cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.List.filter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2efilter,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2efilter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Permutation.Permutation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eclos__refl,V_24X1) = chahn_2eHahnRelationsBasic_2eclos__refl___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_avoid_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_Coq.Lists.List.nth_default_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth__default,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth__default___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.firstn_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2efirstn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2efirstn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_26270_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__26270,V_24X1),V_24X2) = c_24__prop__26270___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.fold_right_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Operators.Ltl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eLtl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnList.flatten_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnList_2eflatten,V_24X1),V_24X2) = chahn_2eHahnList_2eflatten___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_hahn.HahnFuneq.funeq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnFuneq_2efuneq,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnFuneq_2efuneq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.tl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2etl,V_24X1),V_24X2) = cCoq_2eLists_2eList_2etl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.Symmetric_$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('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.inter_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2einter__rel,V_24X1) = chahn_2eHahnRelationsBasic_2einter__rel___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.List.flat_map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2eflat__map,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2eflat__map___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_hahn.Zorn.Private.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eZorn_2ePrivate_2ele,V_24X1),V_24X2) = chahn_2eZorn_2ePrivate_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.FinFun.bInjective_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2ebInjective,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2ebInjective___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_3000_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__3000,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__3000___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_$_let_var_6_p_15959_15961_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__15959__15961,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__15959__15961___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2) = cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_hahn.HahnSets.set_equiv_$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('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_613_$a1',axiom,
! [V_24X1] : happ(c_24__lam__613,V_24X1) = c_24__lam__613___24a1(V_24X1) ).
fof('$adef_$_lam_33250_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33250,V_24X1),V_24X2) = c_24__lam__33250___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_619_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__619,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__619___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.NFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eNFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1150_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1150,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1150___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.symmetric_$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('$adef_$_case_Coq.setoid_ring.Ring_polynom.Pol$27670_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2427670,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2427670___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).
fof('$adef_hahn.HahnRelationsBasic.seq_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eseq,V_24X1) = chahn_2eHahnRelationsBasic_2eseq___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEeval_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.collect_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ecollect__rel,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_74_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__74,V_24X1),V_24X2))
<=> c_24__lam__74___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_aux_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_fix_10440_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__10440__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__10440__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_$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('$adef_Coq.Relations.Relation_Operators.clos_trans_$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('$adef_Coq.setoid_ring.Field_theory.denum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2edenum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Specif.sumbool$25580_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eSpecif_2esumbool_2425580,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_2425580___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Classes.RelationClasses.PreOrder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2ePreOrder,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_common_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__common,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.incl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eincl,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eincl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_11_subst_l_2928_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__11__subst__l__2928,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__11__subst__l__2928___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$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.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_$_lam_1172_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__1172,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__1172___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_1268_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1268,V_24X1),V_24X2),V_24X3) = c_24__lam__1268___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_25594_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__25594,V_24X1),V_24X2),V_24X3) = c_24__prop__25594___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] :
( p(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] :
( p(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] :
( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$tdef_$_type_17375',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17375___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17375___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_33039',axiom,
! [V_24Y] :
( c_24__type__33039___24t(V_24Y)
<=> t(V_24Y,c_24__type__33039) ) ).
fof('$tdef_$_type_24684',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24684___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24684___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_28216',axiom,
! [V_24Y] :
( c_24__type__28216___24t(V_24Y)
<=> t(V_24Y,c_24__type__28216) ) ).
fof('$tdef_$_type_24951',axiom,
! [V_24Y] :
( c_24__type__24951___24t(V_24Y)
<=> t(V_24Y,c_24__type__24951) ) ).
fof('$tdef_$_type_3770',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__3770___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__3770___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_31035',axiom,
! [V_24Y] :
( c_24__type__31035___24t(V_24Y)
<=> t(V_24Y,c_24__type__31035) ) ).
fof('$tdef_hahn.Zorn.Private.Le',axiom,
! [V_24X1,V_24Y] :
( chahn_2eZorn_2ePrivate_2eLe___24t(V_24X1,V_24Y)
<=> t(V_24Y,chahn_2eZorn_2ePrivate_2eLe___24a1(V_24X1)) ) ).
fof('$tdef_$_type_225',axiom,
! [V_24Y] :
( c_24__type__225___24t(V_24Y)
<=> t(V_24Y,c_24__type__225) ) ).
fof('$tdef_$_type_1750',axiom,
! [V_24Y] :
( c_24__type__1750___24t(V_24Y)
<=> t(V_24Y,c_24__type__1750) ) ).
fof('$tdef_$_type_1623',axiom,
! [V_24Y] :
( c_24__type__1623___24t(V_24Y)
<=> t(V_24Y,c_24__type__1623) ) ).
fof('$tdef_$_type_3368',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3368___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3368___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_21861',axiom,
! [V_24Y] :
( c_24__type__21861___24t(V_24Y)
<=> t(V_24Y,c_24__type__21861) ) ).
fof('$tdef_$_type_19810',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19810___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19810___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_6482',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6482___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6482___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3137',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3137___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3137___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33647',axiom,
! [V_24Y] :
( c_24__type__33647___24t(V_24Y)
<=> t(V_24Y,c_24__type__33647) ) ).
fof('$tdef_$_type_1660',axiom,
! [V_24Y] :
( c_24__type__1660___24t(V_24Y)
<=> t(V_24Y,c_24__type__1660) ) ).
fof('$tdef_$_type_17570',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17570___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17570___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3792',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__3792___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__3792___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_69',axiom,
! [V_24Y] :
( c_24__type__69___24t(V_24Y)
<=> t(V_24Y,c_24__type__69) ) ).
fof('$tdef_$_type_862',axiom,
! [V_24Y] :
( c_24__type__862___24t(V_24Y)
<=> t(V_24Y,c_24__type__862) ) ).
fof('$tdef_$_type_16669',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__16669___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__16669___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_28265',axiom,
! [V_24X1,V_24Y] :
( c_24__type__28265___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__28265___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6307',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6307___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6307___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3427',axiom,
! [V_24Y] :
( c_24__type__3427___24t(V_24Y)
<=> t(V_24Y,c_24__type__3427) ) ).
fof('$tdef_$_type_34159',axiom,
! [V_24Y] :
( c_24__type__34159___24t(V_24Y)
<=> t(V_24Y,c_24__type__34159) ) ).
fof('$tdef_$_type_4674',axiom,
! [V_24Y] :
( c_24__type__4674___24t(V_24Y)
<=> t(V_24Y,c_24__type__4674) ) ).
fof('$tdef_$_type_33655',axiom,
! [V_24Y] :
( c_24__type__33655___24t(V_24Y)
<=> t(V_24Y,c_24__type__33655) ) ).
fof('$tdef_$_type_22161',axiom,
! [V_24Y] :
( c_24__type__22161___24t(V_24Y)
<=> t(V_24Y,c_24__type__22161) ) ).
fof('$tdef_$_type_21627',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21627___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21627___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5314',axiom,
! [V_24Y] :
( c_24__type__5314___24t(V_24Y)
<=> t(V_24Y,c_24__type__5314) ) ).
fof('$tdef_$_type_17765',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17765___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17765___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_28187',axiom,
! [V_24X1,V_24Y] :
( c_24__type__28187___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__28187___24a1(V_24X1)) ) ).
fof('$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_4867',axiom,
! [V_24Y] :
( c_24__type__4867___24t(V_24Y)
<=> t(V_24Y,c_24__type__4867) ) ).
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_$_type_36217',axiom,
! [V_24Y] :
( c_24__type__36217___24t(V_24Y)
<=> t(V_24Y,c_24__type__36217) ) ).
fof('$tdef_$_type_32226',axiom,
! [V_24Y] :
( c_24__type__32226___24t(V_24Y)
<=> t(V_24Y,c_24__type__32226) ) ).
fof('$tdef_$_type_16489',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__16489___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__16489___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_36',axiom,
! [V_24X1,V_24Y] :
( c_24__type__36___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__36___24a1(V_24X1)) ) ).
fof('$tdef_$_type_259',axiom,
! [V_24Y] :
( c_24__type__259___24t(V_24Y)
<=> t(V_24Y,c_24__type__259) ) ).
fof('$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_$_type_21382',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21382___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21382___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_32321',axiom,
! [V_24Y] :
( c_24__type__32321___24t(V_24Y)
<=> t(V_24Y,c_24__type__32321) ) ).
fof('$tdef_$_type_29203',axiom,
! [V_24Y] :
( c_24__type__29203___24t(V_24Y)
<=> t(V_24Y,c_24__type__29203) ) ).
fof('$tdef_$_type_15971',axiom,
! [V_24Y] :
( c_24__type__15971___24t(V_24Y)
<=> t(V_24Y,c_24__type__15971) ) ).
fof('$tdef_$_type_24400',axiom,
! [V_24Y] :
( c_24__type__24400___24t(V_24Y)
<=> t(V_24Y,c_24__type__24400) ) ).
fof('$tdef_$_type_24183',axiom,
! [V_24Y] :
( c_24__type__24183___24t(V_24Y)
<=> t(V_24Y,c_24__type__24183) ) ).
fof('$tdef_$_type_9374',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9374___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9374___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_2916',axiom,
! [V_24Y] :
( c_24__type__2916___24t(V_24Y)
<=> t(V_24Y,c_24__type__2916) ) ).
fof('$tdef_$_type_33247',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33247___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33247___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_21070',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__21070___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__21070___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_8546',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__8546___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__8546___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_34126',axiom,
! [V_24Y] :
( c_24__type__34126___24t(V_24Y)
<=> t(V_24Y,c_24__type__34126) ) ).
fof('$tdef_$_type_32132',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32132___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32132___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_21613',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21613___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21613___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5398',axiom,
! [V_24Y] :
( c_24__type__5398___24t(V_24Y)
<=> t(V_24Y,c_24__type__5398) ) ).
fof('$tdef_$_type_1879',axiom,
! [V_24Y] :
( c_24__type__1879___24t(V_24Y)
<=> t(V_24Y,c_24__type__1879) ) ).
fof('$tdef_$_type_19402',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19402___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19402___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_6400',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6400___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6400___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_$_type_1612',axiom,
! [V_24Y] :
( c_24__type__1612___24t(V_24Y)
<=> t(V_24Y,c_24__type__1612) ) ).
fof('$tdef_$_type_3651',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__3651___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__3651___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_33387',axiom,
! [V_24Y] :
( c_24__type__33387___24t(V_24Y)
<=> t(V_24Y,c_24__type__33387) ) ).
fof('$tdef_$_type_21871',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21871___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21871___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_56',axiom,
! [V_24Y] :
( c_24__type__56___24t(V_24Y)
<=> t(V_24Y,c_24__type__56) ) ).
fof('$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_$_type_8265',axiom,
! [V_24Y] :
( c_24__type__8265___24t(V_24Y)
<=> t(V_24Y,c_24__type__8265) ) ).
fof('$tdef_$_type_41',axiom,
! [V_24Y] :
( c_24__type__41___24t(V_24Y)
<=> t(V_24Y,c_24__type__41) ) ).
fof('$tdef_$_type_1153',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1153___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1153___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_24693',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24693___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24693___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_27923',axiom,
! [V_24Y] :
( c_24__type__27923___24t(V_24Y)
<=> t(V_24Y,c_24__type__27923) ) ).
fof('$tdef_$_type_22871',axiom,
! [V_24Y] :
( c_24__type__22871___24t(V_24Y)
<=> t(V_24Y,c_24__type__22871) ) ).
fof('$tdef_$_type_3154',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3154___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3154___24a1(V_24X1)) ) ).
fof('$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_21265',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__21265___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__21265___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_436',axiom,
! [V_24Y] :
( c_24__type__436___24t(V_24Y)
<=> t(V_24Y,c_24__type__436) ) ).
fof('$tdef_$_type_28072',axiom,
! [V_24Y] :
( c_24__type__28072___24t(V_24Y)
<=> t(V_24Y,c_24__type__28072) ) ).
fof('$tdef_$_type_21914',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21914___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21914___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_33600',axiom,
! [V_24Y] :
( c_24__type__33600___24t(V_24Y)
<=> t(V_24Y,c_24__type__33600) ) ).
fof('$tdef_$_type_23452',axiom,
! [V_24Y] :
( c_24__type__23452___24t(V_24Y)
<=> t(V_24Y,c_24__type__23452) ) ).
fof('$tdef_$_type_9082',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__9082___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__9082___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_33086',axiom,
! [V_24Y] :
( c_24__type__33086___24t(V_24Y)
<=> t(V_24Y,c_24__type__33086) ) ).
fof('$tdef_$_type_2921',axiom,
! [V_24Y] :
( c_24__type__2921___24t(V_24Y)
<=> t(V_24Y,c_24__type__2921) ) ).
fof('$tdef_$_type_24324',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__24324___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__24324___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8981',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__8981___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__8981___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_21634',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21634___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21634___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32282',axiom,
! [V_24Y] :
( c_24__type__32282___24t(V_24Y)
<=> t(V_24Y,c_24__type__32282) ) ).
fof('$tdef_$_type_3132',axiom,
! [V_24Y] :
( c_24__type__3132___24t(V_24Y)
<=> t(V_24Y,c_24__type__3132) ) ).
fof('$tdef_$_type_32036',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__32036___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__32036___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_29005',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__29005___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__29005___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_467',axiom,
! [V_24Y] :
( c_24__type__467___24t(V_24Y)
<=> t(V_24Y,c_24__type__467) ) ).
fof('$tdef_$_type_28958',axiom,
! [V_24Y] :
( c_24__type__28958___24t(V_24Y)
<=> t(V_24Y,c_24__type__28958) ) ).
fof('$tdef_$_type_31986',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__31986___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__31986___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_17624',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17624___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17624___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_6575',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__6575___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__6575___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_31894',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__31894___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__31894___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_17684',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17684___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17684___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_36555',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__36555___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__36555___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_26103',axiom,
! [V_24Y] :
( c_24__type__26103___24t(V_24Y)
<=> t(V_24Y,c_24__type__26103) ) ).
fof('$tdef_$_type_24115',axiom,
! [V_24Y] :
( c_24__type__24115___24t(V_24Y)
<=> t(V_24Y,c_24__type__24115) ) ).
fof('$tdef_$_type_29396',axiom,
! [V_24Y] :
( c_24__type__29396___24t(V_24Y)
<=> t(V_24Y,c_24__type__29396) ) ).
fof('$tdef_$_type_1',axiom,
! [V_24Y] :
( c_24__type__1___24t(V_24Y)
<=> t(V_24Y,c_24__type__1) ) ).
fof('$tdef_$_type_3390',axiom,
! [V_24Y] :
( c_24__type__3390___24t(V_24Y)
<=> t(V_24Y,c_24__type__3390) ) ).
fof('$tdef_$_type_2653',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2653___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2653___24a1(V_24X1)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15950',axiom,
! [V_24Y] :
( c_24__type__15950___24t(V_24Y)
<=> t(V_24Y,c_24__type__15950) ) ).
fof('$tdef_$_type_33243',axiom,
! [V_24Y] :
( c_24__type__33243___24t(V_24Y)
<=> t(V_24Y,c_24__type__33243) ) ).
fof('$tdef_$_type_33',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1012',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1012___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1012___24a1(V_24X1)) ) ).
fof('$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_3407',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3407___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3407___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_500',axiom,
! [V_24Y] :
( c_24__type__500___24t(V_24Y)
<=> t(V_24Y,c_24__type__500) ) ).
fof('$tdef_$_type_135',axiom,
! [V_24Y] :
( c_24__type__135___24t(V_24Y)
<=> t(V_24Y,c_24__type__135) ) ).
fof('$tdef_$_type_3646',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__3646___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__3646___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32293',axiom,
! [V_24Y] :
( c_24__type__32293___24t(V_24Y)
<=> t(V_24Y,c_24__type__32293) ) ).
fof('$tdef_$_type_6214',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__6214___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__6214___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3146',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3146___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3146___24a1(V_24X1)) ) ).
fof('$tdef_$_type_24395',axiom,
! [V_24Y] :
( c_24__type__24395___24t(V_24Y)
<=> t(V_24Y,c_24__type__24395) ) ).
fof('$tdef_$_type_25773',axiom,
! [V_24Y] :
( c_24__type__25773___24t(V_24Y)
<=> t(V_24Y,c_24__type__25773) ) ).
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_$_type_33642',axiom,
! [V_24Y] :
( c_24__type__33642___24t(V_24Y)
<=> t(V_24Y,c_24__type__33642) ) ).
fof('$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_5033',axiom,
! [V_24Y] :
( c_24__type__5033___24t(V_24Y)
<=> t(V_24Y,c_24__type__5033) ) ).
fof('$tdef_$_type_24312',axiom,
! [V_24X1,V_24Y] :
( c_24__type__24312___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__24312___24a1(V_24X1)) ) ).
fof('$tdef_$_type_27947',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__27947___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__27947___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21426',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21426___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21426___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_5304',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5304___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5304___24a1(V_24X1)) ) ).
fof('$tdef_$_type_17708',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17708___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17708___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_949',axiom,
! [V_24Y] :
( c_24__type__949___24t(V_24Y)
<=> t(V_24Y,c_24__type__949) ) ).
fof('$tdef_$_type_33884',axiom,
! [V_24Y] :
( c_24__type__33884___24t(V_24Y)
<=> t(V_24Y,c_24__type__33884) ) ).
fof('$tdef_$_type_1845',axiom,
! [V_24Y] :
( c_24__type__1845___24t(V_24Y)
<=> t(V_24Y,c_24__type__1845) ) ).
fof('$tdef_$_type_30447',axiom,
! [V_24Y] :
( c_24__type__30447___24t(V_24Y)
<=> t(V_24Y,c_24__type__30447) ) ).
fof('$tdef_$_type_257',axiom,
! [V_24Y] :
( c_24__type__257___24t(V_24Y)
<=> t(V_24Y,c_24__type__257) ) ).
fof('$tdef_$_type_23438',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23438___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23438___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_787',axiom,
! [V_24Y] :
( c_24__type__787___24t(V_24Y)
<=> t(V_24Y,c_24__type__787) ) ).
fof('$tdef_$_type_28124',axiom,
! [V_24Y] :
( c_24__type__28124___24t(V_24Y)
<=> t(V_24Y,c_24__type__28124) ) ).
fof('$tdef_$_type_10',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35871',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35871___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35871___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34112',axiom,
! [V_24Y] :
( c_24__type__34112___24t(V_24Y)
<=> t(V_24Y,c_24__type__34112) ) ).
fof('$tdef_$_type_24732',axiom,
! [V_24Y] :
( c_24__type__24732___24t(V_24Y)
<=> t(V_24Y,c_24__type__24732) ) ).
fof('$tdef_$_type_1918',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1918___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1918___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21801',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__21801___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__21801___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1906',axiom,
! [V_24Y] :
( c_24__type__1906___24t(V_24Y)
<=> t(V_24Y,c_24__type__1906) ) ).
fof('$tdef_$_type_20023',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20023___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20023___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_24403',axiom,
! [V_24Y] :
( c_24__type__24403___24t(V_24Y)
<=> t(V_24Y,c_24__type__24403) ) ).
fof('$tdef_$_type_24712',axiom,
! [V_24Y] :
( c_24__type__24712___24t(V_24Y)
<=> t(V_24Y,c_24__type__24712) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.linear',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1)) ) ).
fof('$tdef_$_type_90',axiom,
! [V_24Y] :
( c_24__type__90___24t(V_24Y)
<=> t(V_24Y,c_24__type__90) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_33779',axiom,
! [V_24Y] :
( c_24__type__33779___24t(V_24Y)
<=> t(V_24Y,c_24__type__33779) ) ).
fof('$tdef_$_type_31844',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__31844___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__31844___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_20857',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20857___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20857___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_803',axiom,
! [V_24Y] :
( c_24__type__803___24t(V_24Y)
<=> t(V_24Y,c_24__type__803) ) ).
fof('$tdef_$_type_31685',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31685___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31685___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_31666',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31666___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31666___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_33523',axiom,
! [V_24Y] :
( c_24__type__33523___24t(V_24Y)
<=> t(V_24Y,c_24__type__33523) ) ).
fof('$tdef_$_type_1735',axiom,
! [V_24Y] :
( c_24__type__1735___24t(V_24Y)
<=> t(V_24Y,c_24__type__1735) ) ).
fof('$tdef_$_type_17352',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17352___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17352___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_22011',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22011___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22011___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_32274',axiom,
! [V_24Y] :
( c_24__type__32274___24t(V_24Y)
<=> t(V_24Y,c_24__type__32274) ) ).
fof('$tdef_$_type_831',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__831___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__831___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_25406',axiom,
! [V_24Y] :
( c_24__type__25406___24t(V_24Y)
<=> t(V_24Y,c_24__type__25406) ) ).
fof('$tdef_$_type_23493',axiom,
! [V_24Y] :
( c_24__type__23493___24t(V_24Y)
<=> t(V_24Y,c_24__type__23493) ) ).
fof('$tdef_$_type_492',axiom,
! [V_24Y] :
( c_24__type__492___24t(V_24Y)
<=> t(V_24Y,c_24__type__492) ) ).
fof('$tdef_$_type_17654',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17654___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17654___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_23348',axiom,
! [V_24Y] :
( c_24__type__23348___24t(V_24Y)
<=> t(V_24Y,c_24__type__23348) ) ).
fof('$tdef_$_type_28232',axiom,
! [V_24Y] :
( c_24__type__28232___24t(V_24Y)
<=> t(V_24Y,c_24__type__28232) ) ).
fof('$tdef_$_type_255',axiom,
! [V_24Y] :
( c_24__type__255___24t(V_24Y)
<=> t(V_24Y,c_24__type__255) ) ).
fof('$tdef_$_type_22157',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22157___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22157___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34266',axiom,
! [V_24Y] :
( c_24__type__34266___24t(V_24Y)
<=> t(V_24Y,c_24__type__34266) ) ).
fof('$tdef_$_type_24188',axiom,
! [V_24Y] :
( c_24__type__24188___24t(V_24Y)
<=> t(V_24Y,c_24__type__24188) ) ).
fof('$tdef_$_type_2011',axiom,
! [V_24Y] :
( c_24__type__2011___24t(V_24Y)
<=> t(V_24Y,c_24__type__2011) ) ).
fof('$tdef_$_type_33187',axiom,
! [V_24Y] :
( c_24__type__33187___24t(V_24Y)
<=> t(V_24Y,c_24__type__33187) ) ).
fof('$tdef_$_type_32666',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__32666___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__32666___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_83',axiom,
! [V_24X1,V_24Y] :
( c_24__type__83___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__83___24a1(V_24X1)) ) ).
fof('$tdef_$_type_934',axiom,
! [V_24Y] :
( c_24__type__934___24t(V_24Y)
<=> t(V_24Y,c_24__type__934) ) ).
fof('$tdef_$_type_33002',axiom,
! [V_24Y] :
( c_24__type__33002___24t(V_24Y)
<=> t(V_24Y,c_24__type__33002) ) ).
fof('$tdef_$_type_26647',axiom,
! [V_24Y] :
( c_24__type__26647___24t(V_24Y)
<=> t(V_24Y,c_24__type__26647) ) ).
fof('$tdef_$_type_2664',axiom,
! [V_24Y] :
( c_24__type__2664___24t(V_24Y)
<=> t(V_24Y,c_24__type__2664) ) ).
fof('$tdef_$_type_33585',axiom,
! [V_24Y] :
( c_24__type__33585___24t(V_24Y)
<=> t(V_24Y,c_24__type__33585) ) ).
fof('$tdef_$_type_33359',axiom,
! [V_24Y] :
( c_24__type__33359___24t(V_24Y)
<=> t(V_24Y,c_24__type__33359) ) ).
fof('$tdef_$_type_33500',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__33500___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__33500___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1758',axiom,
! [V_24Y] :
( c_24__type__1758___24t(V_24Y)
<=> t(V_24Y,c_24__type__1758) ) ).
fof('$tdef_$_type_32307',axiom,
! [V_24Y] :
( c_24__type__32307___24t(V_24Y)
<=> t(V_24Y,c_24__type__32307) ) ).
fof('$tdef_$_type_34152',axiom,
! [V_24Y] :
( c_24__type__34152___24t(V_24Y)
<=> t(V_24Y,c_24__type__34152) ) ).
fof('$tdef_$_type_20662',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20662___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20662___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_3944',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3944___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3944___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_hahn.Zorn.Private.Equiv',axiom,
! [V_24X1,V_24Y] :
( chahn_2eZorn_2ePrivate_2eEquiv___24t(V_24X1,V_24Y)
<=> t(V_24Y,chahn_2eZorn_2ePrivate_2eEquiv___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28919',axiom,
! [V_24Y] :
( c_24__type__28919___24t(V_24Y)
<=> t(V_24Y,c_24__type__28919) ) ).
fof('$tdef_$_type_4679',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4679___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4679___24a1(V_24X1)) ) ).
fof('$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_5224',axiom,
! [V_24Y] :
( c_24__type__5224___24t(V_24Y)
<=> t(V_24Y,c_24__type__5224) ) ).
fof('$tdef_$_type_34117',axiom,
! [V_24Y] :
( c_24__type__34117___24t(V_24Y)
<=> t(V_24Y,c_24__type__34117) ) ).
fof('$tdef_$_type_3934',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3934___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3934___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_158',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__158___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__158___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3517',axiom,
! [V_24Y] :
( c_24__type__3517___24t(V_24Y)
<=> t(V_24Y,c_24__type__3517) ) ).
fof('$tdef_$_type_36311',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__36311___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__36311___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28146',axiom,
! [V_24Y] :
( c_24__type__28146___24t(V_24Y)
<=> t(V_24Y,c_24__type__28146) ) ).
fof('$tdef_$_type_20449',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20449___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20449___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_19189',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19189___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19189___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_6750',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__6750___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__6750___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4776',axiom,
! [V_24Y] :
( c_24__type__4776___24t(V_24Y)
<=> t(V_24Y,c_24__type__4776) ) ).
fof('$tdef_$_type_2036',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2036___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2036___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33660',axiom,
! [V_24Y] :
( c_24__type__33660___24t(V_24Y)
<=> t(V_24Y,c_24__type__33660) ) ).
fof('$tdef_$_type_4124',axiom,
! [V_24Y] :
( c_24__type__4124___24t(V_24Y)
<=> t(V_24Y,c_24__type__4124) ) ).
fof('$tdef_$_type_1568',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1568___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1568___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_31944',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__31944___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__31944___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_33155',axiom,
! [V_24Y] :
( c_24__type__33155___24t(V_24Y)
<=> t(V_24Y,c_24__type__33155) ) ).
fof('$tdef_$_type_24370',axiom,
! [V_24X1,V_24Y] :
( c_24__type__24370___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__24370___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1405',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1405___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1405___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_3',axiom,
! [V_24Y] :
( c_24__type__3___24t(V_24Y)
<=> t(V_24Y,c_24__type__3) ) ).
fof('$tdef_$_type_4873',axiom,
! [V_24Y] :
( c_24__type__4873___24t(V_24Y)
<=> t(V_24Y,c_24__type__4873) ) ).
fof('$tdef_$_type_187',axiom,
! [V_24Y] :
( c_24__type__187___24t(V_24Y)
<=> t(V_24Y,c_24__type__187) ) ).
fof('$tdef_$_type_19615',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19615___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19615___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_25634',axiom,
! [V_24Y] :
( c_24__type__25634___24t(V_24Y)
<=> t(V_24Y,c_24__type__25634) ) ).
fof('$tdef_$_type_961',axiom,
! [V_24Y] :
( c_24__type__961___24t(V_24Y)
<=> t(V_24Y,c_24__type__961) ) ).
fof('$tdef_$_type_3800',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__3800___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__3800___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_36222',axiom,
! [V_24Y] :
( c_24__type__36222___24t(V_24Y)
<=> t(V_24Y,c_24__type__36222) ) ).
fof('$tdef_$_type_810',axiom,
! [V_24Y] :
( c_24__type__810___24t(V_24Y)
<=> t(V_24Y,c_24__type__810) ) ).
fof('$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_3348',axiom,
! [V_24Y] :
( c_24__type__3348___24t(V_24Y)
<=> t(V_24Y,c_24__type__3348) ) ).
fof('$tdef_$_type_85',axiom,
! [V_24Y] :
( c_24__type__85___24t(V_24Y)
<=> t(V_24Y,c_24__type__85) ) ).
fof('$tdef_$_type_33146',axiom,
! [V_24Y] :
( c_24__type__33146___24t(V_24Y)
<=> t(V_24Y,c_24__type__33146) ) ).
fof('$tdef_$_type_17398',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17398___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17398___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_16615',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__16615___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__16615___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_23323',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23323___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23323___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_26929',axiom,
! [V_24Y] :
( c_24__type__26929___24t(V_24Y)
<=> t(V_24Y,c_24__type__26929) ) ).
fof('$tdef_$_type_21904',axiom,
! [V_24Y] :
( c_24__type__21904___24t(V_24Y)
<=> t(V_24Y,c_24__type__21904) ) ).
fof('$tdef_$_type_505',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__505___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__505___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_874',axiom,
! [V_24Y] :
( c_24__type__874___24t(V_24Y)
<=> t(V_24Y,c_24__type__874) ) ).
fof('$tdef_$_type_36268',axiom,
! [V_24Y] :
( c_24__type__36268___24t(V_24Y)
<=> t(V_24Y,c_24__type__36268) ) ).
fof('$tdef_$_type_23006',axiom,
! [V_24Y] :
( c_24__type__23006___24t(V_24Y)
<=> t(V_24Y,c_24__type__23006) ) ).
fof('$tdef_$_type_22238',axiom,
! [V_24Y] :
( c_24__type__22238___24t(V_24Y)
<=> t(V_24Y,c_24__type__22238) ) ).
fof('$tdef_$_type_35906',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35906___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35906___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_17460',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17460___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17460___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Bool.Bool.reflect',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_16732',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__16732___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__16732___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_21841',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__21841___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__21841___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_8499',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__8499___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__8499___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_22325',axiom,
! [V_24Y] :
( c_24__type__22325___24t(V_24Y)
<=> t(V_24Y,c_24__type__22325) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22760',axiom,
! [V_24Y] :
( c_24__type__22760___24t(V_24Y)
<=> t(V_24Y,c_24__type__22760) ) ).
fof('$tdef_$_type_5402',axiom,
! [V_24Y] :
( c_24__type__5402___24t(V_24Y)
<=> t(V_24Y,c_24__type__5402) ) ).
fof('$tdef_$_type_5239',axiom,
! [V_24Y] :
( c_24__type__5239___24t(V_24Y)
<=> t(V_24Y,c_24__type__5239) ) ).
fof('$tdef_$_type_3372',axiom,
! [V_24Y] :
( c_24__type__3372___24t(V_24Y)
<=> t(V_24Y,c_24__type__3372) ) ).
fof('$tdef_$_type_33346',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33346___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33346___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32125',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32125___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32125___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_33199',axiom,
! [V_24Y] :
( c_24__type__33199___24t(V_24Y)
<=> t(V_24Y,c_24__type__33199) ) ).
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_$_type_220',axiom,
! [V_24Y] :
( c_24__type__220___24t(V_24Y)
<=> t(V_24Y,c_24__type__220) ) ).
fof('$tdef_$_type_4593',axiom,
! [V_24Y] :
( c_24__type__4593___24t(V_24Y)
<=> t(V_24Y,c_24__type__4593) ) ).
fof('$tdef_$_type_25215',axiom,
! [V_24X1,V_24Y] :
( c_24__type__25215___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__25215___24a1(V_24X1)) ) ).
fof('$tdef_$_type_292',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__292___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__292___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_$_type_5542',axiom,
! [V_24Y] :
( c_24__type__5542___24t(V_24Y)
<=> t(V_24Y,c_24__type__5542) ) ).
fof('$tdef_$_type_17600',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17600___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17600___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_$_type_10110',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__10110___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__10110___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_21766',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__21766___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__21766___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_21462',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21462___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21462___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_939',axiom,
! [V_24Y] :
( c_24__type__939___24t(V_24Y)
<=> t(V_24Y,c_24__type__939) ) ).
fof('$tdef_$_type_914',axiom,
! [V_24Y] :
( c_24__type__914___24t(V_24Y)
<=> t(V_24Y,c_24__type__914) ) ).
fof('$tdef_$_type_34167',axiom,
! [V_24Y] :
( c_24__type__34167___24t(V_24Y)
<=> t(V_24Y,c_24__type__34167) ) ).
fof('$tdef_$_type_33481',axiom,
! [V_24Y] :
( c_24__type__33481___24t(V_24Y)
<=> t(V_24Y,c_24__type__33481) ) ).
fof('$tdef_$_type_25788',axiom,
! [V_24Y] :
( c_24__type__25788___24t(V_24Y)
<=> t(V_24Y,c_24__type__25788) ) ).
fof('$tdef_$_type_24074',axiom,
! [V_24Y] :
( c_24__type__24074___24t(V_24Y)
<=> t(V_24Y,c_24__type__24074) ) ).
fof('$tdef_$_type_5029',axiom,
! [V_24Y] :
( c_24__type__5029___24t(V_24Y)
<=> t(V_24Y,c_24__type__5029) ) ).
fof('$tdef_$_type_33726',axiom,
! [V_24Y] :
( c_24__type__33726___24t(V_24Y)
<=> t(V_24Y,c_24__type__33726) ) ).
fof('$tdef_$_type_20236',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20236___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20236___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_33076',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33076___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33076___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Datatypes.prod',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28193',axiom,
! [V_24Y] :
( c_24__type__28193___24t(V_24Y)
<=> t(V_24Y,c_24__type__28193) ) ).
fof('$tdef_$_type_25793',axiom,
! [V_24Y] :
( c_24__type__25793___24t(V_24Y)
<=> t(V_24Y,c_24__type__25793) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Formula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_52',axiom,
! [V_24Y] :
( c_24__type__52___24t(V_24Y)
<=> t(V_24Y,c_24__type__52) ) ).
fof('$tdef_$_type_509',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__509___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__509___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_16552',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__16552___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__16552___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_23288',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23288___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23288___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_63',axiom,
! [V_24Y] :
( c_24__type__63___24t(V_24Y)
<=> t(V_24Y,c_24__type__63) ) ).
fof('$tdef_$_type_2913',axiom,
! [V_24Y] :
( c_24__type__2913___24t(V_24Y)
<=> t(V_24Y,c_24__type__2913) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4781',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4781___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4781___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33339',axiom,
! [V_24Y] :
( c_24__type__33339___24t(V_24Y)
<=> t(V_24Y,c_24__type__33339) ) ).
fof('$tdef_Coq.Init.Datatypes.ID',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).
fof('$tdef_$_type_24284',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__24284___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__24284___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_33310',axiom,
! [V_24Y] :
( c_24__type__33310___24t(V_24Y)
<=> t(V_24Y,c_24__type__33310) ) ).
fof('$tdef_$_type_28060',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__28060___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__28060___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_3585',axiom,
! [V_24Y] :
( c_24__type__3585___24t(V_24Y)
<=> t(V_24Y,c_24__type__3585) ) ).
fof('$tdef_$_type_1896',axiom,
! [V_24Y] :
( c_24__type__1896___24t(V_24Y)
<=> t(V_24Y,c_24__type__1896) ) ).
fof('$tdef_$_type_902',axiom,
! [V_24Y] :
( c_24__type__902___24t(V_24Y)
<=> t(V_24Y,c_24__type__902) ) ).
fof('$tdef_$_type_34240',axiom,
! [V_24Y] :
( c_24__type__34240___24t(V_24Y)
<=> t(V_24Y,c_24__type__34240) ) ).
fof('$tdef_$_type_35894',axiom,
! [V_24Y] :
( c_24__type__35894___24t(V_24Y)
<=> t(V_24Y,c_24__type__35894) ) ).
fof('$tdef_$_type_17416',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17416___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17416___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
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_$_type_864',axiom,
! [V_24Y] :
( c_24__type__864___24t(V_24Y)
<=> t(V_24Y,c_24__type__864) ) ).
fof('$tdef_Coq.Sets.Relations_1.Relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3413',axiom,
! [V_24Y] :
( c_24__type__3413___24t(V_24Y)
<=> t(V_24Y,c_24__type__3413) ) ).
fof('$tdef_$_type_209',axiom,
! [V_24Y] :
( c_24__type__209___24t(V_24Y)
<=> t(V_24Y,c_24__type__209) ) ).
fof('$tdef_$_type_1929',axiom,
! [V_24Y] :
( c_24__type__1929___24t(V_24Y)
<=> t(V_24Y,c_24__type__1929) ) ).
fof('$tdef_$_type_17329',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17329___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17329___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_13',axiom,
! [V_24X1,V_24Y] :
( c_24__type__13___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__13___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35853',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35853___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35853___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22085',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22085___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22085___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_9273',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__9273___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__9273___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_21506',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21506___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21506___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_9475',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__9475___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__9475___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_33129',axiom,
! [V_24Y] :
( c_24__type__33129___24t(V_24Y)
<=> t(V_24Y,c_24__type__33129) ) ).
fof('$tdef_$_type_24663',axiom,
! [V_24Y] :
( c_24__type__24663___24t(V_24Y)
<=> t(V_24Y,c_24__type__24663) ) ).
fof('$tdef_$_type_17442',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17442___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17442___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_479',axiom,
! [V_24Y] :
( c_24__type__479___24t(V_24Y)
<=> t(V_24Y,c_24__type__479) ) ).
fof('$tdef_$_type_25782',axiom,
! [V_24Y] :
( c_24__type__25782___24t(V_24Y)
<=> t(V_24Y,c_24__type__25782) ) ).
fof('$tdef_$_type_890',axiom,
! [V_24Y] :
( c_24__type__890___24t(V_24Y)
<=> t(V_24Y,c_24__type__890) ) ).
fof('$tdef_$_type_1833',axiom,
! [V_24Y] :
( c_24__type__1833___24t(V_24Y)
<=> t(V_24Y,c_24__type__1833) ) ).
fof('$tdef_$_type_35862',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35862___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35862___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_17792',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17792___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17792___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_23400',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23400___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23400___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_25605',axiom,
! [V_24Y] :
( c_24__type__25605___24t(V_24Y)
<=> t(V_24Y,c_24__type__25605) ) ).
fof('$tdef_$_type_8276',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__8276___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__8276___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34263',axiom,
! [V_24Y] :
( c_24__type__34263___24t(V_24Y)
<=> t(V_24Y,c_24__type__34263) ) ).
fof('$tdef_$_type_1827',axiom,
! [V_24Y] :
( c_24__type__1827___24t(V_24Y)
<=> t(V_24Y,c_24__type__1827) ) ).
fof('$tdef_$_type_78',axiom,
! [V_24Y] :
( c_24__type__78___24t(V_24Y)
<=> t(V_24Y,c_24__type__78) ) ).
fof('$tdef_$_type_1740',axiom,
! [V_24Y] :
( c_24__type__1740___24t(V_24Y)
<=> t(V_24Y,c_24__type__1740) ) ).
fof('$tdef_$_type_35755',axiom,
! [V_24Y] :
( c_24__type__35755___24t(V_24Y)
<=> t(V_24Y,c_24__type__35755) ) ).
fof('$tdef_$_type_17741',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17741___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17741___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_22050',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__22050___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__22050___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_25210',axiom,
! [V_24Y] :
( c_24__type__25210___24t(V_24Y)
<=> t(V_24Y,c_24__type__25210) ) ).
fof('$tdef_$_type_9576',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9576___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9576___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3482',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__3482___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__3482___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_27149',axiom,
! [V_24Y] :
( c_24__type__27149___24t(V_24Y)
<=> t(V_24Y,c_24__type__27149) ) ).
fof('$tdef_$_type_31699',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31699___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31699___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_22888',axiom,
! [V_24Y] :
( c_24__type__22888___24t(V_24Y)
<=> t(V_24Y,c_24__type__22888) ) ).
fof('$tdef_$_type_6657',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6657___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6657___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4150',axiom,
! [V_24Y] :
( c_24__type__4150___24t(V_24Y)
<=> t(V_24Y,c_24__type__4150) ) ).
fof('$tdef_$_type_823',axiom,
! [V_24Y] :
( c_24__type__823___24t(V_24Y)
<=> t(V_24Y,c_24__type__823) ) ).
fof('$tdef_$_type_4814',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4814___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4814___24a1(V_24X1)) ) ).
fof('$tdef_$_type_9183',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9183___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9183___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4586',axiom,
! [V_24Y] :
( c_24__type__4586___24t(V_24Y)
<=> t(V_24Y,c_24__type__4586) ) ).
fof('$tdef_$_type_21278',axiom,
! [V_24Y] :
( c_24__type__21278___24t(V_24Y)
<=> t(V_24Y,c_24__type__21278) ) ).
fof('$tdef_$_type_3778',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__3778___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__3778___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_24392',axiom,
! [V_24Y] :
( c_24__type__24392___24t(V_24Y)
<=> t(V_24Y,c_24__type__24392) ) ).
fof('$tdef_$_type_23255',axiom,
! [V_24Y] :
( c_24__type__23255___24t(V_24Y)
<=> t(V_24Y,c_24__type__23255) ) ).
fof('$tdef_$_type_24309',axiom,
! [V_24Y] :
( c_24__type__24309___24t(V_24Y)
<=> t(V_24Y,c_24__type__24309) ) ).
fof('_HAMMER_GOAL',conjecture,
cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(cA,cHahnTotalExt_2etot__ext___24a3(cA,cdom,cr)) ).
%------------------------------------------------------------------------------