TPTP Problem File: SEV675+1.p
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%------------------------------------------------------------------------------
% File : SEV675+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - TaitCoreNc NormalizationProofNc app ass
% 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 : TaitCoreNc.NormalizationProofNc.app'.ass.p [Kal26]
% Status : Theorem
% Rating : 0.91 v9.3.0
% Syntax : Number of formulae : 3188 (1271 unt; 0 def)
% Number of atoms : 11962 (3403 equ)
% Maximal formula atoms : 413 ( 3 avg)
% Number of connectives : 8875 ( 101 ~; 969 |;2372 &)
% (1248 <=>;4185 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 7 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 640 ( 639 usr; 0 prp; 1-23 aty)
% Number of functors : 1891 (1891 usr;1211 con; 0-22 aty)
% Number of variables : 11422 (10382 !;1040 ?)
% 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$15359',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2415446___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2415359___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__15363] :
( t(Vvar__1___24Anonymous__15363,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__15364] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__15364)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2415446___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__15363,Vvar__2___24Anonymous__15364)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2415359___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__15363,c_24__fix__15491__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__15364,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$15446',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2415446___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__15450] :
( t(Vvar__1___24Anonymous__15450,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__15451] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__15451)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__15450,Vvar__2___24Anonymous__15451)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2415446___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__15450,c_24__fix__15491__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__15451,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$37850',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2437850___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__37851] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__37851)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__37851)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2437850___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__37851)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$37872',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2437872___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__37873] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__37873)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__37873)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2437872___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__37873)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$28377',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__28390___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__28382] :
( t(Vvar__2___24Anonymous__28382,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__28383] :
( t(Vvar__3___24Anonymous__28383,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__28382,Vvar__3___24Anonymous__28383)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2428377___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__28382)),Vvar__3___24Anonymous__28383)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Specif.sumbool$12598',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( c_24__type__12431___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__3 = Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__12610___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__12611___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_2412598___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__let__var__var__7__n__12567__12571__12580___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)) )
| ( Vv__CANONICAL__3 != Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__12612___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__12613___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_2412598___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__let__var__var__7__n__12567__12571__12580___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$35204',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZ0
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2435204___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) )
| ? [Vvar__0___24Anonymous__35205] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35205)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35205)
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2435204___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__35205) ) )
| ? [Vvar__0___24Anonymous__35206] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35206)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35206)
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2435204___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__1 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__35206) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$37867',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2437872___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2437867___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__37868] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37868)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2437872___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37868)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2437867___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37868) )
| ? [Vvar__0___24Anonymous__37869] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37869)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2437872___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37869)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2437867___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37869) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.positive$46022',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__46023] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46023)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__46023)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2446022___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__46038__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__46023)) )
| ? [Vvar__0___24Anonymous__46030] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46030)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__46030)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2446022___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__46030) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2446022___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_case_Coq.setoid_ring.Ring_polynom.Pol$10401',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__10404] :
( t(Vvar__1___24Anonymous__10404,Vv__CANONICAL__8)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ( c_24__type__10424___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__11)
=> ( cType___24t(Vv__CANONICAL__13)
=> ( t(Vvar__1___24Anonymous__10404,Vv__CANONICAL__8)
=> ( Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vv__CANONICAL__8,Vvar__1___24Anonymous__10404)
& ( ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__10404),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2410401___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__10097___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__10404),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2410401___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__10097___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__10407] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10407)
& ? [Vvar__2___24Anonymous__10408] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__2___24Anonymous__10408)
& Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vv__CANONICAL__8,Vvar__1___24Anonymous__10407,Vvar__2___24Anonymous__10408)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2410401___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__10097___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__10411] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__1___24Anonymous__10411)
& ? [Vvar__2___24Anonymous__10412] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__10412)
& ? [Vvar__3___24Anonymous__10413] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__3___24Anonymous__10413)
& Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vv__CANONICAL__8,Vvar__1___24Anonymous__10411,Vvar__2___24Anonymous__10412,Vvar__3___24Anonymous__10413)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2410401___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__10097___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_$_cast_13804',axiom,
! [V0__A] : c_24__cast__13804___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ).
fof('$_def_$_cast_35424',axiom,
! [Vvar__35425] :
( c_24__cast__35424___24t(Vvar__35425)
<=> cTait_2eTerm_2etype___24t(Vvar__35425) ) ).
fof('$_def_$_cast_35426',axiom,
! [Vvar__35427] :
( c_24__cast__35426___24t(Vvar__35427)
<=> cTait_2eTerm_2etype___24t(Vvar__35427) ) ).
fof('$_def_$_cast_35428',axiom,
! [Vvar__35429] :
( c_24__cast__35428___24t(Vvar__35429)
<=> cTait_2eTerm_2etype___24t(Vvar__35429) ) ).
fof('$_def_$_cast_35430',axiom,
! [Vvar__35431] :
( c_24__cast__35430___24t(Vvar__35431)
<=> cTait_2eTerm_2etype___24t(Vvar__35431) ) ).
fof('$_def_$_cast_35432',axiom,
! [Vvar__35433] :
( c_24__cast__35432___24t(Vvar__35433)
<=> cTait_2eTerm_2etype___24t(Vvar__35433) ) ).
fof('$_def_$_cast_35434',axiom,
! [Vvar__35435] :
( c_24__cast__35434___24t(Vvar__35435)
<=> cTait_2eTerm_2etype___24t(Vvar__35435) ) ).
fof('$_def_$_cast_35436',axiom,
! [Vvar__35437] :
( c_24__cast__35436___24t(Vvar__35437)
<=> cTait_2eTerm_2etype___24t(Vvar__35437) ) ).
fof('$_def_$_cast_35438',axiom,
! [Vvar__35439] :
( c_24__cast__35438___24t(Vvar__35439)
<=> cTait_2eTerm_2etype___24t(Vvar__35439) ) ).
fof('$_def_$_cast_35440',axiom,
! [Vvar__35441] :
( c_24__cast__35440___24t(Vvar__35441)
<=> cTait_2eTerm_2etype___24t(Vvar__35441) ) ).
fof('$_def_$_cast_35442',axiom,
! [Vvar__35443] :
( c_24__cast__35442___24t(Vvar__35443)
<=> cTait_2eTerm_2etype___24t(Vvar__35443) ) ).
fof('$_def_$_cast_35444',axiom,
! [Vvar__35445] :
( c_24__cast__35444___24t(Vvar__35445)
<=> cTait_2eTerm_2etype___24t(Vvar__35445) ) ).
fof('$_def_$_cast_35446',axiom,
! [Vvar__35447] :
( c_24__cast__35446___24t(Vvar__35447)
<=> cTait_2eTerm_2etype___24t(Vvar__35447) ) ).
fof('$_def_$_cast_35448',axiom,
! [Vvar__35449] :
( c_24__cast__35448___24t(Vvar__35449)
<=> cTait_2eTerm_2etype___24t(Vvar__35449) ) ).
fof('$_def_$_cast_35450',axiom,
! [Vvar__35451] :
( c_24__cast__35450___24t(Vvar__35451)
<=> cTait_2eTerm_2etype___24t(Vvar__35451) ) ).
fof('$_def_$_cast_35452',axiom,
! [Vvar__35453] :
( c_24__cast__35452___24t(Vvar__35453)
<=> cTait_2eTerm_2etype___24t(Vvar__35453) ) ).
fof('$_def_$_cast_35454',axiom,
! [Vvar__35455] :
( c_24__cast__35454___24t(Vvar__35455)
<=> cTait_2eTerm_2etype___24t(Vvar__35455) ) ).
fof('$_def_$_let_11_subst_l_20426',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__20426___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_23561',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__23564] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23564)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23564)
& c_24__let__16__mkpow__23561___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__23565] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23565)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23565)
& c_24__let__16__mkpow__23561___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__23561___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_mkopp_pow_23562',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__23562___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__23561___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_23563',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__23563___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__23561___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_20_lnum_10097',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num] : c_24__let__20__lnum__10097___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num) ).
fof('$_def_$_let_var_6_p_24281_24284',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24280] : c_24__let__var__6__p__24281__24284___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24280) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24280) ).
fof('$_def_$_let_var_6_p_24283_24285',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24282] : c_24__let__var__6__p__24283__24285___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24282) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24282) ).
fof('$_def_$_let_var_v_CANONICAL_4_683_687',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__0___24Anonymous__682] : c_24__let__var__v__CANONICAL__4__683__687___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__0___24Anonymous__682) = happ(Vv__CANONICAL__1,Vvar__0___24Anonymous__682) ).
fof('$_def_$_let_var_var_7_n_12567_12571_12580',axiom,
! [V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__12564] : c_24__let__var__var__7__n__12567__12571__12580___24a4(V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__12564) = cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,Vvar__2___24Anonymous__12564,V4__x) ).
fof('$_def_Coq.Arith.Compare_dec.le_gt_dec',axiom,
! [V0__n,V1__m] : cCoq_2eArith_2eCompare__dec_2ele__gt__dec___24a2(V0__n,V1__m) = cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V0__n,V1__m) ).
fof('$_def_Coq.Arith.EqNat.eq_nat',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__35586] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35586)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35586)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__35587] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35587)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35587)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__35590] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35590)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35590)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__35587,Vvar__0___24Anonymous__35590) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eq',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eq_dec',axiom,
! [V0__n] : cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enat__rec___24a4(c_24__lam__588,c_24__lam__596,c_24__lam__681,V0__n) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.Arith.Wf_nat.ltof',axiom,
! [V0__A,V1__f,V2__a,V3__b] :
( cCoq_2eArith_2eWf__nat_2eltof___24a4(V0__A,V1__f,V2__a,V3__b)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(happ(V1__f,V2__a),happ(V1__f,V3__b))) ) ).
fof('$_def_Coq.Bool.Bool.Is_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24True) ) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24False) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.eqb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.E.eq',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V0__s)
<=> ! [V1__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__a)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__a,V0__s) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
! [V0__i,V1__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__i,V1__t)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__i,V1__t) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.add',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& ( ? [Vvar__0___24Anonymous__35115] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35115)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35115)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__35115,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf)) )
| ? [Vvar__0___24Anonymous__35116] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35116)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35116)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__35116,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf),cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ) ) ) )
| ? [Vvar__0___24Anonymous__35117] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__35117)
& ? [Vvar__1___24Anonymous__35118] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__35118)
& ? [Vvar__2___24Anonymous__35119] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__35119)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__35117,Vvar__1___24Anonymous__35118,Vvar__2___24Anonymous__35119)
& ( ? [Vvar__0___24Anonymous__35132] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35132)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35132)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__35117,Vvar__1___24Anonymous__35118,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__35132,Vvar__2___24Anonymous__35119)) )
| ? [Vvar__0___24Anonymous__35133] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35133)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35133)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__35133,Vvar__0___24Anonymous__35117),Vvar__1___24Anonymous__35118,Vvar__2___24Anonymous__35119) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__35117,cCoq_2eInit_2eDatatypes_2etrue,Vvar__2___24Anonymous__35119) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.cardinal',axiom,
! [V1__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__m)
=> ( ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V1__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__35169] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__35169)
& ? [Vvar__1___24Anonymous__35170] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__35170)
& ? [Vvar__2___24Anonymous__35171] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__35171)
& ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__35170)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__35169,Vvar__1___24Anonymous__35170,Vvar__2___24Anonymous__35171)
& ( ( Vvar__1___24Anonymous__35170 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V1__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(Vvar__0___24Anonymous__35169),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(Vvar__2___24Anonymous__35171))) )
| ( Vvar__1___24Anonymous__35170 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(Vvar__0___24Anonymous__35169),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(Vvar__2___24Anonymous__35171)) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elements',axiom,
! [V0__m] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V0__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V0__m,cCoq_2eNumbers_2eBinNums_2exH,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt)) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__35099] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__35099)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__35099) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.fold',axiom,
! [V0__B,V1__f,V2__m,V3__i] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold___24a4(V0__B,V1__f,V2__m,V3__i) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfold___24a5(V0__B,V1__f,V2__m,V3__i,cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__46097] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__46097)
& ? [Vvar__1___24Anonymous__46098] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__46098)
& ? [Vvar__2___24Anonymous__46099] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__46099)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__46097,Vvar__1___24Anonymous__46098,Vvar__2___24Anonymous__46099)
& ( ? [Vvar__0___24Anonymous__46112] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46112)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__46112)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__46112,Vvar__2___24Anonymous__46099) )
| ? [Vvar__0___24Anonymous__46113] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46113)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__46113)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__46113,Vvar__0___24Anonymous__46097) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__46098 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.rev',axiom,
! [V0__x] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev___24a1(V0__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
! [V1__y,V2__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__y)
=> ( ? [Vvar__0___24Anonymous__46118] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46118)
& V1__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__46118)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__46118,cCoq_2eNumbers_2eBinNums_2exI___24a1(V2__x)) )
| ? [Vvar__0___24Anonymous__46119] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46119)
& V1__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__46119)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__46119,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__x)) )
| ( V1__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = V2__x ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__35113] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__35113)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__35113) ) ).
fof('$_def_Coq.Init.Datatypes.IDProp',axiom,
( p(cCoq_2eInit_2eDatatypes_2eIDProp)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> p(V0__A) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.andb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__64] :
( t(Vvar__1___24Anonymous__64,V0__A)
& ? [Vvar__2___24Anonymous__65] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__65)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__64,Vvar__2___24Anonymous__65)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__64,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__65,V3__m)) ) ) ) ) ) ).
fof('$_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__2762] :
( t(Vvar__2___24Anonymous__2762,V0__A)
& ? [Vvar__3___24Anonymous__2763] :
( t(Vvar__3___24Anonymous__2763,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__2762,Vvar__3___24Anonymous__2763)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__2762 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__234] :
( t(Vvar__1___24Anonymous__234,V0__A)
& ? [Vvar__2___24Anonymous__235] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__235)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__234,Vvar__2___24Anonymous__235)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__235)) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Datatypes.list_rect',axiom,
! [V0__A,V1__P,V2__f,V3__f,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__2792___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = V2__f )
| ? [Vvar__1___24Anonymous__2786] :
( t(Vvar__1___24Anonymous__2786,V0__A)
& ? [Vvar__2___24Anonymous__2787] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2787)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2786,Vvar__2___24Anonymous__2787)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = happ(happ(happ(V3__f,Vvar__1___24Anonymous__2786),Vvar__2___24Anonymous__2787),cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,Vvar__2___24Anonymous__2787)) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__2698___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
| ? [Vvar__0___24Anonymous__2696] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2696)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2696)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__2696),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__2696)) ) ) ) ) ).
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('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__2774] :
( t(Vvar__2___24Anonymous__2774,V0__A)
& ? [Vvar__3___24Anonymous__2775] :
( t(Vvar__3___24Anonymous__2775,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__2774,Vvar__3___24Anonymous__2775)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__2775 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.xorb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__268] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__268)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__268)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__268,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.even',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__36498] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36498)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36498)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36498)
& ( ( Vvar__0___24Anonymous__36498 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__36501] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36501)
& Vvar__0___24Anonymous__36498 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36501)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__36501) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__14649] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14649)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14649)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__14652] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14652)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14652)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__14649,Vvar__0___24Anonymous__14652)) ) ) ) ) ) ) ) ).
fof('$_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__14655] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14655)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14655)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__14658] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14658)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14658)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__14655,Vvar__0___24Anonymous__14658)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__36495] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36495)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36495)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__36495,V2__m)) ) ) ) ).
fof('$_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__1149] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1149)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1149)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__1149 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__408] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__408)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__408)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__411] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__411)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__411)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__408,Vvar__0___24Anonymous__411) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__30775___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__30769] :
( t(Vvar__2__x__30769,V0__A)
& p(happ(V1__P,Vvar__2__x__30769))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__30769)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__30769 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.sumbool_rec',axiom,
! [V0__A,V1__B,V2__P] : cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V0__A,V1__B,V2__P) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V0__A,V1__B,V2__P) ).
fof('$_def_Coq.Lists.List.ForallPairs',axiom,
! [V0__A,V1__R,V2__l] :
( cCoq_2eLists_2eList_2eForallPairs___24a3(V0__A,V1__R,V2__l)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__b,V2__l)
=> p(happ(happ(V1__R,V3__a),V4__b)) ) ) ) ) ) ).
fof('$_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)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__950] :
( t(Vvar__1___24Anonymous__950,V0__A)
& ? [Vvar__2___24Anonymous__951] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__951)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__950,Vvar__2___24Anonymous__951)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__950 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__951) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.combine',axiom,
! [V0__A,V1__B,V3__l,V4__l_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__13736] :
( t(Vvar__1___24Anonymous__13736,V0__A)
& ? [Vvar__2___24Anonymous__13737] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__13737)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l_27)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__13736,Vvar__2___24Anonymous__13737)
& ( ( V4__l_27 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__13748] :
( t(Vvar__1___24Anonymous__13748,V1__B)
& ? [Vvar__2___24Anonymous__13749] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__13749)
& V4__l_27 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__13748,Vvar__2___24Anonymous__13749)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__1___24Anonymous__13736,Vvar__1___24Anonymous__13748),cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,Vvar__2___24Anonymous__13737,Vvar__2___24Anonymous__13749)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__1024] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__1___24Anonymous__1024)
& ? [Vvar__2___24Anonymous__1025] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__1025)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__1___24Anonymous__1024,Vvar__2___24Anonymous__1025)
& cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__1___24Anonymous__1024,cCoq_2eLists_2eList_2econcat___24a2(V0__A,Vvar__2___24Anonymous__1025)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.count_occ',axiom,
! [V0__A,V1__eq__dec,V3__l,V4__x] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__12563] :
( t(Vvar__1___24Anonymous__12563,V0__A)
& ? [Vvar__2___24Anonymous__12564] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12564)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12563,Vvar__2___24Anonymous__12564)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_2412598___24a5(V0__A,V1__eq__dec,V4__x,Vvar__1___24Anonymous__12563,Vvar__2___24Anonymous__12564) ) ) ) ) ) ).
fof('$_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__13612] :
( t(Vvar__1___24Anonymous__13612,V0__A)
& ? [Vvar__2___24Anonymous__13613] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__13613)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__13612,Vvar__2___24Anonymous__13613)
& cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(happ(V1__f,Vvar__1___24Anonymous__13612),cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__13613)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.filter',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__1055] :
( t(Vvar__1___24Anonymous__1055,V0__A)
& ? [Vvar__2___24Anonymous__1056] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1056)
& ( cType___24t(V0__A)
=> ( c_24__type__1061___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__1055,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1055,Vvar__2___24Anonymous__1056)
& ( ( happ(V1__f,Vvar__1___24Anonymous__1055) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1055,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__1056)) )
| ( happ(V1__f,Vvar__1___24Anonymous__1055) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__1056) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__13639] :
( t(Vvar__1___24Anonymous__13639,V0__A)
& ? [Vvar__2___24Anonymous__13640] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__13640)
& ( cType___24t(V0__A)
=> ( c_24__type__1061___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__13639,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__13639,Vvar__2___24Anonymous__13640)
& ( ( happ(V1__f,Vvar__1___24Anonymous__13639) = 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__13639) )
| ( happ(V1__f,Vvar__1___24Anonymous__13639) = 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__13640) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.firstn',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__0___24Anonymous__1071] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1071)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1071)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__1078] :
( t(Vvar__1___24Anonymous__1078,V0__A)
& ? [Vvar__2___24Anonymous__1079] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1079)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1078,Vvar__2___24Anonymous__1079)
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1078,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,Vvar__0___24Anonymous__1071,Vvar__2___24Anonymous__1079)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__13438] :
( t(Vvar__1___24Anonymous__13438,V0__A)
& ? [Vvar__2___24Anonymous__13439] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__13439)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__13438,Vvar__2___24Anonymous__13439)
& 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__13438),cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__13439)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_left',axiom,
! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
| ? [Vvar__1___24Anonymous__13504] :
( t(Vvar__1___24Anonymous__13504,V1__B)
& ? [Vvar__2___24Anonymous__13505] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__13505)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__13504,Vvar__2___24Anonymous__13505)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__13505,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__13504)) ) ) ) ) ) ) ).
fof('$_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__13540] :
( t(Vvar__1___24Anonymous__13540,V1__B)
& ? [Vvar__2___24Anonymous__13541] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__13541)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__13540,Vvar__2___24Anonymous__13541)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__13540),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__13541)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.forallb',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__1___24Anonymous__13627] :
( t(Vvar__1___24Anonymous__13627,V0__A)
& ? [Vvar__2___24Anonymous__13628] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__13628)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__13627,Vvar__2___24Anonymous__13628)
& cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eandb___24a2(happ(V1__f,Vvar__1___24Anonymous__13627),cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__13628)) ) ) ) ) ) ).
fof('$_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__12285] :
( t(Vvar__1___24Anonymous__12285,V0__A)
& ? [Vvar__2___24Anonymous__12286] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12286)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12285,Vvar__2___24Anonymous__12286)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__12285 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd_error',axiom,
! [V0__A,V1__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__12296] :
( t(Vvar__1___24Anonymous__12296,V0__A)
& ? [Vvar__2___24Anonymous__12297] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12297)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12296,Vvar__2___24Anonymous__12297)
& cCoq_2eLists_2eList_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__12296) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.incl',axiom,
! [V0__A,V1__l,V2__m] :
( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__12519] :
( t(Vvar__1___24Anonymous__12519,V0__A)
& ? [Vvar__2___24Anonymous__12520] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12520)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12520)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12519,Vvar__2___24Anonymous__12520)
& ( ( Vvar__2___24Anonymous__12520 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__12519 )
| ? [Vvar__1___24Anonymous__12531] :
( t(Vvar__1___24Anonymous__12531,V0__A)
& ? [Vvar__2___24Anonymous__12532] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12532)
& Vvar__2___24Anonymous__12520 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12531,Vvar__2___24Anonymous__12532)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__12520,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.lel',axiom,
! [V0__A,V1__l,V2__m] :
( cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V2__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__m))) ) ).
fof('$_def_Coq.Lists.List.list_prod',axiom,
! [V0__A,V1__B,V3__l,V4__l_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__13781] :
( t(Vvar__1___24Anonymous__13781,V0__A)
& ? [Vvar__2___24Anonymous__13782] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__13782)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__13781,Vvar__2___24Anonymous__13782)
& cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eLists_2eList_2emap___24a4(V1__B,cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),c_24__lam__13789___24a3(V0__A,V1__B,Vvar__1___24Anonymous__13781),V4__l_27),cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,Vvar__2___24Anonymous__13782,V4__l_27)) ) ) ) ) ) ) ).
fof('$_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__1034] :
( t(Vvar__1___24Anonymous__1034,V0__A)
& ? [Vvar__2___24Anonymous__1035] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1035)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1034,Vvar__2___24Anonymous__1035)
& 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__1034),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__1035)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__246] :
( t(Vvar__1___24Anonymous__246,V0__A)
& ? [Vvar__2___24Anonymous__247] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__247)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__246,Vvar__2___24Anonymous__247)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__246 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__249] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__249)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__249)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__256] :
( t(Vvar__1___24Anonymous__256,V0__A)
& ? [Vvar__2___24Anonymous__257] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__257)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__256,Vvar__2___24Anonymous__257)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__249,Vvar__2___24Anonymous__257,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__12463] :
( t(Vvar__1___24Anonymous__12463,V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__12463)
& cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V1__default,V2__l,V3__n) = Vvar__1___24Anonymous__12463 )
| ( 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('$_def_Coq.Lists.List.nth_error',axiom,
! [V0__A,V2__l,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__962] :
( t(Vvar__1___24Anonymous__962,V0__A)
& ? [Vvar__2___24Anonymous__963] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__963)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__962,Vvar__2___24Anonymous__963)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__962) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__965] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__965)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__965)
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__972] :
( t(Vvar__1___24Anonymous__972,V0__A)
& ? [Vvar__2___24Anonymous__973] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__973)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__972,Vvar__2___24Anonymous__973)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,Vvar__2___24Anonymous__973,Vvar__0___24Anonymous__965) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__12440] :
( t(Vvar__1___24Anonymous__12440,V0__A)
& ? [Vvar__2___24Anonymous__12441] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12441)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12440,Vvar__2___24Anonymous__12441)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__12443] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12443)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12443)
& ( ( 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__12450] :
( t(Vvar__1___24Anonymous__12450,V0__A)
& ? [Vvar__2___24Anonymous__12451] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12451)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12450,Vvar__2___24Anonymous__12451)
& 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__12443,Vvar__2___24Anonymous__12451,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.removelast',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__984] :
( t(Vvar__1___24Anonymous__984,V0__A)
& ? [Vvar__2___24Anonymous__985] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__985)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__985)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__984,Vvar__2___24Anonymous__985)
& ( ( Vvar__2___24Anonymous__985 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__996] :
( t(Vvar__1___24Anonymous__996,V0__A)
& ? [Vvar__2___24Anonymous__997] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__997)
& Vvar__2___24Anonymous__985 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__996,Vvar__2___24Anonymous__997)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__984,cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,Vvar__2___24Anonymous__985)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.repeat',axiom,
! [V0__A,V2__x,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,V3__n) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__0___24Anonymous__14542] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14542)
& V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14542)
& cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,V3__n) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,Vvar__0___24Anonymous__14542)) ) ) ) ) ).
fof('$_def_Coq.Lists.List.rev',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__1006] :
( t(Vvar__1___24Anonymous__1006,V0__A)
& ? [Vvar__2___24Anonymous__1007] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1007)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1006,Vvar__2___24Anonymous__1007)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,Vvar__2___24Anonymous__1007),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1006,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Lists.List.rev_append',axiom,
! [V0__A,V2__l,V3__l_27] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V2__l,V3__l_27) = V3__l_27 )
| ? [Vvar__1___24Anonymous__1014] :
( t(Vvar__1___24Anonymous__1014,V0__A)
& ? [Vvar__2___24Anonymous__1015] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1015)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1014,Vvar__2___24Anonymous__1015)
& cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V2__l,V3__l_27) = cCoq_2eLists_2eList_2erev__append___24a3(V0__A,Vvar__2___24Anonymous__1015,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1014,V3__l_27)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.seq',axiom,
! [V1__start,V2__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__len)
=> ( ( V2__len = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__0___24Anonymous__13884] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13884)
& V2__len = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13884)
& cCoq_2eLists_2eList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,V1__start,cCoq_2eLists_2eList_2eseq___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__start),Vvar__0___24Anonymous__13884)) ) ) ) ).
fof('$_def_Coq.Lists.List.skipn',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = V3__l )
| ? [Vvar__0___24Anonymous__1087] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1087)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1087)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__1094] :
( t(Vvar__1___24Anonymous__1094,V0__A)
& ? [Vvar__2___24Anonymous__1095] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1095)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1094,Vvar__2___24Anonymous__1095)
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = cCoq_2eLists_2eList_2eskipn___24a3(V0__A,Vvar__0___24Anonymous__1087,Vvar__2___24Anonymous__1095) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__12305] :
( t(Vvar__1___24Anonymous__12305,V0__A)
& ? [Vvar__2___24Anonymous__12306] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12306)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12305,Vvar__2___24Anonymous__12306)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__12306 ) ) ) ) ) ).
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('$_def_Coq.Lists.SetoidList.transpose',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V6__z)))) ) ) ) ) ).
fof('$_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.NArith.BinNat.N.eq',axiom,
cCoq_2eNArith_2eBinNat_2eN_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.NArith.BinNat.N.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.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__35029] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35029)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35029)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__35032] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35032)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35032)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__35029,Vvar__0___24Anonymous__35032)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div_eucl',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
| ? [Vvar__0___24Anonymous__35048] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35048)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35048)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,V0__a) )
| ? [Vvar__0___24Anonymous__35051] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35051)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35051)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__35048,V1__b) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__35040] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35040)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35040)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__35041] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35041)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35041)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__35044] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35044)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35044)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__35041,Vvar__0___24Anonymous__35044) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__35034] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35034)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35034)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__35037] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35037)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35037)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__35034,Vvar__0___24Anonymous__35037)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__35055] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35055)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35055)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__35055) ) ) ) ).
fof('$_def_Coq.NArith.Ndigits.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eNdigits_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.eq',axiom,
cCoq_2ePArith_2eBinPos_2ePos_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__35065] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35065)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35065)
& ( ? [Vvar__0___24Anonymous__35069] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35069)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35069)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__35064__1__add__carry___24a2(Vvar__0___24Anonymous__35065,Vvar__0___24Anonymous__35069)) )
| ? [Vvar__0___24Anonymous__35070] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35070)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35070)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__35065,Vvar__0___24Anonymous__35070)) )
| ( 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__35065)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__35071] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35071)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35071)
& ( ? [Vvar__0___24Anonymous__35075] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35075)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35075)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__35071,Vvar__0___24Anonymous__35075)) )
| ? [Vvar__0___24Anonymous__35076] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35076)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35076)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__35071,Vvar__0___24Anonymous__35076)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35071) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__35077] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35077)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35077)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__35077)) )
| ? [Vvar__0___24Anonymous__35078] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35078)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35078)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35078) )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__46060] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46060)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__46060)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__46060),Vvar__0___24Anonymous__46060)) )
| ? [Vvar__0___24Anonymous__46061] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46061)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__46061)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__46061),Vvar__0___24Anonymous__46061) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
! [V0__A,V1__op,V3__p,V4__a] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__46073] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46073)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__46073)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__46073,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__46074] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46074)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__46074)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__46074,happ(happ(V1__op,V4__a),V4__a)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__35097] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35097)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35097)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35097)) )
| ? [Vvar__0___24Anonymous__35098] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35098)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35098)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__35098)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_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__46057] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46057)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__46057)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__46057 )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__35062] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35062)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35062)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__35062)) )
| ? [Vvar__0___24Anonymous__35063] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35063)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35063)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35063) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__37803] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__37803)
& ? [Vvar__1__Qden__37804] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__37804)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__37803,Vvar__1__Qden__37804)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__37804 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qdiv',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQdiv___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V0__x,cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V1__y)) ).
fof('$_def_Coq.QArith.QArith_base.Qeq',axiom,
! [V0__p,V1__q] :
( cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__p,V1__q)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__p),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__q))) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__q),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__p))) ) ).
fof('$_def_Coq.QArith.QArith_base.Qeq_bool',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)))) ).
fof('$_def_Coq.QArith.QArith_base.Qminus',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQminus___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQplus___24a2(V0__x,cCoq_2eQArith_2eQArith__base_2eQopp___24a1(V1__y)) ).
fof('$_def_Coq.QArith.QArith_base.Qmult',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y)),cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__37798] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__37798)
& ? [Vvar__1__Qden__37799] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__37799)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__37798,Vvar__1__Qden__37799)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__37798 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qopp',axiom,
! [V0__x] : cCoq_2eQArith_2eQArith__base_2eQopp___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x)),cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)) ).
fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
| ? [Vvar__0___24Anonymous__14907] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14907)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__14907)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__14907) )
| ? [Vvar__0___24Anonymous__14908] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14908)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__14908)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__14908)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__28776] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28776)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28776)
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r,cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,Vvar__0___24Anonymous__28776)) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__1173___24a1(V0__A) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__1173___24a1(V0__U) ).
fof('$_def_Coq.Strings.String.append',axiom,
! [V1__s1,V2__s2] :
( cCoq_2eStrings_2eString_2estring___24t(V1__s1)
=> ( ( V1__s1 = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2eappend___24a2(V1__s1,V2__s2) = V2__s2 )
| ? [Vvar__0___24Anonymous__30837] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__30837)
& ? [Vvar__1___24Anonymous__30838] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__30838)
& V1__s1 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__30837,Vvar__1___24Anonymous__30838)
& cCoq_2eStrings_2eString_2eappend___24a2(V1__s1,V2__s2) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__30837,cCoq_2eStrings_2eString_2eappend___24a2(Vvar__1___24Anonymous__30838,V2__s2)) ) ) ) ) ).
fof('$_def_Coq.Strings.String.list_ascii_of_string',axiom,
! [V1__s] :
( cCoq_2eStrings_2eString_2estring___24t(V1__s)
=> ( ( V1__s = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2elist__ascii__of__string___24a1(V1__s) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eStrings_2eAscii_2eascii) )
| ? [Vvar__0___24Anonymous__30875] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__30875)
& ? [Vvar__1___24Anonymous__30876] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__30876)
& V1__s = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__30875,Vvar__1___24Anonymous__30876)
& cCoq_2eStrings_2eString_2elist__ascii__of__string___24a1(V1__s) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eStrings_2eAscii_2eascii,Vvar__0___24Anonymous__30875,cCoq_2eStrings_2eString_2elist__ascii__of__string___24a1(Vvar__1___24Anonymous__30876)) ) ) ) ) ).
fof('$_def_Coq.Strings.String.string_of_list_ascii',axiom,
! [V1__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,V1__s)
=> ( ( V1__s = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eStrings_2eAscii_2eascii)
& cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(V1__s) = cCoq_2eStrings_2eString_2eEmptyString )
| ? [Vvar__1___24Anonymous__30869] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1___24Anonymous__30869)
& ? [Vvar__2___24Anonymous__30870] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,Vvar__2___24Anonymous__30870)
& V1__s = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eStrings_2eAscii_2eascii,Vvar__1___24Anonymous__30869,Vvar__2___24Anonymous__30870)
& cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(V1__s) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1___24Anonymous__30869,cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(Vvar__2___24Anonymous__30870)) ) ) ) ) ).
fof('$_def_Coq.Structures.DecidableTypeEx.N_as_DT.eq',axiom,
cCoq_2eStructures_2eDecidableTypeEx_2eN__as__DT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.Structures.DecidableTypeEx.Nat_as_DT.eq',axiom,
cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Structures.DecidableTypeEx.Positive_as_DT.eq',axiom,
cCoq_2eStructures_2eDecidableTypeEx_2ePositive__as__DT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.DecidableTypeEx.Z_as_DT.eq',axiom,
cCoq_2eStructures_2eDecidableTypeEx_2eZ__as__DT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [Vvar__45973] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__45973)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__45973) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt = cCoq_2eInit_2ePeano_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__45979] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__45979)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__45979) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__46089] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__46089)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__46089) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__46124] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__46124)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__46124) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__46126] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__46126)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__46126) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__46160] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__46160)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__46160) ) ).
fof('$_def_Coq.Vectors.Vector.to_list',axiom,
! [V0__A,V1__n,V2__v] : cCoq_2eVectors_2eVector_2eto__list___24a3(V0__A,V1__n,V2__v) = c_24__fix__33859__v__CANONICAL__2___24a5(V0__A,V1__n,V1__n,V2__v,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ).
fof('$_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__33859__v__CANONICAL__2___24a5(V0__A,V1__n,V1__n,V2__v,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ).
fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
& V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eq',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__46141] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46141)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__46141)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__46141) )
| ? [Vvar__0___24Anonymous__46142] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46142)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__46142)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__46142) ) ) ) ).
fof('$_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__701] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__701)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__701)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__705] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__705)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__705)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__701,Vvar__0___24Anonymous__705)) )
| ? [Vvar__0___24Anonymous__706] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__706)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__706)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__701,Vvar__0___24Anonymous__706) ) ) ) ) )
| ? [Vvar__0___24Anonymous__707] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__707)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__707)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__711] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__711)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__711)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__711,Vvar__0___24Anonymous__707) )
| ? [Vvar__0___24Anonymous__712] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__712)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__712)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__707,Vvar__0___24Anonymous__712)) ) ) ) ) ) ) ) ).
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__733] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__733)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__733)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__734] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__734)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__734)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__735] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__735)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__735)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__739] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__739)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__739)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__735,Vvar__0___24Anonymous__739) )
| ? [Vvar__0___24Anonymous__740] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__740)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__740)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__741] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__741)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__741)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__745] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__745)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__745)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__746] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__746)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__746)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__741,Vvar__0___24Anonymous__746)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.gtb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___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_2eBinIntDef_2eZ_2egtb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.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__720] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__720)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__720)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__724] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__724)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__724)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__720,Vvar__0___24Anonymous__724)) )
| ? [Vvar__0___24Anonymous__725] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__725)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__725)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__720,Vvar__0___24Anonymous__725)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__726] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__726)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__726)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__730] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__730)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__730)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__726,Vvar__0___24Anonymous__730)) )
| ? [Vvar__0___24Anonymous__731] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__731)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__731)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__726,Vvar__0___24Anonymous__731)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.odd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__46147] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46147)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46147)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__46147)
& ( ? [Vvar__0___24Anonymous__46151] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46151)
& Vvar__0___24Anonymous__46147 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__46151)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__46152] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46152)
& Vvar__0___24Anonymous__46147 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__46152)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__46147 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__46153] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46153)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46153)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__46153)
& ( ? [Vvar__0___24Anonymous__46157] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46157)
& Vvar__0___24Anonymous__46153 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__46157)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__46158] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46158)
& Vvar__0___24Anonymous__46153 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__46158)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__46153 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__35226] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35226)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35226)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35226) ) ) ) ).
fof('$_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__750] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__750)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__750)
& 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__750)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__716] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__716)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__716)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__716) )
| ? [Vvar__0___24Anonymous__717] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__717)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__717)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__717) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__46136] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46136)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__46136)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__46136) )
| ? [Vvar__0___24Anonymous__46137] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46137)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__46137)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__35229] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35229)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35229)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
| ? [Vvar__0___24Anonymous__35239] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35239)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35229)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35239)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35239)
& ? [Vvar__2___24Anonymous__35247] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__35247)
& ? [Vvar__3___24Anonymous__35248] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__35248)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__35229,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35239)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__35247,Vvar__3___24Anonymous__35248)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__35247),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__35248)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__35250] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35250)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35229)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35250)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35250)
& ? [Vvar__2___24Anonymous__35258] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__35258)
& ? [Vvar__3___24Anonymous__35259] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__35259)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__35229,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35250)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__35258,Vvar__3___24Anonymous__35259)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__35258)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__35259)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__35261] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35261)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35261)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
| ? [Vvar__0___24Anonymous__35271] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35271)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35261)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35271)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35271)
& ? [Vvar__2___24Anonymous__35279] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__35279)
& ? [Vvar__3___24Anonymous__35280] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__35280)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__35261,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35271)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__35279,Vvar__3___24Anonymous__35280)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__35279)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__35280))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__35282] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35282)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35261)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35282)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35282)
& ? [Vvar__2___24Anonymous__35290] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__35290)
& ? [Vvar__3___24Anonymous__35291] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__35291)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__35261,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35282)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__35290,Vvar__3___24Anonymous__35291)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__35290),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__35291))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__46143] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46143)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__46143)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__46143 )
| ? [Vvar__0___24Anonymous__46144] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46144)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__46144)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zcomplements.Zlength',axiom,
cCoq_2eZArith_2eZcomplements_2eZlength = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('$_def_Coq.ZArith.Zcomplements.Zlength_aux',axiom,
! [V1__acc,V2__A,V3__l] :
( cType___24t(V2__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V2__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__A)
& cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V1__acc,V2__A,V3__l) = V1__acc )
| ? [Vvar__1___24Anonymous__34996] :
( t(Vvar__1___24Anonymous__34996,V2__A)
& ? [Vvar__2___24Anonymous__34997] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V2__A,Vvar__2___24Anonymous__34997)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__A,Vvar__1___24Anonymous__34996,Vvar__2___24Anonymous__34997)
& cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V1__acc,V2__A,V3__l) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__acc),V2__A,Vvar__2___24Anonymous__34997) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zeven',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__45782] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45782)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45782)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45782)
& ( ? [Vvar__0___24Anonymous__45786] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45786)
& Vvar__0___24Anonymous__45782 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45786)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__45787] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45787)
& Vvar__0___24Anonymous__45782 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45787)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__45782 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__45788] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45788)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45788)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__45788)
& ( ? [Vvar__0___24Anonymous__45792] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45792)
& Vvar__0___24Anonymous__45788 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45792)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__45793] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45793)
& Vvar__0___24Anonymous__45788 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45793)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__45788 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zodd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__45794] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45794)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45794)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45794)
& ( ? [Vvar__0___24Anonymous__45798] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45798)
& Vvar__0___24Anonymous__45794 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45798)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__45799] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45799)
& Vvar__0___24Anonymous__45794 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45799)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__45794 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__45800] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45800)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45800)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__45800)
& ( ? [Vvar__0___24Anonymous__45804] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45804)
& Vvar__0___24Anonymous__45800 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45804)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__45805] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45805)
& Vvar__0___24Anonymous__45800 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45805)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__45800 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zlogarithm.Is_power',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__45807] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45807)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45807)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__45808] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45808)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45808)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__45808) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__2862___24a1(V0__D) ).
fof('$_def_Coq.micromega.QMicromega.QWitness',axiom,
! [Vvar__14693] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(Vvar__14693)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__14693) ) ).
fof('$_def_Coq.micromega.RMicromega.RWitness',axiom,
! [Vvar__14886] :
( cCoq_2emicromega_2eRMicromega_2eRWitness___24t(Vvar__14886)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__14886) ) ).
fof('$_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__14934] :
( t(Vvar__1___24Anonymous__14934,V1__A)
& ? [Vvar__2___24Anonymous__14935] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__14935)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__14935)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__14934,Vvar__2___24Anonymous__14935)
& ( ( Vvar__2___24Anonymous__14935 = 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__14934)) ) )
| ? [Vvar__1___24Anonymous__14946] :
( t(Vvar__1___24Anonymous__14946,V1__A)
& ? [Vvar__2___24Anonymous__14947] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__14947)
& Vvar__2___24Anonymous__14935 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__14946,Vvar__2___24Anonymous__14947)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__14934))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__14935) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__14915] :
( t(Vvar__1___24Anonymous__14915,V1__A)
& ? [Vvar__2___24Anonymous__14916] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__14916)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__14915,Vvar__2___24Anonymous__14916)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__14915))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__14916,V4__goal) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.micromega.RingMicromega.PolC',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V0__C) ).
fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).
fof('$_def_Coq.micromega.RingMicromega.cltb',axiom,
! [V0__C,V1__ceqb,V2__cleb,V3__x,V4__y] : cCoq_2emicromega_2eRingMicromega_2ecltb___24a5(V0__C,V1__ceqb,V2__cleb,V3__x,V4__y) = cCoq_2eInit_2eDatatypes_2eandb___24a2(happ(happ(V2__cleb,V3__x),V4__y),cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V0__C,V1__ceqb,V3__x,V4__y)) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op1',axiom,
! [V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V5__o)
=> ( ( V5__o = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__43214___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__43222___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__43230___24a3(V0__R,V1__rO,V4__rlt) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__43238___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.ge_bool',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__16291] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__16291)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__16291)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__16292] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__16292)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__16292)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__16295] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__16295)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__16295)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(Vvar__0___24Anonymous__16292,Vvar__0___24Anonymous__16295) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.map_option',axiom,
! [V0__A,V1__B,V2__f,V3__o] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V3__o)
=> ( ? [Vvar__1___24Anonymous__15839] :
( t(Vvar__1___24Anonymous__15839,V0__A)
& V3__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__15839)
& cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = happ(V2__f,Vvar__1___24Anonymous__15839) )
| ( V3__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.map_option2',axiom,
! [V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cType___24t(V2__C)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V4__o)
=> ( ? [Vvar__1___24Anonymous__15857] :
( t(Vvar__1___24Anonymous__15857,V0__A)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cType___24t(V2__C)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V1__B,V5__o_27)
=> ( V4__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__15857)
& ( ? [Vvar__1___24Anonymous__15862] :
( t(Vvar__1___24Anonymous__15862,V1__B)
& V5__o_27 = cCoq_2eInit_2eDatatypes_2eSome___24a2(V1__B,Vvar__1___24Anonymous__15862)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = happ(happ(V3__f,Vvar__1___24Anonymous__15857),Vvar__1___24Anonymous__15862) )
| ( V5__o_27 = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V2__C) ) ) ) ) ) ) ) )
| ( V4__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V2__C) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.nhyps_of_psatz',axiom,
! [V0__C,V2__prf] :
( cType___24t(V0__C)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,V2__prf)
=> ( ? [Vvar__1___24Anonymous__16332] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__16332)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V0__C,Vvar__1___24Anonymous__16332)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__1___24Anonymous__16332,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat)) )
| ? [Vvar__1___24Anonymous__16334] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V0__C,Vvar__1___24Anonymous__16334)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V0__C,Vvar__1___24Anonymous__16334)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__1___24Anonymous__16336] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V0__C,Vvar__1___24Anonymous__16336)
& ? [Vvar__2___24Anonymous__16337] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__2___24Anonymous__16337)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V0__C,Vvar__1___24Anonymous__16336,Vvar__2___24Anonymous__16337)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__2___24Anonymous__16337) ) )
| ? [Vvar__1___24Anonymous__16340] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__1___24Anonymous__16340)
& ? [Vvar__2___24Anonymous__16341] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__2___24Anonymous__16341)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V0__C,Vvar__1___24Anonymous__16340,Vvar__2___24Anonymous__16341)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__1___24Anonymous__16340),cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__2___24Anonymous__16341)) ) )
| ? [Vvar__1___24Anonymous__16344] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__1___24Anonymous__16344)
& ? [Vvar__2___24Anonymous__16345] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__2___24Anonymous__16345)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V0__C,Vvar__1___24Anonymous__16344,Vvar__2___24Anonymous__16345)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__1___24Anonymous__16344),cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__2___24Anonymous__16345)) ) )
| ? [Vvar__1___24Anonymous__16348] :
( t(Vvar__1___24Anonymous__16348,V0__C)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V0__C,Vvar__1___24Anonymous__16348)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ( V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V0__C)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.psub',axiom,
! [V0__C,V1__cO,V2__cplus,V3__cminus,V4__copp,V5__ceqb] : cCoq_2emicromega_2eRingMicromega_2epsub___24a6(V0__C,V1__cO,V2__cplus,V3__cminus,V4__copp,V5__ceqb) = cCoq_2emicromega_2eEnvRing_2ePsub___24a6(V0__C,V1__cO,V2__cplus,V3__cminus,V4__copp,V5__ceqb) ).
fof('$_def_Coq.micromega.Tauto.BFormula',axiom,
! [V0__A] : cCoq_2emicromega_2eTauto_2eBFormula___24a1(V0__A) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__A,cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_def_Coq.micromega.Tauto.TFormula',axiom,
! [V0__Term,V1__Annot,V2__TX,V3__AF] : cCoq_2emicromega_2eTauto_2eTFormula___24a4(V0__Term,V1__Annot,V2__TX,V3__AF) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__Term,V2__TX,V1__Annot,V3__AF) ).
fof('$_def_Coq.micromega.Tauto.and_cnf',axiom,
! [V0__Term_27,V1__Annot,V2__f1,V3__f2] : cCoq_2emicromega_2eTauto_2eand__cnf___24a4(V0__Term_27,V1__Annot,V2__f1,V3__f2) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot),V2__f1,V3__f2) ).
fof('$_def_Coq.micromega.Tauto.clause',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.cnf',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.cnf_ff',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf__ff___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)))) ).
fof('$_def_Coq.micromega.Tauto.cnf_tt',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.collect_annot',axiom,
! [V0__TA,V1__TX,V2__AA,V3__AF,V5__f] :
( cType___24t(V0__TA)
=> ( cType___24t(V1__TX)
=> ( cType___24t(V2__AA)
=> ( cType___24t(V3__AF)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,V5__f)
=> ( ( V5__f = cCoq_2emicromega_2eTauto_2eTT___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__AA) )
| ( V5__f = cCoq_2emicromega_2eTauto_2eFF___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__AA) )
| ? [Vvar__4___24Anonymous__31422] :
( t(Vvar__4___24Anonymous__31422,V1__TX)
& V5__f = cCoq_2emicromega_2eTauto_2eX___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31422)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__AA) )
| ? [Vvar__4___24Anonymous__31427] :
( t(Vvar__4___24Anonymous__31427,V0__TA)
& ? [Vvar__5___24Anonymous__31428] :
( t(Vvar__5___24Anonymous__31428,V2__AA)
& V5__f = cCoq_2emicromega_2eTauto_2eA___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31427,Vvar__5___24Anonymous__31428)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__AA,Vvar__5___24Anonymous__31428,cCoq_2eInit_2eDatatypes_2enil___24a1(V2__AA)) ) )
| ? [Vvar__4___24Anonymous__31434] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31434)
& ? [Vvar__5___24Anonymous__31435] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__31435)
& V5__f = cCoq_2emicromega_2eTauto_2eCj___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31434,Vvar__5___24Anonymous__31435)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V2__AA,cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31434),cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__31435)) ) )
| ? [Vvar__4___24Anonymous__31441] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31441)
& ? [Vvar__5___24Anonymous__31442] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__31442)
& V5__f = cCoq_2emicromega_2eTauto_2eD___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31441,Vvar__5___24Anonymous__31442)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V2__AA,cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31441),cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__31442)) ) )
| ? [Vvar__4___24Anonymous__31448] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31448)
& V5__f = cCoq_2emicromega_2eTauto_2eN___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31448)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31448) )
| ? [Vvar__4___24Anonymous__31453] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31453)
& ? [Vvar__5___24Anonymous__31454] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V3__AF,Vvar__5___24Anonymous__31454)
& ? [Vvar__6___24Anonymous__31455] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__31455)
& V5__f = cCoq_2emicromega_2eTauto_2eI___24a7(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31453,Vvar__5___24Anonymous__31454,Vvar__6___24Anonymous__31455)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V2__AA,cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31453),cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__31455)) ) ) ) ) ) ) ) ) ) ).
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__31332] :
( t(Vvar__1___24Anonymous__31332,V0__AF)
& V1__id = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__AF,Vvar__1___24Anonymous__31332)
& cCoq_2emicromega_2eTauto_2econs__id___24a3(V0__AF,V1__id,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__AF,Vvar__1___24Anonymous__31332,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('$_def_Coq.micromega.Tauto.eval_cnf',axiom,
! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__f] :
( cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__f)
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V1__Term_27,V2__Annot),cCoq_2emicromega_2eTauto_2eeval__clause___24a5(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env),V5__f) ) ).
fof('$_def_Coq.micromega.Tauto.eval_f',axiom,
! [V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f] :
( cType___24t(V0__TA)
=> ( cType___24t(V1__TX)
=> ( cType___24t(V2__AA)
=> ( cType___24t(V3__AF)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,V7__f)
=> ( ( V7__f = cCoq_2emicromega_2eTauto_2eTT___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(c_24True) ) )
| ( V7__f = cCoq_2emicromega_2eTauto_2eFF___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(c_24False) ) )
| ? [Vvar__4___24Anonymous__31488] :
( t(Vvar__4___24Anonymous__31488,V1__TX)
& V7__f = cCoq_2emicromega_2eTauto_2eX___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31488)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(happ(V4__ex,Vvar__4___24Anonymous__31488)) ) )
| ? [Vvar__4___24Anonymous__31493] :
( t(Vvar__4___24Anonymous__31493,V0__TA)
& ? [Vvar__5___24Anonymous__31494] :
( t(Vvar__5___24Anonymous__31494,V2__AA)
& V7__f = cCoq_2emicromega_2eTauto_2eA___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31493,Vvar__5___24Anonymous__31494)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(happ(V5__ea,Vvar__4___24Anonymous__31493)) ) ) )
| ? [Vvar__4___24Anonymous__31500] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31500)
& ? [Vvar__5___24Anonymous__31501] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__31501)
& V7__f = cCoq_2emicromega_2eTauto_2eCj___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31500,Vvar__5___24Anonymous__31501)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__31500)
& cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__31501) ) ) ) )
| ? [Vvar__4___24Anonymous__31507] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31507)
& ? [Vvar__5___24Anonymous__31508] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__31508)
& V7__f = cCoq_2emicromega_2eTauto_2eD___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31507,Vvar__5___24Anonymous__31508)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__31507)
| cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__31508) ) ) ) )
| ? [Vvar__4___24Anonymous__31514] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31514)
& V7__f = cCoq_2emicromega_2eTauto_2eN___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31514)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ~ cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__31514) ) )
| ? [Vvar__4___24Anonymous__31519] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31519)
& ? [Vvar__5___24Anonymous__31520] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V3__AF,Vvar__5___24Anonymous__31520)
& ? [Vvar__6___24Anonymous__31521] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__31521)
& V7__f = cCoq_2emicromega_2eTauto_2eI___24a7(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__31519,Vvar__5___24Anonymous__31520,Vvar__6___24Anonymous__31521)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__31519)
=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__6___24Anonymous__31521) ) ) ) ) ) ) ) ) ) ) ) ).
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.Tauto.or_cnf',axiom,
! [V0__Term_27,V1__Annot,V2__unsat,V3__deduce,V5__f,V6__f_27] :
( cType___24t(V0__Term_27)
=> ( cType___24t(V1__Annot)
=> ( cCoq_2emicromega_2eTauto_2ecnf___24t(V0__Term_27,V1__Annot,V5__f)
=> ( ( V5__f = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot))
& cCoq_2emicromega_2eTauto_2eor__cnf___24a6(V0__Term_27,V1__Annot,V2__unsat,V3__deduce,V5__f,V6__f_27) = cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V0__Term_27,V1__Annot) )
| ? [Vvar__1___24Anonymous__31913] :
( cCoq_2emicromega_2eTauto_2eclause___24t(V0__Term_27,V1__Annot,Vvar__1___24Anonymous__31913)
& ? [Vvar__2___24Anonymous__31914] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot),Vvar__2___24Anonymous__31914)
& V5__f = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot),Vvar__1___24Anonymous__31913,Vvar__2___24Anonymous__31914)
& cCoq_2emicromega_2eTauto_2eor__cnf___24a6(V0__Term_27,V1__Annot,V2__unsat,V3__deduce,V5__f,V6__f_27) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot),cCoq_2emicromega_2eTauto_2eor__cnf___24a6(V0__Term_27,V1__Annot,V2__unsat,V3__deduce,Vvar__2___24Anonymous__31914,V6__f_27),cCoq_2emicromega_2eTauto_2eor__clause__cnf___24a6(V0__Term_27,V1__Annot,V2__unsat,V3__deduce,Vvar__1___24Anonymous__31913,V6__f_27)) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.Vars.E.eq',axiom,
cCoq_2emicromega_2eZMicromega_2eVars_2eE_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.micromega.ZMicromega.Vars.Facts.MP.to_list',axiom,
cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eto__list = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements ).
fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
! [Vvar__33979] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__33979)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__33979) ) ).
fof('$_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.micromega.ZMicromega.valid_cut_sign',axiom,
! [V0__op] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V0__op)
=> ( ( V0__op = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V0__op = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__op = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__op = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_def_Coq.omega.PreOmega.Z_of_nat\'',axiom,
cCoq_2eomega_2ePreOmega_2eZ__of__nat_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat ).
fof('$_def_Coq.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__2596] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2596)
& V2__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2596)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__2596,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__2596,cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l))) )
| ? [Vvar__0___24Anonymous__2597] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2597)
& V2__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2597)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__2597,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__2597,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('$_def_Coq.setoid_ring.BinList.nth',axiom,
! [V0__A,V1__default,V3__p,V4__l] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__2604] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2604)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2604)
& cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,V3__p,V4__l) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,Vvar__0___24Anonymous__2604,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__2604,cCoq_2eLists_2eList_2etl___24a2(V0__A,V4__l))) )
| ? [Vvar__0___24Anonymous__2605] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2605)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2605)
& cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,V3__p,V4__l) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,Vvar__0___24Anonymous__2605,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__2605,V4__l)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,V3__p,V4__l) = cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V4__l) ) ) ) ) ).
fof('$_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__8350] :
( t(Vvar__1___24Anonymous__8350,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__8350)
& 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__8350) )
| ? [Vvar__1___24Anonymous__8352] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8352)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__8352)
& 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__8352,V15__l) )
| ? [Vvar__1___24Anonymous__8354] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__8354)
& ? [Vvar__2___24Anonymous__8355] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__8355)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__8354,Vvar__2___24Anonymous__8355)
& 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__8354)),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__8355)) ) )
| ? [Vvar__1___24Anonymous__8358] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__8358)
& ? [Vvar__2___24Anonymous__8359] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__8359)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__8358,Vvar__2___24Anonymous__8359)
& 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__8358)),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__8359)) ) )
| ? [Vvar__1___24Anonymous__8362] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__8362)
& ? [Vvar__2___24Anonymous__8363] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__8363)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__8362,Vvar__2___24Anonymous__8363)
& 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__8362)),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__8363)) ) )
| ? [Vvar__1___24Anonymous__8366] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__8366)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__8366)
& 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__8366)) )
| ? [Vvar__1___24Anonymous__8368] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__8368)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__8368)
& 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__8368)) )
| ? [Vvar__1___24Anonymous__8370] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__8370)
& ? [Vvar__2___24Anonymous__8371] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__8371)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__8370,Vvar__2___24Anonymous__8371)
& 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__8370)),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__8371)) ) )
| ? [Vvar__1___24Anonymous__8374] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__8374)
& ? [Vvar__2___24Anonymous__8375] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8375)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__8374,Vvar__2___24Anonymous__8375)
& 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__8374)),happ(V12__Cp__phi,Vvar__2___24Anonymous__8375)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__11174] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__11174)
& ? [Vvar__2___24Anonymous__11175] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__11175)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__11174,Vvar__2___24Anonymous__11175)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__11174),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__11175,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fcons2',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__e,V10__l] : cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__e,V10__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons1___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2esetoid__ring_2eField__theory_2ePEsimp___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e),V10__l) ).
fof('$_def_Coq.setoid_ring.Field_theory.NPEadd',axiom,
! [V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e1)
=> ( ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6179] :
( t(Vvar__1___24Anonymous__6179,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6179,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6179)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6179),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6179),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6182] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6182)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6182)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6184] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6184)
& ? [Vvar__2___24Anonymous__6185] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6185)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6184,Vvar__2___24Anonymous__6185)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6188] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6188)
& ? [Vvar__2___24Anonymous__6189] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6189)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6188,Vvar__2___24Anonymous__6189)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6192] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6192)
& ? [Vvar__2___24Anonymous__6193] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6193)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6192,Vvar__2___24Anonymous__6193)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6196] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6196)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6196)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6198] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6198)
& ? [Vvar__2___24Anonymous__6199] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6199)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6198,Vvar__2___24Anonymous__6199)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6206] :
( t(Vvar__1___24Anonymous__6206,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6206,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6206)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6206),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6206),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6209] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6209)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6209)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6211] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6211)
& ? [Vvar__2___24Anonymous__6212] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6212)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6211,Vvar__2___24Anonymous__6212)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6215] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6215)
& ? [Vvar__2___24Anonymous__6216] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6216)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6215,Vvar__2___24Anonymous__6216)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6219] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6219)
& ? [Vvar__2___24Anonymous__6220] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6220)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6219,Vvar__2___24Anonymous__6220)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6223] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6223)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6223)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6225] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6225)
& ? [Vvar__2___24Anonymous__6226] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6226)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6225,Vvar__2___24Anonymous__6226)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6229] :
( t(Vvar__1___24Anonymous__6229,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6229)
& ( ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6229,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6229,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6254] :
( t(Vvar__1___24Anonymous__6254,V0__C)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6254)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,happ(happ(V2__cadd,Vvar__1___24Anonymous__6229),Vvar__1___24Anonymous__6254)) )
| ? [Vvar__1___24Anonymous__6256] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6256)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6229,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6256)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6259] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6259)
& ? [Vvar__2___24Anonymous__6260] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6260)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6229,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6259,Vvar__2___24Anonymous__6260)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6265] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6265)
& ? [Vvar__2___24Anonymous__6266] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6266)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6229,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6265,Vvar__2___24Anonymous__6266)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6271] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6271)
& ? [Vvar__2___24Anonymous__6272] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6272)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6229,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6271,Vvar__2___24Anonymous__6272)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6277] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6277)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6229,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6277)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6280] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6280)
& ? [Vvar__2___24Anonymous__6281] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6281)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6229,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6280,Vvar__2___24Anonymous__6281)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6229),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6286] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6286)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6286)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6304] :
( t(Vvar__1___24Anonymous__6304,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6304,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6304)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6304),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6304),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6307] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6307)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6307)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6309] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6309)
& ? [Vvar__2___24Anonymous__6310] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6310)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6309,Vvar__2___24Anonymous__6310)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6313] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6313)
& ? [Vvar__2___24Anonymous__6314] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6314)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6313,Vvar__2___24Anonymous__6314)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6317] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6317)
& ? [Vvar__2___24Anonymous__6318] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6318)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6317,Vvar__2___24Anonymous__6318)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6321] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6321)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6321)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6323] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6323)
& ? [Vvar__2___24Anonymous__6324] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6324)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6323,Vvar__2___24Anonymous__6324)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6327] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6327)
& ? [Vvar__2___24Anonymous__6328] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6328)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6327,Vvar__2___24Anonymous__6328)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6360] :
( t(Vvar__1___24Anonymous__6360,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6360,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6360)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6360),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6360),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6363] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6363)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6363)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6365] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6365)
& ? [Vvar__2___24Anonymous__6366] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6366)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6365,Vvar__2___24Anonymous__6366)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6369] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6369)
& ? [Vvar__2___24Anonymous__6370] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6370)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6369,Vvar__2___24Anonymous__6370)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6373] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6373)
& ? [Vvar__2___24Anonymous__6374] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6374)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6373,Vvar__2___24Anonymous__6374)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6377] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6377)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6377)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6379] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6379)
& ? [Vvar__2___24Anonymous__6380] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6380)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6379,Vvar__2___24Anonymous__6380)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6383] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6383)
& ? [Vvar__2___24Anonymous__6384] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6384)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6383,Vvar__2___24Anonymous__6384)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6416] :
( t(Vvar__1___24Anonymous__6416,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6416,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6416)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6416),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6416),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6419] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6419)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6419)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6421] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6421)
& ? [Vvar__2___24Anonymous__6422] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6422)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6421,Vvar__2___24Anonymous__6422)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6425] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6425)
& ? [Vvar__2___24Anonymous__6426] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6426)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6425,Vvar__2___24Anonymous__6426)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6429] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6429)
& ? [Vvar__2___24Anonymous__6430] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6430)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6429,Vvar__2___24Anonymous__6430)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6433] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6433)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6433)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6435] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6435)
& ? [Vvar__2___24Anonymous__6436] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6436)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6435,Vvar__2___24Anonymous__6436)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6439] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6439)
& ? [Vvar__2___24Anonymous__6440] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6440)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6439,Vvar__2___24Anonymous__6440)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6472] :
( t(Vvar__1___24Anonymous__6472,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6472,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6472)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6472),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6472),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6475] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6475)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6475)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6477] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6477)
& ? [Vvar__2___24Anonymous__6478] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6478)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6477,Vvar__2___24Anonymous__6478)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6481] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6481)
& ? [Vvar__2___24Anonymous__6482] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6482)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6481,Vvar__2___24Anonymous__6482)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6485] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6485)
& ? [Vvar__2___24Anonymous__6486] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6486)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6485,Vvar__2___24Anonymous__6486)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6489] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6489)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6489)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6491] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6491)
& ? [Vvar__2___24Anonymous__6492] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6492)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6491,Vvar__2___24Anonymous__6492)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6495] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6495)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6495)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6513] :
( t(Vvar__1___24Anonymous__6513,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6513,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6513)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6513),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6513),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6516] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6516)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6516)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6518] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6518)
& ? [Vvar__2___24Anonymous__6519] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6519)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6518,Vvar__2___24Anonymous__6519)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6522] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6522)
& ? [Vvar__2___24Anonymous__6523] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6523)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6522,Vvar__2___24Anonymous__6523)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6526] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6526)
& ? [Vvar__2___24Anonymous__6527] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6527)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6526,Vvar__2___24Anonymous__6527)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6530] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6530)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6530)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6532] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6532)
& ? [Vvar__2___24Anonymous__6533] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6533)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6532,Vvar__2___24Anonymous__6533)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6536] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6536)
& ? [Vvar__2___24Anonymous__6537] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6537)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6536,Vvar__2___24Anonymous__6537)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6569] :
( t(Vvar__1___24Anonymous__6569,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6569,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6569)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6569),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6569),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6572] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6572)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6572)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6574] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6574)
& ? [Vvar__2___24Anonymous__6575] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6575)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6574,Vvar__2___24Anonymous__6575)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6578] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6578)
& ? [Vvar__2___24Anonymous__6579] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6579)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6578,Vvar__2___24Anonymous__6579)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6582] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6582)
& ? [Vvar__2___24Anonymous__6583] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6583)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6582,Vvar__2___24Anonymous__6583)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6586] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6586)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6586)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6588] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6588)
& ? [Vvar__2___24Anonymous__6589] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6589)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6588,Vvar__2___24Anonymous__6589)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) ) ) ) ).
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.NPEopp',axiom,
! [V0__C,V1__copp,V2__e1] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V2__e1)
=> ( ( V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) )
| ( V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) )
| ? [Vvar__1___24Anonymous__7171] :
( t(Vvar__1___24Anonymous__7171,V0__C)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7171)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,happ(V1__copp,Vvar__1___24Anonymous__7171)) )
| ? [Vvar__1___24Anonymous__7173] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7173)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7173)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) )
| ? [Vvar__1___24Anonymous__7175] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7175)
& ? [Vvar__2___24Anonymous__7176] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7176)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7175,Vvar__2___24Anonymous__7176)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) ) )
| ? [Vvar__1___24Anonymous__7179] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7179)
& ? [Vvar__2___24Anonymous__7180] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7180)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7179,Vvar__2___24Anonymous__7180)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) ) )
| ? [Vvar__1___24Anonymous__7183] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7183)
& ? [Vvar__2___24Anonymous__7184] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7184)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7183,Vvar__2___24Anonymous__7184)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) ) )
| ? [Vvar__1___24Anonymous__7187] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7187)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7187)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) )
| ? [Vvar__1___24Anonymous__7189] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7189)
& ? [Vvar__2___24Anonymous__7190] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7190)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7189,Vvar__2___24Anonymous__7190)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.NPEsub',axiom,
! [V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e1)
=> ( ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6680] :
( t(Vvar__1___24Anonymous__6680,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6680,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6680)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6680),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6680),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6683] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6683)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6683)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6685] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6685)
& ? [Vvar__2___24Anonymous__6686] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6686)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6685,Vvar__2___24Anonymous__6686)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6689] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6689)
& ? [Vvar__2___24Anonymous__6690] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6690)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6689,Vvar__2___24Anonymous__6690)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6693] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6693)
& ? [Vvar__2___24Anonymous__6694] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6694)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6693,Vvar__2___24Anonymous__6694)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6697] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6697)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6697)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6699] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6699)
& ? [Vvar__2___24Anonymous__6700] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6700)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6699,Vvar__2___24Anonymous__6700)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6707] :
( t(Vvar__1___24Anonymous__6707,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6707,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6707)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6707),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6707),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6710] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6710)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6710)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6712] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6712)
& ? [Vvar__2___24Anonymous__6713] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6713)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6712,Vvar__2___24Anonymous__6713)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6716] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6716)
& ? [Vvar__2___24Anonymous__6717] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6717)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6716,Vvar__2___24Anonymous__6717)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6720] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6720)
& ? [Vvar__2___24Anonymous__6721] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6721)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6720,Vvar__2___24Anonymous__6721)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6724] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6724)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6724)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6726] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6726)
& ? [Vvar__2___24Anonymous__6727] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6727)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6726,Vvar__2___24Anonymous__6727)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6730] :
( t(Vvar__1___24Anonymous__6730,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6730)
& ( ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6730,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6730,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6755] :
( t(Vvar__1___24Anonymous__6755,V0__C)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6755)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,happ(happ(V2__csub,Vvar__1___24Anonymous__6730),Vvar__1___24Anonymous__6755)) )
| ? [Vvar__1___24Anonymous__6757] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6757)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6730,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6757)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6760] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6760)
& ? [Vvar__2___24Anonymous__6761] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6761)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6730,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6760,Vvar__2___24Anonymous__6761)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6766] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6766)
& ? [Vvar__2___24Anonymous__6767] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6767)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6730,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6766,Vvar__2___24Anonymous__6767)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6772] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6772)
& ? [Vvar__2___24Anonymous__6773] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6773)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6730,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6772,Vvar__2___24Anonymous__6773)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6778] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6778)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6730,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6778)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6781] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6781)
& ? [Vvar__2___24Anonymous__6782] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6782)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6730,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6781,Vvar__2___24Anonymous__6782)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6730),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6787] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6787)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6787)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6805] :
( t(Vvar__1___24Anonymous__6805,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6805,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6805)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6805),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6805),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6808] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6808)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6808)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6810] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6810)
& ? [Vvar__2___24Anonymous__6811] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6811)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6810,Vvar__2___24Anonymous__6811)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6814] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6814)
& ? [Vvar__2___24Anonymous__6815] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6815)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6814,Vvar__2___24Anonymous__6815)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6818] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6818)
& ? [Vvar__2___24Anonymous__6819] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6819)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6818,Vvar__2___24Anonymous__6819)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6822] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6822)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6822)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6824] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6824)
& ? [Vvar__2___24Anonymous__6825] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6825)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6824,Vvar__2___24Anonymous__6825)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6828] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6828)
& ? [Vvar__2___24Anonymous__6829] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6829)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6828,Vvar__2___24Anonymous__6829)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6861] :
( t(Vvar__1___24Anonymous__6861,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6861,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6861)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6861),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6861),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6864] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6864)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6864)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6866] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6866)
& ? [Vvar__2___24Anonymous__6867] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6867)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6866,Vvar__2___24Anonymous__6867)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6870] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6870)
& ? [Vvar__2___24Anonymous__6871] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6871)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6870,Vvar__2___24Anonymous__6871)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6874] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6874)
& ? [Vvar__2___24Anonymous__6875] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6875)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6874,Vvar__2___24Anonymous__6875)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6878] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6878)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6878)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6880] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6880)
& ? [Vvar__2___24Anonymous__6881] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6881)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6880,Vvar__2___24Anonymous__6881)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6884] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6884)
& ? [Vvar__2___24Anonymous__6885] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6885)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6884,Vvar__2___24Anonymous__6885)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6917] :
( t(Vvar__1___24Anonymous__6917,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6917,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6917)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6917),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6917),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6920] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6920)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6920)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6922] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6922)
& ? [Vvar__2___24Anonymous__6923] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6923)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6922,Vvar__2___24Anonymous__6923)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6926] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6926)
& ? [Vvar__2___24Anonymous__6927] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6927)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6926,Vvar__2___24Anonymous__6927)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6930] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6930)
& ? [Vvar__2___24Anonymous__6931] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6931)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6930,Vvar__2___24Anonymous__6931)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6934] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6934)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6934)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6936] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6936)
& ? [Vvar__2___24Anonymous__6937] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6937)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6936,Vvar__2___24Anonymous__6937)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6940] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6940)
& ? [Vvar__2___24Anonymous__6941] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6941)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6940,Vvar__2___24Anonymous__6941)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6973] :
( t(Vvar__1___24Anonymous__6973,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__6973,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__6973)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6973),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__6973),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6976] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6976)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__6976)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6978] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6978)
& ? [Vvar__2___24Anonymous__6979] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6979)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__6978,Vvar__2___24Anonymous__6979)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6982] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6982)
& ? [Vvar__2___24Anonymous__6983] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6983)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__6982,Vvar__2___24Anonymous__6983)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6986] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6986)
& ? [Vvar__2___24Anonymous__6987] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__6987)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__6986,Vvar__2___24Anonymous__6987)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__6990] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6990)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6990)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__6992] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6992)
& ? [Vvar__2___24Anonymous__6993] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6993)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__6992,Vvar__2___24Anonymous__6993)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__6996] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__6996)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__6996)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__7014] :
( t(Vvar__1___24Anonymous__7014,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__7014,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7014)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__7014),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__7014),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7017] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7017)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7017)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__7019] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7019)
& ? [Vvar__2___24Anonymous__7020] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7020)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7019,Vvar__2___24Anonymous__7020)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__7023] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7023)
& ? [Vvar__2___24Anonymous__7024] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7024)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7023,Vvar__2___24Anonymous__7024)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__7027] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7027)
& ? [Vvar__2___24Anonymous__7028] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7028)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7027,Vvar__2___24Anonymous__7028)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__7031] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7031)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7031)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__7033] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7033)
& ? [Vvar__2___24Anonymous__7034] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7034)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7033,Vvar__2___24Anonymous__7034)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7037] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7037)
& ? [Vvar__2___24Anonymous__7038] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7038)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7037,Vvar__2___24Anonymous__7038)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__7070] :
( t(Vvar__1___24Anonymous__7070,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__7070,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7070)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__7070),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__7070),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7073] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7073)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7073)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__7075] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7075)
& ? [Vvar__2___24Anonymous__7076] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7076)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7075,Vvar__2___24Anonymous__7076)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__7079] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7079)
& ? [Vvar__2___24Anonymous__7080] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7080)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7079,Vvar__2___24Anonymous__7080)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__7083] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7083)
& ? [Vvar__2___24Anonymous__7084] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7084)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7083,Vvar__2___24Anonymous__7084)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__7087] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7087)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7087)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__7089] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7089)
& ? [Vvar__2___24Anonymous__7090] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7090)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7089,Vvar__2___24Anonymous__7090)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) ) ) ) ).
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__8687] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__8687)
& ? [Vvar__2___24Anonymous__8688] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__8688)
& ( 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__8688)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__8687,Vvar__2___24Anonymous__8688)
& ( ( Vvar__2___24Anonymous__8688 = 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__8687)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__8699] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__8699)
& ? [Vvar__2___24Anonymous__8700] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__8700)
& Vvar__2___24Anonymous__8688 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__8699,Vvar__2___24Anonymous__8700)
& ( 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__8687)),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__8688) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__8674] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__8674)
& ? [Vvar__2__denum__8675] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__8675)
& ? [Vvar__3__condition__8676] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__8676)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__8674,Vvar__2__denum__8675,Vvar__3__condition__8676)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__8676 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__8665] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__8665)
& ? [Vvar__2__denum__8666] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__8666)
& ? [Vvar__3__condition__8667] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__8667)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__8665,Vvar__2__denum__8666,Vvar__3__condition__8667)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__8666 ) ) ) ) ) ).
fof('$_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_2410401___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('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__8654] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__8654)
& ? [Vvar__2__denum__8655] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__8655)
& ? [Vvar__3__condition__8656] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__8656)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__8654,Vvar__2__denum__8655,Vvar__3__condition__8656)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__8654 ) ) ) ) ) ).
fof('$_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__9007] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__9007)
& ? [Vvar__2__rsplit__common__9008] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__9008)
& ? [Vvar__3__rsplit__right__9009] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__9009)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__9007,Vvar__2__rsplit__common__9008,Vvar__3__rsplit__right__9009)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,V1__r) = Vvar__2__rsplit__common__9008 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__8996] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__8996)
& ? [Vvar__2__rsplit__common__8997] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__8997)
& ? [Vvar__3__rsplit__right__8998] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__8998)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__8996,Vvar__2__rsplit__common__8997,Vvar__3__rsplit__right__8998)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,V1__r) = Vvar__1__rsplit__left__8996 ) ) ) ) ) ).
fof('$_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__9016] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__9016)
& ? [Vvar__2__rsplit__common__9017] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__9017)
& ? [Vvar__3__rsplit__right__9018] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__9018)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__9016,Vvar__2__rsplit__common__9017,Vvar__3__rsplit__right__9018)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,V1__r) = Vvar__3__rsplit__right__9018 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.split',axiom,
! [V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,V6__e2] : cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,V6__e2) = cCoq_2esetoid__ring_2eField__theory_2esplit__aux___24a8(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,cCoq_2eNumbers_2eBinNums_2exH,V6__e2) ).
fof('$_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.Nw_is0',axiom,
! [V1__w] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V1__w)
=> ( ( V1__w = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2eNw__is0___24a1(V1__w) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__1___24Anonymous__12061] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__12061)
& ? [Vvar__2___24Anonymous__12062] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__12062)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__12061)
=> ( V1__w = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__12061,Vvar__2___24Anonymous__12062)
& ( ( Vvar__1___24Anonymous__12061 = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2eNw__is0___24a1(V1__w) = cCoq_2esetoid__ring_2eInitialRing_2eNw__is0___24a1(Vvar__2___24Anonymous__12062) )
| ? [Vvar__0___24Anonymous__12068] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12068)
& Vvar__1___24Anonymous__12061 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12068)
& cCoq_2esetoid__ring_2eInitialRing_2eNw__is0___24a1(V1__w) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
! [Vvar__12000] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__12000)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__12000) ) ).
fof('$_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__11960] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11960)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11960)
& 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__11960) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiNword',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w] :
( cType___24t(V0__R)
=> ( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V8__w)
=> ( ( V8__w = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = V1__rO )
| ? [Vvar__1___24Anonymous__12101] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__12101)
& ? [Vvar__2___24Anonymous__12102] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__12102)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__12101)
=> ( V8__w = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__12101,Vvar__2___24Anonymous__12102)
& ( ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__12102)
=> ( Vvar__1___24Anonymous__12101 = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( Vvar__2___24Anonymous__12102 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,Vvar__1___24Anonymous__12101) )
| ? [Vvar__1___24Anonymous__12123] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__12123)
& ? [Vvar__2___24Anonymous__12124] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__12124)
& Vvar__2___24Anonymous__12102 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__12123,Vvar__2___24Anonymous__12124)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = happ(V6__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,Vvar__2___24Anonymous__12102)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__12126] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12126)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__12102)
=> ( Vvar__1___24Anonymous__12101 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12126)
& ( ( Vvar__2___24Anonymous__12102 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,Vvar__1___24Anonymous__12101) )
| ? [Vvar__1___24Anonymous__12133] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__12133)
& ? [Vvar__2___24Anonymous__12134] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__12134)
& Vvar__2___24Anonymous__12102 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__12133,Vvar__2___24Anonymous__12134)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,Vvar__1___24Anonymous__12101)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,Vvar__2___24Anonymous__12102)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__36460] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36460)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36460)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__36460)
& ( ? [Vvar__0___24Anonymous__36464] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36464)
& Vvar__0___24Anonymous__36460 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__36464)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__36460))) )
| ? [Vvar__0___24Anonymous__36465] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36465)
& Vvar__0___24Anonymous__36460 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__36465)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__36460))) )
| ( Vvar__0___24Anonymous__36460 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V2__radd,V1__rI),V1__rI)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__36466] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36466)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36466)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__36466)
& ( ? [Vvar__0___24Anonymous__36470] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36470)
& Vvar__0___24Anonymous__36466 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__36470)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__36466)) )
| ? [Vvar__0___24Anonymous__36471] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36471)
& Vvar__0___24Anonymous__36466 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__36471)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__36466)) )
| ( Vvar__0___24Anonymous__36466 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),V1__rI) ) ) ) ) ) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__36427] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36427)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__36427)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__36427))) )
| ? [Vvar__0___24Anonymous__36428] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36428)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__36428)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__36428)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__11885] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11885)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11885)
& 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__11885) )
| ? [Vvar__0___24Anonymous__11886] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11886)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11886)
& 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__11886)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.get_signZ',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__11938] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11938)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11938)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__11939] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11939)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11939)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11939)) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.triv_div',axiom,
! [V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y] :
( cType___24t(V0__C)
=> ( c_24__type__3122___24t(V0__C,V3__ceqb)
=> ( t(V4__x,V0__C)
=> ( t(V5__y,V0__C)
=> ( ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V2__cI,V1__cO) )
| ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V1__cO,V4__x) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring.bool_eq',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V1__b2) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.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.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__19524] :
( t(Vvar__1___24Anonymous__19524,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__19524)
& 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__19524) )
| ? [Vvar__1___24Anonymous__19526] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__19526)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__19526)
& 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__19526,V13__l) )
| ? [Vvar__1___24Anonymous__19528] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__19528)
& ? [Vvar__2___24Anonymous__19529] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__19529)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__19528,Vvar__2___24Anonymous__19529)
& 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__19528)),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__19529)) ) )
| ? [Vvar__1___24Anonymous__19532] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__19532)
& ? [Vvar__2___24Anonymous__19533] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__19533)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__19532,Vvar__2___24Anonymous__19533)
& 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__19532)),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__19533)) ) )
| ? [Vvar__1___24Anonymous__19536] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__19536)
& ? [Vvar__2___24Anonymous__19537] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__19537)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__19536,Vvar__2___24Anonymous__19537)
& 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__19536)),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__19537)) ) )
| ? [Vvar__1___24Anonymous__19540] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__19540)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__19540)
& 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__19540)) )
| ? [Vvar__1___24Anonymous__19542] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__19542)
& ? [Vvar__2___24Anonymous__19543] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__19543)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__19542,Vvar__2___24Anonymous__19543)
& 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__19542)),happ(V10__Cp__phi,Vvar__2___24Anonymous__19543)) ) ) ) ) ) ) ) ).
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__17393] :
( t(Vvar__1___24Anonymous__17393,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__17393)
& ( ? [Vvar__1___24Anonymous__17403] :
( t(Vvar__1___24Anonymous__17403,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__17403)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__17393),Vvar__1___24Anonymous__17403) )
| ? [Vvar__1___24Anonymous__17405] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17405)
& ? [Vvar__2___24Anonymous__17406] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__17406)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__17405,Vvar__2___24Anonymous__17406)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__17409] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17409)
& ? [Vvar__2___24Anonymous__17410] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17410)
& ? [Vvar__3___24Anonymous__17411] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__17411)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__17409,Vvar__2___24Anonymous__17410,Vvar__3___24Anonymous__17411)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__17416] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17416)
& ? [Vvar__2___24Anonymous__17417] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__17417)
& ( 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__17416,Vvar__2___24Anonymous__17417)
& ( ? [Vvar__1___24Anonymous__17437] :
( t(Vvar__1___24Anonymous__17437,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__17437)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__17439] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17439)
& ? [Vvar__2___24Anonymous__17440] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__17440)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17416)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17439)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__17439,Vvar__2___24Anonymous__17440)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__17416,Vvar__1___24Anonymous__17439) = 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__17417,Vvar__2___24Anonymous__17440) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__17416,Vvar__1___24Anonymous__17439) = 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__17416,Vvar__1___24Anonymous__17439) = 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__17445] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17445)
& ? [Vvar__2___24Anonymous__17446] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17446)
& ? [Vvar__3___24Anonymous__17447] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__17447)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__17445,Vvar__2___24Anonymous__17446,Vvar__3___24Anonymous__17447)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__17452] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17452)
& ? [Vvar__2___24Anonymous__17453] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17453)
& ? [Vvar__3___24Anonymous__17454] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__17454)
& ( 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__17452,Vvar__2___24Anonymous__17453,Vvar__3___24Anonymous__17454)
& ( ? [Vvar__1___24Anonymous__17487] :
( t(Vvar__1___24Anonymous__17487,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__17487)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__17489] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17489)
& ? [Vvar__2___24Anonymous__17490] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__17490)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__17489,Vvar__2___24Anonymous__17490)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__17493] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17493)
& ? [Vvar__2___24Anonymous__17494] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17494)
& ? [Vvar__3___24Anonymous__17495] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__17495)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17453)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17494)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__17493,Vvar__2___24Anonymous__17494,Vvar__3___24Anonymous__17495)
& ( ( cType___24t(V0__C)
=> ( c_24__type__3122___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17452)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17493)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__17453,Vvar__2___24Anonymous__17494) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__17452,Vvar__1___24Anonymous__17493) = 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__17454,Vvar__3___24Anonymous__17495) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__17452,Vvar__1___24Anonymous__17493) = 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__17453,Vvar__2___24Anonymous__17494) = 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__17453,Vvar__2___24Anonymous__17494) = 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__18797] :
( t(Vvar__1___24Anonymous__18797,V4__C)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V4__C,Vvar__1___24Anonymous__18797)
& 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__18797) )
| ? [Vvar__1___24Anonymous__18799] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__18799)
& ? [Vvar__2___24Anonymous__18800] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__2___24Anonymous__18800)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V4__C,Vvar__1___24Anonymous__18799,Vvar__2___24Anonymous__18800)
& 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__18799,V7__l),Vvar__2___24Anonymous__18800) ) )
| ? [Vvar__1___24Anonymous__18803] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__1___24Anonymous__18803)
& ? [Vvar__2___24Anonymous__18804] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__18804)
& ? [Vvar__3___24Anonymous__18805] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__3___24Anonymous__18805)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V4__C,Vvar__1___24Anonymous__18803,Vvar__2___24Anonymous__18804,Vvar__3___24Anonymous__18805)
& 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__18803)),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__18804))),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__18805)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V15__get__sign,c_24__let__16__mkpow__23561___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__23562___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__23563___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
fof('$_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__20652] :
( 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__20652)
& ? [Vvar__2___24Anonymous__20653] :
( 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__20653)
& ( 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__20652)
=> ( 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__20652,Vvar__2___24Anonymous__20653)
& ? [Vvar__2___24Anonymous__20671] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__2___24Anonymous__20671)
& ? [Vvar__3___24Anonymous__20672] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__3___24Anonymous__20672)
& ( 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__20653)
=> ( Vvar__1___24Anonymous__20652 = 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__20671,Vvar__3___24Anonymous__20672)
& ( ( Vvar__2___24Anonymous__20653 = 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__20671)),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__20672))) ) )
| ? [Vvar__1___24Anonymous__20683] :
( 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__20683)
& ? [Vvar__2___24Anonymous__20684] :
( 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__20684)
& Vvar__2___24Anonymous__20653 = 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__20683,Vvar__2___24Anonymous__20684)
& ( 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__20671)),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__20672)))
& 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__20653) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkPinj',axiom,
! [V0__C,V1__j,V2__P] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V2__P)
=> ( ? [Vvar__1___24Anonymous__17524] :
( t(Vvar__1___24Anonymous__17524,V0__C)
& V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__17524)
& cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = V2__P )
| ? [Vvar__1___24Anonymous__17526] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17526)
& ? [Vvar__2___24Anonymous__17527] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__17527)
& V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__17526,Vvar__2___24Anonymous__17527)
& cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__j,Vvar__1___24Anonymous__17526),Vvar__2___24Anonymous__17527) ) )
| ? [Vvar__1___24Anonymous__17530] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17530)
& ? [Vvar__2___24Anonymous__17531] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17531)
& ? [Vvar__3___24Anonymous__17532] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__17532)
& V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__17530,Vvar__2___24Anonymous__17531,Vvar__3___24Anonymous__17532)
& cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,V1__j,V2__P) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),V10__lpe)
=> ( ( V10__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__21015] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__21015)
& ? [Vvar__2___24Anonymous__21016] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__2___24Anonymous__21016)
& ( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__21015)
=> ( V10__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__1___24Anonymous__21015,Vvar__2___24Anonymous__21016)
& ? [Vvar__2___24Anonymous__21032] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__21032)
& ? [Vvar__3___24Anonymous__21033] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__21033)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__3114___24t(V0__C,V3__cadd)
=> ( c_24__type__3114___24t(V0__C,V4__cmul)
=> ( c_24__type__3114___24t(V0__C,V5__csub)
=> ( c_24__type__4409___24t(V0__C,V6__copp)
=> ( c_24__type__3122___24t(V0__C,V7__ceqb)
=> ( c_24__type__11290___24t(V0__C,V8__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__21032)
=> ( Vvar__1___24Anonymous__21015 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__21032,Vvar__3___24Anonymous__21033)
& ( ? [Vvar__1___24Anonymous__21041] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__21041)
& cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__21032)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__21041)
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C)),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C),Vvar__1___24Anonymous__21041,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__3___24Anonymous__21033)),cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__21016)) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__21032)) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__21016) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__43319] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43319)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43319)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(happ(V1__rmul,V3__r),V4__x),V4__x,Vvar__0___24Anonymous__43319),V4__x,Vvar__0___24Anonymous__43319) )
| ? [Vvar__0___24Anonymous__43320] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43320)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43320)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,Vvar__0___24Anonymous__43320),V4__x,Vvar__0___24Anonymous__43320) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkmult_rec',axiom,
! [V0__R,V1__mkmult__pow,V3__r,V4__lm] :
( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),V4__lm)
=> ( ( V4__lm = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive))
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec___24a4(V0__R,V1__mkmult__pow,V3__r,V4__lm) = V3__r )
| ? [Vvar__1___24Anonymous__21301] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__21301)
& ? [Vvar__2___24Anonymous__21302] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__2___24Anonymous__21302)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__21301)
=> ( V4__lm = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__1___24Anonymous__21301,Vvar__2___24Anonymous__21302)
& ? [Vvar__2___24Anonymous__21314] :
( t(Vvar__2___24Anonymous__21314,V0__R)
& ? [Vvar__3___24Anonymous__21315] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3___24Anonymous__21315)
& Vvar__1___24Anonymous__21301 = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__2___24Anonymous__21314,Vvar__3___24Anonymous__21315)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec___24a4(V0__R,V1__mkmult__pow,V3__r,V4__lm) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec___24a4(V0__R,V1__mkmult__pow,happ(happ(happ(V1__mkmult__pow,V3__r),Vvar__2___24Anonymous__21314),Vvar__3___24Anonymous__21315),Vvar__2___24Anonymous__21302) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__20498___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_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__23427] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__23427)
& ? [Vvar__2___24Anonymous__23428] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__2___24Anonymous__23428)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__23427)
=> ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__1___24Anonymous__23427,Vvar__2___24Anonymous__23428)
& ? [Vvar__2___24Anonymous__23440] :
( t(Vvar__2___24Anonymous__23440,V0__R)
& ? [Vvar__3___24Anonymous__23441] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3___24Anonymous__23441)
& Vvar__1___24Anonymous__23427 = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__2___24Anonymous__23440,Vvar__3___24Anonymous__23441)
& 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__23440,Vvar__3___24Anonymous__23441)),cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,Vvar__2___24Anonymous__23428)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_Coq.setoid_ring.Ring_theory.IDphi',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRopp',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRsub',axiom,
! [V0__R,V1__radd,V2__x,V3__y] : cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V0__R,V1__radd,V2__x,V3__y) = happ(happ(V1__radd,V2__x),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V3__y)) ).
fof('$_def_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
! [V0__C,V1__c] : cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V0__C,V1__c) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__C) ).
fof('$_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('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__24300] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24300)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24300)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__24300) ) ) ) ) ).
fof('$_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__24280] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24280)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24280)
& 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__24281__24284___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24280)),c_24__let__var__6__p__24281__24284___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24280))) )
| ? [Vvar__0___24Anonymous__24282] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24282)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24282)
& 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__24283__24285___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24282)),c_24__let__var__6__p__24283__24285___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24282)) )
| ( 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('$_def_Tait.MoreList.consn',axiom,
! [V0__A,V1__n,V2__a,V3__l] : cTait_2eMoreList_2econsn___24a4(V0__A,V1__n,V2__a,V3__l) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(c_24__lam__395___24a1(V0__A),V3__l,c_24__lam__398___24a2(V0__A,V2__a),V1__n) ).
fof('$_def_Tait.MoreList.existsb',axiom,
! [V0__A,V2__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)
& cTait_2eMoreList_2eexistsb___24a3(V0__A,V2__f,V3__l) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__14627] :
( t(Vvar__1___24Anonymous__14627,V0__A)
& ? [Vvar__2___24Anonymous__14628] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__14628)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14627,Vvar__2___24Anonymous__14628)
& cTait_2eMoreList_2eexistsb___24a3(V0__A,V2__f,V3__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(happ(V2__f,Vvar__1___24Anonymous__14627),cTait_2eMoreList_2eexistsb___24a3(V0__A,V2__f,Vvar__2___24Anonymous__14628)) ) ) ) ) ) ).
fof('$_def_Tait.MoreList.firstn',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cTait_2eMoreList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__0___24Anonymous__14635] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14635)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14635)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cTait_2eMoreList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__14642] :
( t(Vvar__1___24Anonymous__14642,V0__A)
& ? [Vvar__2___24Anonymous__14643] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__14643)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14642,Vvar__2___24Anonymous__14643)
& cTait_2eMoreList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14642,cTait_2eMoreList_2efirstn___24a3(V0__A,Vvar__0___24Anonymous__14635,Vvar__2___24Anonymous__14643)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Tait.MoreList.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)
& cTait_2eMoreList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__1129] :
( t(Vvar__1___24Anonymous__1129,V0__A)
& ? [Vvar__2___24Anonymous__1130] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1130)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1130)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1129,Vvar__2___24Anonymous__1130)
& ( ( Vvar__2___24Anonymous__1130 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cTait_2eMoreList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__1129 )
| ? [Vvar__1___24Anonymous__1141] :
( t(Vvar__1___24Anonymous__1141,V0__A)
& ? [Vvar__2___24Anonymous__1142] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1142)
& Vvar__2___24Anonymous__1130 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1141,Vvar__2___24Anonymous__1142)
& cTait_2eMoreList_2elast___24a3(V0__A,V2__l,V3__d) = cTait_2eMoreList_2elast___24a3(V0__A,Vvar__2___24Anonymous__1130,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Tait.MoreList.removelast',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cTait_2eMoreList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__14597] :
( t(Vvar__1___24Anonymous__14597,V0__A)
& ? [Vvar__2___24Anonymous__14598] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__14598)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__14598)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14597,Vvar__2___24Anonymous__14598)
& ( ( Vvar__2___24Anonymous__14598 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cTait_2eMoreList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__14609] :
( t(Vvar__1___24Anonymous__14609,V0__A)
& ? [Vvar__2___24Anonymous__14610] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__14610)
& Vvar__2___24Anonymous__14598 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14609,Vvar__2___24Anonymous__14610)
& cTait_2eMoreList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14597,cTait_2eMoreList_2eremovelast___24a2(V0__A,Vvar__2___24Anonymous__14598)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Tait.MoreList.rev_acc',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)
& cTait_2eMoreList_2erev__acc___24a3(V0__A,V2__l,V3__l_27) = V3__l_27 )
| ? [Vvar__1___24Anonymous__14557] :
( t(Vvar__1___24Anonymous__14557,V0__A)
& ? [Vvar__2___24Anonymous__14558] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__14558)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14557,Vvar__2___24Anonymous__14558)
& cTait_2eMoreList_2erev__acc___24a3(V0__A,V2__l,V3__l_27) = cTait_2eMoreList_2erev__acc___24a3(V0__A,Vvar__2___24Anonymous__14558,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14557,V3__l_27)) ) ) ) ) ) ).
fof('$_def_Tait.MoreList.seq',axiom,
! [V1__start,V2__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__len)
=> ( ( V2__len = cCoq_2eInit_2eDatatypes_2eO
& cTait_2eMoreList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__0___24Anonymous__14564] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14564)
& V2__len = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14564)
& cTait_2eMoreList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,V1__start,cTait_2eMoreList_2eseq___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__start),Vvar__0___24Anonymous__14564)) ) ) ) ).
fof('$_def_Tait.Subst.shift',axiom,
! [V0__s] :
( cTait_2eSubst_2esubstitution___24t(V0__s)
=> ? [Vvar__0__support__463] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__0__support__463)
& ? [Vvar__1__shift__464] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__shift__464)
& V0__s = cTait_2eSubst_2emk__sub___24a2(Vvar__0__support__463,Vvar__1__shift__464)
& cTait_2eSubst_2eshift___24a1(V0__s) = Vvar__1__shift__464 ) ) ) ).
fof('$_def_Tait.Subst.sub',axiom,
! [V1__r,V2__rs] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> ( ? [Vvar__0___24Anonymous__471] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__471)
& V1__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__471)
& cTait_2eSubst_2esub___24a2(V1__r,V2__rs) = cCoq_2eLists_2eList_2enth___24a4(cTait_2eTerm_2eterm,Vvar__0___24Anonymous__471,cTait_2eSubst_2esupport___24a1(V2__rs),cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__471,cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2eterm,cTait_2eSubst_2esupport___24a1(V2__rs))),cTait_2eSubst_2eshift___24a1(V2__rs)))) )
| ? [Vvar__0___24Anonymous__472] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__472)
& ? [Vvar__1___24Anonymous__473] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__473)
& V1__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__472,Vvar__1___24Anonymous__473)
& cTait_2eSubst_2esub___24a2(V1__r,V2__rs) = cTait_2eTerm_2eApp___24a2(cTait_2eSubst_2esub___24a2(Vvar__0___24Anonymous__472,V2__rs),cTait_2eSubst_2esub___24a2(Vvar__1___24Anonymous__473,V2__rs)) ) )
| ? [Vvar__0___24Anonymous__475] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__475)
& ? [Vvar__1___24Anonymous__476] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__476)
& V1__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__475,Vvar__1___24Anonymous__476)
& cTait_2eSubst_2esub___24a2(V1__r,V2__rs) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__475,cTait_2eSubst_2esub___24a2(Vvar__1___24Anonymous__476,cTait_2eSubst_2esublift___24a1(V2__rs))) ) ) ) ) ).
fof('$_def_Tait.Subst.sub1',axiom,
! [V0__r] : cTait_2eSubst_2esub1___24a1(V0__r) = cTait_2eSubst_2emk__sub___24a2(cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,V0__r,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)),cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_def_Tait.Subst.sublift',axiom,
! [V0__rs] : cTait_2eSubst_2esublift___24a1(V0__rs) = cTait_2eSubst_2emk__sub___24a2(cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eLists_2eList_2emap___24a4(cTait_2eTerm_2eterm,cTait_2eTerm_2eterm,cTait_2eTerm_2eup___24a1(cCoq_2eInit_2eDatatypes_2eO),cTait_2eSubst_2esupport___24a1(V0__rs))),cCoq_2eInit_2eDatatypes_2eS___24a1(cTait_2eSubst_2eshift___24a1(V0__rs))) ).
fof('$_def_Tait.Subst.support',axiom,
! [V0__s] :
( cTait_2eSubst_2esubstitution___24t(V0__s)
=> ? [Vvar__0__support__458] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__0__support__458)
& ? [Vvar__1__shift__459] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__shift__459)
& V0__s = cTait_2eSubst_2emk__sub___24a2(Vvar__0__support__458,Vvar__1__shift__459)
& cTait_2eSubst_2esupport___24a1(V0__s) = Vvar__0__support__458 ) ) ) ).
fof('$_def_Tait.Subst2.Joachimski.PushList',axiom,
! [V1__l,V2__theta] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)
& cTait_2eSubst2_2eJoachimski_2ePushList___24a2(V1__l,V2__theta) = V2__theta )
| ? [Vvar__1___24Anonymous__35011] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__35011)
& ? [Vvar__2___24Anonymous__35012] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__2___24Anonymous__35012)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__1___24Anonymous__35011,Vvar__2___24Anonymous__35012)
& cTait_2eSubst2_2eJoachimski_2ePushList___24a2(V1__l,V2__theta) = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__1___24Anonymous__35011,cTait_2eSubst2_2eJoachimski_2ePushList___24a2(Vvar__2___24Anonymous__35012,V2__theta)) ) ) ) ) ).
fof('$_def_Tait.Subst2.Joachimski.sub',axiom,
! [V1__r,V2__theta] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> ( ? [Vvar__0___24Anonymous__2299] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2299)
& V1__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__2299)
& cTait_2eSubst2_2eJoachimski_2esub___24a2(V1__r,V2__theta) = cTait_2eSubst2_2eJoachimski_2esub_27___24a2(Vvar__0___24Anonymous__2299,V2__theta) )
| ? [Vvar__0___24Anonymous__2300] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__2300)
& ? [Vvar__1___24Anonymous__2301] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__2301)
& V1__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__2300,Vvar__1___24Anonymous__2301)
& cTait_2eSubst2_2eJoachimski_2esub___24a2(V1__r,V2__theta) = cTait_2eTerm_2eApp___24a2(cTait_2eSubst2_2eJoachimski_2esub___24a2(Vvar__0___24Anonymous__2300,V2__theta),cTait_2eSubst2_2eJoachimski_2esub___24a2(Vvar__1___24Anonymous__2301,V2__theta)) ) )
| ? [Vvar__0___24Anonymous__2303] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__2303)
& ? [Vvar__1___24Anonymous__2304] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__2304)
& V1__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__2303,Vvar__1___24Anonymous__2304)
& cTait_2eSubst2_2eJoachimski_2esub___24a2(V1__r,V2__theta) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__2303,cTait_2eSubst2_2eJoachimski_2esub___24a2(Vvar__1___24Anonymous__2304,cTait_2eSubst2_2eJoachimski_2eDot___24a2(cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eDatatypes_2eO),cTait_2eSubst2_2eJoachimski_2esublift___24a2(V2__theta,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))) ) ) ) ) ).
fof('$_def_Tait.Subst2.Joachimski.sub\'',axiom,
! [V1__k,V2__theta] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( ( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V2__theta)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eO
& ( ? [Vvar__0___24Anonymous__2282] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__2282)
& ? [Vvar__1___24Anonymous__2283] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vvar__1___24Anonymous__2283)
& V2__theta = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__2282,Vvar__1___24Anonymous__2283)
& cTait_2eSubst2_2eJoachimski_2esub_27___24a2(V1__k,V2__theta) = Vvar__0___24Anonymous__2282 ) )
| ? [Vvar__0___24Anonymous__2285] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2285)
& V2__theta = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__2285)
& cTait_2eSubst2_2eJoachimski_2esub_27___24a2(V1__k,V2__theta) = cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__k,Vvar__0___24Anonymous__2285)) ) ) ) )
| ? [Vvar__0___24Anonymous__2286] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2286)
& ( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V2__theta)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2286)
& ( ? [Vvar__0___24Anonymous__2291] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__2291)
& ? [Vvar__1___24Anonymous__2292] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vvar__1___24Anonymous__2292)
& V2__theta = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__2291,Vvar__1___24Anonymous__2292)
& cTait_2eSubst2_2eJoachimski_2esub_27___24a2(V1__k,V2__theta) = cTait_2eSubst2_2eJoachimski_2esub_27___24a2(Vvar__0___24Anonymous__2286,Vvar__1___24Anonymous__2292) ) )
| ? [Vvar__0___24Anonymous__2294] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2294)
& V2__theta = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__2294)
& cTait_2eSubst2_2eJoachimski_2esub_27___24a2(V1__k,V2__theta) = cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__k,Vvar__0___24Anonymous__2294)) ) ) ) ) ) ) ) ).
fof('$_def_Tait.Subst2.Joachimski.sublift',axiom,
! [V1__theta,V2__n] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V1__theta)
=> ( ? [Vvar__0___24Anonymous__2274] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__2274)
& ? [Vvar__1___24Anonymous__2275] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vvar__1___24Anonymous__2275)
& V1__theta = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__2274,Vvar__1___24Anonymous__2275)
& cTait_2eSubst2_2eJoachimski_2esublift___24a2(V1__theta,V2__n) = cTait_2eSubst2_2eJoachimski_2eDot___24a2(cTait_2eTerm_2elift___24a3(cCoq_2eInit_2eDatatypes_2eO,V2__n,Vvar__0___24Anonymous__2274),cTait_2eSubst2_2eJoachimski_2esublift___24a2(Vvar__1___24Anonymous__2275,V2__n)) ) )
| ? [Vvar__0___24Anonymous__2277] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2277)
& V1__theta = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__2277)
& cTait_2eSubst2_2eJoachimski_2esublift___24a2(V1__theta,V2__n) = cTait_2eSubst2_2eJoachimski_2eUp___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__2277,V2__n)) ) ) ) ).
fof('$_def_Tait.Subst2.above',axiom,
! [V0__k,V1__r] :
( cTait_2eSubst2_2eabove___24a2(V0__k,V1__r)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__k,V2__n))
=> cTait_2eTerm_2eoccurs___24a2(V2__n,V1__r) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Tait.TaitCore.F',axiom,
! [V0__rhos,V1__rho,V2__r,V3__k] :
( cTait_2eTaitCore_2eF___24a4(V0__rhos,V1__rho,V2__r,V3__k)
<=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,V2__r,V1__rho)
& p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V0__rhos),V3__k)) ) ) ).
fof('$_def_Tait.Term.arrow_left',axiom,
! [V0__sigma] :
( cTait_2eTerm_2etype___24t(V0__sigma)
=> ( ( V0__sigma = cTait_2eTerm_2eIota
& cTait_2eTerm_2earrow__left___24a1(V0__sigma) = cTait_2eTerm_2edtype )
| ? [Vvar__0___24Anonymous__1533] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__1533)
& ? [Vvar__1___24Anonymous__1534] :
( cTait_2eTerm_2etype___24t(Vvar__1___24Anonymous__1534)
& V0__sigma = cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__1533,Vvar__1___24Anonymous__1534)
& cTait_2eTerm_2earrow__left___24a1(V0__sigma) = Vvar__0___24Anonymous__1533 ) ) ) ) ).
fof('$_def_Tait.Term.arrow_right',axiom,
! [V0__sigma] :
( cTait_2eTerm_2etype___24t(V0__sigma)
=> ( ( V0__sigma = cTait_2eTerm_2eIota
& cTait_2eTerm_2earrow__right___24a1(V0__sigma) = cTait_2eTerm_2edtype )
| ? [Vvar__0___24Anonymous__297] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__297)
& ? [Vvar__1___24Anonymous__298] :
( cTait_2eTerm_2etype___24t(Vvar__1___24Anonymous__298)
& V0__sigma = cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__297,Vvar__1___24Anonymous__298)
& cTait_2eTerm_2earrow__right___24a1(V0__sigma) = Vvar__1___24Anonymous__298 ) ) ) ) ).
fof('$_def_Tait.Term.down',axiom,
! [V1__l,V2__r] :
( cTait_2eTerm_2eterm___24t(V2__r)
=> ( ? [Vvar__0___24Anonymous__2234] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2234)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2234)
=> ( V2__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__2234)
& ( ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__2234))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V1__l,Vvar__0___24Anonymous__2234) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__2234),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__2234,V1__l))
& cTait_2eTerm_2edown___24a2(V1__l,V2__r) = cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2epred___24a1(Vvar__0___24Anonymous__2234)) )
| ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__2234,V1__l))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V1__l,Vvar__0___24Anonymous__2234) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__2234),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__2234,V1__l))
& cTait_2eTerm_2edown___24a2(V1__l,V2__r) = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__2234) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2246] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__2246)
& ? [Vvar__1___24Anonymous__2247] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__2247)
& V2__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__2246,Vvar__1___24Anonymous__2247)
& cTait_2eTerm_2edown___24a2(V1__l,V2__r) = cTait_2eTerm_2eApp___24a2(cTait_2eTerm_2edown___24a2(V1__l,Vvar__0___24Anonymous__2246),cTait_2eTerm_2edown___24a2(V1__l,Vvar__1___24Anonymous__2247)) ) )
| ? [Vvar__0___24Anonymous__2249] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__2249)
& ? [Vvar__1___24Anonymous__2250] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__2250)
& V2__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__2249,Vvar__1___24Anonymous__2250)
& cTait_2eTerm_2edown___24a2(V1__l,V2__r) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__2249,cTait_2eTerm_2edown___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__l),Vvar__1___24Anonymous__2250)) ) ) ) ) ).
fof('$_def_Tait.Term.lift',axiom,
! [V1__l,V2__k,V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ( ? [Vvar__0___24Anonymous__2210] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2210)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2210)
=> ( V3__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__2210)
& ( ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__2210))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V1__l,Vvar__0___24Anonymous__2210) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__2210),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__2210,V1__l))
& cTait_2eTerm_2elift___24a3(V1__l,V2__k,V3__r) = cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V2__k,Vvar__0___24Anonymous__2210)) )
| ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__2210,V1__l))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V1__l,Vvar__0___24Anonymous__2210) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__2210),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__2210,V1__l))
& cTait_2eTerm_2elift___24a3(V1__l,V2__k,V3__r) = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__2210) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2222] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__2222)
& ? [Vvar__1___24Anonymous__2223] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__2223)
& V3__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__2222,Vvar__1___24Anonymous__2223)
& cTait_2eTerm_2elift___24a3(V1__l,V2__k,V3__r) = cTait_2eTerm_2eApp___24a2(cTait_2eTerm_2elift___24a3(V1__l,V2__k,Vvar__0___24Anonymous__2222),cTait_2eTerm_2elift___24a3(V1__l,V2__k,Vvar__1___24Anonymous__2223)) ) )
| ? [Vvar__0___24Anonymous__2225] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__2225)
& ? [Vvar__1___24Anonymous__2226] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__2226)
& V3__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__2225,Vvar__1___24Anonymous__2226)
& cTait_2eTerm_2elift___24a3(V1__l,V2__k,V3__r) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__2225,cTait_2eTerm_2elift___24a3(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__l),V2__k,Vvar__1___24Anonymous__2226)) ) ) ) ) ).
fof('$_def_Tait.Term.occurs',axiom,
! [V1__k,V2__r] :
( cTait_2eTerm_2eterm___24t(V2__r)
=> ( ? [Vvar__0___24Anonymous__490] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__490)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__490)
=> ( V2__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__490)
& ( ( Vvar__0___24Anonymous__490 = V1__k
& cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a2(Vvar__0___24Anonymous__490,V1__k) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__508___24a2(V1__k,Vvar__0___24Anonymous__490),c_24__prop__509___24a2(V1__k,Vvar__0___24Anonymous__490))
& cTait_2eTerm_2eoccurs___24a2(V1__k,V2__r) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__490 != V1__k
& cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a2(Vvar__0___24Anonymous__490,V1__k) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__510___24a2(V1__k,Vvar__0___24Anonymous__490),c_24__prop__511___24a2(V1__k,Vvar__0___24Anonymous__490))
& cTait_2eTerm_2eoccurs___24a2(V1__k,V2__r) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__502] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__502)
& ? [Vvar__1___24Anonymous__503] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__503)
& V2__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__502,Vvar__1___24Anonymous__503)
& cTait_2eTerm_2eoccurs___24a2(V1__k,V2__r) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cTait_2eTerm_2eoccurs___24a2(V1__k,Vvar__0___24Anonymous__502),cTait_2eTerm_2eoccurs___24a2(V1__k,Vvar__1___24Anonymous__503)) ) )
| ? [Vvar__0___24Anonymous__505] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__505)
& ? [Vvar__1___24Anonymous__506] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__506)
& V2__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__505,Vvar__1___24Anonymous__506)
& cTait_2eTerm_2eoccurs___24a2(V1__k,V2__r) = cTait_2eTerm_2eoccurs___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__k),Vvar__1___24Anonymous__506) ) ) ) ) ).
fof('$_def_Tait.Term.term_rec',axiom,
! [V0__P] : cTait_2eTerm_2eterm__rec___24a1(V0__P) = cTait_2eTerm_2eterm__rect___24a1(V0__P) ).
fof('$_def_Tait.Term.term_rect',axiom,
! [V0__P,V1__f,V2__f,V3__f,V5__t] :
( c_24__type__1430___24t(V0__P,V0__P)
=> ( cTait_2eTerm_2eterm___24t(V5__t)
=> ( ? [Vvar__0___24Anonymous__1422] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1422)
& V5__t = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__1422)
& cTait_2eTerm_2eterm__rect___24a5(V0__P,V1__f,V2__f,V3__f,V5__t) = happ(V1__f,Vvar__0___24Anonymous__1422) )
| ? [Vvar__0___24Anonymous__1423] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__1423)
& ? [Vvar__1___24Anonymous__1424] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__1424)
& V5__t = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__1423,Vvar__1___24Anonymous__1424)
& cTait_2eTerm_2eterm__rect___24a5(V0__P,V1__f,V2__f,V3__f,V5__t) = happ(happ(happ(happ(V2__f,Vvar__0___24Anonymous__1423),cTait_2eTerm_2eterm__rect___24a5(V0__P,V1__f,V2__f,V3__f,Vvar__0___24Anonymous__1423)),Vvar__1___24Anonymous__1424),cTait_2eTerm_2eterm__rect___24a5(V0__P,V1__f,V2__f,V3__f,Vvar__1___24Anonymous__1424)) ) )
| ? [Vvar__0___24Anonymous__1426] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__1426)
& ? [Vvar__1___24Anonymous__1427] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__1427)
& V5__t = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__1426,Vvar__1___24Anonymous__1427)
& cTait_2eTerm_2eterm__rect___24a5(V0__P,V1__f,V2__f,V3__f,V5__t) = happ(happ(happ(V3__f,Vvar__0___24Anonymous__1426),Vvar__1___24Anonymous__1427),cTait_2eTerm_2eterm__rect___24a5(V0__P,V1__f,V2__f,V3__f,Vvar__1___24Anonymous__1427)) ) ) ) ) ) ).
fof('$_def_Tait.Term.type_rec',axiom,
! [V0__P] : cTait_2eTerm_2etype__rec___24a1(V0__P) = cTait_2eTerm_2etype__rect___24a1(V0__P) ).
fof('$_def_Tait.Term.type_rect',axiom,
! [V0__P,V1__f,V2__f,V4__t] :
( c_24__type__1357___24t(V0__P,V0__P)
=> ( cTait_2eTerm_2etype___24t(V4__t)
=> ( ( V4__t = cTait_2eTerm_2eIota
& cTait_2eTerm_2etype__rect___24a4(V0__P,V1__f,V2__f,V4__t) = V1__f )
| ? [Vvar__0___24Anonymous__1353] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__1353)
& ? [Vvar__1___24Anonymous__1354] :
( cTait_2eTerm_2etype___24t(Vvar__1___24Anonymous__1354)
& V4__t = cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__1353,Vvar__1___24Anonymous__1354)
& cTait_2eTerm_2etype__rect___24a4(V0__P,V1__f,V2__f,V4__t) = happ(happ(happ(happ(V2__f,Vvar__0___24Anonymous__1353),cTait_2eTerm_2etype__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__1353)),Vvar__1___24Anonymous__1354),cTait_2eTerm_2etype__rect___24a4(V0__P,V1__f,V2__f,Vvar__1___24Anonymous__1354)) ) ) ) ) ) ).
fof('$_def_Tait.Term.up',axiom,
! [V1__l,V2__r] :
( cTait_2eTerm_2eterm___24t(V2__r)
=> ( ? [Vvar__0___24Anonymous__516] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__516)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__516)
=> ( V2__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__516)
& ( ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__516))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V1__l,Vvar__0___24Anonymous__516) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__516),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__516,V1__l))
& cTait_2eTerm_2eup___24a2(V1__l,V2__r) = cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__516)) )
| ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__516,V1__l))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V1__l,Vvar__0___24Anonymous__516) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__516),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__516,V1__l))
& cTait_2eTerm_2eup___24a2(V1__l,V2__r) = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__516) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__528] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__528)
& ? [Vvar__1___24Anonymous__529] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__529)
& V2__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__528,Vvar__1___24Anonymous__529)
& cTait_2eTerm_2eup___24a2(V1__l,V2__r) = cTait_2eTerm_2eApp___24a2(cTait_2eTerm_2eup___24a2(V1__l,Vvar__0___24Anonymous__528),cTait_2eTerm_2eup___24a2(V1__l,Vvar__1___24Anonymous__529)) ) )
| ? [Vvar__0___24Anonymous__531] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__531)
& ? [Vvar__1___24Anonymous__532] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__532)
& V2__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__531,Vvar__1___24Anonymous__532)
& cTait_2eTerm_2eup___24a2(V1__l,V2__r) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__531,cTait_2eTerm_2eup___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__l),Vvar__1___24Anonymous__532)) ) ) ) ) ).
fof('$_def_Tait.Typing.TypJ',axiom,
! [V0__rhos,V1__r,V2__rho] :
( cTait_2eTyping_2eTypJ___24a3(V0__rhos,V1__r,V2__rho)
<=> ( cTait_2eTyping_2eCorTyp___24a2(V0__rhos,V1__r)
& cTait_2eTyping_2etyp___24a2(V0__rhos,V1__r) = V2__rho ) ) ).
fof('$_def_Tait.Typing.context',axiom,
! [Vvar__109] :
( cTait_2eTyping_2econtext___24t(Vvar__109)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__109) ) ).
fof('$_def_Tait.Typing.ext_ctx',axiom,
! [V0__rhos,V1__k,V2__rho] : cTait_2eTyping_2eext__ctx___24a3(V0__rhos,V1__k,V2__rho) = cTait_2eMoreList_2econsn___24a4(cTait_2eTerm_2etype,cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__k),cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V0__rhos)),V2__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)) ).
fof('$_def_Tait.Typing.typ',axiom,
! [V1__rhos,V2__r] :
( cTait_2eTerm_2eterm___24t(V2__r)
=> ( ? [Vvar__0___24Anonymous__303] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__303)
& V2__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__303)
& cTait_2eTyping_2etyp___24a2(V1__rhos,V2__r) = cCoq_2eLists_2eList_2enth___24a4(cTait_2eTerm_2etype,Vvar__0___24Anonymous__303,V1__rhos,cTait_2eTerm_2edtype) )
| ? [Vvar__0___24Anonymous__304] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__304)
& ? [Vvar__1___24Anonymous__305] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__305)
& V2__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__304,Vvar__1___24Anonymous__305)
& cTait_2eTyping_2etyp___24a2(V1__rhos,V2__r) = cTait_2eTerm_2earrow__right___24a1(cTait_2eTyping_2etyp___24a2(V1__rhos,Vvar__0___24Anonymous__304)) ) )
| ? [Vvar__0___24Anonymous__307] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__307)
& ? [Vvar__1___24Anonymous__308] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__308)
& V2__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__307,Vvar__1___24Anonymous__308)
& cTait_2eTyping_2etyp___24a2(V1__rhos,V2__r) = cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__307,cTait_2eTyping_2etyp___24a2(cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,Vvar__0___24Anonymous__307,V1__rhos),Vvar__1___24Anonymous__308)) ) ) ) ) ).
fof('$_def_Tait.nc.ncP',axiom,
! [V0__A,V1__P] :
( cTait_2enc_2encP___24a2(V0__A,V1__P)
<=> ! [V3__a_27] :
( t(V3__a_27,V0__A)
=> ( cTait_2enc_2enc___24a2(V0__A,V3__a_27) = c_24Proof
=> p(happ(V1__P,V3__a_27)) ) ) ) ).
fof('$_def_Tait.nc.ncP2',axiom,
! [V0__A,V1__B,V2__P] :
( cTait_2enc_2encP2___24a3(V0__A,V1__B,V2__P)
<=> ! [V5__a_27] :
( t(V5__a_27,V0__A)
=> ( cTait_2enc_2enc___24a2(V0__A,V5__a_27) = c_24Proof
=> ! [V7__b_27] :
( t(V7__b_27,V1__B)
=> ( cTait_2enc_2enc___24a2(V1__B,V7__b_27) = c_24Proof
=> p(happ(happ(V2__P,V5__a_27),V7__b_27)) ) ) ) ) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__35469,Vvar__1___24Anonymous__35470,Vvar__0__P__35471,Vvar__1___24Anonymous__35472] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__35469) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__35471) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__35104,Vvar__1___24Anonymous__35105,Vvar__2___24Anonymous__35106] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__35104,Vvar__1___24Anonymous__35105,Vvar__2___24Anonymous__35106) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__35549,Vvar__1__Plt__35550,Vvar__2__Pgt__35551,Vvar__3___24Anonymous__35552,Vvar__0__Peq__35553,Vvar__1__Plt__35554,Vvar__2__Pgt__35555,Vvar__3___24Anonymous__35556] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__35549,Vvar__1__Plt__35550,Vvar__2__Pgt__35551) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__35553,Vvar__1__Plt__35554,Vvar__2__Pgt__35555) ).
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__35] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__850,Vvar__1___24Anonymous__851,Vvar__0__A__852] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__850,Vvar__1___24Anonymous__851) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__852) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__2730,Vvar__1__B__2731,Vvar__2___24Anonymous__2732,Vvar__0__A__2733,Vvar__1__B__2734,Vvar__2___24Anonymous__2735] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__2730,Vvar__1__B__2731,Vvar__2___24Anonymous__2732) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__2733,Vvar__1__B__2734,Vvar__2___24Anonymous__2735) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__48,Vvar__0__A__49,Vvar__1___24Anonymous__50,Vvar__2___24Anonymous__51] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__48) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__49,Vvar__1___24Anonymous__50,Vvar__2___24Anonymous__51) ).
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__30796,Vvar__1__B__30797,Vvar__2___24Anonymous__30798,Vvar__0__A__30799,Vvar__1__B__30800,Vvar__2___24Anonymous__30801] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__30796,Vvar__1__B__30797,Vvar__2___24Anonymous__30798) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__30799,Vvar__1__B__30800) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__433,Vvar__1__B__434,Vvar__2___24Anonymous__435,Vvar__0__A__436,Vvar__1__B__437,Vvar__2___24Anonymous__438] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__433,Vvar__1__B__434) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__436,Vvar__1__B__437) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__2622] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2622) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__379] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__379) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__367,Vvar__0___24Anonymous__368] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__367) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__368) ).
fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__46043,Vvar__1___24Anonymous__46044] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__46043,Vvar__1___24Anonymous__46044) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__46052] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__46052) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__37892,Vvar__1___24Anonymous__37893,Vvar__0__x__37894,Vvar__1__n__37895,Vvar__2___24Anonymous__37896] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__37892) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__37894,Vvar__1__n__37895) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__30827,Vvar__1___24Anonymous__30828] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__30827,Vvar__1___24Anonymous__30828) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__37749,Vvar__1__lt__37750,Vvar__2__eq__37751,Vvar__3__x__37752,Vvar__4__y__37753,Vvar__5___24Anonymous__37754,Vvar__0__X__37755,Vvar__1__lt__37756,Vvar__2__eq__37757,Vvar__3__x__37758,Vvar__4__y__37759,Vvar__5___24Anonymous__37760] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__37749,Vvar__1__lt__37750,Vvar__2__eq__37751,Vvar__3__x__37752,Vvar__4__y__37753) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__37755,Vvar__1__lt__37756,Vvar__2__eq__37757,Vvar__3__x__37758,Vvar__4__y__37759) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__36417,Vvar__0__n__36418,Vvar__1___24Anonymous__36419] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__36417) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__36418,Vvar__1___24Anonymous__36419) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__33886,Vvar__0__A__33887,Vvar__1__h__33888,Vvar__2__n__33889,Vvar__3___24Anonymous__33890] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__33886) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__33887,Vvar__1__h__33888,Vvar__2__n__33889,Vvar__3___24Anonymous__33890) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__2988,Vvar__1___24Anonymous__2989,Vvar__0__C__2990,Vvar__1___24Anonymous__2991] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__2988,Vvar__1___24Anonymous__2989) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__2990,Vvar__1___24Anonymous__2991) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__920,Vvar__1___24Anonymous__921,Vvar__0__C__922,Vvar__1___24Anonymous__923,Vvar__2___24Anonymous__924] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__920,Vvar__1___24Anonymous__921) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__922,Vvar__1___24Anonymous__923,Vvar__2___24Anonymous__924) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__3135,Vvar__1___24Anonymous__3136] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__3135,Vvar__1___24Anonymous__3136) ).
fof('$_discrim_Coq.micromega.RMicromega.C0$Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eC0 != cCoq_2emicromega_2eRMicromega_2eC1 ).
fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).
fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).
fof('$_discrim_Coq.micromega.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__15801,Vvar__1___24Anonymous__15802,Vvar__0__C__15803,Vvar__1___24Anonymous__15804] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__15801,Vvar__1___24Anonymous__15802) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__15803,Vvar__1___24Anonymous__15804) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__31236,Vvar__1__TX__31237,Vvar__2__AA__31238,Vvar__3__AF__31239,Vvar__0__TA__31240,Vvar__1__TX__31241,Vvar__2__AA__31242,Vvar__3__AF__31243] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__31236,Vvar__1__TX__31237,Vvar__2__AA__31238,Vvar__3__AF__31239) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__31240,Vvar__1__TX__31241,Vvar__2__AA__31242,Vvar__3__AF__31243) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__34106,Vvar__1___24Anonymous__34107] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__34106,Vvar__1___24Anonymous__34107) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__8293,Vvar__0__C__8294] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8293) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8294) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__19464,Vvar__0__C__19465] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__19464) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__19465) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__17338,Vvar__1___24Anonymous__17339,Vvar__0__C__17340,Vvar__1___24Anonymous__17341,Vvar__2___24Anonymous__17342] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__17338,Vvar__1___24Anonymous__17339) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__17340,Vvar__1___24Anonymous__17341,Vvar__2___24Anonymous__17342) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__18136,Vvar__1___24Anonymous__18137] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__18136,Vvar__1___24Anonymous__18137) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__45518,Vvar__1__req__45519,Vvar__2__reqb__45520,Vvar__3___24Anonymous__45521] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__45518,Vvar__1__req__45519,Vvar__2__reqb__45520) ).
fof('$_discrim_Tait.Subst2.Joachimski.Dot$Tait.Subst2.Joachimski.Up',axiom,
! [Vvar__0___24Anonymous__2261,Vvar__1___24Anonymous__2262,Vvar__0___24Anonymous__2263] : cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__2261,Vvar__1___24Anonymous__2262) != cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__2263) ).
fof('$_discrim_Tait.Term.Iota$Tait.Term.Arrow',axiom,
! [Vvar__0___24Anonymous__77,Vvar__1___24Anonymous__78] : cTait_2eTerm_2eIota != cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__77,Vvar__1___24Anonymous__78) ).
fof('$_discrim_Tait.Term.Var$Tait.Term.App',axiom,
! [Vvar__0___24Anonymous__96,Vvar__0___24Anonymous__97,Vvar__1___24Anonymous__98] : cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__96) != cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__97,Vvar__1___24Anonymous__98) ).
fof('$_fix_15491_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__15491__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__15495] :
( t(Vvar__1___24Anonymous__15495,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__15496] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__15496)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__15495,Vvar__2___24Anonymous__15496)
& c_24__fix__15491__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__15495,c_24__fix__15491__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__15496,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_33859_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__33859__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__33864] :
( t(Vvar__1__h__33864,Vv__CANONICAL__0)
& ? [Vvar__2__n__33865] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__33865)
& ? [Vvar__3___24Anonymous__33866] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vvar__2__n__33865,Vvar__3___24Anonymous__33866)
& Vv__CANONICAL__4 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vvar__1__h__33864,Vvar__2__n__33865,Vvar__3___24Anonymous__33866)
& c_24__fix__33859__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__33864,c_24__fix__33859__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2__n__33865,Vvar__3___24Anonymous__33866,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_fix_35064_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__35079] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35079)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35079)
& ( ? [Vvar__0___24Anonymous__35083] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35083)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35083)
& c_24__fix__35064__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__35064__1__add__carry___24a2(Vvar__0___24Anonymous__35079,Vvar__0___24Anonymous__35083)) )
| ? [Vvar__0___24Anonymous__35084] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35084)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35084)
& c_24__fix__35064__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__35064__1__add__carry___24a2(Vvar__0___24Anonymous__35079,Vvar__0___24Anonymous__35084)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__35064__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__35079)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__35085] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35085)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35085)
& ( ? [Vvar__0___24Anonymous__35089] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35089)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35089)
& c_24__fix__35064__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__35064__1__add__carry___24a2(Vvar__0___24Anonymous__35085,Vvar__0___24Anonymous__35089)) )
| ? [Vvar__0___24Anonymous__35090] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35090)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35090)
& c_24__fix__35064__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__35085,Vvar__0___24Anonymous__35090)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__35064__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__35085)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__35091] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35091)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35091)
& c_24__fix__35064__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__35091)) )
| ? [Vvar__0___24Anonymous__35092] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35092)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35092)
& c_24__fix__35064__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__35092)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__35064__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_fix_46038_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__46039] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46039)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__46039)
& c_24__fix__46038__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__46038__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__46039)) )
| ? [Vvar__0___24Anonymous__46040] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46040)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__46040)
& c_24__fix__46038__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__46040) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__46038__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__35477,Vvar__0__P__35478,Vvar__1___24Anonymous__35479,Vvar__1___24Anonymous__35480] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__35477) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__35478)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__35477 = Vvar__0__P__35478 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__35473,Vvar__0__P__35474,Vvar__1___24Anonymous__35475,Vvar__1___24Anonymous__35476] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__35473) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__35474)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__35473 = Vvar__0__P__35474 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__35107,Vvar__0___24Anonymous__35108,Vvar__1___24Anonymous__35109,Vvar__1___24Anonymous__35110,Vvar__2___24Anonymous__35111,Vvar__2___24Anonymous__35112] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__35107,Vvar__1___24Anonymous__35109,Vvar__2___24Anonymous__35111) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__35108,Vvar__1___24Anonymous__35110,Vvar__2___24Anonymous__35112)
=> ( Vvar__2___24Anonymous__35111 = Vvar__2___24Anonymous__35112
& Vvar__1___24Anonymous__35109 = Vvar__1___24Anonymous__35110
& Vvar__0___24Anonymous__35107 = Vvar__0___24Anonymous__35108 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__35557,Vvar__0__Peq__35558,Vvar__1__Plt__35559,Vvar__1__Plt__35560,Vvar__2__Pgt__35561,Vvar__2__Pgt__35562,Vvar__3___24Anonymous__35563,Vvar__3___24Anonymous__35564] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__35557,Vvar__1__Plt__35559,Vvar__2__Pgt__35561) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__35558,Vvar__1__Plt__35560,Vvar__2__Pgt__35562)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__35561 = Vvar__2__Pgt__35562
& Vvar__1__Plt__35559 = Vvar__1__Plt__35560
& Vvar__0__Peq__35557 = Vvar__0__Peq__35558 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__35573,Vvar__0__Peq__35574,Vvar__1__Plt__35575,Vvar__1__Plt__35576,Vvar__2__Pgt__35577,Vvar__2__Pgt__35578,Vvar__3___24Anonymous__35579,Vvar__3___24Anonymous__35580] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__35573,Vvar__1__Plt__35575,Vvar__2__Pgt__35577) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__35574,Vvar__1__Plt__35576,Vvar__2__Pgt__35578)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__35577 = Vvar__2__Pgt__35578
& Vvar__1__Plt__35575 = Vvar__1__Plt__35576
& Vvar__0__Peq__35573 = Vvar__0__Peq__35574 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__35565,Vvar__0__Peq__35566,Vvar__1__Plt__35567,Vvar__1__Plt__35568,Vvar__2__Pgt__35569,Vvar__2__Pgt__35570,Vvar__3___24Anonymous__35571,Vvar__3___24Anonymous__35572] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__35565,Vvar__1__Plt__35567,Vvar__2__Pgt__35569) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__35566,Vvar__1__Plt__35568,Vvar__2__Pgt__35570)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__35569 = Vvar__2__Pgt__35570
& Vvar__1__Plt__35567 = Vvar__1__Plt__35568
& Vvar__0__Peq__35565 = Vvar__0__Peq__35566 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__857,Vvar__0__A__858] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__857) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__858)
=> Vvar__0__A__857 = Vvar__0__A__858 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__36,Vvar__0___24Anonymous__37] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__37)
=> Vvar__0___24Anonymous__36 = Vvar__0___24Anonymous__37 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__853,Vvar__0__A__854,Vvar__1___24Anonymous__855,Vvar__1___24Anonymous__856] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__853,Vvar__1___24Anonymous__855) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__854,Vvar__1___24Anonymous__856)
=> ( Vvar__1___24Anonymous__855 = Vvar__1___24Anonymous__856
& Vvar__0__A__853 = Vvar__0__A__854 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__54,Vvar__0__A__55,Vvar__1___24Anonymous__56,Vvar__1___24Anonymous__57,Vvar__2___24Anonymous__58,Vvar__2___24Anonymous__59] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__54,Vvar__1___24Anonymous__56,Vvar__2___24Anonymous__58) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__55,Vvar__1___24Anonymous__57,Vvar__2___24Anonymous__59)
=> ( Vvar__2___24Anonymous__58 = Vvar__2___24Anonymous__59
& Vvar__1___24Anonymous__56 = Vvar__1___24Anonymous__57
& Vvar__0__A__54 = Vvar__0__A__55 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__2736,Vvar__0__A__2737,Vvar__1__B__2738,Vvar__1__B__2739,Vvar__2___24Anonymous__2740,Vvar__2___24Anonymous__2741] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__2736,Vvar__1__B__2738,Vvar__2___24Anonymous__2740) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__2737,Vvar__1__B__2739,Vvar__2___24Anonymous__2741)
=> ( Vvar__2___24Anonymous__2740 = Vvar__2___24Anonymous__2741
& Vvar__1__B__2738 = Vvar__1__B__2739
& Vvar__0__A__2736 = Vvar__0__A__2737 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__2742,Vvar__0__A__2743,Vvar__1__B__2744,Vvar__1__B__2745,Vvar__2___24Anonymous__2746,Vvar__2___24Anonymous__2747] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__2742,Vvar__1__B__2744,Vvar__2___24Anonymous__2746) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__2743,Vvar__1__B__2745,Vvar__2___24Anonymous__2747)
=> ( Vvar__2___24Anonymous__2746 = Vvar__2___24Anonymous__2747
& Vvar__1__B__2744 = Vvar__1__B__2745
& Vvar__0__A__2742 = Vvar__0__A__2743 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__52,Vvar__0__A__53] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__52) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__53)
=> Vvar__0__A__52 = Vvar__0__A__53 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__874,Vvar__0__A__875,Vvar__1__B__876,Vvar__1__B__877,Vvar__2___24Anonymous__878,Vvar__2___24Anonymous__879,Vvar__3___24Anonymous__880,Vvar__3___24Anonymous__881] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__874,Vvar__1__B__876,Vvar__2___24Anonymous__878,Vvar__3___24Anonymous__880) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__875,Vvar__1__B__877,Vvar__2___24Anonymous__879,Vvar__3___24Anonymous__881)
=> ( Vvar__3___24Anonymous__880 = Vvar__3___24Anonymous__881
& Vvar__2___24Anonymous__878 = Vvar__2___24Anonymous__879
& Vvar__1__B__876 = Vvar__1__B__877
& Vvar__0__A__874 = Vvar__0__A__875 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__30702,Vvar__0__A__30703,Vvar__1__P__30704,Vvar__1__P__30705,Vvar__2__x__30706,Vvar__2__x__30707,Vvar__3___24Anonymous__30708,Vvar__3___24Anonymous__30709] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__30702,Vvar__1__P__30704,Vvar__2__x__30706) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__30703,Vvar__1__P__30705,Vvar__2__x__30707)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__30706 = Vvar__2__x__30707
& Vvar__1__P__30704 = Vvar__1__P__30705
& Vvar__0__A__30702 = Vvar__0__A__30703 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__45613,Vvar__0__A__45614,Vvar__1__P__45615,Vvar__1__P__45616,Vvar__2__Q__45617,Vvar__2__Q__45618,Vvar__3__x__45619,Vvar__3__x__45620,Vvar__4___24Anonymous__45621,Vvar__4___24Anonymous__45622,Vvar__5___24Anonymous__45623,Vvar__5___24Anonymous__45624] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__45613,Vvar__1__P__45615,Vvar__2__Q__45617,Vvar__3__x__45619) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__45614,Vvar__1__P__45616,Vvar__2__Q__45618,Vvar__3__x__45620)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__45619 = Vvar__3__x__45620
& Vvar__2__Q__45617 = Vvar__2__Q__45618
& Vvar__1__P__45615 = Vvar__1__P__45616
& Vvar__0__A__45613 = Vvar__0__A__45614 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__30743,Vvar__0__A__30744,Vvar__1__P__30745,Vvar__1__P__30746,Vvar__2__x__30747,Vvar__2__x__30748,Vvar__3___24Anonymous__30749,Vvar__3___24Anonymous__30750] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__30743,Vvar__1__P__30745,Vvar__2__x__30747,Vvar__3___24Anonymous__30749) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__30744,Vvar__1__P__30746,Vvar__2__x__30748,Vvar__3___24Anonymous__30750)
=> ( Vvar__3___24Anonymous__30749 = Vvar__3___24Anonymous__30750
& Vvar__2__x__30747 = Vvar__2__x__30748
& Vvar__1__P__30745 = Vvar__1__P__30746
& Vvar__0__A__30743 = Vvar__0__A__30744 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__45669,Vvar__0__A__45670,Vvar__1__P__45671,Vvar__1__P__45672,Vvar__2__Q__45673,Vvar__2__Q__45674,Vvar__3__x__45675,Vvar__3__x__45676,Vvar__4___24Anonymous__45677,Vvar__4___24Anonymous__45678,Vvar__5___24Anonymous__45679,Vvar__5___24Anonymous__45680] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__45669,Vvar__1__P__45671,Vvar__2__Q__45673,Vvar__3__x__45675,Vvar__4___24Anonymous__45677,Vvar__5___24Anonymous__45679) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__45670,Vvar__1__P__45672,Vvar__2__Q__45674,Vvar__3__x__45676,Vvar__4___24Anonymous__45678,Vvar__5___24Anonymous__45680)
=> ( Vvar__5___24Anonymous__45679 = Vvar__5___24Anonymous__45680
& Vvar__4___24Anonymous__45677 = Vvar__4___24Anonymous__45678
& Vvar__3__x__45675 = Vvar__3__x__45676
& Vvar__2__Q__45673 = Vvar__2__Q__45674
& Vvar__1__P__45671 = Vvar__1__P__45672
& Vvar__0__A__45669 = Vvar__0__A__45670 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__30802,Vvar__0__A__30803,Vvar__1__B__30804,Vvar__1__B__30805,Vvar__2___24Anonymous__30806,Vvar__2___24Anonymous__30807] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__30802,Vvar__1__B__30804,Vvar__2___24Anonymous__30806) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__30803,Vvar__1__B__30805,Vvar__2___24Anonymous__30807)
=> ( Vvar__2___24Anonymous__30806 = Vvar__2___24Anonymous__30807
& Vvar__1__B__30804 = Vvar__1__B__30805
& Vvar__0__A__30802 = Vvar__0__A__30803 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__30808,Vvar__0__A__30809,Vvar__1__B__30810,Vvar__1__B__30811,Vvar__2___24Anonymous__30812,Vvar__2___24Anonymous__30813] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__30808,Vvar__1__B__30810) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__30809,Vvar__1__B__30811)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__30810 = Vvar__1__B__30811
& Vvar__0__A__30808 = Vvar__0__A__30809 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__439,Vvar__0__A__440,Vvar__1__B__441,Vvar__1__B__442,Vvar__2___24Anonymous__443,Vvar__2___24Anonymous__444] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__439,Vvar__1__B__441) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__440,Vvar__1__B__442)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__441 = Vvar__1__B__442
& Vvar__0__A__439 = Vvar__0__A__440 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__445,Vvar__0__A__446,Vvar__1__B__447,Vvar__1__B__448,Vvar__2___24Anonymous__449,Vvar__2___24Anonymous__450] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__445,Vvar__1__B__447) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__446,Vvar__1__B__448)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__447 = Vvar__1__B__448
& Vvar__0__A__445 = Vvar__0__A__446 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__2623,Vvar__0___24Anonymous__2624] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2623) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2624)
=> Vvar__0___24Anonymous__2623 = Vvar__0___24Anonymous__2624 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__382,Vvar__0___24Anonymous__383] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__382) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__383)
=> Vvar__0___24Anonymous__382 = Vvar__0___24Anonymous__383 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__380,Vvar__0___24Anonymous__381] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__380) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__381)
=> Vvar__0___24Anonymous__380 = Vvar__0___24Anonymous__381 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__369,Vvar__0___24Anonymous__370] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__369) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__370)
=> Vvar__0___24Anonymous__369 = Vvar__0___24Anonymous__370 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__371,Vvar__0___24Anonymous__372] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__371) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__372)
=> Vvar__0___24Anonymous__371 = Vvar__0___24Anonymous__372 ) ).
fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__46045,Vvar__0__p__46046,Vvar__1___24Anonymous__46047,Vvar__1___24Anonymous__46048] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__46045,Vvar__1___24Anonymous__46047) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__46046,Vvar__1___24Anonymous__46048)
=> ( Vvar__1___24Anonymous__46047 = Vvar__1___24Anonymous__46048
& Vvar__0__p__46045 = Vvar__0__p__46046 ) ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__46053,Vvar__0___24Anonymous__46054] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__46053) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__46054)
=> Vvar__0___24Anonymous__46053 = Vvar__0___24Anonymous__46054 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__14663,Vvar__0__Qnum__14664,Vvar__1__Qden__14665,Vvar__1__Qden__14666] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__14663,Vvar__1__Qden__14665) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__14664,Vvar__1__Qden__14666)
=> ( Vvar__1__Qden__14665 = Vvar__1__Qden__14666
& Vvar__0__Qnum__14663 = Vvar__0__Qnum__14664 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__37811,Vvar__0__nonzero__37812,Vvar__1__cond__nonzero__37813,Vvar__1__cond__nonzero__37814] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__37811) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__37812)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__37811 = Vvar__0__nonzero__37812 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__37907,Vvar__0__x__37908,Vvar__1__n__37909,Vvar__1__n__37910,Vvar__2___24Anonymous__37911,Vvar__2___24Anonymous__37912] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__37907,Vvar__1__n__37909) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__37908,Vvar__1__n__37910)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__37909 = Vvar__1__n__37910
& Vvar__0__x__37907 = Vvar__0__x__37908 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__37897,Vvar__0__x__37898,Vvar__1___24Anonymous__37899,Vvar__1___24Anonymous__37900] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__37897) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__37898)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__37897 = Vvar__0__x__37898 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__37901,Vvar__0__x__37902,Vvar__1__n__37903,Vvar__1__n__37904,Vvar__2___24Anonymous__37905,Vvar__2___24Anonymous__37906] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__37901,Vvar__1__n__37903) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__37902,Vvar__1__n__37904)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__37903 = Vvar__1__n__37904
& Vvar__0__x__37901 = Vvar__0__x__37902 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__2351,Vvar__0___24Anonymous__2352,Vvar__1___24Anonymous__2353,Vvar__1___24Anonymous__2354,Vvar__2___24Anonymous__2355,Vvar__2___24Anonymous__2356,Vvar__3___24Anonymous__2357,Vvar__3___24Anonymous__2358,Vvar__4___24Anonymous__2359,Vvar__4___24Anonymous__2360,Vvar__5___24Anonymous__2361,Vvar__5___24Anonymous__2362,Vvar__6___24Anonymous__2363,Vvar__6___24Anonymous__2364,Vvar__7___24Anonymous__2365,Vvar__7___24Anonymous__2366] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__2351,Vvar__1___24Anonymous__2353,Vvar__2___24Anonymous__2355,Vvar__3___24Anonymous__2357,Vvar__4___24Anonymous__2359,Vvar__5___24Anonymous__2361,Vvar__6___24Anonymous__2363,Vvar__7___24Anonymous__2365) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__2352,Vvar__1___24Anonymous__2354,Vvar__2___24Anonymous__2356,Vvar__3___24Anonymous__2358,Vvar__4___24Anonymous__2360,Vvar__5___24Anonymous__2362,Vvar__6___24Anonymous__2364,Vvar__7___24Anonymous__2366)
=> ( Vvar__7___24Anonymous__2365 = Vvar__7___24Anonymous__2366
& Vvar__6___24Anonymous__2363 = Vvar__6___24Anonymous__2364
& Vvar__5___24Anonymous__2361 = Vvar__5___24Anonymous__2362
& Vvar__4___24Anonymous__2359 = Vvar__4___24Anonymous__2360
& Vvar__3___24Anonymous__2357 = Vvar__3___24Anonymous__2358
& Vvar__2___24Anonymous__2355 = Vvar__2___24Anonymous__2356
& Vvar__1___24Anonymous__2353 = Vvar__1___24Anonymous__2354
& Vvar__0___24Anonymous__2351 = Vvar__0___24Anonymous__2352 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__30829,Vvar__0___24Anonymous__30830,Vvar__1___24Anonymous__30831,Vvar__1___24Anonymous__30832] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__30829,Vvar__1___24Anonymous__30831) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__30830,Vvar__1___24Anonymous__30832)
=> ( Vvar__1___24Anonymous__30831 = Vvar__1___24Anonymous__30832
& Vvar__0___24Anonymous__30829 = Vvar__0___24Anonymous__30830 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__37773,Vvar__0__X__37774,Vvar__1__lt__37775,Vvar__1__lt__37776,Vvar__2__eq__37777,Vvar__2__eq__37778,Vvar__3__x__37779,Vvar__3__x__37780,Vvar__4__y__37781,Vvar__4__y__37782,Vvar__5___24Anonymous__37783,Vvar__5___24Anonymous__37784] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__37773,Vvar__1__lt__37775,Vvar__2__eq__37777,Vvar__3__x__37779,Vvar__4__y__37781) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__37774,Vvar__1__lt__37776,Vvar__2__eq__37778,Vvar__3__x__37780,Vvar__4__y__37782)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__37781 = Vvar__4__y__37782
& Vvar__3__x__37779 = Vvar__3__x__37780
& Vvar__2__eq__37777 = Vvar__2__eq__37778
& Vvar__1__lt__37775 = Vvar__1__lt__37776
& Vvar__0__X__37773 = Vvar__0__X__37774 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__37785,Vvar__0__X__37786,Vvar__1__lt__37787,Vvar__1__lt__37788,Vvar__2__eq__37789,Vvar__2__eq__37790,Vvar__3__x__37791,Vvar__3__x__37792,Vvar__4__y__37793,Vvar__4__y__37794,Vvar__5___24Anonymous__37795,Vvar__5___24Anonymous__37796] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__37785,Vvar__1__lt__37787,Vvar__2__eq__37789,Vvar__3__x__37791,Vvar__4__y__37793) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__37786,Vvar__1__lt__37788,Vvar__2__eq__37790,Vvar__3__x__37792,Vvar__4__y__37794)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__37793 = Vvar__4__y__37794
& Vvar__3__x__37791 = Vvar__3__x__37792
& Vvar__2__eq__37789 = Vvar__2__eq__37790
& Vvar__1__lt__37787 = Vvar__1__lt__37788
& Vvar__0__X__37785 = Vvar__0__X__37786 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__37761,Vvar__0__X__37762,Vvar__1__lt__37763,Vvar__1__lt__37764,Vvar__2__eq__37765,Vvar__2__eq__37766,Vvar__3__x__37767,Vvar__3__x__37768,Vvar__4__y__37769,Vvar__4__y__37770,Vvar__5___24Anonymous__37771,Vvar__5___24Anonymous__37772] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__37761,Vvar__1__lt__37763,Vvar__2__eq__37765,Vvar__3__x__37767,Vvar__4__y__37769) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__37762,Vvar__1__lt__37764,Vvar__2__eq__37766,Vvar__3__x__37768,Vvar__4__y__37770)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__37769 = Vvar__4__y__37770
& Vvar__3__x__37767 = Vvar__3__x__37768
& Vvar__2__eq__37765 = Vvar__2__eq__37766
& Vvar__1__lt__37763 = Vvar__1__lt__37764
& Vvar__0__X__37761 = Vvar__0__X__37762 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__36420,Vvar__0__n__36421] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__36420) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__36421)
=> Vvar__0__n__36420 = Vvar__0__n__36421 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__36422,Vvar__0__n__36423,Vvar__1___24Anonymous__36424,Vvar__1___24Anonymous__36425] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__36422,Vvar__1___24Anonymous__36424) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__36423,Vvar__1___24Anonymous__36425)
=> ( Vvar__1___24Anonymous__36424 = Vvar__1___24Anonymous__36425
& Vvar__0__n__36422 = Vvar__0__n__36423 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__33893,Vvar__0__A__33894,Vvar__1__h__33895,Vvar__1__h__33896,Vvar__2__n__33897,Vvar__2__n__33898,Vvar__3___24Anonymous__33899,Vvar__3___24Anonymous__33900] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__33893,Vvar__1__h__33895,Vvar__2__n__33897,Vvar__3___24Anonymous__33899) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__33894,Vvar__1__h__33896,Vvar__2__n__33898,Vvar__3___24Anonymous__33900)
=> ( Vvar__3___24Anonymous__33899 = Vvar__3___24Anonymous__33900
& Vvar__2__n__33897 = Vvar__2__n__33898
& Vvar__1__h__33895 = Vvar__1__h__33896
& Vvar__0__A__33893 = Vvar__0__A__33894 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__33891,Vvar__0__A__33892] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__33891) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__33892)
=> Vvar__0__A__33891 = Vvar__0__A__33892 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__45848,Vvar__0__a__45849,Vvar__1__b__45850,Vvar__1__b__45851,Vvar__2__u__45852,Vvar__2__u__45853,Vvar__3__v__45854,Vvar__3__v__45855,Vvar__4__d__45856,Vvar__4__d__45857,Vvar__5___24Anonymous__45858,Vvar__5___24Anonymous__45859,Vvar__6___24Anonymous__45860,Vvar__6___24Anonymous__45861] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__45848,Vvar__1__b__45850,Vvar__2__u__45852,Vvar__3__v__45854,Vvar__4__d__45856) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__45849,Vvar__1__b__45851,Vvar__2__u__45853,Vvar__3__v__45855,Vvar__4__d__45857)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__45856 = Vvar__4__d__45857
& Vvar__3__v__45854 = Vvar__3__v__45855
& Vvar__2__u__45852 = Vvar__2__u__45853
& Vvar__1__b__45850 = Vvar__1__b__45851
& Vvar__0__a__45848 = Vvar__0__a__45849 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__45909,Vvar__0__x__45910,Vvar__1__p__45911,Vvar__1__p__45912,Vvar__2__q__45913,Vvar__2__q__45914,Vvar__3__r__45915,Vvar__3__r__45916,Vvar__4___24Anonymous__45917,Vvar__4___24Anonymous__45918,Vvar__5___24Anonymous__45919,Vvar__5___24Anonymous__45920,Vvar__6___24Anonymous__45921,Vvar__6___24Anonymous__45922] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__45909,Vvar__1__p__45911,Vvar__2__q__45913,Vvar__3__r__45915) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__45910,Vvar__1__p__45912,Vvar__2__q__45914,Vvar__3__r__45916)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__45915 = Vvar__3__r__45916
& Vvar__2__q__45913 = Vvar__2__q__45914
& Vvar__1__p__45911 = Vvar__1__p__45912
& Vvar__0__x__45909 = Vvar__0__x__45910 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__2996,Vvar__0__C__2997,Vvar__1___24Anonymous__2998,Vvar__1___24Anonymous__2999] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__2996,Vvar__1___24Anonymous__2998) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__2997,Vvar__1___24Anonymous__2999)
=> ( Vvar__1___24Anonymous__2998 = Vvar__1___24Anonymous__2999
& Vvar__0__C__2996 = Vvar__0__C__2997 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__3000,Vvar__0__C__3001,Vvar__1___24Anonymous__3002,Vvar__1___24Anonymous__3003,Vvar__2___24Anonymous__3004,Vvar__2___24Anonymous__3005] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__3000,Vvar__1___24Anonymous__3002,Vvar__2___24Anonymous__3004) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__3001,Vvar__1___24Anonymous__3003,Vvar__2___24Anonymous__3005)
=> ( Vvar__2___24Anonymous__3004 = Vvar__2___24Anonymous__3005
& Vvar__1___24Anonymous__3002 = Vvar__1___24Anonymous__3003
& Vvar__0__C__3000 = Vvar__0__C__3001 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__2992,Vvar__0__C__2993,Vvar__1___24Anonymous__2994,Vvar__1___24Anonymous__2995] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__2992,Vvar__1___24Anonymous__2994) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__2993,Vvar__1___24Anonymous__2995)
=> ( Vvar__1___24Anonymous__2994 = Vvar__1___24Anonymous__2995
& Vvar__0__C__2992 = Vvar__0__C__2993 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__3012,Vvar__0__C__3013,Vvar__1___24Anonymous__3014,Vvar__1___24Anonymous__3015,Vvar__2___24Anonymous__3016,Vvar__2___24Anonymous__3017] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__3012,Vvar__1___24Anonymous__3014,Vvar__2___24Anonymous__3016) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__3013,Vvar__1___24Anonymous__3015,Vvar__2___24Anonymous__3017)
=> ( Vvar__2___24Anonymous__3016 = Vvar__2___24Anonymous__3017
& Vvar__1___24Anonymous__3014 = Vvar__1___24Anonymous__3015
& Vvar__0__C__3012 = Vvar__0__C__3013 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__3018,Vvar__0__C__3019,Vvar__1___24Anonymous__3020,Vvar__1___24Anonymous__3021] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__3018,Vvar__1___24Anonymous__3020) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__3019,Vvar__1___24Anonymous__3021)
=> ( Vvar__1___24Anonymous__3020 = Vvar__1___24Anonymous__3021
& Vvar__0__C__3018 = Vvar__0__C__3019 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__3022,Vvar__0__C__3023,Vvar__1___24Anonymous__3024,Vvar__1___24Anonymous__3025,Vvar__2___24Anonymous__3026,Vvar__2___24Anonymous__3027] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__3022,Vvar__1___24Anonymous__3024,Vvar__2___24Anonymous__3026) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__3023,Vvar__1___24Anonymous__3025,Vvar__2___24Anonymous__3027)
=> ( Vvar__2___24Anonymous__3026 = Vvar__2___24Anonymous__3027
& Vvar__1___24Anonymous__3024 = Vvar__1___24Anonymous__3025
& Vvar__0__C__3022 = Vvar__0__C__3023 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__3006,Vvar__0__C__3007,Vvar__1___24Anonymous__3008,Vvar__1___24Anonymous__3009,Vvar__2___24Anonymous__3010,Vvar__2___24Anonymous__3011] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__3006,Vvar__1___24Anonymous__3008,Vvar__2___24Anonymous__3010) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__3007,Vvar__1___24Anonymous__3009,Vvar__2___24Anonymous__3011)
=> ( Vvar__2___24Anonymous__3010 = Vvar__2___24Anonymous__3011
& Vvar__1___24Anonymous__3008 = Vvar__1___24Anonymous__3009
& Vvar__0__C__3006 = Vvar__0__C__3007 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__935,Vvar__0__C__936,Vvar__1___24Anonymous__937,Vvar__1___24Anonymous__938,Vvar__2___24Anonymous__939,Vvar__2___24Anonymous__940,Vvar__3___24Anonymous__941,Vvar__3___24Anonymous__942] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__935,Vvar__1___24Anonymous__937,Vvar__2___24Anonymous__939,Vvar__3___24Anonymous__941) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__936,Vvar__1___24Anonymous__938,Vvar__2___24Anonymous__940,Vvar__3___24Anonymous__942)
=> ( Vvar__3___24Anonymous__941 = Vvar__3___24Anonymous__942
& Vvar__2___24Anonymous__939 = Vvar__2___24Anonymous__940
& Vvar__1___24Anonymous__937 = Vvar__1___24Anonymous__938
& Vvar__0__C__935 = Vvar__0__C__936 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__925,Vvar__0__C__926,Vvar__1___24Anonymous__927,Vvar__1___24Anonymous__928] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__925,Vvar__1___24Anonymous__927) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__926,Vvar__1___24Anonymous__928)
=> ( Vvar__1___24Anonymous__927 = Vvar__1___24Anonymous__928
& Vvar__0__C__925 = Vvar__0__C__926 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__929,Vvar__0__C__930,Vvar__1___24Anonymous__931,Vvar__1___24Anonymous__932,Vvar__2___24Anonymous__933,Vvar__2___24Anonymous__934] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__929,Vvar__1___24Anonymous__931,Vvar__2___24Anonymous__933) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__930,Vvar__1___24Anonymous__932,Vvar__2___24Anonymous__934)
=> ( Vvar__2___24Anonymous__933 = Vvar__2___24Anonymous__934
& Vvar__1___24Anonymous__931 = Vvar__1___24Anonymous__932
& Vvar__0__C__929 = Vvar__0__C__930 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__3141,Vvar__0___24Anonymous__3142,Vvar__1___24Anonymous__3143,Vvar__1___24Anonymous__3144] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__3141,Vvar__1___24Anonymous__3143) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__3142,Vvar__1___24Anonymous__3144)
=> ( Vvar__1___24Anonymous__3143 = Vvar__1___24Anonymous__3144
& Vvar__0___24Anonymous__3141 = Vvar__0___24Anonymous__3142 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__3137,Vvar__0___24Anonymous__3138,Vvar__1___24Anonymous__3139,Vvar__1___24Anonymous__3140] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__3137,Vvar__1___24Anonymous__3139) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__3138,Vvar__1___24Anonymous__3140)
=> ( Vvar__1___24Anonymous__3139 = Vvar__1___24Anonymous__3140
& Vvar__0___24Anonymous__3137 = Vvar__0___24Anonymous__3138 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__14863,Vvar__0__r__14864] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__14863) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__14864)
=> Vvar__0__r__14863 = Vvar__0__r__14864 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__14851,Vvar__0__r1__14852,Vvar__1__r2__14853,Vvar__1__r2__14854] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__14851,Vvar__1__r2__14853) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__14852,Vvar__1__r2__14854)
=> ( Vvar__1__r2__14853 = Vvar__1__r2__14854
& Vvar__0__r1__14851 = Vvar__0__r1__14852 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__14855,Vvar__0__r1__14856,Vvar__1__r2__14857,Vvar__1__r2__14858] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__14855,Vvar__1__r2__14857) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__14856,Vvar__1__r2__14858)
=> ( Vvar__1__r2__14857 = Vvar__1__r2__14858
& Vvar__0__r1__14855 = Vvar__0__r1__14856 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__14865,Vvar__0__r__14866] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__14865) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__14866)
=> Vvar__0__r__14865 = Vvar__0__r__14866 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__14847,Vvar__0__r1__14848,Vvar__1__r2__14849,Vvar__1__r2__14850] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__14847,Vvar__1__r2__14849) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__14848,Vvar__1__r2__14850)
=> ( Vvar__1__r2__14849 = Vvar__1__r2__14850
& Vvar__0__r1__14847 = Vvar__0__r1__14848 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__14859,Vvar__0__r1__14860,Vvar__1__z__14861,Vvar__1__z__14862] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__14859,Vvar__1__z__14861) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__14860,Vvar__1__z__14862)
=> ( Vvar__1__z__14861 = Vvar__1__z__14862
& Vvar__0__r1__14859 = Vvar__0__r1__14860 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__14843,Vvar__0__r__14844] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__14843) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__14844)
=> Vvar__0__r__14843 = Vvar__0__r__14844 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__14845,Vvar__0__r__14846] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__14845) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__14846)
=> Vvar__0__r__14845 = Vvar__0__r__14846 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__16534,Vvar__0__T__16535,Vvar__1__Flhs__16536,Vvar__1__Flhs__16537,Vvar__2__Fop__16538,Vvar__2__Fop__16539,Vvar__3__Frhs__16540,Vvar__3__Frhs__16541] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__16534,Vvar__1__Flhs__16536,Vvar__2__Fop__16538,Vvar__3__Frhs__16540) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__16535,Vvar__1__Flhs__16537,Vvar__2__Fop__16539,Vvar__3__Frhs__16541)
=> ( Vvar__3__Frhs__16540 = Vvar__3__Frhs__16541
& Vvar__2__Fop__16538 = Vvar__2__Fop__16539
& Vvar__1__Flhs__16536 = Vvar__1__Flhs__16537
& Vvar__0__T__16534 = Vvar__0__T__16535 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__15825,Vvar__0__C__15826,Vvar__1___24Anonymous__15827,Vvar__1___24Anonymous__15828,Vvar__2___24Anonymous__15829,Vvar__2___24Anonymous__15830] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__15825,Vvar__1___24Anonymous__15827,Vvar__2___24Anonymous__15829) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__15826,Vvar__1___24Anonymous__15828,Vvar__2___24Anonymous__15830)
=> ( Vvar__2___24Anonymous__15829 = Vvar__2___24Anonymous__15830
& Vvar__1___24Anonymous__15827 = Vvar__1___24Anonymous__15828
& Vvar__0__C__15825 = Vvar__0__C__15826 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__15831,Vvar__0__C__15832,Vvar__1___24Anonymous__15833,Vvar__1___24Anonymous__15834] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__15831,Vvar__1___24Anonymous__15833) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__15832,Vvar__1___24Anonymous__15834)
=> ( Vvar__1___24Anonymous__15833 = Vvar__1___24Anonymous__15834
& Vvar__0__C__15831 = Vvar__0__C__15832 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__15805,Vvar__0__C__15806,Vvar__1___24Anonymous__15807,Vvar__1___24Anonymous__15808] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__15805,Vvar__1___24Anonymous__15807) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__15806,Vvar__1___24Anonymous__15808)
=> ( Vvar__1___24Anonymous__15807 = Vvar__1___24Anonymous__15808
& Vvar__0__C__15805 = Vvar__0__C__15806 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__15813,Vvar__0__C__15814,Vvar__1___24Anonymous__15815,Vvar__1___24Anonymous__15816,Vvar__2___24Anonymous__15817,Vvar__2___24Anonymous__15818] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__15813,Vvar__1___24Anonymous__15815,Vvar__2___24Anonymous__15817) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__15814,Vvar__1___24Anonymous__15816,Vvar__2___24Anonymous__15818)
=> ( Vvar__2___24Anonymous__15817 = Vvar__2___24Anonymous__15818
& Vvar__1___24Anonymous__15815 = Vvar__1___24Anonymous__15816
& Vvar__0__C__15813 = Vvar__0__C__15814 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__15819,Vvar__0__C__15820,Vvar__1___24Anonymous__15821,Vvar__1___24Anonymous__15822,Vvar__2___24Anonymous__15823,Vvar__2___24Anonymous__15824] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__15819,Vvar__1___24Anonymous__15821,Vvar__2___24Anonymous__15823) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__15820,Vvar__1___24Anonymous__15822,Vvar__2___24Anonymous__15824)
=> ( Vvar__2___24Anonymous__15823 = Vvar__2___24Anonymous__15824
& Vvar__1___24Anonymous__15821 = Vvar__1___24Anonymous__15822
& Vvar__0__C__15819 = Vvar__0__C__15820 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__15809,Vvar__0__C__15810,Vvar__1___24Anonymous__15811,Vvar__1___24Anonymous__15812] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__15809,Vvar__1___24Anonymous__15811) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__15810,Vvar__1___24Anonymous__15812)
=> ( Vvar__1___24Anonymous__15811 = Vvar__1___24Anonymous__15812
& Vvar__0__C__15809 = Vvar__0__C__15810 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__15835,Vvar__0__C__15836] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__15835) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__15836)
=> Vvar__0__C__15835 = Vvar__0__C__15836 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__31270,Vvar__0__TA__31271,Vvar__1__TX__31272,Vvar__1__TX__31273,Vvar__2__AA__31274,Vvar__2__AA__31275,Vvar__3__AF__31276,Vvar__3__AF__31277,Vvar__4___24Anonymous__31278,Vvar__4___24Anonymous__31279,Vvar__5___24Anonymous__31280,Vvar__5___24Anonymous__31281] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__31270,Vvar__1__TX__31272,Vvar__2__AA__31274,Vvar__3__AF__31276,Vvar__4___24Anonymous__31278,Vvar__5___24Anonymous__31280) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__31271,Vvar__1__TX__31273,Vvar__2__AA__31275,Vvar__3__AF__31277,Vvar__4___24Anonymous__31279,Vvar__5___24Anonymous__31281)
=> ( Vvar__5___24Anonymous__31280 = Vvar__5___24Anonymous__31281
& Vvar__4___24Anonymous__31278 = Vvar__4___24Anonymous__31279
& Vvar__3__AF__31276 = Vvar__3__AF__31277
& Vvar__2__AA__31274 = Vvar__2__AA__31275
& Vvar__1__TX__31272 = Vvar__1__TX__31273
& Vvar__0__TA__31270 = Vvar__0__TA__31271 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__31282,Vvar__0__TA__31283,Vvar__1__TX__31284,Vvar__1__TX__31285,Vvar__2__AA__31286,Vvar__2__AA__31287,Vvar__3__AF__31288,Vvar__3__AF__31289,Vvar__4___24Anonymous__31290,Vvar__4___24Anonymous__31291,Vvar__5___24Anonymous__31292,Vvar__5___24Anonymous__31293] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__31282,Vvar__1__TX__31284,Vvar__2__AA__31286,Vvar__3__AF__31288,Vvar__4___24Anonymous__31290,Vvar__5___24Anonymous__31292) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__31283,Vvar__1__TX__31285,Vvar__2__AA__31287,Vvar__3__AF__31289,Vvar__4___24Anonymous__31291,Vvar__5___24Anonymous__31293)
=> ( Vvar__5___24Anonymous__31292 = Vvar__5___24Anonymous__31293
& Vvar__4___24Anonymous__31290 = Vvar__4___24Anonymous__31291
& Vvar__3__AF__31288 = Vvar__3__AF__31289
& Vvar__2__AA__31286 = Vvar__2__AA__31287
& Vvar__1__TX__31284 = Vvar__1__TX__31285
& Vvar__0__TA__31282 = Vvar__0__TA__31283 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__31294,Vvar__0__TA__31295,Vvar__1__TX__31296,Vvar__1__TX__31297,Vvar__2__AA__31298,Vvar__2__AA__31299,Vvar__3__AF__31300,Vvar__3__AF__31301,Vvar__4___24Anonymous__31302,Vvar__4___24Anonymous__31303,Vvar__5___24Anonymous__31304,Vvar__5___24Anonymous__31305] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__31294,Vvar__1__TX__31296,Vvar__2__AA__31298,Vvar__3__AF__31300,Vvar__4___24Anonymous__31302,Vvar__5___24Anonymous__31304) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__31295,Vvar__1__TX__31297,Vvar__2__AA__31299,Vvar__3__AF__31301,Vvar__4___24Anonymous__31303,Vvar__5___24Anonymous__31305)
=> ( Vvar__5___24Anonymous__31304 = Vvar__5___24Anonymous__31305
& Vvar__4___24Anonymous__31302 = Vvar__4___24Anonymous__31303
& Vvar__3__AF__31300 = Vvar__3__AF__31301
& Vvar__2__AA__31298 = Vvar__2__AA__31299
& Vvar__1__TX__31296 = Vvar__1__TX__31297
& Vvar__0__TA__31294 = Vvar__0__TA__31295 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__31252,Vvar__0__TA__31253,Vvar__1__TX__31254,Vvar__1__TX__31255,Vvar__2__AA__31256,Vvar__2__AA__31257,Vvar__3__AF__31258,Vvar__3__AF__31259] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__31252,Vvar__1__TX__31254,Vvar__2__AA__31256,Vvar__3__AF__31258) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__31253,Vvar__1__TX__31255,Vvar__2__AA__31257,Vvar__3__AF__31259)
=> ( Vvar__3__AF__31258 = Vvar__3__AF__31259
& Vvar__2__AA__31256 = Vvar__2__AA__31257
& Vvar__1__TX__31254 = Vvar__1__TX__31255
& Vvar__0__TA__31252 = Vvar__0__TA__31253 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__31316,Vvar__0__TA__31317,Vvar__1__TX__31318,Vvar__1__TX__31319,Vvar__2__AA__31320,Vvar__2__AA__31321,Vvar__3__AF__31322,Vvar__3__AF__31323,Vvar__4___24Anonymous__31324,Vvar__4___24Anonymous__31325,Vvar__5___24Anonymous__31326,Vvar__5___24Anonymous__31327,Vvar__6___24Anonymous__31328,Vvar__6___24Anonymous__31329] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__31316,Vvar__1__TX__31318,Vvar__2__AA__31320,Vvar__3__AF__31322,Vvar__4___24Anonymous__31324,Vvar__5___24Anonymous__31326,Vvar__6___24Anonymous__31328) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__31317,Vvar__1__TX__31319,Vvar__2__AA__31321,Vvar__3__AF__31323,Vvar__4___24Anonymous__31325,Vvar__5___24Anonymous__31327,Vvar__6___24Anonymous__31329)
=> ( Vvar__6___24Anonymous__31328 = Vvar__6___24Anonymous__31329
& Vvar__5___24Anonymous__31326 = Vvar__5___24Anonymous__31327
& Vvar__4___24Anonymous__31324 = Vvar__4___24Anonymous__31325
& Vvar__3__AF__31322 = Vvar__3__AF__31323
& Vvar__2__AA__31320 = Vvar__2__AA__31321
& Vvar__1__TX__31318 = Vvar__1__TX__31319
& Vvar__0__TA__31316 = Vvar__0__TA__31317 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__31306,Vvar__0__TA__31307,Vvar__1__TX__31308,Vvar__1__TX__31309,Vvar__2__AA__31310,Vvar__2__AA__31311,Vvar__3__AF__31312,Vvar__3__AF__31313,Vvar__4___24Anonymous__31314,Vvar__4___24Anonymous__31315] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__31306,Vvar__1__TX__31308,Vvar__2__AA__31310,Vvar__3__AF__31312,Vvar__4___24Anonymous__31314) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__31307,Vvar__1__TX__31309,Vvar__2__AA__31311,Vvar__3__AF__31313,Vvar__4___24Anonymous__31315)
=> ( Vvar__4___24Anonymous__31314 = Vvar__4___24Anonymous__31315
& Vvar__3__AF__31312 = Vvar__3__AF__31313
& Vvar__2__AA__31310 = Vvar__2__AA__31311
& Vvar__1__TX__31308 = Vvar__1__TX__31309
& Vvar__0__TA__31306 = Vvar__0__TA__31307 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__31244,Vvar__0__TA__31245,Vvar__1__TX__31246,Vvar__1__TX__31247,Vvar__2__AA__31248,Vvar__2__AA__31249,Vvar__3__AF__31250,Vvar__3__AF__31251] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__31244,Vvar__1__TX__31246,Vvar__2__AA__31248,Vvar__3__AF__31250) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__31245,Vvar__1__TX__31247,Vvar__2__AA__31249,Vvar__3__AF__31251)
=> ( Vvar__3__AF__31250 = Vvar__3__AF__31251
& Vvar__2__AA__31248 = Vvar__2__AA__31249
& Vvar__1__TX__31246 = Vvar__1__TX__31247
& Vvar__0__TA__31244 = Vvar__0__TA__31245 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__31260,Vvar__0__TA__31261,Vvar__1__TX__31262,Vvar__1__TX__31263,Vvar__2__AA__31264,Vvar__2__AA__31265,Vvar__3__AF__31266,Vvar__3__AF__31267,Vvar__4___24Anonymous__31268,Vvar__4___24Anonymous__31269] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__31260,Vvar__1__TX__31262,Vvar__2__AA__31264,Vvar__3__AF__31266,Vvar__4___24Anonymous__31268) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__31261,Vvar__1__TX__31263,Vvar__2__AA__31265,Vvar__3__AF__31267,Vvar__4___24Anonymous__31269)
=> ( Vvar__4___24Anonymous__31268 = Vvar__4___24Anonymous__31269
& Vvar__3__AF__31266 = Vvar__3__AF__31267
& Vvar__2__AA__31264 = Vvar__2__AA__31265
& Vvar__1__TX__31262 = Vvar__1__TX__31263
& Vvar__0__TA__31260 = Vvar__0__TA__31261 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__34112,Vvar__0___24Anonymous__34113,Vvar__1___24Anonymous__34114,Vvar__1___24Anonymous__34115] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__34112,Vvar__1___24Anonymous__34114) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__34113,Vvar__1___24Anonymous__34115)
=> ( Vvar__1___24Anonymous__34114 = Vvar__1___24Anonymous__34115
& Vvar__0___24Anonymous__34112 = Vvar__0___24Anonymous__34113 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__34116,Vvar__0___24Anonymous__34117,Vvar__1___24Anonymous__34118,Vvar__1___24Anonymous__34119,Vvar__2___24Anonymous__34120,Vvar__2___24Anonymous__34121] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__34116,Vvar__1___24Anonymous__34118,Vvar__2___24Anonymous__34120) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__34117,Vvar__1___24Anonymous__34119,Vvar__2___24Anonymous__34121)
=> ( Vvar__2___24Anonymous__34120 = Vvar__2___24Anonymous__34121
& Vvar__1___24Anonymous__34118 = Vvar__1___24Anonymous__34119
& Vvar__0___24Anonymous__34116 = Vvar__0___24Anonymous__34117 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__34108,Vvar__0___24Anonymous__34109,Vvar__1___24Anonymous__34110,Vvar__1___24Anonymous__34111] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__34108,Vvar__1___24Anonymous__34110) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__34109,Vvar__1___24Anonymous__34111)
=> ( Vvar__1___24Anonymous__34110 = Vvar__1___24Anonymous__34111
& Vvar__0___24Anonymous__34108 = Vvar__0___24Anonymous__34109 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__8297,Vvar__0__C__8298] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8297) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8298)
=> Vvar__0__C__8297 = Vvar__0__C__8298 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__8295,Vvar__0__C__8296] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8295) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8296)
=> Vvar__0__C__8295 = Vvar__0__C__8296 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__8303,Vvar__0__C__8304,Vvar__1___24Anonymous__8305,Vvar__1___24Anonymous__8306] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__8303,Vvar__1___24Anonymous__8305) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__8304,Vvar__1___24Anonymous__8306)
=> ( Vvar__1___24Anonymous__8305 = Vvar__1___24Anonymous__8306
& Vvar__0__C__8303 = Vvar__0__C__8304 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__8307,Vvar__0__C__8308,Vvar__1___24Anonymous__8309,Vvar__1___24Anonymous__8310,Vvar__2___24Anonymous__8311,Vvar__2___24Anonymous__8312] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__8307,Vvar__1___24Anonymous__8309,Vvar__2___24Anonymous__8311) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__8308,Vvar__1___24Anonymous__8310,Vvar__2___24Anonymous__8312)
=> ( Vvar__2___24Anonymous__8311 = Vvar__2___24Anonymous__8312
& Vvar__1___24Anonymous__8309 = Vvar__1___24Anonymous__8310
& Vvar__0__C__8307 = Vvar__0__C__8308 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__8299,Vvar__0__C__8300,Vvar__1___24Anonymous__8301,Vvar__1___24Anonymous__8302] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__8299,Vvar__1___24Anonymous__8301) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__8300,Vvar__1___24Anonymous__8302)
=> ( Vvar__1___24Anonymous__8301 = Vvar__1___24Anonymous__8302
& Vvar__0__C__8299 = Vvar__0__C__8300 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__8333,Vvar__0__C__8334,Vvar__1___24Anonymous__8335,Vvar__1___24Anonymous__8336,Vvar__2___24Anonymous__8337,Vvar__2___24Anonymous__8338] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__8333,Vvar__1___24Anonymous__8335,Vvar__2___24Anonymous__8337) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__8334,Vvar__1___24Anonymous__8336,Vvar__2___24Anonymous__8338)
=> ( Vvar__2___24Anonymous__8337 = Vvar__2___24Anonymous__8338
& Vvar__1___24Anonymous__8335 = Vvar__1___24Anonymous__8336
& Vvar__0__C__8333 = Vvar__0__C__8334 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__8329,Vvar__0__C__8330,Vvar__1___24Anonymous__8331,Vvar__1___24Anonymous__8332] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__8329,Vvar__1___24Anonymous__8331) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__8330,Vvar__1___24Anonymous__8332)
=> ( Vvar__1___24Anonymous__8331 = Vvar__1___24Anonymous__8332
& Vvar__0__C__8329 = Vvar__0__C__8330 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__8319,Vvar__0__C__8320,Vvar__1___24Anonymous__8321,Vvar__1___24Anonymous__8322,Vvar__2___24Anonymous__8323,Vvar__2___24Anonymous__8324] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__8319,Vvar__1___24Anonymous__8321,Vvar__2___24Anonymous__8323) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__8320,Vvar__1___24Anonymous__8322,Vvar__2___24Anonymous__8324)
=> ( Vvar__2___24Anonymous__8323 = Vvar__2___24Anonymous__8324
& Vvar__1___24Anonymous__8321 = Vvar__1___24Anonymous__8322
& Vvar__0__C__8319 = Vvar__0__C__8320 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__8325,Vvar__0__C__8326,Vvar__1___24Anonymous__8327,Vvar__1___24Anonymous__8328] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__8325,Vvar__1___24Anonymous__8327) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__8326,Vvar__1___24Anonymous__8328)
=> ( Vvar__1___24Anonymous__8327 = Vvar__1___24Anonymous__8328
& Vvar__0__C__8325 = Vvar__0__C__8326 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__8339,Vvar__0__C__8340,Vvar__1___24Anonymous__8341,Vvar__1___24Anonymous__8342,Vvar__2___24Anonymous__8343,Vvar__2___24Anonymous__8344] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__8339,Vvar__1___24Anonymous__8341,Vvar__2___24Anonymous__8343) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__8340,Vvar__1___24Anonymous__8342,Vvar__2___24Anonymous__8344)
=> ( Vvar__2___24Anonymous__8343 = Vvar__2___24Anonymous__8344
& Vvar__1___24Anonymous__8341 = Vvar__1___24Anonymous__8342
& Vvar__0__C__8339 = Vvar__0__C__8340 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__8313,Vvar__0__C__8314,Vvar__1___24Anonymous__8315,Vvar__1___24Anonymous__8316,Vvar__2___24Anonymous__8317,Vvar__2___24Anonymous__8318] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__8313,Vvar__1___24Anonymous__8315,Vvar__2___24Anonymous__8317) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__8314,Vvar__1___24Anonymous__8316,Vvar__2___24Anonymous__8318)
=> ( Vvar__2___24Anonymous__8317 = Vvar__2___24Anonymous__8318
& Vvar__1___24Anonymous__8315 = Vvar__1___24Anonymous__8316
& Vvar__0__C__8313 = Vvar__0__C__8314 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__8636,Vvar__0__C__8637,Vvar__1__num__8638,Vvar__1__num__8639,Vvar__2__denum__8640,Vvar__2__denum__8641,Vvar__3__condition__8642,Vvar__3__condition__8643] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__8636,Vvar__1__num__8638,Vvar__2__denum__8640,Vvar__3__condition__8642) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__8637,Vvar__1__num__8639,Vvar__2__denum__8641,Vvar__3__condition__8643)
=> ( Vvar__3__condition__8642 = Vvar__3__condition__8643
& Vvar__2__denum__8640 = Vvar__2__denum__8641
& Vvar__1__num__8638 = Vvar__1__num__8639
& Vvar__0__C__8636 = Vvar__0__C__8637 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__8986,Vvar__0__C__8987,Vvar__1__rsplit__left__8988,Vvar__1__rsplit__left__8989,Vvar__2__rsplit__common__8990,Vvar__2__rsplit__common__8991,Vvar__3__rsplit__right__8992,Vvar__3__rsplit__right__8993] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__8986,Vvar__1__rsplit__left__8988,Vvar__2__rsplit__common__8990,Vvar__3__rsplit__right__8992) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__8987,Vvar__1__rsplit__left__8989,Vvar__2__rsplit__common__8991,Vvar__3__rsplit__right__8993)
=> ( Vvar__3__rsplit__right__8992 = Vvar__3__rsplit__right__8993
& Vvar__2__rsplit__common__8990 = Vvar__2__rsplit__common__8991
& Vvar__1__rsplit__left__8988 = Vvar__1__rsplit__left__8989
& Vvar__0__C__8986 = Vvar__0__C__8987 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__19468,Vvar__0__C__19469] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__19468) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__19469)
=> Vvar__0__C__19468 = Vvar__0__C__19469 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__19466,Vvar__0__C__19467] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__19466) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__19467)
=> Vvar__0__C__19466 = Vvar__0__C__19467 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__19474,Vvar__0__C__19475,Vvar__1___24Anonymous__19476,Vvar__1___24Anonymous__19477] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__19474,Vvar__1___24Anonymous__19476) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__19475,Vvar__1___24Anonymous__19477)
=> ( Vvar__1___24Anonymous__19476 = Vvar__1___24Anonymous__19477
& Vvar__0__C__19474 = Vvar__0__C__19475 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__19478,Vvar__0__C__19479,Vvar__1___24Anonymous__19480,Vvar__1___24Anonymous__19481,Vvar__2___24Anonymous__19482,Vvar__2___24Anonymous__19483] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__19478,Vvar__1___24Anonymous__19480,Vvar__2___24Anonymous__19482) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__19479,Vvar__1___24Anonymous__19481,Vvar__2___24Anonymous__19483)
=> ( Vvar__2___24Anonymous__19482 = Vvar__2___24Anonymous__19483
& Vvar__1___24Anonymous__19480 = Vvar__1___24Anonymous__19481
& Vvar__0__C__19478 = Vvar__0__C__19479 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__19470,Vvar__0__C__19471,Vvar__1___24Anonymous__19472,Vvar__1___24Anonymous__19473] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__19470,Vvar__1___24Anonymous__19472) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__19471,Vvar__1___24Anonymous__19473)
=> ( Vvar__1___24Anonymous__19472 = Vvar__1___24Anonymous__19473
& Vvar__0__C__19470 = Vvar__0__C__19471 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__19490,Vvar__0__C__19491,Vvar__1___24Anonymous__19492,Vvar__1___24Anonymous__19493,Vvar__2___24Anonymous__19494,Vvar__2___24Anonymous__19495] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__19490,Vvar__1___24Anonymous__19492,Vvar__2___24Anonymous__19494) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__19491,Vvar__1___24Anonymous__19493,Vvar__2___24Anonymous__19495)
=> ( Vvar__2___24Anonymous__19494 = Vvar__2___24Anonymous__19495
& Vvar__1___24Anonymous__19492 = Vvar__1___24Anonymous__19493
& Vvar__0__C__19490 = Vvar__0__C__19491 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__19496,Vvar__0__C__19497,Vvar__1___24Anonymous__19498,Vvar__1___24Anonymous__19499] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__19496,Vvar__1___24Anonymous__19498) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__19497,Vvar__1___24Anonymous__19499)
=> ( Vvar__1___24Anonymous__19498 = Vvar__1___24Anonymous__19499
& Vvar__0__C__19496 = Vvar__0__C__19497 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__19500,Vvar__0__C__19501,Vvar__1___24Anonymous__19502,Vvar__1___24Anonymous__19503,Vvar__2___24Anonymous__19504,Vvar__2___24Anonymous__19505] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__19500,Vvar__1___24Anonymous__19502,Vvar__2___24Anonymous__19504) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__19501,Vvar__1___24Anonymous__19503,Vvar__2___24Anonymous__19505)
=> ( Vvar__2___24Anonymous__19504 = Vvar__2___24Anonymous__19505
& Vvar__1___24Anonymous__19502 = Vvar__1___24Anonymous__19503
& Vvar__0__C__19500 = Vvar__0__C__19501 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__19484,Vvar__0__C__19485,Vvar__1___24Anonymous__19486,Vvar__1___24Anonymous__19487,Vvar__2___24Anonymous__19488,Vvar__2___24Anonymous__19489] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__19484,Vvar__1___24Anonymous__19486,Vvar__2___24Anonymous__19488) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__19485,Vvar__1___24Anonymous__19487,Vvar__2___24Anonymous__19489)
=> ( Vvar__2___24Anonymous__19488 = Vvar__2___24Anonymous__19489
& Vvar__1___24Anonymous__19486 = Vvar__1___24Anonymous__19487
& Vvar__0__C__19484 = Vvar__0__C__19485 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__17353,Vvar__0__C__17354,Vvar__1___24Anonymous__17355,Vvar__1___24Anonymous__17356,Vvar__2___24Anonymous__17357,Vvar__2___24Anonymous__17358,Vvar__3___24Anonymous__17359,Vvar__3___24Anonymous__17360] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__17353,Vvar__1___24Anonymous__17355,Vvar__2___24Anonymous__17357,Vvar__3___24Anonymous__17359) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__17354,Vvar__1___24Anonymous__17356,Vvar__2___24Anonymous__17358,Vvar__3___24Anonymous__17360)
=> ( Vvar__3___24Anonymous__17359 = Vvar__3___24Anonymous__17360
& Vvar__2___24Anonymous__17357 = Vvar__2___24Anonymous__17358
& Vvar__1___24Anonymous__17355 = Vvar__1___24Anonymous__17356
& Vvar__0__C__17353 = Vvar__0__C__17354 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__17343,Vvar__0__C__17344,Vvar__1___24Anonymous__17345,Vvar__1___24Anonymous__17346] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__17343,Vvar__1___24Anonymous__17345) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__17344,Vvar__1___24Anonymous__17346)
=> ( Vvar__1___24Anonymous__17345 = Vvar__1___24Anonymous__17346
& Vvar__0__C__17343 = Vvar__0__C__17344 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__17347,Vvar__0__C__17348,Vvar__1___24Anonymous__17349,Vvar__1___24Anonymous__17350,Vvar__2___24Anonymous__17351,Vvar__2___24Anonymous__17352] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__17347,Vvar__1___24Anonymous__17349,Vvar__2___24Anonymous__17351) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__17348,Vvar__1___24Anonymous__17350,Vvar__2___24Anonymous__17352)
=> ( Vvar__2___24Anonymous__17351 = Vvar__2___24Anonymous__17352
& Vvar__1___24Anonymous__17349 = Vvar__1___24Anonymous__17350
& Vvar__0__C__17347 = Vvar__0__C__17348 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__18142,Vvar__0___24Anonymous__18143,Vvar__1___24Anonymous__18144,Vvar__1___24Anonymous__18145] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__18142,Vvar__1___24Anonymous__18144) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__18143,Vvar__1___24Anonymous__18145)
=> ( Vvar__1___24Anonymous__18144 = Vvar__1___24Anonymous__18145
& Vvar__0___24Anonymous__18142 = Vvar__0___24Anonymous__18143 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__18138,Vvar__0___24Anonymous__18139,Vvar__1___24Anonymous__18140,Vvar__1___24Anonymous__18141] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__18138,Vvar__1___24Anonymous__18140) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__18139,Vvar__1___24Anonymous__18141)
=> ( Vvar__1___24Anonymous__18140 = Vvar__1___24Anonymous__18141
& Vvar__0___24Anonymous__18138 = Vvar__0___24Anonymous__18139 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__45522,Vvar__0__R__45523,Vvar__1__req__45524,Vvar__1__req__45525,Vvar__2__reqb__45526,Vvar__2__reqb__45527,Vvar__3___24Anonymous__45528,Vvar__3___24Anonymous__45529] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__45522,Vvar__1__req__45524,Vvar__2__reqb__45526) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__45523,Vvar__1__req__45525,Vvar__2__reqb__45527)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__45526 = Vvar__2__reqb__45527
& Vvar__1__req__45524 = Vvar__1__req__45525
& Vvar__0__R__45522 = Vvar__0__R__45523 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__45530,Vvar__0__R__45531,Vvar__1__rO__45532,Vvar__1__rO__45533,Vvar__2__rI__45534,Vvar__2__rI__45535,Vvar__3__radd__45536,Vvar__3__radd__45537,Vvar__4__rmul__45538,Vvar__4__rmul__45539,Vvar__5__rsub__45540,Vvar__5__rsub__45541,Vvar__6__ropp__45542,Vvar__6__ropp__45543,Vvar__7__req__45544,Vvar__7__req__45545,Vvar__8__C__45546,Vvar__8__C__45547,Vvar__9__cO__45548,Vvar__9__cO__45549,Vvar__10__cI__45550,Vvar__10__cI__45551,Vvar__11__cadd__45552,Vvar__11__cadd__45553,Vvar__12__cmul__45554,Vvar__12__cmul__45555,Vvar__13__csub__45556,Vvar__13__csub__45557,Vvar__14__copp__45558,Vvar__14__copp__45559,Vvar__15__ceqb__45560,Vvar__15__ceqb__45561,Vvar__16__phi__45562,Vvar__16__phi__45563,Vvar__17___24Anonymous__45564,Vvar__17___24Anonymous__45565] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__45530,Vvar__1__rO__45532,Vvar__2__rI__45534,Vvar__3__radd__45536,Vvar__4__rmul__45538,Vvar__5__rsub__45540,Vvar__6__ropp__45542,Vvar__7__req__45544,Vvar__8__C__45546,Vvar__9__cO__45548,Vvar__10__cI__45550,Vvar__11__cadd__45552,Vvar__12__cmul__45554,Vvar__13__csub__45556,Vvar__14__copp__45558,Vvar__15__ceqb__45560,Vvar__16__phi__45562) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__45531,Vvar__1__rO__45533,Vvar__2__rI__45535,Vvar__3__radd__45537,Vvar__4__rmul__45539,Vvar__5__rsub__45541,Vvar__6__ropp__45543,Vvar__7__req__45545,Vvar__8__C__45547,Vvar__9__cO__45549,Vvar__10__cI__45551,Vvar__11__cadd__45553,Vvar__12__cmul__45555,Vvar__13__csub__45557,Vvar__14__copp__45559,Vvar__15__ceqb__45561,Vvar__16__phi__45563)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__45562 = Vvar__16__phi__45563
& Vvar__15__ceqb__45560 = Vvar__15__ceqb__45561
& Vvar__14__copp__45558 = Vvar__14__copp__45559
& Vvar__13__csub__45556 = Vvar__13__csub__45557
& Vvar__12__cmul__45554 = Vvar__12__cmul__45555
& Vvar__11__cadd__45552 = Vvar__11__cadd__45553
& Vvar__10__cI__45550 = Vvar__10__cI__45551
& Vvar__9__cO__45548 = Vvar__9__cO__45549
& Vvar__8__C__45546 = Vvar__8__C__45547
& Vvar__7__req__45544 = Vvar__7__req__45545
& Vvar__6__ropp__45542 = Vvar__6__ropp__45543
& Vvar__5__rsub__45540 = Vvar__5__rsub__45541
& Vvar__4__rmul__45538 = Vvar__4__rmul__45539
& Vvar__3__radd__45536 = Vvar__3__radd__45537
& Vvar__2__rI__45534 = Vvar__2__rI__45535
& Vvar__1__rO__45532 = Vvar__1__rO__45533
& Vvar__0__R__45530 = Vvar__0__R__45531 ) ) ).
fof('$_inj_Tait.Subst.mk_sub',axiom,
! [Vvar__0__support__454,Vvar__0__support__455,Vvar__1__shift__456,Vvar__1__shift__457] :
( cTait_2eSubst_2emk__sub___24a2(Vvar__0__support__454,Vvar__1__shift__456) = cTait_2eSubst_2emk__sub___24a2(Vvar__0__support__455,Vvar__1__shift__457)
=> ( Vvar__1__shift__456 = Vvar__1__shift__457
& Vvar__0__support__454 = Vvar__0__support__455 ) ) ).
fof('$_inj_Tait.Subst2.Joachimski.Dot',axiom,
! [Vvar__0___24Anonymous__2264,Vvar__0___24Anonymous__2265,Vvar__1___24Anonymous__2266,Vvar__1___24Anonymous__2267] :
( cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__2264,Vvar__1___24Anonymous__2266) = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__2265,Vvar__1___24Anonymous__2267)
=> ( Vvar__1___24Anonymous__2266 = Vvar__1___24Anonymous__2267
& Vvar__0___24Anonymous__2264 = Vvar__0___24Anonymous__2265 ) ) ).
fof('$_inj_Tait.Subst2.Joachimski.Up',axiom,
! [Vvar__0___24Anonymous__2268,Vvar__0___24Anonymous__2269] :
( cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__2268) = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__2269)
=> Vvar__0___24Anonymous__2268 = Vvar__0___24Anonymous__2269 ) ).
fof('$_inj_Tait.Term.Abs',axiom,
! [Vvar__0___24Anonymous__105,Vvar__0___24Anonymous__106,Vvar__1___24Anonymous__107,Vvar__1___24Anonymous__108] :
( cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__105,Vvar__1___24Anonymous__107) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__106,Vvar__1___24Anonymous__108)
=> ( Vvar__1___24Anonymous__107 = Vvar__1___24Anonymous__108
& Vvar__0___24Anonymous__105 = Vvar__0___24Anonymous__106 ) ) ).
fof('$_inj_Tait.Term.App',axiom,
! [Vvar__0___24Anonymous__101,Vvar__0___24Anonymous__102,Vvar__1___24Anonymous__103,Vvar__1___24Anonymous__104] :
( cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__101,Vvar__1___24Anonymous__103) = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__102,Vvar__1___24Anonymous__104)
=> ( Vvar__1___24Anonymous__103 = Vvar__1___24Anonymous__104
& Vvar__0___24Anonymous__101 = Vvar__0___24Anonymous__102 ) ) ).
fof('$_inj_Tait.Term.Arrow',axiom,
! [Vvar__0___24Anonymous__79,Vvar__0___24Anonymous__80,Vvar__1___24Anonymous__81,Vvar__1___24Anonymous__82] :
( cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__79,Vvar__1___24Anonymous__81) = cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__80,Vvar__1___24Anonymous__82)
=> ( Vvar__1___24Anonymous__81 = Vvar__1___24Anonymous__82
& Vvar__0___24Anonymous__79 = Vvar__0___24Anonymous__80 ) ) ).
fof('$_inj_Tait.Term.Var',axiom,
! [Vvar__0___24Anonymous__99,Vvar__0___24Anonymous__100] :
( cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__99) = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__100)
=> Vvar__0___24Anonymous__99 = Vvar__0___24Anonymous__100 ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__35644] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35644)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__35644)
=> ( Vvar__0___24Anonymous__35644 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__35646] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__35646)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__35646)
& Vvar__0___24Anonymous__35644 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__35646) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__35648] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35648)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__35648)
=> ? [Vvar__0__n__35650] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__35650)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__35650)
& Vvar__0___24Anonymous__35648 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__35650) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__35459,Vvar__1___24Anonymous__35460,VX35461] :
( cProp___24t(Vvar__0__P__35459)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__35460)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__35459,Vvar__1___24Anonymous__35460,VX35461)
=> ( ( p(Vvar__0__P__35459)
& Vvar__1___24Anonymous__35460 = cCoq_2eInit_2eDatatypes_2etrue
& VX35461 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__35459) )
| ( ~ p(Vvar__0__P__35459)
& Vvar__1___24Anonymous__35460 = cCoq_2eInit_2eDatatypes_2efalse
& VX35461 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__35459) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX35100] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX35100)
=> ( VX35100 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__35101] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__35101)
& ? [Vvar__1___24Anonymous__35102] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__35102)
& ? [Vvar__2___24Anonymous__35103] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__35103)
& VX35100 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__35101,Vvar__1___24Anonymous__35102,Vvar__2___24Anonymous__35103) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX2627] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX2627)
=> ( VX2627 = cCoq_2eInit_2eByte_2ex00
| VX2627 = cCoq_2eInit_2eByte_2ex01
| VX2627 = cCoq_2eInit_2eByte_2ex02
| VX2627 = cCoq_2eInit_2eByte_2ex03
| VX2627 = cCoq_2eInit_2eByte_2ex04
| VX2627 = cCoq_2eInit_2eByte_2ex05
| VX2627 = cCoq_2eInit_2eByte_2ex06
| VX2627 = cCoq_2eInit_2eByte_2ex07
| VX2627 = cCoq_2eInit_2eByte_2ex08
| VX2627 = cCoq_2eInit_2eByte_2ex09
| VX2627 = cCoq_2eInit_2eByte_2ex0a
| VX2627 = cCoq_2eInit_2eByte_2ex0b
| VX2627 = cCoq_2eInit_2eByte_2ex0c
| VX2627 = cCoq_2eInit_2eByte_2ex0d
| VX2627 = cCoq_2eInit_2eByte_2ex0e
| VX2627 = cCoq_2eInit_2eByte_2ex0f
| VX2627 = cCoq_2eInit_2eByte_2ex10
| VX2627 = cCoq_2eInit_2eByte_2ex11
| VX2627 = cCoq_2eInit_2eByte_2ex12
| VX2627 = cCoq_2eInit_2eByte_2ex13
| VX2627 = cCoq_2eInit_2eByte_2ex14
| VX2627 = cCoq_2eInit_2eByte_2ex15
| VX2627 = cCoq_2eInit_2eByte_2ex16
| VX2627 = cCoq_2eInit_2eByte_2ex17
| VX2627 = cCoq_2eInit_2eByte_2ex18
| VX2627 = cCoq_2eInit_2eByte_2ex19
| VX2627 = cCoq_2eInit_2eByte_2ex1a
| VX2627 = cCoq_2eInit_2eByte_2ex1b
| VX2627 = cCoq_2eInit_2eByte_2ex1c
| VX2627 = cCoq_2eInit_2eByte_2ex1d
| VX2627 = cCoq_2eInit_2eByte_2ex1e
| VX2627 = cCoq_2eInit_2eByte_2ex1f
| VX2627 = cCoq_2eInit_2eByte_2ex20
| VX2627 = cCoq_2eInit_2eByte_2ex21
| VX2627 = cCoq_2eInit_2eByte_2ex22
| VX2627 = cCoq_2eInit_2eByte_2ex23
| VX2627 = cCoq_2eInit_2eByte_2ex24
| VX2627 = cCoq_2eInit_2eByte_2ex25
| VX2627 = cCoq_2eInit_2eByte_2ex26
| VX2627 = cCoq_2eInit_2eByte_2ex27
| VX2627 = cCoq_2eInit_2eByte_2ex28
| VX2627 = cCoq_2eInit_2eByte_2ex29
| VX2627 = cCoq_2eInit_2eByte_2ex2a
| VX2627 = cCoq_2eInit_2eByte_2ex2b
| VX2627 = cCoq_2eInit_2eByte_2ex2c
| VX2627 = cCoq_2eInit_2eByte_2ex2d
| VX2627 = cCoq_2eInit_2eByte_2ex2e
| VX2627 = cCoq_2eInit_2eByte_2ex2f
| VX2627 = cCoq_2eInit_2eByte_2ex30
| VX2627 = cCoq_2eInit_2eByte_2ex31
| VX2627 = cCoq_2eInit_2eByte_2ex32
| VX2627 = cCoq_2eInit_2eByte_2ex33
| VX2627 = cCoq_2eInit_2eByte_2ex34
| VX2627 = cCoq_2eInit_2eByte_2ex35
| VX2627 = cCoq_2eInit_2eByte_2ex36
| VX2627 = cCoq_2eInit_2eByte_2ex37
| VX2627 = cCoq_2eInit_2eByte_2ex38
| VX2627 = cCoq_2eInit_2eByte_2ex39
| VX2627 = cCoq_2eInit_2eByte_2ex3a
| VX2627 = cCoq_2eInit_2eByte_2ex3b
| VX2627 = cCoq_2eInit_2eByte_2ex3c
| VX2627 = cCoq_2eInit_2eByte_2ex3d
| VX2627 = cCoq_2eInit_2eByte_2ex3e
| VX2627 = cCoq_2eInit_2eByte_2ex3f
| VX2627 = cCoq_2eInit_2eByte_2ex40
| VX2627 = cCoq_2eInit_2eByte_2ex41
| VX2627 = cCoq_2eInit_2eByte_2ex42
| VX2627 = cCoq_2eInit_2eByte_2ex43
| VX2627 = cCoq_2eInit_2eByte_2ex44
| VX2627 = cCoq_2eInit_2eByte_2ex45
| VX2627 = cCoq_2eInit_2eByte_2ex46
| VX2627 = cCoq_2eInit_2eByte_2ex47
| VX2627 = cCoq_2eInit_2eByte_2ex48
| VX2627 = cCoq_2eInit_2eByte_2ex49
| VX2627 = cCoq_2eInit_2eByte_2ex4a
| VX2627 = cCoq_2eInit_2eByte_2ex4b
| VX2627 = cCoq_2eInit_2eByte_2ex4c
| VX2627 = cCoq_2eInit_2eByte_2ex4d
| VX2627 = cCoq_2eInit_2eByte_2ex4e
| VX2627 = cCoq_2eInit_2eByte_2ex4f
| VX2627 = cCoq_2eInit_2eByte_2ex50
| VX2627 = cCoq_2eInit_2eByte_2ex51
| VX2627 = cCoq_2eInit_2eByte_2ex52
| VX2627 = cCoq_2eInit_2eByte_2ex53
| VX2627 = cCoq_2eInit_2eByte_2ex54
| VX2627 = cCoq_2eInit_2eByte_2ex55
| VX2627 = cCoq_2eInit_2eByte_2ex56
| VX2627 = cCoq_2eInit_2eByte_2ex57
| VX2627 = cCoq_2eInit_2eByte_2ex58
| VX2627 = cCoq_2eInit_2eByte_2ex59
| VX2627 = cCoq_2eInit_2eByte_2ex5a
| VX2627 = cCoq_2eInit_2eByte_2ex5b
| VX2627 = cCoq_2eInit_2eByte_2ex5c
| VX2627 = cCoq_2eInit_2eByte_2ex5d
| VX2627 = cCoq_2eInit_2eByte_2ex5e
| VX2627 = cCoq_2eInit_2eByte_2ex5f
| VX2627 = cCoq_2eInit_2eByte_2ex60
| VX2627 = cCoq_2eInit_2eByte_2ex61
| VX2627 = cCoq_2eInit_2eByte_2ex62
| VX2627 = cCoq_2eInit_2eByte_2ex63
| VX2627 = cCoq_2eInit_2eByte_2ex64
| VX2627 = cCoq_2eInit_2eByte_2ex65
| VX2627 = cCoq_2eInit_2eByte_2ex66
| VX2627 = cCoq_2eInit_2eByte_2ex67
| VX2627 = cCoq_2eInit_2eByte_2ex68
| VX2627 = cCoq_2eInit_2eByte_2ex69
| VX2627 = cCoq_2eInit_2eByte_2ex6a
| VX2627 = cCoq_2eInit_2eByte_2ex6b
| VX2627 = cCoq_2eInit_2eByte_2ex6c
| VX2627 = cCoq_2eInit_2eByte_2ex6d
| VX2627 = cCoq_2eInit_2eByte_2ex6e
| VX2627 = cCoq_2eInit_2eByte_2ex6f
| VX2627 = cCoq_2eInit_2eByte_2ex70
| VX2627 = cCoq_2eInit_2eByte_2ex71
| VX2627 = cCoq_2eInit_2eByte_2ex72
| VX2627 = cCoq_2eInit_2eByte_2ex73
| VX2627 = cCoq_2eInit_2eByte_2ex74
| VX2627 = cCoq_2eInit_2eByte_2ex75
| VX2627 = cCoq_2eInit_2eByte_2ex76
| VX2627 = cCoq_2eInit_2eByte_2ex77
| VX2627 = cCoq_2eInit_2eByte_2ex78
| VX2627 = cCoq_2eInit_2eByte_2ex79
| VX2627 = cCoq_2eInit_2eByte_2ex7a
| VX2627 = cCoq_2eInit_2eByte_2ex7b
| VX2627 = cCoq_2eInit_2eByte_2ex7c
| VX2627 = cCoq_2eInit_2eByte_2ex7d
| VX2627 = cCoq_2eInit_2eByte_2ex7e
| VX2627 = cCoq_2eInit_2eByte_2ex7f
| VX2627 = cCoq_2eInit_2eByte_2ex80
| VX2627 = cCoq_2eInit_2eByte_2ex81
| VX2627 = cCoq_2eInit_2eByte_2ex82
| VX2627 = cCoq_2eInit_2eByte_2ex83
| VX2627 = cCoq_2eInit_2eByte_2ex84
| VX2627 = cCoq_2eInit_2eByte_2ex85
| VX2627 = cCoq_2eInit_2eByte_2ex86
| VX2627 = cCoq_2eInit_2eByte_2ex87
| VX2627 = cCoq_2eInit_2eByte_2ex88
| VX2627 = cCoq_2eInit_2eByte_2ex89
| VX2627 = cCoq_2eInit_2eByte_2ex8a
| VX2627 = cCoq_2eInit_2eByte_2ex8b
| VX2627 = cCoq_2eInit_2eByte_2ex8c
| VX2627 = cCoq_2eInit_2eByte_2ex8d
| VX2627 = cCoq_2eInit_2eByte_2ex8e
| VX2627 = cCoq_2eInit_2eByte_2ex8f
| VX2627 = cCoq_2eInit_2eByte_2ex90
| VX2627 = cCoq_2eInit_2eByte_2ex91
| VX2627 = cCoq_2eInit_2eByte_2ex92
| VX2627 = cCoq_2eInit_2eByte_2ex93
| VX2627 = cCoq_2eInit_2eByte_2ex94
| VX2627 = cCoq_2eInit_2eByte_2ex95
| VX2627 = cCoq_2eInit_2eByte_2ex96
| VX2627 = cCoq_2eInit_2eByte_2ex97
| VX2627 = cCoq_2eInit_2eByte_2ex98
| VX2627 = cCoq_2eInit_2eByte_2ex99
| VX2627 = cCoq_2eInit_2eByte_2ex9a
| VX2627 = cCoq_2eInit_2eByte_2ex9b
| VX2627 = cCoq_2eInit_2eByte_2ex9c
| VX2627 = cCoq_2eInit_2eByte_2ex9d
| VX2627 = cCoq_2eInit_2eByte_2ex9e
| VX2627 = cCoq_2eInit_2eByte_2ex9f
| VX2627 = cCoq_2eInit_2eByte_2exa0
| VX2627 = cCoq_2eInit_2eByte_2exa1
| VX2627 = cCoq_2eInit_2eByte_2exa2
| VX2627 = cCoq_2eInit_2eByte_2exa3
| VX2627 = cCoq_2eInit_2eByte_2exa4
| VX2627 = cCoq_2eInit_2eByte_2exa5
| VX2627 = cCoq_2eInit_2eByte_2exa6
| VX2627 = cCoq_2eInit_2eByte_2exa7
| VX2627 = cCoq_2eInit_2eByte_2exa8
| VX2627 = cCoq_2eInit_2eByte_2exa9
| VX2627 = cCoq_2eInit_2eByte_2exaa
| VX2627 = cCoq_2eInit_2eByte_2exab
| VX2627 = cCoq_2eInit_2eByte_2exac
| VX2627 = cCoq_2eInit_2eByte_2exad
| VX2627 = cCoq_2eInit_2eByte_2exae
| VX2627 = cCoq_2eInit_2eByte_2exaf
| VX2627 = cCoq_2eInit_2eByte_2exb0
| VX2627 = cCoq_2eInit_2eByte_2exb1
| VX2627 = cCoq_2eInit_2eByte_2exb2
| VX2627 = cCoq_2eInit_2eByte_2exb3
| VX2627 = cCoq_2eInit_2eByte_2exb4
| VX2627 = cCoq_2eInit_2eByte_2exb5
| VX2627 = cCoq_2eInit_2eByte_2exb6
| VX2627 = cCoq_2eInit_2eByte_2exb7
| VX2627 = cCoq_2eInit_2eByte_2exb8
| VX2627 = cCoq_2eInit_2eByte_2exb9
| VX2627 = cCoq_2eInit_2eByte_2exba
| VX2627 = cCoq_2eInit_2eByte_2exbb
| VX2627 = cCoq_2eInit_2eByte_2exbc
| VX2627 = cCoq_2eInit_2eByte_2exbd
| VX2627 = cCoq_2eInit_2eByte_2exbe
| VX2627 = cCoq_2eInit_2eByte_2exbf
| VX2627 = cCoq_2eInit_2eByte_2exc0
| VX2627 = cCoq_2eInit_2eByte_2exc1
| VX2627 = cCoq_2eInit_2eByte_2exc2
| VX2627 = cCoq_2eInit_2eByte_2exc3
| VX2627 = cCoq_2eInit_2eByte_2exc4
| VX2627 = cCoq_2eInit_2eByte_2exc5
| VX2627 = cCoq_2eInit_2eByte_2exc6
| VX2627 = cCoq_2eInit_2eByte_2exc7
| VX2627 = cCoq_2eInit_2eByte_2exc8
| VX2627 = cCoq_2eInit_2eByte_2exc9
| VX2627 = cCoq_2eInit_2eByte_2exca
| VX2627 = cCoq_2eInit_2eByte_2excb
| VX2627 = cCoq_2eInit_2eByte_2excc
| VX2627 = cCoq_2eInit_2eByte_2excd
| VX2627 = cCoq_2eInit_2eByte_2exce
| VX2627 = cCoq_2eInit_2eByte_2excf
| VX2627 = cCoq_2eInit_2eByte_2exd0
| VX2627 = cCoq_2eInit_2eByte_2exd1
| VX2627 = cCoq_2eInit_2eByte_2exd2
| VX2627 = cCoq_2eInit_2eByte_2exd3
| VX2627 = cCoq_2eInit_2eByte_2exd4
| VX2627 = cCoq_2eInit_2eByte_2exd5
| VX2627 = cCoq_2eInit_2eByte_2exd6
| VX2627 = cCoq_2eInit_2eByte_2exd7
| VX2627 = cCoq_2eInit_2eByte_2exd8
| VX2627 = cCoq_2eInit_2eByte_2exd9
| VX2627 = cCoq_2eInit_2eByte_2exda
| VX2627 = cCoq_2eInit_2eByte_2exdb
| VX2627 = cCoq_2eInit_2eByte_2exdc
| VX2627 = cCoq_2eInit_2eByte_2exdd
| VX2627 = cCoq_2eInit_2eByte_2exde
| VX2627 = cCoq_2eInit_2eByte_2exdf
| VX2627 = cCoq_2eInit_2eByte_2exe0
| VX2627 = cCoq_2eInit_2eByte_2exe1
| VX2627 = cCoq_2eInit_2eByte_2exe2
| VX2627 = cCoq_2eInit_2eByte_2exe3
| VX2627 = cCoq_2eInit_2eByte_2exe4
| VX2627 = cCoq_2eInit_2eByte_2exe5
| VX2627 = cCoq_2eInit_2eByte_2exe6
| VX2627 = cCoq_2eInit_2eByte_2exe7
| VX2627 = cCoq_2eInit_2eByte_2exe8
| VX2627 = cCoq_2eInit_2eByte_2exe9
| VX2627 = cCoq_2eInit_2eByte_2exea
| VX2627 = cCoq_2eInit_2eByte_2exeb
| VX2627 = cCoq_2eInit_2eByte_2exec
| VX2627 = cCoq_2eInit_2eByte_2exed
| VX2627 = cCoq_2eInit_2eByte_2exee
| VX2627 = cCoq_2eInit_2eByte_2exef
| VX2627 = cCoq_2eInit_2eByte_2exf0
| VX2627 = cCoq_2eInit_2eByte_2exf1
| VX2627 = cCoq_2eInit_2eByte_2exf2
| VX2627 = cCoq_2eInit_2eByte_2exf3
| VX2627 = cCoq_2eInit_2eByte_2exf4
| VX2627 = cCoq_2eInit_2eByte_2exf5
| VX2627 = cCoq_2eInit_2eByte_2exf6
| VX2627 = cCoq_2eInit_2eByte_2exf7
| VX2627 = cCoq_2eInit_2eByte_2exf8
| VX2627 = cCoq_2eInit_2eByte_2exf9
| VX2627 = cCoq_2eInit_2eByte_2exfa
| VX2627 = cCoq_2eInit_2eByte_2exfb
| VX2627 = cCoq_2eInit_2eByte_2exfc
| VX2627 = cCoq_2eInit_2eByte_2exfd
| VX2627 = cCoq_2eInit_2eByte_2exfe
| VX2627 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__35481,Vvar__1__Q__35482,Vvar__2___24Anonymous__35483] :
( cProp___24t(Vvar__0__P__35481)
=> ( cProp___24t(Vvar__1__Q__35482)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__35483)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__35481,Vvar__1__Q__35482,Vvar__2___24Anonymous__35483)
=> ( ( p(Vvar__0__P__35481)
& Vvar__2___24Anonymous__35483 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__35482)
& Vvar__2___24Anonymous__35483 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__35491,Vvar__1__Plt__35492,Vvar__2__Pgt__35493,Vvar__3___24Anonymous__35494] :
( cProp___24t(Vvar__0__Peq__35491)
=> ( cProp___24t(Vvar__1__Plt__35492)
=> ( cProp___24t(Vvar__2__Pgt__35493)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__35494)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__35491,Vvar__1__Plt__35492,Vvar__2__Pgt__35493,Vvar__3___24Anonymous__35494)
=> ( ( p(Vvar__0__Peq__35491)
& Vvar__3___24Anonymous__35494 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__35492)
& Vvar__3___24Anonymous__35494 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__35493)
& Vvar__3___24Anonymous__35494 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__35508,Vvar__1__Plt__35509,Vvar__2__Pgt__35510,Vvar__3___24Anonymous__35511,VX35512] :
( cProp___24t(Vvar__0__Peq__35508)
=> ( cProp___24t(Vvar__1__Plt__35509)
=> ( cProp___24t(Vvar__2__Pgt__35510)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__35511)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__35508,Vvar__1__Plt__35509,Vvar__2__Pgt__35510,Vvar__3___24Anonymous__35511,VX35512)
=> ( ( p(Vvar__0__Peq__35508)
& Vvar__3___24Anonymous__35511 = cCoq_2eInit_2eDatatypes_2eEq
& VX35512 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__35508,Vvar__1__Plt__35509,Vvar__2__Pgt__35510) )
| ( p(Vvar__1__Plt__35509)
& Vvar__3___24Anonymous__35511 = cCoq_2eInit_2eDatatypes_2eLt
& VX35512 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__35508,Vvar__1__Plt__35509,Vvar__2__Pgt__35510) )
| ( p(Vvar__2__Pgt__35510)
& Vvar__3___24Anonymous__35511 = cCoq_2eInit_2eDatatypes_2eGt
& VX35512 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__35508,Vvar__1__Plt__35509,Vvar__2__Pgt__35510) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX384] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX384)
=> ( VX384 = cCoq_2eInit_2eDatatypes_2etrue
| VX384 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX240] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX240)
=> ( VX240 = cCoq_2eInit_2eDatatypes_2eEq
| VX240 = cCoq_2eInit_2eDatatypes_2eLt
| VX240 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__40,VX41] :
( cType___24t(Vvar__0__A__40)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__40,VX41)
=> ( VX41 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__40)
| ? [Vvar__1___24Anonymous__44] :
( t(Vvar__1___24Anonymous__44,Vvar__0__A__40)
& ? [Vvar__2___24Anonymous__45] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__40,Vvar__2___24Anonymous__45)
& VX41 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__40,Vvar__1___24Anonymous__44,Vvar__2___24Anonymous__45) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX33] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX33)
=> ( VX33 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__34] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34)
& VX33 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__845,VX846] :
( cType___24t(Vvar__0__A__845)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__845,VX846)
=> ( ? [Vvar__1___24Anonymous__848] :
( t(Vvar__1___24Anonymous__848,Vvar__0__A__845)
& VX846 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__845,Vvar__1___24Anonymous__848) )
| VX846 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__845) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__864,Vvar__1__B__865,VX866] :
( cType___24t(Vvar__0__A__864)
=> ( cType___24t(Vvar__1__B__865)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__864,Vvar__1__B__865,VX866)
=> ? [Vvar__2___24Anonymous__869] :
( t(Vvar__2___24Anonymous__869,Vvar__0__A__864)
& ? [Vvar__3___24Anonymous__870] :
( t(Vvar__3___24Anonymous__870,Vvar__1__B__865)
& VX866 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__864,Vvar__1__B__865,Vvar__2___24Anonymous__869,Vvar__3___24Anonymous__870) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__2720,Vvar__1__B__2721,VX2722] :
( cType___24t(Vvar__0__A__2720)
=> ( cType___24t(Vvar__1__B__2721)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__2720,Vvar__1__B__2721,VX2722)
=> ( ? [Vvar__2___24Anonymous__2725] :
( t(Vvar__2___24Anonymous__2725,Vvar__0__A__2720)
& VX2722 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__2720,Vvar__1__B__2721,Vvar__2___24Anonymous__2725) )
| ? [Vvar__2___24Anonymous__2728] :
( t(Vvar__2___24Anonymous__2728,Vvar__1__B__2721)
& VX2722 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__2720,Vvar__1__B__2721,Vvar__2___24Anonymous__2728) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX2692] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX2692)
=> VX2692 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__413,Vvar__1___24Anonymous__414] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__413)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__414)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__413,Vvar__1___24Anonymous__414))
=> ( Vvar__1___24Anonymous__414 = Vvar__0__n__413
| ? [Vvar__1__m__418] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__418)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__413,Vvar__1__m__418))
& Vvar__1___24Anonymous__414 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__418) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__30681,Vvar__1__P__30682,VX30685] :
( cType___24t(Vvar__0__A__30681)
=> ( c_24__type__30695___24t(Vvar__0__A__30681,Vvar__1__P__30682,Vvar__1__P__30682)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__30681,Vvar__1__P__30682,VX30685)
=> ? [Vvar__2__x__30690] :
( t(Vvar__2__x__30690,Vvar__0__A__30681)
& p(happ(Vvar__1__P__30682,Vvar__2__x__30690))
& VX30685 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__30681,Vvar__1__P__30682,Vvar__2__x__30690) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__45569,Vvar__1__P__45570,Vvar__2__Q__45573,VX45576] :
( cType___24t(Vvar__0__A__45569)
=> ( c_24__type__45593___24t(Vvar__0__A__45569,Vvar__1__P__45570,Vvar__2__Q__45573,Vvar__1__P__45570)
=> ( c_24__type__45601___24t(Vvar__0__A__45569,Vvar__1__P__45570,Vvar__2__Q__45573,Vvar__2__Q__45573)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__45569,Vvar__1__P__45570,Vvar__2__Q__45573,VX45576)
=> ? [Vvar__3__x__45584] :
( t(Vvar__3__x__45584,Vvar__0__A__45569)
& p(happ(Vvar__1__P__45570,Vvar__3__x__45584))
& p(happ(Vvar__2__Q__45573,Vvar__3__x__45584))
& VX45576 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__45569,Vvar__1__P__45570,Vvar__2__Q__45573,Vvar__3__x__45584) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__30720,Vvar__1__P__30721,VX30724] :
( cType___24t(Vvar__0__A__30720)
=> ( c_24__type__30734___24t(Vvar__0__A__30720,Vvar__1__P__30721,Vvar__1__P__30721)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__30720,Vvar__1__P__30721,VX30724)
=> ? [Vvar__2__x__30729] :
( t(Vvar__2__x__30729,Vvar__0__A__30720)
& ? [Vvar__3___24Anonymous__30730] :
( t(Vvar__3___24Anonymous__30730,happ(Vvar__1__P__30721,Vvar__2__x__30729))
& VX30724 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__30720,Vvar__1__P__30721,Vvar__2__x__30729,Vvar__3___24Anonymous__30730) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__45625,Vvar__1__P__45626,Vvar__2__Q__45629,VX45632] :
( cType___24t(Vvar__0__A__45625)
=> ( c_24__type__45649___24t(Vvar__0__A__45625,Vvar__1__P__45626,Vvar__2__Q__45629,Vvar__1__P__45626)
=> ( c_24__type__45657___24t(Vvar__0__A__45625,Vvar__1__P__45626,Vvar__2__Q__45629,Vvar__2__Q__45629)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__45625,Vvar__1__P__45626,Vvar__2__Q__45629,VX45632)
=> ? [Vvar__3__x__45640] :
( t(Vvar__3__x__45640,Vvar__0__A__45625)
& ? [Vvar__4___24Anonymous__45641] :
( t(Vvar__4___24Anonymous__45641,happ(Vvar__1__P__45626,Vvar__3__x__45640))
& ? [Vvar__5___24Anonymous__45642] :
( t(Vvar__5___24Anonymous__45642,happ(Vvar__2__Q__45629,Vvar__3__x__45640))
& VX45632 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__45625,Vvar__1__P__45626,Vvar__2__Q__45629,Vvar__3__x__45640,Vvar__4___24Anonymous__45641,Vvar__5___24Anonymous__45642) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__421,Vvar__1__B__422,VX423] :
( cProp___24t(Vvar__0__A__421)
=> ( cProp___24t(Vvar__1__B__422)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__421,Vvar__1__B__422,VX423)
=> ( ( p(Vvar__0__A__421)
& VX423 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__421,Vvar__1__B__422) )
| ( p(Vvar__1__B__422)
& VX423 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__421,Vvar__1__B__422) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__30784,Vvar__1__B__30785,VX30786] :
( cType___24t(Vvar__0__A__30784)
=> ( cProp___24t(Vvar__1__B__30785)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__30784,Vvar__1__B__30785,VX30786)
=> ( ? [Vvar__2___24Anonymous__30789] :
( t(Vvar__2___24Anonymous__30789,Vvar__0__A__30784)
& VX30786 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__30784,Vvar__1__B__30785,Vvar__2___24Anonymous__30789) )
| ( p(Vvar__1__B__30785)
& VX30786 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__30784,Vvar__1__B__30785) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__45681,Vvar__1__R__45682,Vvar__2__x__45687] :
( cType___24t(Vvar__0__A__45681)
=> ( c_24__type__45716___24t(Vvar__0__A__45681,Vvar__1__R__45682,Vvar__2__x__45687,Vvar__1__R__45682)
=> ( t(Vvar__2__x__45687,Vvar__0__A__45681)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__45681,Vvar__1__R__45682,Vvar__2__x__45687)
=> ( ! [Vvar__var__var__var__var__3__y__45697__45699__45701__45703__45705] :
( t(Vvar__var__var__var__var__3__y__45697__45699__45701__45703__45705,Vvar__0__A__45681)
=> ( p(happ(happ(Vvar__1__R__45682,Vvar__var__var__var__var__3__y__45697__45699__45701__45703__45705),Vvar__2__x__45687))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__45681,Vvar__1__R__45682,Vvar__var__var__var__var__3__y__45697__45699__45701__45703__45705) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__1100,Vvar__1__a__1101,Vvar__2___24Anonymous__1102,Vvar__3___24Anonymous__1103] :
( cType___24t(Vvar__0__A__1100)
=> ( t(Vvar__1__a__1101,Vvar__0__A__1100)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1100,Vvar__2___24Anonymous__1102)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1100,Vvar__3___24Anonymous__1103)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__1100,Vvar__1__a__1101,Vvar__2___24Anonymous__1102,Vvar__3___24Anonymous__1103)
=> ( ? [Vvar__2__l__1107] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1100,Vvar__2__l__1107)
& Vvar__3___24Anonymous__1103 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1100,Vvar__1__a__1101,Vvar__2__l__1107)
& Vvar__2___24Anonymous__1102 = Vvar__2__l__1107 )
| ? [Vvar__2__x__1110] :
( t(Vvar__2__x__1110,Vvar__0__A__1100)
& ? [Vvar__3__l__1111] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1100,Vvar__3__l__1111)
& ? [Vvar__4__l_27__1112] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1100,Vvar__4__l_27__1112)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__1100,Vvar__1__a__1101,Vvar__3__l__1111,Vvar__4__l_27__1112)
& Vvar__3___24Anonymous__1103 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1100,Vvar__2__x__1110,Vvar__4__l_27__1112)
& Vvar__2___24Anonymous__1102 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1100,Vvar__2__x__1110,Vvar__3__l__1111) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__13888,Vvar__1__P__13889,Vvar__2___24Anonymous__13892] :
( cType___24t(Vvar__0__A__13888)
=> ( c_24__type__13912___24t(Vvar__0__A__13888,Vvar__1__P__13889,Vvar__2___24Anonymous__13892,Vvar__1__P__13889)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13888,Vvar__2___24Anonymous__13892)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__13888,Vvar__1__P__13889,Vvar__2___24Anonymous__13892)
=> ( ? [Vvar__2__x__13898] :
( t(Vvar__2__x__13898,Vvar__0__A__13888)
& ? [Vvar__3__l__13899] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13888,Vvar__3__l__13899)
& p(happ(Vvar__1__P__13889,Vvar__2__x__13898))
& Vvar__2___24Anonymous__13892 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13888,Vvar__2__x__13898,Vvar__3__l__13899) ) )
| ? [Vvar__2__x__13905] :
( t(Vvar__2__x__13905,Vvar__0__A__13888)
& ? [Vvar__3__l__13906] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13888,Vvar__3__l__13906)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__13888,Vvar__1__P__13889,Vvar__3__l__13906)
& Vvar__2___24Anonymous__13892 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13888,Vvar__2__x__13905,Vvar__3__l__13906) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__14045,Vvar__1__P__14046,Vvar__2___24Anonymous__14049] :
( cType___24t(Vvar__0__A__14045)
=> ( c_24__type__14067___24t(Vvar__0__A__14045,Vvar__1__P__14046,Vvar__2___24Anonymous__14049,Vvar__1__P__14046)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14045,Vvar__2___24Anonymous__14049)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__14045,Vvar__1__P__14046,Vvar__2___24Anonymous__14049)
=> ( Vvar__2___24Anonymous__14049 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__14045)
| ? [Vvar__2__x__14059] :
( t(Vvar__2__x__14059,Vvar__0__A__14045)
& ? [Vvar__3__l__14060] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14045,Vvar__3__l__14060)
& p(happ(Vvar__1__P__14046,Vvar__2__x__14059))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__14045,Vvar__1__P__14046,Vvar__3__l__14060)
& Vvar__2___24Anonymous__14049 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__14045,Vvar__2__x__14059,Vvar__3__l__14060) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__14369,Vvar__1__B__14370,Vvar__2__R__14371,Vvar__3___24Anonymous__14376,Vvar__4___24Anonymous__14377] :
( cType___24t(Vvar__0__A__14369)
=> ( cType___24t(Vvar__1__B__14370)
=> ( c_24__type__14414___24t(Vvar__0__A__14369,Vvar__1__B__14370,Vvar__2__R__14371,Vvar__3___24Anonymous__14376,Vvar__4___24Anonymous__14377,Vvar__2__R__14371)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14369,Vvar__3___24Anonymous__14376)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__14370,Vvar__4___24Anonymous__14377)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__14369,Vvar__1__B__14370,Vvar__2__R__14371,Vvar__3___24Anonymous__14376,Vvar__4___24Anonymous__14377)
=> ( ( Vvar__4___24Anonymous__14377 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__14370)
& Vvar__3___24Anonymous__14376 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__14369) )
| ? [Vvar__3__x__14393] :
( t(Vvar__3__x__14393,Vvar__0__A__14369)
& ? [Vvar__4__y__14394] :
( t(Vvar__4__y__14394,Vvar__1__B__14370)
& ? [Vvar__5__l__14395] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14369,Vvar__5__l__14395)
& ? [Vvar__6__l_27__14396] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__14370,Vvar__6__l_27__14396)
& p(happ(happ(Vvar__2__R__14371,Vvar__3__x__14393),Vvar__4__y__14394))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__14369,Vvar__1__B__14370,Vvar__2__R__14371,Vvar__5__l__14395,Vvar__6__l_27__14396)
& Vvar__4___24Anonymous__14377 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__14370,Vvar__4__y__14394,Vvar__6__l_27__14396)
& Vvar__3___24Anonymous__14376 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__14369,Vvar__3__x__14393,Vvar__5__l__14395) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__14488,Vvar__1__R__14489,Vvar__2___24Anonymous__14494] :
( cType___24t(Vvar__0__A__14488)
=> ( c_24__type__14521___24t(Vvar__0__A__14488,Vvar__1__R__14489,Vvar__2___24Anonymous__14494,Vvar__1__R__14489)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14488,Vvar__2___24Anonymous__14494)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__14488,Vvar__1__R__14489,Vvar__2___24Anonymous__14494)
=> ( Vvar__2___24Anonymous__14494 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__14488)
| ? [Vvar__2__a__14508] :
( t(Vvar__2__a__14508,Vvar__0__A__14488)
& ? [Vvar__3__l__14509] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14488,Vvar__3__l__14509)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__14488,happ(Vvar__1__R__14489,Vvar__2__a__14508),Vvar__3__l__14509)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__14488,Vvar__1__R__14489,Vvar__3__l__14509)
& Vvar__2___24Anonymous__14494 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__14488,Vvar__2__a__14508,Vvar__3__l__14509) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__13814,Vvar__1___24Anonymous__13815] :
( cType___24t(Vvar__0__A__13814)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13814,Vvar__1___24Anonymous__13815)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__13814,Vvar__1___24Anonymous__13815)
=> ( Vvar__1___24Anonymous__13815 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__13814)
| ? [Vvar__1__x__13819] :
( t(Vvar__1__x__13819,Vvar__0__A__13814)
& ? [Vvar__2__l__13820] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13814,Vvar__2__l__13820)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__13814,Vvar__1__x__13819,Vvar__2__l__13820)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__13814,Vvar__2__l__13820)
& Vvar__1___24Anonymous__13815 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13814,Vvar__1__x__13819,Vvar__2__l__13820) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__28780,Vvar__1__eqA__28781,Vvar__2__x__28786,Vvar__3___24Anonymous__28787] :
( cType___24t(Vvar__0__A__28780)
=> ( c_24__type__28820___24t(Vvar__0__A__28780,Vvar__1__eqA__28781,Vvar__2__x__28786,Vvar__3___24Anonymous__28787,Vvar__1__eqA__28781)
=> ( t(Vvar__2__x__28786,Vvar__0__A__28780)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28780,Vvar__3___24Anonymous__28787)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__28780,Vvar__1__eqA__28781,Vvar__2__x__28786,Vvar__3___24Anonymous__28787)
=> ( ? [Vvar__3__y__28796] :
( t(Vvar__3__y__28796,Vvar__0__A__28780)
& ? [Vvar__4__l__28797] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28780,Vvar__4__l__28797)
& p(happ(happ(Vvar__1__eqA__28781,Vvar__2__x__28786),Vvar__3__y__28796))
& Vvar__3___24Anonymous__28787 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28780,Vvar__3__y__28796,Vvar__4__l__28797) ) )
| ? [Vvar__3__y__28806] :
( t(Vvar__3__y__28806,Vvar__0__A__28780)
& ? [Vvar__4__l__28807] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28780,Vvar__4__l__28807)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__28780,Vvar__1__eqA__28781,Vvar__2__x__28786,Vvar__4__l__28807)
& Vvar__3___24Anonymous__28787 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28780,Vvar__3__y__28806,Vvar__4__l__28807) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__28856,Vvar__1__eqA__28857,Vvar__2___24Anonymous__28862] :
( cType___24t(Vvar__0__A__28856)
=> ( c_24__type__28889___24t(Vvar__0__A__28856,Vvar__1__eqA__28857,Vvar__2___24Anonymous__28862,Vvar__1__eqA__28857)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28856,Vvar__2___24Anonymous__28862)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__28856,Vvar__1__eqA__28857,Vvar__2___24Anonymous__28862)
=> ( Vvar__2___24Anonymous__28862 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28856)
| ? [Vvar__2__x__28876] :
( t(Vvar__2__x__28876,Vvar__0__A__28856)
& ? [Vvar__3__l__28877] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28856,Vvar__3__l__28877)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__28856,Vvar__1__eqA__28857,Vvar__2__x__28876,Vvar__3__l__28877)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__28856,Vvar__1__eqA__28857,Vvar__3__l__28877)
& Vvar__2___24Anonymous__28862 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28856,Vvar__2__x__28876,Vvar__3__l__28877) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__28935,Vvar__1__eqA__28936,Vvar__2___24Anonymous__28941,Vvar__3___24Anonymous__28942] :
( cType___24t(Vvar__0__A__28935)
=> ( c_24__type__28973___24t(Vvar__0__A__28935,Vvar__1__eqA__28936,Vvar__2___24Anonymous__28941,Vvar__3___24Anonymous__28942,Vvar__1__eqA__28936)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28935,Vvar__2___24Anonymous__28941)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28935,Vvar__3___24Anonymous__28942)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__28935,Vvar__1__eqA__28936,Vvar__2___24Anonymous__28941,Vvar__3___24Anonymous__28942)
=> ( ( Vvar__3___24Anonymous__28942 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28935)
& Vvar__2___24Anonymous__28941 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28935) )
| ? [Vvar__2__x__28956] :
( t(Vvar__2__x__28956,Vvar__0__A__28935)
& ? [Vvar__3__x_27__28957] :
( t(Vvar__3__x_27__28957,Vvar__0__A__28935)
& ? [Vvar__4__l__28958] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28935,Vvar__4__l__28958)
& ? [Vvar__5__l_27__28959] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28935,Vvar__5__l_27__28959)
& p(happ(happ(Vvar__1__eqA__28936,Vvar__2__x__28956),Vvar__3__x_27__28957))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__28935,Vvar__1__eqA__28936,Vvar__4__l__28958,Vvar__5__l_27__28959)
& Vvar__3___24Anonymous__28942 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28935,Vvar__3__x_27__28957,Vvar__5__l_27__28959)
& Vvar__2___24Anonymous__28941 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28935,Vvar__2__x__28956,Vvar__4__l__28958) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__35592,Vvar__1__P__35593,Vvar__2__p__35596,Vvar__3__x__35597,Vvar__4__q__35598,Vvar__5___24Anonymous__35599] :
( cType___24t(Vvar__0__U__35592)
=> ( c_24__type__35614___24t(Vvar__0__U__35592,Vvar__1__P__35593,Vvar__2__p__35596,Vvar__3__x__35597,Vvar__4__q__35598,Vvar__5___24Anonymous__35599,Vvar__1__P__35593)
=> ( t(Vvar__2__p__35596,Vvar__0__U__35592)
=> ( t(Vvar__3__x__35597,happ(Vvar__1__P__35593,Vvar__2__p__35596))
=> ( t(Vvar__4__q__35598,Vvar__0__U__35592)
=> ( t(Vvar__5___24Anonymous__35599,happ(Vvar__1__P__35593,Vvar__4__q__35598))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__35592,Vvar__1__P__35593,Vvar__2__p__35596,Vvar__3__x__35597,Vvar__4__q__35598,Vvar__5___24Anonymous__35599)
=> ( Vvar__5___24Anonymous__35599 = Vvar__3__x__35597
& Vvar__4__q__35598 = Vvar__2__p__35596 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__35616,Vvar__1__P__35617,Vvar__2__p__35620,Vvar__3__x__35621,Vvar__4__q__35622,Vvar__5__y__35623] :
( cType___24t(Vvar__0__U__35616)
=> ( c_24__type__35642___24t(Vvar__0__U__35616,Vvar__1__P__35617,Vvar__2__p__35620,Vvar__3__x__35621,Vvar__4__q__35622,Vvar__5__y__35623,Vvar__1__P__35617)
=> ( t(Vvar__2__p__35620,Vvar__0__U__35616)
=> ( t(Vvar__3__x__35621,happ(Vvar__1__P__35617,Vvar__2__p__35620))
=> ( t(Vvar__4__q__35622,Vvar__0__U__35616)
=> ( t(Vvar__5__y__35623,happ(Vvar__1__P__35617,Vvar__4__q__35622))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__35616,Vvar__1__P__35617,Vvar__2__p__35620,Vvar__3__x__35621,Vvar__4__q__35622,Vvar__5__y__35623)
=> ( Vvar__4__q__35622 = Vvar__2__p__35620
& Vvar__3__x__35621 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__35616,Vvar__4__q__35622,Vvar__1__P__35617,Vvar__5__y__35623,Vvar__2__p__35620)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX2620] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX2620)
=> ( VX2620 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__2621] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2621)
& VX2620 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2621) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX373] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX373)
=> ( VX373 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__374] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__374)
& VX373 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__374) )
| ? [Vvar__0___24Anonymous__375] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__375)
& VX373 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__375) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX362] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX362)
=> ( ? [Vvar__0___24Anonymous__363] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__363)
& VX362 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__363) )
| ? [Vvar__0___24Anonymous__364] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__364)
& VX362 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__364) )
| VX362 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [Vvar__0___24Anonymous__45984,VX45985] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45984)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__45984,VX45985)
=> ( ( Vvar__0___24Anonymous__45984 = cCoq_2eNumbers_2eBinNums_2exH
& VX45985 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
| ? [Vvar__0__p__45986] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__45986)
& ? [Vvar__1___24Anonymous__45987] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__45986,Vvar__1___24Anonymous__45987)
& Vvar__0___24Anonymous__45984 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2446022___24a2(Vvar__0___24Anonymous__45984,Vvar__0__p__45986)
& VX45985 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__45986,Vvar__1___24Anonymous__45987) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX46049] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX46049)
=> ( VX46049 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__46050] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46050)
& VX46049 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__46050) )
| VX46049 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX14660] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX14660)
=> ? [Vvar__0__Qnum__14661] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__14661)
& ? [Vvar__1__Qden__14662] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__14662)
& VX14660 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__14661,Vvar__1__Qden__14662) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX37808] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX37808)
=> ? [Vvar__0__nonzero__37809] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__37809)
& Vvar__0__nonzero__37809 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX37808 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__37809) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__37824,Vvar__1___24Anonymous__37825,VX37826] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__37824)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__37825)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__37824,Vvar__1___24Anonymous__37825,VX37826)
=> ( ( Vvar__0__x__37824 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__37825 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX37826 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__37824) )
| ? [Vvar__1__n__37830] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__37830)
& Vvar__0__x__37824 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__37830)
& Vvar__1___24Anonymous__37825 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2437850___24a3(Vvar__0__x__37824,Vvar__1___24Anonymous__37825,Vvar__1__n__37830)
& VX37826 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__37824,Vvar__1__n__37830) )
| ? [Vvar__1__n__37835] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__37835)
& Vvar__0__x__37824 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__37835))
& Vvar__1___24Anonymous__37825 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2437867___24a3(Vvar__0__x__37824,Vvar__1___24Anonymous__37825,Vvar__1__n__37835)
& VX37826 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__37824,Vvar__1__n__37835) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__15065,Vvar__1__leA__15066,Vvar__2___24Anonymous__15071] :
( cType___24t(Vvar__0__A__15065)
=> ( c_24__type__15161___24t(Vvar__0__A__15065,Vvar__1__leA__15066,Vvar__2___24Anonymous__15071,Vvar__1__leA__15066)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__15065,Vvar__2___24Anonymous__15071)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__15065,Vvar__1__leA__15066,Vvar__2___24Anonymous__15071)
=> ( Vvar__2___24Anonymous__15071 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__15065)
| ? [Vvar__2__x__15085] :
( t(Vvar__2__x__15085,Vvar__0__A__15065)
& Vvar__2___24Anonymous__15071 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__15065,Vvar__2__x__15085,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__15065)) )
| ? [Vvar__2__x__15092] :
( t(Vvar__2__x__15092,Vvar__0__A__15065)
& ? [Vvar__3__y__15093] :
( t(Vvar__3__y__15093,Vvar__0__A__15065)
& ? [Vvar__4__l__15094] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__15065,Vvar__4__l__15094)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__15065,Vvar__1__leA__15066,Vvar__2__x__15092,Vvar__3__y__15093)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__15065,Vvar__1__leA__15066,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__15065,Vvar__4__l__15094,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__15065,Vvar__3__y__15093,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__15065))))
& Vvar__2___24Anonymous__15071 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2415359___24a6(Vvar__0__A__15065,Vvar__1__leA__15066,Vvar__2___24Anonymous__15071,Vvar__2__x__15092,Vvar__3__y__15093,Vvar__4__l__15094) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__14978,Vvar__1__leA__14979,Vvar__2___24Anonymous__14984,Vvar__3___24Anonymous__14985] :
( cType___24t(Vvar__0__A__14978)
=> ( c_24__type__15027___24t(Vvar__0__A__14978,Vvar__1__leA__14979,Vvar__2___24Anonymous__14984,Vvar__3___24Anonymous__14985,Vvar__1__leA__14979)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14978,Vvar__2___24Anonymous__14984)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14978,Vvar__3___24Anonymous__14985)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__14978,Vvar__1__leA__14979,Vvar__2___24Anonymous__14984,Vvar__3___24Anonymous__14985)
=> ( ? [Vvar__2__a__14993] :
( t(Vvar__2__a__14993,Vvar__0__A__14978)
& ? [Vvar__3__x__14994] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14978,Vvar__3__x__14994)
& Vvar__3___24Anonymous__14985 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__14978,Vvar__2__a__14993,Vvar__3__x__14994)
& Vvar__2___24Anonymous__14984 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__14978) ) )
| ? [Vvar__2__a__15001] :
( t(Vvar__2__a__15001,Vvar__0__A__14978)
& ? [Vvar__3__b__15002] :
( t(Vvar__3__b__15002,Vvar__0__A__14978)
& p(happ(happ(Vvar__1__leA__14979,Vvar__2__a__15001),Vvar__3__b__15002))
& ? [Vvar__5__x__15004] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14978,Vvar__5__x__15004)
& ? [Vvar__6__y__15005] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14978,Vvar__6__y__15005)
& Vvar__3___24Anonymous__14985 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__14978,Vvar__3__b__15002,Vvar__6__y__15005)
& Vvar__2___24Anonymous__14984 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__14978,Vvar__2__a__15001,Vvar__5__x__15004) ) ) ) )
| ? [Vvar__2__a__15012] :
( t(Vvar__2__a__15012,Vvar__0__A__14978)
& ? [Vvar__3__x__15013] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14978,Vvar__3__x__15013)
& ? [Vvar__4__y__15014] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14978,Vvar__4__y__15014)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__14978,Vvar__1__leA__14979,Vvar__3__x__15013,Vvar__4__y__15014)
& Vvar__3___24Anonymous__14985 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__14978,Vvar__2__a__15012,Vvar__4__y__15014)
& Vvar__2___24Anonymous__14984 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__14978,Vvar__2__a__15012,Vvar__3__x__15013) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__14965,Vvar__1__R__14966,Vvar__2__x__14967,Vvar__3___24Anonymous__14968] :
( cType___24t(Vvar__0__A__14965)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__14965,Vvar__1__R__14966)
=> ( t(Vvar__2__x__14967,Vvar__0__A__14965)
=> ( t(Vvar__3___24Anonymous__14968,Vvar__0__A__14965)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__14965,Vvar__1__R__14966,Vvar__2__x__14967,Vvar__3___24Anonymous__14968)
=> ( ? [Vvar__3__y__14973] :
( t(Vvar__3__y__14973,Vvar__0__A__14965)
& p(happ(happ(Vvar__1__R__14966,Vvar__2__x__14967),Vvar__3__y__14973))
& Vvar__3___24Anonymous__14968 = Vvar__3__y__14973 )
| Vvar__3___24Anonymous__14968 = Vvar__2__x__14967 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__1210,Vvar__1__R__1211,Vvar__2__a__1216,Vvar__3___24Anonymous__1217] :
( cType___24t(Vvar__0__A__1210)
=> ( c_24__type__1247___24t(Vvar__0__A__1210,Vvar__1__R__1211,Vvar__2__a__1216,Vvar__3___24Anonymous__1217,Vvar__1__R__1211)
=> ( t(Vvar__2__a__1216,Vvar__0__A__1210)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1210,Vvar__3___24Anonymous__1217)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__1210,Vvar__1__R__1211,Vvar__2__a__1216,Vvar__3___24Anonymous__1217)
=> ( Vvar__3___24Anonymous__1217 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1210)
| ? [Vvar__3__b__1233] :
( t(Vvar__3__b__1233,Vvar__0__A__1210)
& ? [Vvar__4__l__1234] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1210,Vvar__4__l__1234)
& p(happ(happ(Vvar__1__R__1211,Vvar__2__a__1216),Vvar__3__b__1233))
& Vvar__3___24Anonymous__1217 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1210,Vvar__3__b__1233,Vvar__4__l__1234) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__30131,Vvar__1__R__30132,Vvar__2___24Anonymous__30137] :
( cType___24t(Vvar__0__A__30131)
=> ( c_24__type__30172___24t(Vvar__0__A__30131,Vvar__1__R__30132,Vvar__2___24Anonymous__30137,Vvar__1__R__30132)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30131,Vvar__2___24Anonymous__30137)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__30131,Vvar__1__R__30132,Vvar__2___24Anonymous__30137)
=> ( Vvar__2___24Anonymous__30137 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30131)
| ? [Vvar__2__a__30151] :
( t(Vvar__2__a__30151,Vvar__0__A__30131)
& Vvar__2___24Anonymous__30137 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30131,Vvar__2__a__30151,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30131)) )
| ? [Vvar__2__a__30158] :
( t(Vvar__2__a__30158,Vvar__0__A__30131)
& ? [Vvar__3__b__30159] :
( t(Vvar__3__b__30159,Vvar__0__A__30131)
& ? [Vvar__4__l__30160] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30131,Vvar__4__l__30160)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__30131,Vvar__1__R__30132,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30131,Vvar__3__b__30159,Vvar__4__l__30160))
& p(happ(happ(Vvar__1__R__30132,Vvar__2__a__30158),Vvar__3__b__30159))
& Vvar__2___24Anonymous__30137 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30131,Vvar__2__a__30158,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30131,Vvar__3__b__30159,Vvar__4__l__30160)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__1249,Vvar__1__R__1250,Vvar__2___24Anonymous__1255] :
( cType___24t(Vvar__0__A__1249)
=> ( c_24__type__1282___24t(Vvar__0__A__1249,Vvar__1__R__1250,Vvar__2___24Anonymous__1255,Vvar__1__R__1250)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1249,Vvar__2___24Anonymous__1255)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__1249,Vvar__1__R__1250,Vvar__2___24Anonymous__1255)
=> ( Vvar__2___24Anonymous__1255 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1249)
| ? [Vvar__2__a__1269] :
( t(Vvar__2__a__1269,Vvar__0__A__1249)
& ? [Vvar__3__l__1270] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1249,Vvar__3__l__1270)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__1249,Vvar__1__R__1250,Vvar__3__l__1270)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__1249,Vvar__1__R__1250,Vvar__2__a__1269,Vvar__3__l__1270)
& Vvar__2___24Anonymous__1255 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1249,Vvar__2__a__1269,Vvar__3__l__1270) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__30333,Vvar__1__R__30334,Vvar__2___24Anonymous__30339] :
( cType___24t(Vvar__0__A__30333)
=> ( c_24__type__30366___24t(Vvar__0__A__30333,Vvar__1__R__30334,Vvar__2___24Anonymous__30339,Vvar__1__R__30334)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30333,Vvar__2___24Anonymous__30339)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__30333,Vvar__1__R__30334,Vvar__2___24Anonymous__30339)
=> ( Vvar__2___24Anonymous__30339 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30333)
| ? [Vvar__2__a__30353] :
( t(Vvar__2__a__30353,Vvar__0__A__30333)
& ? [Vvar__3__l__30354] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30333,Vvar__3__l__30354)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__30333,Vvar__1__R__30334,Vvar__3__l__30354)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__30333,happ(Vvar__1__R__30334,Vvar__2__a__30353),Vvar__3__l__30354)
& Vvar__2___24Anonymous__30339 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30333,Vvar__2__a__30353,Vvar__3__l__30354) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX2342] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX2342)
=> ? [Vvar__0___24Anonymous__2343] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__2343)
& ? [Vvar__1___24Anonymous__2344] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__2344)
& ? [Vvar__2___24Anonymous__2345] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__2345)
& ? [Vvar__3___24Anonymous__2346] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__2346)
& ? [Vvar__4___24Anonymous__2347] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__2347)
& ? [Vvar__5___24Anonymous__2348] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__2348)
& ? [Vvar__6___24Anonymous__2349] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__2349)
& ? [Vvar__7___24Anonymous__2350] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__2350)
& VX2342 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__2343,Vvar__1___24Anonymous__2344,Vvar__2___24Anonymous__2345,Vvar__3___24Anonymous__2346,Vvar__4___24Anonymous__2347,Vvar__5___24Anonymous__2348,Vvar__6___24Anonymous__2349,Vvar__7___24Anonymous__2350) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX30824] :
( cCoq_2eStrings_2eString_2estring___24t(VX30824)
=> ( VX30824 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__30825] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__30825)
& ? [Vvar__1___24Anonymous__30826] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__30826)
& VX30824 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__30825,Vvar__1___24Anonymous__30826) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__37605,Vvar__1__lt__37606,Vvar__2__eq__37611,Vvar__3__x__37616,Vvar__4__y__37617,VX37618] :
( cType___24t(Vvar__0__X__37605)
=> ( c_24__type__37678___24t(Vvar__0__X__37605,Vvar__1__lt__37606,Vvar__2__eq__37611,Vvar__3__x__37616,Vvar__4__y__37617,Vvar__1__lt__37606)
=> ( c_24__type__37697___24t(Vvar__0__X__37605,Vvar__1__lt__37606,Vvar__2__eq__37611,Vvar__3__x__37616,Vvar__4__y__37617,Vvar__2__eq__37611)
=> ( t(Vvar__3__x__37616,Vvar__0__X__37605)
=> ( t(Vvar__4__y__37617,Vvar__0__X__37605)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__37605,Vvar__1__lt__37606,Vvar__2__eq__37611,Vvar__3__x__37616,Vvar__4__y__37617,VX37618)
=> ( ( p(happ(happ(Vvar__1__lt__37606,Vvar__3__x__37616),Vvar__4__y__37617))
& VX37618 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__37605,Vvar__1__lt__37606,Vvar__2__eq__37611,Vvar__3__x__37616,Vvar__4__y__37617) )
| ( p(happ(happ(Vvar__2__eq__37611,Vvar__3__x__37616),Vvar__4__y__37617))
& VX37618 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__37605,Vvar__1__lt__37606,Vvar__2__eq__37611,Vvar__3__x__37616,Vvar__4__y__37617) )
| ( p(happ(happ(Vvar__1__lt__37606,Vvar__4__y__37617),Vvar__3__x__37616))
& VX37618 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__37605,Vvar__1__lt__37606,Vvar__2__eq__37611,Vvar__3__x__37616,Vvar__4__y__37617) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX37797] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX37797)
=> ( VX37797 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX37797 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX37797 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__36412,VX36413] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36412)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__36412,VX36413)
=> ( ? [Vvar__0__n__36414] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__36414)
& Vvar__0___24Anonymous__36412 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__36414)
& VX36413 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__36414) )
| ? [Vvar__0__n__36415] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__36415)
& ? [Vvar__1___24Anonymous__36416] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__36415,Vvar__1___24Anonymous__36416)
& Vvar__0___24Anonymous__36412 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__36415)
& VX36413 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__36415,Vvar__1___24Anonymous__36416) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__33875,Vvar__1___24Anonymous__33876,VX33877] :
( cType___24t(Vvar__0__A__33875)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__33876)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__33875,Vvar__1___24Anonymous__33876,VX33877)
=> ( ( Vvar__1___24Anonymous__33876 = cCoq_2eInit_2eDatatypes_2eO
& VX33877 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__33875) )
| ? [Vvar__1__h__33880] :
( t(Vvar__1__h__33880,Vvar__0__A__33875)
& ? [Vvar__2__n__33881] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__33881)
& ? [Vvar__3___24Anonymous__33882] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__33875,Vvar__2__n__33881,Vvar__3___24Anonymous__33882)
& Vvar__1___24Anonymous__33876 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__33881)
& VX33877 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__33875,Vvar__1__h__33880,Vvar__2__n__33881,Vvar__3___24Anonymous__33882) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__45862,Vvar__1__b__45863,Vvar__2__d__45864] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__45862)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__45863)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__45864)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__45862,Vvar__1__b__45863,Vvar__2__d__45864)
=> ? [Vvar__3__u__45869] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__45869)
& ? [Vvar__4__v__45870] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__45870)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__45869,Vvar__0__a__45862),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__45870,Vvar__1__b__45863)) = Vvar__2__d__45864
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__45837,Vvar__1__b__45838,VX45839] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__45837)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__45838)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__45837,Vvar__1__b__45838,VX45839)
=> ? [Vvar__2__u__45842] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__45842)
& ? [Vvar__3__v__45843] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__45843)
& ? [Vvar__4__d__45844] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__45844)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__45842,Vvar__0__a__45837),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__45843,Vvar__1__b__45838)) = Vvar__4__d__45844
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__45837,Vvar__1__b__45838,Vvar__4__d__45844)
& VX45839 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__45837,Vvar__1__b__45838,Vvar__2__u__45842,Vvar__3__v__45843,Vvar__4__d__45844) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__45809,Vvar__1__b__45810,Vvar__2__g__45811] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__45809)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__45810)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__45811)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__45809,Vvar__1__b__45810,Vvar__2__g__45811)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__45811,Vvar__0__a__45809)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__45811,Vvar__1__b__45810)
& ! [Vvar__var__var__var__var__5__x__45819__45822__45825__45828__45831] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__45819__45822__45825__45828__45831)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__45819__45822__45825__45828__45831,Vvar__0__a__45809)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__45819__45822__45825__45828__45831,Vvar__1__b__45810)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__45819__45822__45825__45828__45831,Vvar__2__g__45811) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__45872] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__45872)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__45872)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__45872))
& ! [Vvar__var__var__2__n__45877__45879__45881] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__45877__45879__45881)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__45877__45879__45881))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__45877__45879__45881,Vvar__0__p__45872)) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__45877__45879__45881,Vvar__0__p__45872) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__45885,Vvar__1__p__45886,VX45887] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__45885)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__45886)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__45885,Vvar__1__p__45886,VX45887)
=> ? [Vvar__2__q__45890] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__45890)
& ? [Vvar__3__r__45891] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__45891)
& Vvar__0__x__45885 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__45890,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__45886)),Vvar__3__r__45891)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__45891))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__45891,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__45886)))
& VX45887 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__45885,Vvar__1__p__45886,Vvar__2__q__45890,Vvar__3__r__45891) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX3124] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX3124)
=> ( VX3124 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__3125] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3125)
& ? [Vvar__1___24Anonymous__3126] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__3126)
& VX3124 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__3125,Vvar__1___24Anonymous__3126) ) )
| ? [Vvar__0___24Anonymous__3127] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3127)
& ? [Vvar__1___24Anonymous__3128] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__3128)
& VX3124 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__3127,Vvar__1___24Anonymous__3128) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__2864,VX2865] :
( cType___24t(Vvar__0__C__2864)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2864,VX2865)
=> ( ? [Vvar__1___24Anonymous__2867] :
( t(Vvar__1___24Anonymous__2867,Vvar__0__C__2864)
& VX2865 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__2864,Vvar__1___24Anonymous__2867) )
| ? [Vvar__1___24Anonymous__2869] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2869)
& VX2865 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__2864,Vvar__1___24Anonymous__2869) )
| ? [Vvar__1___24Anonymous__2871] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2864,Vvar__1___24Anonymous__2871)
& ? [Vvar__2___24Anonymous__2872] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2864,Vvar__2___24Anonymous__2872)
& VX2865 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__2864,Vvar__1___24Anonymous__2871,Vvar__2___24Anonymous__2872) ) )
| ? [Vvar__1___24Anonymous__2874] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2864,Vvar__1___24Anonymous__2874)
& ? [Vvar__2___24Anonymous__2875] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2864,Vvar__2___24Anonymous__2875)
& VX2865 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__2864,Vvar__1___24Anonymous__2874,Vvar__2___24Anonymous__2875) ) )
| ? [Vvar__1___24Anonymous__2877] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2864,Vvar__1___24Anonymous__2877)
& ? [Vvar__2___24Anonymous__2878] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2864,Vvar__2___24Anonymous__2878)
& VX2865 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__2864,Vvar__1___24Anonymous__2877,Vvar__2___24Anonymous__2878) ) )
| ? [Vvar__1___24Anonymous__2880] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2864,Vvar__1___24Anonymous__2880)
& VX2865 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__2864,Vvar__1___24Anonymous__2880) )
| ? [Vvar__1___24Anonymous__2882] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2864,Vvar__1___24Anonymous__2882)
& ? [Vvar__2___24Anonymous__2883] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2883)
& VX2865 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__2864,Vvar__1___24Anonymous__2882,Vvar__2___24Anonymous__2883) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__896,VX897] :
( cType___24t(Vvar__0__C__896)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__896,VX897)
=> ( ? [Vvar__1___24Anonymous__899] :
( t(Vvar__1___24Anonymous__899,Vvar__0__C__896)
& VX897 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__896,Vvar__1___24Anonymous__899) )
| ? [Vvar__1___24Anonymous__901] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__901)
& ? [Vvar__2___24Anonymous__902] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__896,Vvar__2___24Anonymous__902)
& VX897 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__896,Vvar__1___24Anonymous__901,Vvar__2___24Anonymous__902) ) )
| ? [Vvar__1___24Anonymous__904] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__896,Vvar__1___24Anonymous__904)
& ? [Vvar__2___24Anonymous__905] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__905)
& ? [Vvar__3___24Anonymous__906] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__896,Vvar__3___24Anonymous__906)
& VX897 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__896,Vvar__1___24Anonymous__904,Vvar__2___24Anonymous__905,Vvar__3___24Anonymous__906) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__36508,Vvar__1__rO__36509,Vvar__2__rI__36510,Vvar__3__rplus__36511,Vvar__4__rtimes__36516,Vvar__5__rminus__36521,Vvar__6__ropp__36526,Vvar__7__req__36529,Vvar__8__rle__36534,Vvar__9__rlt__36539] :
( cType___24t(Vvar__0__R__36508)
=> ( t(Vvar__1__rO__36509,Vvar__0__R__36508)
=> ( t(Vvar__2__rI__36510,Vvar__0__R__36508)
=> ( c_24__type__36940___24t(Vvar__0__R__36508,Vvar__1__rO__36509,Vvar__2__rI__36510,Vvar__3__rplus__36511,Vvar__4__rtimes__36516,Vvar__5__rminus__36521,Vvar__6__ropp__36526,Vvar__7__req__36529,Vvar__8__rle__36534,Vvar__9__rlt__36539,Vvar__3__rplus__36511)
=> ( c_24__type__37041___24t(Vvar__0__R__36508,Vvar__1__rO__36509,Vvar__2__rI__36510,Vvar__3__rplus__36511,Vvar__4__rtimes__36516,Vvar__5__rminus__36521,Vvar__6__ropp__36526,Vvar__7__req__36529,Vvar__8__rle__36534,Vvar__9__rlt__36539,Vvar__4__rtimes__36516)
=> ( c_24__type__37142___24t(Vvar__0__R__36508,Vvar__1__rO__36509,Vvar__2__rI__36510,Vvar__3__rplus__36511,Vvar__4__rtimes__36516,Vvar__5__rminus__36521,Vvar__6__ropp__36526,Vvar__7__req__36529,Vvar__8__rle__36534,Vvar__9__rlt__36539,Vvar__5__rminus__36521)
=> ( c_24__type__37232___24t(Vvar__0__R__36508,Vvar__1__rO__36509,Vvar__2__rI__36510,Vvar__3__rplus__36511,Vvar__4__rtimes__36516,Vvar__5__rminus__36521,Vvar__6__ropp__36526,Vvar__7__req__36529,Vvar__8__rle__36534,Vvar__9__rlt__36539,Vvar__6__ropp__36526)
=> ( c_24__type__37333___24t(Vvar__0__R__36508,Vvar__1__rO__36509,Vvar__2__rI__36510,Vvar__3__rplus__36511,Vvar__4__rtimes__36516,Vvar__5__rminus__36521,Vvar__6__ropp__36526,Vvar__7__req__36529,Vvar__8__rle__36534,Vvar__9__rlt__36539,Vvar__7__req__36529)
=> ( c_24__type__37434___24t(Vvar__0__R__36508,Vvar__1__rO__36509,Vvar__2__rI__36510,Vvar__3__rplus__36511,Vvar__4__rtimes__36516,Vvar__5__rminus__36521,Vvar__6__ropp__36526,Vvar__7__req__36529,Vvar__8__rle__36534,Vvar__9__rlt__36539,Vvar__8__rle__36534)
=> ( c_24__type__37535___24t(Vvar__0__R__36508,Vvar__1__rO__36509,Vvar__2__rI__36510,Vvar__3__rplus__36511,Vvar__4__rtimes__36516,Vvar__5__rminus__36521,Vvar__6__ropp__36526,Vvar__7__req__36529,Vvar__8__rle__36534,Vvar__9__rlt__36539,Vvar__9__rlt__36539)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__36508,Vvar__1__rO__36509,Vvar__2__rI__36510,Vvar__3__rplus__36511,Vvar__4__rtimes__36516,Vvar__5__rminus__36521,Vvar__6__ropp__36526,Vvar__7__req__36529,Vvar__8__rle__36534,Vvar__9__rlt__36539)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__36508,Vvar__7__req__36529)
& ! [Vvar__var__var__var__var__11__x1__36583__36589__36694__36700__36706] :
( t(Vvar__var__var__var__var__11__x1__36583__36589__36694__36700__36706,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__12__x2__36584__36590__36695__36701__36707] :
( t(Vvar__var__var__var__var__12__x2__36584__36590__36695__36701__36707,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__7__req__36529,Vvar__var__var__var__var__11__x1__36583__36589__36694__36700__36706),Vvar__var__var__var__var__12__x2__36584__36590__36695__36701__36707))
=> ! [Vvar__var__var__var__var__14__y1__36585__36591__36696__36702__36708] :
( t(Vvar__var__var__var__var__14__y1__36585__36591__36696__36702__36708,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__15__y2__36586__36592__36697__36703__36709] :
( t(Vvar__var__var__var__var__15__y2__36586__36592__36697__36703__36709,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__7__req__36529,Vvar__var__var__var__var__14__y1__36585__36591__36696__36702__36708),Vvar__var__var__var__var__15__y2__36586__36592__36697__36703__36709))
=> p(happ(happ(Vvar__7__req__36529,happ(happ(Vvar__3__rplus__36511,Vvar__var__var__var__var__11__x1__36583__36589__36694__36700__36706),Vvar__var__var__var__var__14__y1__36585__36591__36696__36702__36708)),happ(happ(Vvar__3__rplus__36511,Vvar__var__var__var__var__12__x2__36584__36590__36695__36701__36707),Vvar__var__var__var__var__15__y2__36586__36592__36697__36703__36709))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__36596__36602__36712__36718__36724] :
( t(Vvar__var__var__var__var__12__x1__36596__36602__36712__36718__36724,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__13__x2__36597__36603__36713__36719__36725] :
( t(Vvar__var__var__var__var__13__x2__36597__36603__36713__36719__36725,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__7__req__36529,Vvar__var__var__var__var__12__x1__36596__36602__36712__36718__36724),Vvar__var__var__var__var__13__x2__36597__36603__36713__36719__36725))
=> ! [Vvar__var__var__var__var__15__y1__36598__36604__36714__36720__36726] :
( t(Vvar__var__var__var__var__15__y1__36598__36604__36714__36720__36726,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__16__y2__36599__36605__36715__36721__36727] :
( t(Vvar__var__var__var__var__16__y2__36599__36605__36715__36721__36727,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__7__req__36529,Vvar__var__var__var__var__15__y1__36598__36604__36714__36720__36726),Vvar__var__var__var__var__16__y2__36599__36605__36715__36721__36727))
=> p(happ(happ(Vvar__7__req__36529,happ(happ(Vvar__4__rtimes__36516,Vvar__var__var__var__var__12__x1__36596__36602__36712__36718__36724),Vvar__var__var__var__var__15__y1__36598__36604__36714__36720__36726)),happ(happ(Vvar__4__rtimes__36516,Vvar__var__var__var__var__13__x2__36597__36603__36713__36719__36725),Vvar__var__var__var__var__16__y2__36599__36605__36715__36721__36727))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__36609__36612__36730__36733__36736] :
( t(Vvar__var__var__var__var__13__x1__36609__36612__36730__36733__36736,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__14__x2__36610__36613__36731__36734__36737] :
( t(Vvar__var__var__var__var__14__x2__36610__36613__36731__36734__36737,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__7__req__36529,Vvar__var__var__var__var__13__x1__36609__36612__36730__36733__36736),Vvar__var__var__var__var__14__x2__36610__36613__36731__36734__36737))
=> p(happ(happ(Vvar__7__req__36529,happ(Vvar__6__ropp__36526,Vvar__var__var__var__var__13__x1__36609__36612__36730__36733__36736)),happ(Vvar__6__ropp__36526,Vvar__var__var__var__var__14__x2__36610__36613__36731__36734__36737))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__36616__36622__36739__36745__36751] :
( t(Vvar__var__var__var__var__14__x1__36616__36622__36739__36745__36751,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__15__x2__36617__36623__36740__36746__36752] :
( t(Vvar__var__var__var__var__15__x2__36617__36623__36740__36746__36752,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__7__req__36529,Vvar__var__var__var__var__14__x1__36616__36622__36739__36745__36751),Vvar__var__var__var__var__15__x2__36617__36623__36740__36746__36752))
=> ! [Vvar__var__var__var__var__17__y1__36618__36624__36741__36747__36753] :
( t(Vvar__var__var__var__var__17__y1__36618__36624__36741__36747__36753,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__18__y2__36619__36625__36742__36748__36754] :
( t(Vvar__var__var__var__var__18__y2__36619__36625__36742__36748__36754,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__7__req__36529,Vvar__var__var__var__var__17__y1__36618__36624__36741__36747__36753),Vvar__var__var__var__var__18__y2__36619__36625__36742__36748__36754))
=> ( p(happ(happ(Vvar__8__rle__36534,Vvar__var__var__var__var__14__x1__36616__36622__36739__36745__36751),Vvar__var__var__var__var__17__y1__36618__36624__36741__36747__36753))
<=> p(happ(happ(Vvar__8__rle__36534,Vvar__var__var__var__var__15__x2__36617__36623__36740__36746__36752),Vvar__var__var__var__var__18__y2__36619__36625__36742__36748__36754)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__36629__36635__36757__36763__36769] :
( t(Vvar__var__var__var__var__15__x1__36629__36635__36757__36763__36769,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__16__x2__36630__36636__36758__36764__36770] :
( t(Vvar__var__var__var__var__16__x2__36630__36636__36758__36764__36770,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__7__req__36529,Vvar__var__var__var__var__15__x1__36629__36635__36757__36763__36769),Vvar__var__var__var__var__16__x2__36630__36636__36758__36764__36770))
=> ! [Vvar__var__var__var__var__18__y1__36631__36637__36759__36765__36771] :
( t(Vvar__var__var__var__var__18__y1__36631__36637__36759__36765__36771,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__19__y2__36632__36638__36760__36766__36772] :
( t(Vvar__var__var__var__var__19__y2__36632__36638__36760__36766__36772,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__7__req__36529,Vvar__var__var__var__var__18__y1__36631__36637__36759__36765__36771),Vvar__var__var__var__var__19__y2__36632__36638__36760__36766__36772))
=> ( p(happ(happ(Vvar__9__rlt__36539,Vvar__var__var__var__var__15__x1__36629__36635__36757__36763__36769),Vvar__var__var__var__var__18__y1__36631__36637__36759__36765__36771))
<=> p(happ(happ(Vvar__9__rlt__36539,Vvar__var__var__var__var__16__x2__36630__36636__36758__36764__36770),Vvar__var__var__var__var__19__y2__36632__36638__36760__36766__36772)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__36508,Vvar__1__rO__36509,Vvar__2__rI__36510,Vvar__3__rplus__36511,Vvar__4__rtimes__36516,Vvar__5__rminus__36521,Vvar__6__ropp__36526,Vvar__7__req__36529)
& ! [Vvar__var__var__var__17__n__36643__36644__36775__36776] :
( t(Vvar__var__var__var__17__n__36643__36644__36775__36776,Vvar__0__R__36508)
=> p(happ(happ(Vvar__8__rle__36534,Vvar__var__var__var__17__n__36643__36644__36775__36776),Vvar__var__var__var__17__n__36643__36644__36775__36776)) )
& ! [Vvar__var__var__var__var__18__n__36646__36650__36777__36781__36785] :
( t(Vvar__var__var__var__var__18__n__36646__36650__36777__36781__36785,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__19__m__36647__36651__36778__36782__36786] :
( t(Vvar__var__var__var__var__19__m__36647__36651__36778__36782__36786,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__8__rle__36534,Vvar__var__var__var__var__18__n__36646__36650__36777__36781__36785),Vvar__var__var__var__var__19__m__36647__36651__36778__36782__36786))
=> ( p(happ(happ(Vvar__8__rle__36534,Vvar__var__var__var__var__19__m__36647__36651__36778__36782__36786),Vvar__var__var__var__var__18__n__36646__36650__36777__36781__36785))
=> p(happ(happ(Vvar__7__req__36529,Vvar__var__var__var__var__18__n__36646__36650__36777__36781__36785),Vvar__var__var__var__var__19__m__36647__36651__36778__36782__36786)) ) ) ) )
& ! [Vvar__var__var__var__19__n__36655__36660__36789__36794] :
( t(Vvar__var__var__var__19__n__36655__36660__36789__36794,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__20__m__36656__36661__36790__36795] :
( t(Vvar__var__var__var__20__m__36656__36661__36790__36795,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__21__p__36657__36662__36791__36796] :
( t(Vvar__var__var__var__21__p__36657__36662__36791__36796,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__8__rle__36534,Vvar__var__var__var__19__n__36655__36660__36789__36794),Vvar__var__var__var__20__m__36656__36661__36790__36795))
=> ( p(happ(happ(Vvar__8__rle__36534,Vvar__var__var__var__20__m__36656__36661__36790__36795),Vvar__var__var__var__21__p__36657__36662__36791__36796))
=> p(happ(happ(Vvar__8__rle__36534,Vvar__var__var__var__19__n__36655__36660__36789__36794),Vvar__var__var__var__21__p__36657__36662__36791__36796)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__36666__36668__36799__36801__36803__36805] :
( t(Vvar__var__var__var__var__var__20__n__36666__36668__36799__36801__36803__36805,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__var__21__m__36667__36669__36800__36802__36804__36806] :
( t(Vvar__var__var__var__var__var__21__m__36667__36669__36800__36802__36804__36806,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__9__rlt__36539,Vvar__var__var__var__var__var__20__n__36666__36668__36799__36801__36803__36805),Vvar__var__var__var__var__var__21__m__36667__36669__36800__36802__36804__36806))
<=> ( p(happ(happ(Vvar__8__rle__36534,Vvar__var__var__var__var__var__20__n__36666__36668__36799__36801__36803__36805),Vvar__var__var__var__var__var__21__m__36667__36669__36800__36802__36804__36806))
& ~ p(happ(happ(Vvar__7__req__36529,Vvar__var__var__var__var__var__20__n__36666__36668__36799__36801__36803__36805),Vvar__var__var__var__var__var__21__m__36667__36669__36800__36802__36804__36806)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__36671__36673__36807__36809__36811] :
( t(Vvar__var__var__var__var__21__n__36671__36673__36807__36809__36811,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__22__m__36672__36674__36808__36810__36812] :
( t(Vvar__var__var__var__var__22__m__36672__36674__36808__36810__36812,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__9__rlt__36539,Vvar__var__var__var__var__21__n__36671__36673__36807__36809__36811),Vvar__var__var__var__var__22__m__36672__36674__36808__36810__36812))
| p(happ(happ(Vvar__7__req__36529,Vvar__var__var__var__var__21__n__36671__36673__36807__36809__36811),Vvar__var__var__var__var__22__m__36672__36674__36808__36810__36812))
| p(happ(happ(Vvar__9__rlt__36539,Vvar__var__var__var__var__22__m__36672__36674__36808__36810__36812),Vvar__var__var__var__var__21__n__36671__36673__36807__36809__36811)) ) ) )
& ! [Vvar__var__var__var__var__22__n__36676__36680__36813__36817__36821] :
( t(Vvar__var__var__var__var__22__n__36676__36680__36813__36817__36821,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__23__m__36677__36681__36814__36818__36822] :
( t(Vvar__var__var__var__var__23__m__36677__36681__36814__36818__36822,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__24__p__36678__36682__36815__36819__36823] :
( t(Vvar__var__var__var__var__24__p__36678__36682__36815__36819__36823,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__8__rle__36534,Vvar__var__var__var__var__22__n__36676__36680__36813__36817__36821),Vvar__var__var__var__var__23__m__36677__36681__36814__36818__36822))
=> p(happ(happ(Vvar__8__rle__36534,happ(happ(Vvar__3__rplus__36511,Vvar__var__var__var__var__24__p__36678__36682__36815__36819__36823),Vvar__var__var__var__var__22__n__36676__36680__36813__36817__36821)),happ(happ(Vvar__3__rplus__36511,Vvar__var__var__var__var__24__p__36678__36682__36815__36819__36823),Vvar__var__var__var__var__23__m__36677__36681__36814__36818__36822))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__36685__36689__36825__36829__36833__36837] :
( t(Vvar__var__var__var__var__var__23__n__36685__36689__36825__36829__36833__36837,Vvar__0__R__36508)
=> ! [Vvar__var__var__var__var__var__24__m__36686__36690__36826__36830__36834__36838] :
( t(Vvar__var__var__var__var__var__24__m__36686__36690__36826__36830__36834__36838,Vvar__0__R__36508)
=> ( p(happ(happ(Vvar__9__rlt__36539,Vvar__1__rO__36509),Vvar__var__var__var__var__var__23__n__36685__36689__36825__36829__36833__36837))
=> ( p(happ(happ(Vvar__9__rlt__36539,Vvar__1__rO__36509),Vvar__var__var__var__var__var__24__m__36686__36690__36826__36830__36834__36838))
=> p(happ(happ(Vvar__9__rlt__36539,Vvar__1__rO__36509),happ(happ(Vvar__4__rtimes__36516,Vvar__var__var__var__var__var__23__n__36685__36689__36825__36829__36833__36837),Vvar__var__var__var__var__var__24__m__36686__36690__36826__36830__36834__36838))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__36529,Vvar__1__rO__36509),Vvar__2__rI__36510))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX14722] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX14722)
=> ( VX14722 = cCoq_2emicromega_2eRMicromega_2eC0
| VX14722 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__14723] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__14723)
& VX14722 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__14723) )
| ? [Vvar__0__r__14724] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__14724)
& VX14722 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__14724) )
| ? [Vvar__0__r1__14725] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__14725)
& ? [Vvar__1__r2__14726] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__14726)
& VX14722 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__14725,Vvar__1__r2__14726) ) )
| ? [Vvar__0__r1__14727] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__14727)
& ? [Vvar__1__r2__14728] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__14728)
& VX14722 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__14727,Vvar__1__r2__14728) ) )
| ? [Vvar__0__r1__14729] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__14729)
& ? [Vvar__1__r2__14730] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__14730)
& VX14722 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__14729,Vvar__1__r2__14730) ) )
| ? [Vvar__0__r1__14731] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__14731)
& ? [Vvar__1__z__14732] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__14732)
& VX14722 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__14731,Vvar__1__z__14732) ) )
| ? [Vvar__0__r__14733] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__14733)
& VX14722 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__14733) )
| ? [Vvar__0__r__14734] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__14734)
& VX14722 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__14734) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__16528,VX16529] :
( cType___24t(Vvar__0__T__16528)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__16528,VX16529)
=> ? [Vvar__1__Flhs__16531] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__16528,Vvar__1__Flhs__16531)
& ? [Vvar__2__Fop__16532] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__16532)
& ? [Vvar__3__Frhs__16533] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__16528,Vvar__3__Frhs__16533)
& VX16529 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__16528,Vvar__1__Flhs__16531,Vvar__2__Fop__16532,Vvar__3__Frhs__16533) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX1154] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX1154)
=> ( VX1154 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX1154 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX1154 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX1154 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX16527] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX16527)
=> ( VX16527 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX16527 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX16527 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX16527 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX16527 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX16527 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__15691,VX15692] :
( cType___24t(Vvar__0__C__15691)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__15691,VX15692)
=> ( ? [Vvar__1___24Anonymous__15694] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__15694)
& VX15692 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__15691,Vvar__1___24Anonymous__15694) )
| ? [Vvar__1___24Anonymous__15696] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__15691,Vvar__1___24Anonymous__15696)
& VX15692 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__15691,Vvar__1___24Anonymous__15696) )
| ? [Vvar__1___24Anonymous__15698] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__15691,Vvar__1___24Anonymous__15698)
& ? [Vvar__2___24Anonymous__15699] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__15691,Vvar__2___24Anonymous__15699)
& VX15692 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__15691,Vvar__1___24Anonymous__15698,Vvar__2___24Anonymous__15699) ) )
| ? [Vvar__1___24Anonymous__15701] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__15691,Vvar__1___24Anonymous__15701)
& ? [Vvar__2___24Anonymous__15702] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__15691,Vvar__2___24Anonymous__15702)
& VX15692 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__15691,Vvar__1___24Anonymous__15701,Vvar__2___24Anonymous__15702) ) )
| ? [Vvar__1___24Anonymous__15704] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__15691,Vvar__1___24Anonymous__15704)
& ? [Vvar__2___24Anonymous__15705] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__15691,Vvar__2___24Anonymous__15705)
& VX15692 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__15691,Vvar__1___24Anonymous__15704,Vvar__2___24Anonymous__15705) ) )
| ? [Vvar__1___24Anonymous__15707] :
( t(Vvar__1___24Anonymous__15707,Vvar__0__C__15691)
& VX15692 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__15691,Vvar__1___24Anonymous__15707) )
| VX15692 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__15691) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983] :
( cType___24t(Vvar__0__R__37914)
=> ( t(Vvar__1__rO__37915,Vvar__0__R__37914)
=> ( t(Vvar__2__rI__37916,Vvar__0__R__37914)
=> ( c_24__type__38447___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__3__rplus__37917)
=> ( c_24__type__38793___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__4__rtimes__37922)
=> ( c_24__type__39139___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__5__rminus__37927)
=> ( c_24__type__39462___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__6__ropp__37932)
=> ( c_24__type__39808___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__7__req__37935)
=> ( c_24__type__40154___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__8__rle__37940)
=> ( cType___24t(Vvar__9__C__37945)
=> ( t(Vvar__10__cO__37946,Vvar__9__C__37945)
=> ( t(Vvar__11__cI__37947,Vvar__9__C__37945)
=> ( c_24__type__40500___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__12__cplus__37948)
=> ( c_24__type__40846___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__13__ctimes__37953)
=> ( c_24__type__41192___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__14__cminus__37958)
=> ( c_24__type__41515___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__15__copp__37963)
=> ( c_24__type__41861___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__16__ceqb__37966)
=> ( c_24__type__42207___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__17__cleb__37971)
=> ( c_24__type__42530___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__18__phi__37976)
=> ( cType___24t(Vvar__19__E__37979)
=> ( c_24__type__42853___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__20__pow__phi__37980)
=> ( c_24__type__43199___24t(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983,Vvar__21__rpow__37983)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__8__rle__37940,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__17__cleb__37971,Vvar__18__phi__37976,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__37914,Vvar__1__rO__37915,Vvar__2__rI__37916,Vvar__3__rplus__37917,Vvar__4__rtimes__37922,Vvar__5__rminus__37927,Vvar__6__ropp__37932,Vvar__7__req__37935,Vvar__9__C__37945,Vvar__10__cO__37946,Vvar__11__cI__37947,Vvar__12__cplus__37948,Vvar__13__ctimes__37953,Vvar__14__cminus__37958,Vvar__15__copp__37963,Vvar__16__ceqb__37966,Vvar__18__phi__37976)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__37914,Vvar__2__rI__37916,Vvar__4__rtimes__37922,Vvar__7__req__37935,Vvar__19__E__37979,Vvar__20__pow__phi__37980,Vvar__21__rpow__37983)
& ! [Vvar__var__var__var__var__var__24__x__38066__38069__38079__38082__38085__38088] :
( t(Vvar__var__var__var__var__var__24__x__38066__38069__38079__38082__38085__38088,Vvar__9__C__37945)
=> ! [Vvar__var__var__var__var__var__25__y__38067__38070__38080__38083__38086__38089] :
( t(Vvar__var__var__var__var__var__25__y__38067__38070__38080__38083__38086__38089,Vvar__9__C__37945)
=> ( happ(happ(Vvar__16__ceqb__37966,Vvar__var__var__var__var__var__24__x__38066__38069__38079__38082__38085__38088),Vvar__var__var__var__var__var__25__y__38067__38070__38080__38083__38086__38089) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__37935,happ(Vvar__18__phi__37976,Vvar__var__var__var__var__var__24__x__38066__38069__38079__38082__38085__38088)),happ(Vvar__18__phi__37976,Vvar__var__var__var__var__var__25__y__38067__38070__38080__38083__38086__38089))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__38073__38076__38091__38094__38097__38100] :
( t(Vvar__var__var__var__var__var__25__x__38073__38076__38091__38094__38097__38100,Vvar__9__C__37945)
=> ! [Vvar__var__var__var__var__var__26__y__38074__38077__38092__38095__38098__38101] :
( t(Vvar__var__var__var__var__var__26__y__38074__38077__38092__38095__38098__38101,Vvar__9__C__37945)
=> ( happ(happ(Vvar__17__cleb__37971,Vvar__var__var__var__var__var__25__x__38073__38076__38091__38094__38097__38100),Vvar__var__var__var__var__var__26__y__38074__38077__38092__38095__38098__38101) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__37940,happ(Vvar__18__phi__37976,Vvar__var__var__var__var__var__25__x__38073__38076__38091__38094__38097__38100)),happ(Vvar__18__phi__37976,Vvar__var__var__var__var__var__26__y__38074__38077__38092__38095__38098__38101))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,VX30891] :
( cType___24t(Vvar__0__TA__30887)
=> ( cType___24t(Vvar__1__TX__30888)
=> ( cType___24t(Vvar__2__AA__30889)
=> ( cType___24t(Vvar__3__AF__30890)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,VX30891)
=> ( VX30891 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890)
| VX30891 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890)
| ? [Vvar__4___24Anonymous__30904] :
( t(Vvar__4___24Anonymous__30904,Vvar__1__TX__30888)
& VX30891 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__4___24Anonymous__30904) )
| ? [Vvar__4___24Anonymous__30909] :
( t(Vvar__4___24Anonymous__30909,Vvar__0__TA__30887)
& ? [Vvar__5___24Anonymous__30910] :
( t(Vvar__5___24Anonymous__30910,Vvar__2__AA__30889)
& VX30891 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__4___24Anonymous__30909,Vvar__5___24Anonymous__30910) ) )
| ? [Vvar__4___24Anonymous__30915] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__4___24Anonymous__30915)
& ? [Vvar__5___24Anonymous__30916] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__5___24Anonymous__30916)
& VX30891 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__4___24Anonymous__30915,Vvar__5___24Anonymous__30916) ) )
| ? [Vvar__4___24Anonymous__30921] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__4___24Anonymous__30921)
& ? [Vvar__5___24Anonymous__30922] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__5___24Anonymous__30922)
& VX30891 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__4___24Anonymous__30921,Vvar__5___24Anonymous__30922) ) )
| ? [Vvar__4___24Anonymous__30927] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__4___24Anonymous__30927)
& VX30891 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__4___24Anonymous__30927) )
| ? [Vvar__4___24Anonymous__30932] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__4___24Anonymous__30932)
& ? [Vvar__5___24Anonymous__30933] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__30890,Vvar__5___24Anonymous__30933)
& ? [Vvar__6___24Anonymous__30934] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__6___24Anonymous__30934)
& VX30891 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__30887,Vvar__1__TX__30888,Vvar__2__AA__30889,Vvar__3__AF__30890,Vvar__4___24Anonymous__30932,Vvar__5___24Anonymous__30933,Vvar__6___24Anonymous__30934) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__45928] :
( cProp___24t(Vvar__0___24Anonymous__45928)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__45928)
=> ( ? [Vvar__0__S__45930] :
( cType___24t(Vvar__0__S__45930)
& ? [Vvar__1__x__45931] :
( t(Vvar__1__x__45931,Vvar__0__S__45930)
& ? [Vvar__2__y__45932] :
( t(Vvar__2__y__45932,Vvar__0__S__45930)
& Vvar__0___24Anonymous__45928 = c_24__prop__45952___24a4(Vvar__0___24Anonymous__45928,Vvar__0__S__45930,Vvar__1__x__45931,Vvar__2__y__45932) ) ) )
| ? [Vvar__0__x__45933] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__45933)
& ? [Vvar__1__y__45934] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__45934)
& Vvar__0___24Anonymous__45928 = c_24__prop__45953___24a3(Vvar__0___24Anonymous__45928,Vvar__0__x__45933,Vvar__1__y__45934) ) )
| ? [Vvar__0__x__45935] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__45935)
& ? [Vvar__1__s__45936] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__45936)
& Vvar__0___24Anonymous__45928 = c_24__prop__45954___24a3(Vvar__0___24Anonymous__45928,Vvar__0__x__45935,Vvar__1__s__45936) ) )
| Vvar__0___24Anonymous__45928 = c_24True
| Vvar__0___24Anonymous__45928 = c_24False
| ? [Vvar__0__P__45937] :
( cProp___24t(Vvar__0__P__45937)
& ? [Vvar__1__Q__45938] :
( cProp___24t(Vvar__1__Q__45938)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__45937)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__45938)
& Vvar__0___24Anonymous__45928 = c_24__prop__45955___24a3(Vvar__0___24Anonymous__45928,Vvar__0__P__45937,Vvar__1__Q__45938) ) )
| ? [Vvar__0__P__45941] :
( cProp___24t(Vvar__0__P__45941)
& ? [Vvar__1__Q__45942] :
( cProp___24t(Vvar__1__Q__45942)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__45941)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__45942)
& Vvar__0___24Anonymous__45928 = c_24__prop__45956___24a3(Vvar__0___24Anonymous__45928,Vvar__0__P__45941,Vvar__1__Q__45942) ) )
| ? [Vvar__0__P__45945] :
( cProp___24t(Vvar__0__P__45945)
& ? [Vvar__1__Q__45946] :
( cProp___24t(Vvar__1__Q__45946)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__45945)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__45946)
& Vvar__0___24Anonymous__45928 = c_24__prop__45957___24a3(Vvar__0___24Anonymous__45928,Vvar__0__P__45945,Vvar__1__Q__45946) ) )
| ? [Vvar__0__P__45950] :
( cProp___24t(Vvar__0__P__45950)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__45950)
& Vvar__0___24Anonymous__45928 = c_24__prop__45958___24a2(Vvar__0___24Anonymous__45928,Vvar__0__P__45950) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX34079] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX34079)
=> ( VX34079 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__34080] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__34080)
& ? [Vvar__1___24Anonymous__34081] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__34081)
& VX34079 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__34080,Vvar__1___24Anonymous__34081) ) )
| ? [Vvar__0___24Anonymous__34082] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__34082)
& ? [Vvar__1___24Anonymous__34083] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__34083)
& VX34079 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__34082,Vvar__1___24Anonymous__34083) ) )
| ? [Vvar__0___24Anonymous__34084] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__34084)
& ? [Vvar__1___24Anonymous__34085] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__34085)
& ? [Vvar__2___24Anonymous__34086] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__34086)
& VX34079 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__34084,Vvar__1___24Anonymous__34085,Vvar__2___24Anonymous__34086) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__45732,Vvar__1__env__45733,Vvar__2__env_27__45736,Vvar__3__x__45739] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__45732)
=> ( c_24__type__45760___24t(Vvar__0__fr__45732,Vvar__1__env__45733,Vvar__2__env_27__45736,Vvar__3__x__45739,Vvar__1__env__45733)
=> ( c_24__type__45769___24t(Vvar__0__fr__45732,Vvar__1__env__45733,Vvar__2__env_27__45736,Vvar__3__x__45739,Vvar__2__env_27__45736)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__45739)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__45732,Vvar__1__env__45733,Vvar__2__env_27__45736,Vvar__3__x__45739)
=> ( happ(Vvar__1__env__45733,Vvar__3__x__45739) = happ(Vvar__2__env_27__45736,Vvar__3__x__45739)
& happ(Vvar__1__env__45733,Vvar__3__x__45739) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__45736,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__45732,Vvar__3__x__45739))),happ(Vvar__2__env_27__45736,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__45732,Vvar__3__x__45739))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__45736,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__45732,Vvar__3__x__45739))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__45736,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__45732,Vvar__3__x__45739))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__8018,VX8019] :
( cType___24t(Vvar__0__C__8018)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8018,VX8019)
=> ( VX8019 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8018)
| VX8019 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8018)
| ? [Vvar__1___24Anonymous__8023] :
( t(Vvar__1___24Anonymous__8023,Vvar__0__C__8018)
& VX8019 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__8018,Vvar__1___24Anonymous__8023) )
| ? [Vvar__1___24Anonymous__8025] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8025)
& VX8019 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__8018,Vvar__1___24Anonymous__8025) )
| ? [Vvar__1___24Anonymous__8027] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8018,Vvar__1___24Anonymous__8027)
& ? [Vvar__2___24Anonymous__8028] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8018,Vvar__2___24Anonymous__8028)
& VX8019 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__8018,Vvar__1___24Anonymous__8027,Vvar__2___24Anonymous__8028) ) )
| ? [Vvar__1___24Anonymous__8030] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8018,Vvar__1___24Anonymous__8030)
& ? [Vvar__2___24Anonymous__8031] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8018,Vvar__2___24Anonymous__8031)
& VX8019 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__8018,Vvar__1___24Anonymous__8030,Vvar__2___24Anonymous__8031) ) )
| ? [Vvar__1___24Anonymous__8033] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8018,Vvar__1___24Anonymous__8033)
& ? [Vvar__2___24Anonymous__8034] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8018,Vvar__2___24Anonymous__8034)
& VX8019 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__8018,Vvar__1___24Anonymous__8033,Vvar__2___24Anonymous__8034) ) )
| ? [Vvar__1___24Anonymous__8036] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8018,Vvar__1___24Anonymous__8036)
& VX8019 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__8018,Vvar__1___24Anonymous__8036) )
| ? [Vvar__1___24Anonymous__8038] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8018,Vvar__1___24Anonymous__8038)
& VX8019 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__8018,Vvar__1___24Anonymous__8038) )
| ? [Vvar__1___24Anonymous__8040] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8018,Vvar__1___24Anonymous__8040)
& ? [Vvar__2___24Anonymous__8041] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8018,Vvar__2___24Anonymous__8041)
& VX8019 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__8018,Vvar__1___24Anonymous__8040,Vvar__2___24Anonymous__8041) ) )
| ? [Vvar__1___24Anonymous__8043] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8018,Vvar__1___24Anonymous__8043)
& ? [Vvar__2___24Anonymous__8044] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8044)
& VX8019 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__8018,Vvar__1___24Anonymous__8043,Vvar__2___24Anonymous__8044) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__4590,Vvar__1__rO__4591,Vvar__2__rI__4592,Vvar__3__radd__4593,Vvar__4__rmul__4598,Vvar__5__rsub__4603,Vvar__6__ropp__4608,Vvar__7__rdiv__4611,Vvar__8__rinv__4616,Vvar__9__req__4619] :
( cType___24t(Vvar__0__R__4590)
=> ( t(Vvar__1__rO__4591,Vvar__0__R__4590)
=> ( t(Vvar__2__rI__4592,Vvar__0__R__4590)
=> ( c_24__type__4784___24t(Vvar__0__R__4590,Vvar__1__rO__4591,Vvar__2__rI__4592,Vvar__3__radd__4593,Vvar__4__rmul__4598,Vvar__5__rsub__4603,Vvar__6__ropp__4608,Vvar__7__rdiv__4611,Vvar__8__rinv__4616,Vvar__9__req__4619,Vvar__3__radd__4593)
=> ( c_24__type__4877___24t(Vvar__0__R__4590,Vvar__1__rO__4591,Vvar__2__rI__4592,Vvar__3__radd__4593,Vvar__4__rmul__4598,Vvar__5__rsub__4603,Vvar__6__ropp__4608,Vvar__7__rdiv__4611,Vvar__8__rinv__4616,Vvar__9__req__4619,Vvar__4__rmul__4598)
=> ( c_24__type__4970___24t(Vvar__0__R__4590,Vvar__1__rO__4591,Vvar__2__rI__4592,Vvar__3__radd__4593,Vvar__4__rmul__4598,Vvar__5__rsub__4603,Vvar__6__ropp__4608,Vvar__7__rdiv__4611,Vvar__8__rinv__4616,Vvar__9__req__4619,Vvar__5__rsub__4603)
=> ( c_24__type__5052___24t(Vvar__0__R__4590,Vvar__1__rO__4591,Vvar__2__rI__4592,Vvar__3__radd__4593,Vvar__4__rmul__4598,Vvar__5__rsub__4603,Vvar__6__ropp__4608,Vvar__7__rdiv__4611,Vvar__8__rinv__4616,Vvar__9__req__4619,Vvar__6__ropp__4608)
=> ( c_24__type__5145___24t(Vvar__0__R__4590,Vvar__1__rO__4591,Vvar__2__rI__4592,Vvar__3__radd__4593,Vvar__4__rmul__4598,Vvar__5__rsub__4603,Vvar__6__ropp__4608,Vvar__7__rdiv__4611,Vvar__8__rinv__4616,Vvar__9__req__4619,Vvar__7__rdiv__4611)
=> ( c_24__type__5227___24t(Vvar__0__R__4590,Vvar__1__rO__4591,Vvar__2__rI__4592,Vvar__3__radd__4593,Vvar__4__rmul__4598,Vvar__5__rsub__4603,Vvar__6__ropp__4608,Vvar__7__rdiv__4611,Vvar__8__rinv__4616,Vvar__9__req__4619,Vvar__8__rinv__4616)
=> ( c_24__type__5320___24t(Vvar__0__R__4590,Vvar__1__rO__4591,Vvar__2__rI__4592,Vvar__3__radd__4593,Vvar__4__rmul__4598,Vvar__5__rsub__4603,Vvar__6__ropp__4608,Vvar__7__rdiv__4611,Vvar__8__rinv__4616,Vvar__9__req__4619,Vvar__9__req__4619)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__4590,Vvar__1__rO__4591,Vvar__2__rI__4592,Vvar__3__radd__4593,Vvar__4__rmul__4598,Vvar__5__rsub__4603,Vvar__6__ropp__4608,Vvar__7__rdiv__4611,Vvar__8__rinv__4616,Vvar__9__req__4619)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__4590,Vvar__1__rO__4591,Vvar__2__rI__4592,Vvar__3__radd__4593,Vvar__4__rmul__4598,Vvar__5__rsub__4603,Vvar__6__ropp__4608,Vvar__9__req__4619)
& ~ p(happ(happ(Vvar__9__req__4619,Vvar__2__rI__4592),Vvar__1__rO__4591))
& ! [Vvar__var__var__var__var__var__var__12__p__4662__4664__4671__4673__4675__4677__4679] :
( t(Vvar__var__var__var__var__var__var__12__p__4662__4664__4671__4673__4675__4677__4679,Vvar__0__R__4590)
=> ! [Vvar__var__var__var__var__var__var__13__q__4663__4665__4672__4674__4676__4678__4680] :
( t(Vvar__var__var__var__var__var__var__13__q__4663__4665__4672__4674__4676__4678__4680,Vvar__0__R__4590)
=> p(happ(happ(Vvar__9__req__4619,happ(happ(Vvar__7__rdiv__4611,Vvar__var__var__var__var__var__var__12__p__4662__4664__4671__4673__4675__4677__4679),Vvar__var__var__var__var__var__var__13__q__4663__4665__4672__4674__4676__4678__4680)),happ(happ(Vvar__4__rmul__4598,Vvar__var__var__var__var__var__var__12__p__4662__4664__4671__4673__4675__4677__4679),happ(Vvar__8__rinv__4616,Vvar__var__var__var__var__var__var__13__q__4663__4665__4672__4674__4676__4678__4680)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__4667__4669__4681__4683__4685__4687__4689__4691] :
( t(Vvar__var__var__var__var__var__var__var__13__p__4667__4669__4681__4683__4685__4687__4689__4691,Vvar__0__R__4590)
=> ( ~ p(happ(happ(Vvar__9__req__4619,Vvar__var__var__var__var__var__var__var__13__p__4667__4669__4681__4683__4685__4687__4689__4691),Vvar__1__rO__4591))
=> p(happ(happ(Vvar__9__req__4619,happ(happ(Vvar__4__rmul__4598,happ(Vvar__8__rinv__4616,Vvar__var__var__var__var__var__var__var__13__p__4667__4669__4681__4683__4685__4687__4689__4691)),Vvar__var__var__var__var__var__var__var__13__p__4667__4669__4681__4683__4685__4687__4689__4691)),Vvar__2__rI__4592)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__35676,Vvar__1__rO__35677,Vvar__2__rI__35678,Vvar__3__radd__35679,Vvar__4__rmul__35684,Vvar__5__rsub__35689,Vvar__6__ropp__35694,Vvar__7__rdiv__35697,Vvar__8__rinv__35702,Vvar__9__req__35705] :
( cType___24t(Vvar__0__R__35676)
=> ( t(Vvar__1__rO__35677,Vvar__0__R__35676)
=> ( t(Vvar__2__rI__35678,Vvar__0__R__35676)
=> ( c_24__type__35870___24t(Vvar__0__R__35676,Vvar__1__rO__35677,Vvar__2__rI__35678,Vvar__3__radd__35679,Vvar__4__rmul__35684,Vvar__5__rsub__35689,Vvar__6__ropp__35694,Vvar__7__rdiv__35697,Vvar__8__rinv__35702,Vvar__9__req__35705,Vvar__3__radd__35679)
=> ( c_24__type__35963___24t(Vvar__0__R__35676,Vvar__1__rO__35677,Vvar__2__rI__35678,Vvar__3__radd__35679,Vvar__4__rmul__35684,Vvar__5__rsub__35689,Vvar__6__ropp__35694,Vvar__7__rdiv__35697,Vvar__8__rinv__35702,Vvar__9__req__35705,Vvar__4__rmul__35684)
=> ( c_24__type__36056___24t(Vvar__0__R__35676,Vvar__1__rO__35677,Vvar__2__rI__35678,Vvar__3__radd__35679,Vvar__4__rmul__35684,Vvar__5__rsub__35689,Vvar__6__ropp__35694,Vvar__7__rdiv__35697,Vvar__8__rinv__35702,Vvar__9__req__35705,Vvar__5__rsub__35689)
=> ( c_24__type__36138___24t(Vvar__0__R__35676,Vvar__1__rO__35677,Vvar__2__rI__35678,Vvar__3__radd__35679,Vvar__4__rmul__35684,Vvar__5__rsub__35689,Vvar__6__ropp__35694,Vvar__7__rdiv__35697,Vvar__8__rinv__35702,Vvar__9__req__35705,Vvar__6__ropp__35694)
=> ( c_24__type__36231___24t(Vvar__0__R__35676,Vvar__1__rO__35677,Vvar__2__rI__35678,Vvar__3__radd__35679,Vvar__4__rmul__35684,Vvar__5__rsub__35689,Vvar__6__ropp__35694,Vvar__7__rdiv__35697,Vvar__8__rinv__35702,Vvar__9__req__35705,Vvar__7__rdiv__35697)
=> ( c_24__type__36313___24t(Vvar__0__R__35676,Vvar__1__rO__35677,Vvar__2__rI__35678,Vvar__3__radd__35679,Vvar__4__rmul__35684,Vvar__5__rsub__35689,Vvar__6__ropp__35694,Vvar__7__rdiv__35697,Vvar__8__rinv__35702,Vvar__9__req__35705,Vvar__8__rinv__35702)
=> ( c_24__type__36406___24t(Vvar__0__R__35676,Vvar__1__rO__35677,Vvar__2__rI__35678,Vvar__3__radd__35679,Vvar__4__rmul__35684,Vvar__5__rsub__35689,Vvar__6__ropp__35694,Vvar__7__rdiv__35697,Vvar__8__rinv__35702,Vvar__9__req__35705,Vvar__9__req__35705)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__35676,Vvar__1__rO__35677,Vvar__2__rI__35678,Vvar__3__radd__35679,Vvar__4__rmul__35684,Vvar__5__rsub__35689,Vvar__6__ropp__35694,Vvar__7__rdiv__35697,Vvar__8__rinv__35702,Vvar__9__req__35705)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__35676,Vvar__1__rO__35677,Vvar__2__rI__35678,Vvar__3__radd__35679,Vvar__4__rmul__35684,Vvar__5__rsub__35689,Vvar__6__ropp__35694,Vvar__9__req__35705)
& ~ p(happ(happ(Vvar__9__req__35705,Vvar__2__rI__35678),Vvar__1__rO__35677))
& ! [Vvar__var__var__var__var__var__var__12__p__35748__35750__35757__35759__35761__35763__35765] :
( t(Vvar__var__var__var__var__var__var__12__p__35748__35750__35757__35759__35761__35763__35765,Vvar__0__R__35676)
=> ! [Vvar__var__var__var__var__var__var__13__q__35749__35751__35758__35760__35762__35764__35766] :
( t(Vvar__var__var__var__var__var__var__13__q__35749__35751__35758__35760__35762__35764__35766,Vvar__0__R__35676)
=> p(happ(happ(Vvar__9__req__35705,happ(happ(Vvar__7__rdiv__35697,Vvar__var__var__var__var__var__var__12__p__35748__35750__35757__35759__35761__35763__35765),Vvar__var__var__var__var__var__var__13__q__35749__35751__35758__35760__35762__35764__35766)),happ(happ(Vvar__4__rmul__35684,Vvar__var__var__var__var__var__var__12__p__35748__35750__35757__35759__35761__35763__35765),happ(Vvar__8__rinv__35702,Vvar__var__var__var__var__var__var__13__q__35749__35751__35758__35760__35762__35764__35766)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__35753__35755__35767__35769__35771__35773__35775__35777] :
( t(Vvar__var__var__var__var__var__var__var__13__p__35753__35755__35767__35769__35771__35773__35775__35777,Vvar__0__R__35676)
=> ( ~ p(happ(happ(Vvar__9__req__35705,Vvar__var__var__var__var__var__var__var__13__p__35753__35755__35767__35769__35771__35773__35775__35777),Vvar__1__rO__35677))
=> p(happ(happ(Vvar__9__req__35705,happ(happ(Vvar__4__rmul__35684,happ(Vvar__8__rinv__35702,Vvar__var__var__var__var__var__var__var__13__p__35753__35755__35767__35769__35771__35773__35775__35777)),Vvar__var__var__var__var__var__var__var__13__p__35753__35755__35767__35769__35771__35773__35775__35777)),Vvar__2__rI__35678)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__8630,VX8631] :
( cType___24t(Vvar__0__C__8630)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__8630,VX8631)
=> ? [Vvar__1__num__8633] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8630,Vvar__1__num__8633)
& ? [Vvar__2__denum__8634] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8630,Vvar__2__denum__8634)
& ? [Vvar__3__condition__8635] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__8630),Vvar__3__condition__8635)
& VX8631 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__8630,Vvar__1__num__8633,Vvar__2__denum__8634,Vvar__3__condition__8635) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__8980,VX8981] :
( cType___24t(Vvar__0__C__8980)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__8980,VX8981)
=> ? [Vvar__1__rsplit__left__8983] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8980,Vvar__1__rsplit__left__8983)
& ? [Vvar__2__rsplit__common__8984] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8980,Vvar__2__rsplit__common__8984)
& ? [Vvar__3__rsplit__right__8985] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8980,Vvar__3__rsplit__right__8985)
& VX8981 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__8980,Vvar__1__rsplit__left__8983,Vvar__2__rsplit__common__8984,Vvar__3__rsplit__right__8985) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX18125] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX18125)
=> ( VX18125 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__18126] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18126)
& ? [Vvar__1___24Anonymous__18127] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__18127)
& VX18125 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__18126,Vvar__1___24Anonymous__18127) ) )
| ? [Vvar__0___24Anonymous__18128] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18128)
& ? [Vvar__1___24Anonymous__18129] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__18129)
& VX18125 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__18128,Vvar__1___24Anonymous__18129) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__19284,VX19285] :
( cType___24t(Vvar__0__C__19284)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19284,VX19285)
=> ( VX19285 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__19284)
| VX19285 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__19284)
| ? [Vvar__1___24Anonymous__19289] :
( t(Vvar__1___24Anonymous__19289,Vvar__0__C__19284)
& VX19285 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__19284,Vvar__1___24Anonymous__19289) )
| ? [Vvar__1___24Anonymous__19291] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__19291)
& VX19285 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__19284,Vvar__1___24Anonymous__19291) )
| ? [Vvar__1___24Anonymous__19293] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19284,Vvar__1___24Anonymous__19293)
& ? [Vvar__2___24Anonymous__19294] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19284,Vvar__2___24Anonymous__19294)
& VX19285 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__19284,Vvar__1___24Anonymous__19293,Vvar__2___24Anonymous__19294) ) )
| ? [Vvar__1___24Anonymous__19296] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19284,Vvar__1___24Anonymous__19296)
& ? [Vvar__2___24Anonymous__19297] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19284,Vvar__2___24Anonymous__19297)
& VX19285 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__19284,Vvar__1___24Anonymous__19296,Vvar__2___24Anonymous__19297) ) )
| ? [Vvar__1___24Anonymous__19299] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19284,Vvar__1___24Anonymous__19299)
& ? [Vvar__2___24Anonymous__19300] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19284,Vvar__2___24Anonymous__19300)
& VX19285 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__19284,Vvar__1___24Anonymous__19299,Vvar__2___24Anonymous__19300) ) )
| ? [Vvar__1___24Anonymous__19302] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19284,Vvar__1___24Anonymous__19302)
& VX19285 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__19284,Vvar__1___24Anonymous__19302) )
| ? [Vvar__1___24Anonymous__19304] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19284,Vvar__1___24Anonymous__19304)
& ? [Vvar__2___24Anonymous__19305] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__19305)
& VX19285 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__19284,Vvar__1___24Anonymous__19304,Vvar__2___24Anonymous__19305) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__17314,VX17315] :
( cType___24t(Vvar__0__C__17314)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__17314,VX17315)
=> ( ? [Vvar__1___24Anonymous__17317] :
( t(Vvar__1___24Anonymous__17317,Vvar__0__C__17314)
& VX17315 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__17314,Vvar__1___24Anonymous__17317) )
| ? [Vvar__1___24Anonymous__17319] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17319)
& ? [Vvar__2___24Anonymous__17320] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__17314,Vvar__2___24Anonymous__17320)
& VX17315 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__17314,Vvar__1___24Anonymous__17319,Vvar__2___24Anonymous__17320) ) )
| ? [Vvar__1___24Anonymous__17322] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__17314,Vvar__1___24Anonymous__17322)
& ? [Vvar__2___24Anonymous__17323] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17323)
& ? [Vvar__3___24Anonymous__17324] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__17314,Vvar__3___24Anonymous__17324)
& VX17315 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__17314,Vvar__1___24Anonymous__17322,Vvar__2___24Anonymous__17323,Vvar__3___24Anonymous__17324) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__24321,Vvar__1__rO__24322,Vvar__2__rI__24323,Vvar__3__radd__24324,Vvar__4__rmul__24329,Vvar__5__rsub__24334,Vvar__6__ropp__24339,Vvar__7__req__24342] :
( cType___24t(Vvar__0__R__24321)
=> ( t(Vvar__1__rO__24322,Vvar__0__R__24321)
=> ( t(Vvar__2__rI__24323,Vvar__0__R__24321)
=> ( c_24__type__24570___24t(Vvar__0__R__24321,Vvar__1__rO__24322,Vvar__2__rI__24323,Vvar__3__radd__24324,Vvar__4__rmul__24329,Vvar__5__rsub__24334,Vvar__6__ropp__24339,Vvar__7__req__24342,Vvar__3__radd__24324)
=> ( c_24__type__24633___24t(Vvar__0__R__24321,Vvar__1__rO__24322,Vvar__2__rI__24323,Vvar__3__radd__24324,Vvar__4__rmul__24329,Vvar__5__rsub__24334,Vvar__6__ropp__24339,Vvar__7__req__24342,Vvar__4__rmul__24329)
=> ( c_24__type__24696___24t(Vvar__0__R__24321,Vvar__1__rO__24322,Vvar__2__rI__24323,Vvar__3__radd__24324,Vvar__4__rmul__24329,Vvar__5__rsub__24334,Vvar__6__ropp__24339,Vvar__7__req__24342,Vvar__5__rsub__24334)
=> ( c_24__type__24750___24t(Vvar__0__R__24321,Vvar__1__rO__24322,Vvar__2__rI__24323,Vvar__3__radd__24324,Vvar__4__rmul__24329,Vvar__5__rsub__24334,Vvar__6__ropp__24339,Vvar__7__req__24342,Vvar__6__ropp__24339)
=> ( c_24__type__24813___24t(Vvar__0__R__24321,Vvar__1__rO__24322,Vvar__2__rI__24323,Vvar__3__radd__24324,Vvar__4__rmul__24329,Vvar__5__rsub__24334,Vvar__6__ropp__24339,Vvar__7__req__24342,Vvar__7__req__24342)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__24321,Vvar__1__rO__24322,Vvar__2__rI__24323,Vvar__3__radd__24324,Vvar__4__rmul__24329,Vvar__5__rsub__24334,Vvar__6__ropp__24339,Vvar__7__req__24342)
=> ( ! [Vvar__var__var__var__var__var__8__x__24375__24376__24429__24430__24431__24432] :
( t(Vvar__var__var__var__var__var__8__x__24375__24376__24429__24430__24431__24432,Vvar__0__R__24321)
=> p(happ(happ(Vvar__7__req__24342,happ(happ(Vvar__3__radd__24324,Vvar__1__rO__24322),Vvar__var__var__var__var__var__8__x__24375__24376__24429__24430__24431__24432)),Vvar__var__var__var__var__var__8__x__24375__24376__24429__24430__24431__24432)) )
& ! [Vvar__var__var__var__var__9__x__24378__24380__24433__24435__24437] :
( t(Vvar__var__var__var__var__9__x__24378__24380__24433__24435__24437,Vvar__0__R__24321)
=> ! [Vvar__var__var__var__var__10__y__24379__24381__24434__24436__24438] :
( t(Vvar__var__var__var__var__10__y__24379__24381__24434__24436__24438,Vvar__0__R__24321)
=> p(happ(happ(Vvar__7__req__24342,happ(happ(Vvar__3__radd__24324,Vvar__var__var__var__var__9__x__24378__24380__24433__24435__24437),Vvar__var__var__var__var__10__y__24379__24381__24434__24436__24438)),happ(happ(Vvar__3__radd__24324,Vvar__var__var__var__var__10__y__24379__24381__24434__24436__24438),Vvar__var__var__var__var__9__x__24378__24380__24433__24435__24437))) ) )
& ! [Vvar__var__var__var__var__10__x__24383__24386__24439__24442__24445] :
( t(Vvar__var__var__var__var__10__x__24383__24386__24439__24442__24445,Vvar__0__R__24321)
=> ! [Vvar__var__var__var__var__11__y__24384__24387__24440__24443__24446] :
( t(Vvar__var__var__var__var__11__y__24384__24387__24440__24443__24446,Vvar__0__R__24321)
=> ! [Vvar__var__var__var__var__12__z__24385__24388__24441__24444__24447] :
( t(Vvar__var__var__var__var__12__z__24385__24388__24441__24444__24447,Vvar__0__R__24321)
=> p(happ(happ(Vvar__7__req__24342,happ(happ(Vvar__3__radd__24324,Vvar__var__var__var__var__10__x__24383__24386__24439__24442__24445),happ(happ(Vvar__3__radd__24324,Vvar__var__var__var__var__11__y__24384__24387__24440__24443__24446),Vvar__var__var__var__var__12__z__24385__24388__24441__24444__24447))),happ(happ(Vvar__3__radd__24324,happ(happ(Vvar__3__radd__24324,Vvar__var__var__var__var__10__x__24383__24386__24439__24442__24445),Vvar__var__var__var__var__11__y__24384__24387__24440__24443__24446)),Vvar__var__var__var__var__12__z__24385__24388__24441__24444__24447))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__24390__24391__24448__24449__24450__24451] :
( t(Vvar__var__var__var__var__var__11__x__24390__24391__24448__24449__24450__24451,Vvar__0__R__24321)
=> p(happ(happ(Vvar__7__req__24342,happ(happ(Vvar__4__rmul__24329,Vvar__2__rI__24323),Vvar__var__var__var__var__var__11__x__24390__24391__24448__24449__24450__24451)),Vvar__var__var__var__var__var__11__x__24390__24391__24448__24449__24450__24451)) )
& ! [Vvar__var__var__var__var__var__12__x__24393__24394__24452__24453__24454__24455] :
( t(Vvar__var__var__var__var__var__12__x__24393__24394__24452__24453__24454__24455,Vvar__0__R__24321)
=> p(happ(happ(Vvar__7__req__24342,happ(happ(Vvar__4__rmul__24329,Vvar__1__rO__24322),Vvar__var__var__var__var__var__12__x__24393__24394__24452__24453__24454__24455)),Vvar__1__rO__24322)) )
& ! [Vvar__var__var__var__var__13__x__24396__24398__24456__24458__24460] :
( t(Vvar__var__var__var__var__13__x__24396__24398__24456__24458__24460,Vvar__0__R__24321)
=> ! [Vvar__var__var__var__var__14__y__24397__24399__24457__24459__24461] :
( t(Vvar__var__var__var__var__14__y__24397__24399__24457__24459__24461,Vvar__0__R__24321)
=> p(happ(happ(Vvar__7__req__24342,happ(happ(Vvar__4__rmul__24329,Vvar__var__var__var__var__13__x__24396__24398__24456__24458__24460),Vvar__var__var__var__var__14__y__24397__24399__24457__24459__24461)),happ(happ(Vvar__4__rmul__24329,Vvar__var__var__var__var__14__y__24397__24399__24457__24459__24461),Vvar__var__var__var__var__13__x__24396__24398__24456__24458__24460))) ) )
& ! [Vvar__var__var__var__var__14__x__24401__24404__24462__24465__24468] :
( t(Vvar__var__var__var__var__14__x__24401__24404__24462__24465__24468,Vvar__0__R__24321)
=> ! [Vvar__var__var__var__var__15__y__24402__24405__24463__24466__24469] :
( t(Vvar__var__var__var__var__15__y__24402__24405__24463__24466__24469,Vvar__0__R__24321)
=> ! [Vvar__var__var__var__var__16__z__24403__24406__24464__24467__24470] :
( t(Vvar__var__var__var__var__16__z__24403__24406__24464__24467__24470,Vvar__0__R__24321)
=> p(happ(happ(Vvar__7__req__24342,happ(happ(Vvar__4__rmul__24329,Vvar__var__var__var__var__14__x__24401__24404__24462__24465__24468),happ(happ(Vvar__4__rmul__24329,Vvar__var__var__var__var__15__y__24402__24405__24463__24466__24469),Vvar__var__var__var__var__16__z__24403__24406__24464__24467__24470))),happ(happ(Vvar__4__rmul__24329,happ(happ(Vvar__4__rmul__24329,Vvar__var__var__var__var__14__x__24401__24404__24462__24465__24468),Vvar__var__var__var__var__15__y__24402__24405__24463__24466__24469)),Vvar__var__var__var__var__16__z__24403__24406__24464__24467__24470))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__24408__24411__24471__24474__24477__24480] :
( t(Vvar__var__var__var__var__var__15__x__24408__24411__24471__24474__24477__24480,Vvar__0__R__24321)
=> ! [Vvar__var__var__var__var__var__16__y__24409__24412__24472__24475__24478__24481] :
( t(Vvar__var__var__var__var__var__16__y__24409__24412__24472__24475__24478__24481,Vvar__0__R__24321)
=> ! [Vvar__var__var__var__var__var__17__z__24410__24413__24473__24476__24479__24482] :
( t(Vvar__var__var__var__var__var__17__z__24410__24413__24473__24476__24479__24482,Vvar__0__R__24321)
=> p(happ(happ(Vvar__7__req__24342,happ(happ(Vvar__4__rmul__24329,happ(happ(Vvar__3__radd__24324,Vvar__var__var__var__var__var__15__x__24408__24411__24471__24474__24477__24480),Vvar__var__var__var__var__var__16__y__24409__24412__24472__24475__24478__24481)),Vvar__var__var__var__var__var__17__z__24410__24413__24473__24476__24479__24482)),happ(happ(Vvar__3__radd__24324,happ(happ(Vvar__4__rmul__24329,Vvar__var__var__var__var__var__15__x__24408__24411__24471__24474__24477__24480),Vvar__var__var__var__var__var__17__z__24410__24413__24473__24476__24479__24482)),happ(happ(Vvar__4__rmul__24329,Vvar__var__var__var__var__var__16__y__24409__24412__24472__24475__24478__24481),Vvar__var__var__var__var__var__17__z__24410__24413__24473__24476__24479__24482)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__24415__24417__24483__24485__24487__24489] :
( t(Vvar__var__var__var__var__var__16__x__24415__24417__24483__24485__24487__24489,Vvar__0__R__24321)
=> ! [Vvar__var__var__var__var__var__17__y__24416__24418__24484__24486__24488__24490] :
( t(Vvar__var__var__var__var__var__17__y__24416__24418__24484__24486__24488__24490,Vvar__0__R__24321)
=> p(happ(happ(Vvar__7__req__24342,happ(Vvar__6__ropp__24339,happ(happ(Vvar__4__rmul__24329,Vvar__var__var__var__var__var__16__x__24415__24417__24483__24485__24487__24489),Vvar__var__var__var__var__var__17__y__24416__24418__24484__24486__24488__24490))),happ(happ(Vvar__4__rmul__24329,happ(Vvar__6__ropp__24339,Vvar__var__var__var__var__var__16__x__24415__24417__24483__24485__24487__24489)),Vvar__var__var__var__var__var__17__y__24416__24418__24484__24486__24488__24490))) ) )
& ! [Vvar__var__var__var__var__var__17__x__24420__24422__24491__24493__24495__24497] :
( t(Vvar__var__var__var__var__var__17__x__24420__24422__24491__24493__24495__24497,Vvar__0__R__24321)
=> ! [Vvar__var__var__var__var__var__18__y__24421__24423__24492__24494__24496__24498] :
( t(Vvar__var__var__var__var__var__18__y__24421__24423__24492__24494__24496__24498,Vvar__0__R__24321)
=> p(happ(happ(Vvar__7__req__24342,happ(Vvar__6__ropp__24339,happ(happ(Vvar__3__radd__24324,Vvar__var__var__var__var__var__17__x__24420__24422__24491__24493__24495__24497),Vvar__var__var__var__var__var__18__y__24421__24423__24492__24494__24496__24498))),happ(happ(Vvar__3__radd__24324,happ(Vvar__6__ropp__24339,Vvar__var__var__var__var__var__17__x__24420__24422__24491__24493__24495__24497)),happ(Vvar__6__ropp__24339,Vvar__var__var__var__var__var__18__y__24421__24423__24492__24494__24496__24498)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__24425__24427__24499__24501__24503__24505__24507] :
( t(Vvar__var__var__var__var__var__var__18__x__24425__24427__24499__24501__24503__24505__24507,Vvar__0__R__24321)
=> ! [Vvar__var__var__var__var__var__var__19__y__24426__24428__24500__24502__24504__24506__24508] :
( t(Vvar__var__var__var__var__var__var__19__y__24426__24428__24500__24502__24504__24506__24508,Vvar__0__R__24321)
=> p(happ(happ(Vvar__7__req__24342,happ(happ(Vvar__5__rsub__24334,Vvar__var__var__var__var__var__var__18__x__24425__24427__24499__24501__24503__24505__24507),Vvar__var__var__var__var__var__var__19__y__24426__24428__24500__24502__24504__24506__24508)),happ(happ(Vvar__3__radd__24324,Vvar__var__var__var__var__var__var__18__x__24425__24427__24499__24501__24503__24505__24507),happ(Vvar__6__ropp__24339,Vvar__var__var__var__var__var__var__19__y__24426__24428__24500__24502__24504__24506__24508)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__27982,Vvar__1__req__27983,Vvar__2__C__27988,Vvar__3__cadd__27989,Vvar__4__cmul__27994,Vvar__5__phi__27999,Vvar__6__cdiv__28002] :
( cType___24t(Vvar__0__R__27982)
=> ( c_24__type__28122___24t(Vvar__0__R__27982,Vvar__1__req__27983,Vvar__2__C__27988,Vvar__3__cadd__27989,Vvar__4__cmul__27994,Vvar__5__phi__27999,Vvar__6__cdiv__28002,Vvar__1__req__27983)
=> ( cType___24t(Vvar__2__C__27988)
=> ( c_24__type__28172___24t(Vvar__0__R__27982,Vvar__1__req__27983,Vvar__2__C__27988,Vvar__3__cadd__27989,Vvar__4__cmul__27994,Vvar__5__phi__27999,Vvar__6__cdiv__28002,Vvar__3__cadd__27989)
=> ( c_24__type__28222___24t(Vvar__0__R__27982,Vvar__1__req__27983,Vvar__2__C__27988,Vvar__3__cadd__27989,Vvar__4__cmul__27994,Vvar__5__phi__27999,Vvar__6__cdiv__28002,Vvar__4__cmul__27994)
=> ( c_24__type__28264___24t(Vvar__0__R__27982,Vvar__1__req__27983,Vvar__2__C__27988,Vvar__3__cadd__27989,Vvar__4__cmul__27994,Vvar__5__phi__27999,Vvar__6__cdiv__28002,Vvar__5__phi__27999)
=> ( c_24__type__28314___24t(Vvar__0__R__27982,Vvar__1__req__27983,Vvar__2__C__27988,Vvar__3__cadd__27989,Vvar__4__cmul__27994,Vvar__5__phi__27999,Vvar__6__cdiv__28002,Vvar__6__cdiv__28002)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__27982,Vvar__1__req__27983,Vvar__2__C__27988,Vvar__3__cadd__27989,Vvar__4__cmul__27994,Vvar__5__phi__27999,Vvar__6__cdiv__28002)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__28034__28039__28044__28049__28054__28059__28064__28069] :
( t(Vvar__var__var__var__var__var__var__var__7__a__28034__28039__28044__28049__28054__28059__28064__28069,Vvar__2__C__27988)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__28035__28040__28045__28050__28055__28060__28065__28070] :
( t(Vvar__var__var__var__var__var__var__var__8__b__28035__28040__28045__28050__28055__28060__28065__28070,Vvar__2__C__27988)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2428377___24a9(Vvar__0__R__27982,Vvar__1__req__27983,Vvar__2__C__27988,Vvar__3__cadd__27989,Vvar__4__cmul__27994,Vvar__5__phi__27999,Vvar__6__cdiv__28002,Vvar__var__var__var__var__var__var__var__7__a__28034__28039__28044__28049__28054__28059__28064__28069,Vvar__var__var__var__var__var__var__var__8__b__28035__28040__28045__28050__28055__28060__28065__28070) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__28419,Vvar__1__rI__28420,Vvar__2__rmul__28421,Vvar__3__req__28426,Vvar__4__Cpow__28431,Vvar__5__Cp__phi__28432,Vvar__6__rpow__28435] :
( cType___24t(Vvar__0__R__28419)
=> ( t(Vvar__1__rI__28420,Vvar__0__R__28419)
=> ( c_24__type__28521___24t(Vvar__0__R__28419,Vvar__1__rI__28420,Vvar__2__rmul__28421,Vvar__3__req__28426,Vvar__4__Cpow__28431,Vvar__5__Cp__phi__28432,Vvar__6__rpow__28435,Vvar__2__rmul__28421)
=> ( c_24__type__28565___24t(Vvar__0__R__28419,Vvar__1__rI__28420,Vvar__2__rmul__28421,Vvar__3__req__28426,Vvar__4__Cpow__28431,Vvar__5__Cp__phi__28432,Vvar__6__rpow__28435,Vvar__3__req__28426)
=> ( cType___24t(Vvar__4__Cpow__28431)
=> ( c_24__type__28601___24t(Vvar__0__R__28419,Vvar__1__rI__28420,Vvar__2__rmul__28421,Vvar__3__req__28426,Vvar__4__Cpow__28431,Vvar__5__Cp__phi__28432,Vvar__6__rpow__28435,Vvar__5__Cp__phi__28432)
=> ( c_24__type__28645___24t(Vvar__0__R__28419,Vvar__1__rI__28420,Vvar__2__rmul__28421,Vvar__3__req__28426,Vvar__4__Cpow__28431,Vvar__5__Cp__phi__28432,Vvar__6__rpow__28435,Vvar__6__rpow__28435)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__28419,Vvar__1__rI__28420,Vvar__2__rmul__28421,Vvar__3__req__28426,Vvar__4__Cpow__28431,Vvar__5__Cp__phi__28432,Vvar__6__rpow__28435)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__28463__28465__28467__28469__28471__28473__28475__28477] :
( t(Vvar__var__var__var__var__var__var__var__7__r__28463__28465__28467__28469__28471__28473__28475__28477,Vvar__0__R__28419)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__28464__28466__28468__28470__28472__28474__28476__28478] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__28464__28466__28468__28470__28472__28474__28476__28478)
=> p(happ(happ(Vvar__3__req__28426,happ(happ(Vvar__6__rpow__28435,Vvar__var__var__var__var__var__var__var__7__r__28463__28465__28467__28469__28471__28473__28475__28477),happ(Vvar__5__Cp__phi__28432,Vvar__var__var__var__var__var__var__var__8__n__28464__28466__28468__28470__28472__28474__28476__28478))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__28419,Vvar__1__rI__28420,Vvar__2__rmul__28421,Vvar__var__var__var__var__var__var__var__7__r__28463__28465__28467__28469__28471__28473__28475__28477,Vvar__var__var__var__var__var__var__var__8__n__28464__28466__28468__28470__28472__28474__28476__28478))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__24941,Vvar__1__radd__24942,Vvar__2__rmul__24947,Vvar__3__ropp__24952,Vvar__4__req__24955] :
( cType___24t(Vvar__0__R__24941)
=> ( c_24__type__25046___24t(Vvar__0__R__24941,Vvar__1__radd__24942,Vvar__2__rmul__24947,Vvar__3__ropp__24952,Vvar__4__req__24955,Vvar__1__radd__24942)
=> ( c_24__type__25076___24t(Vvar__0__R__24941,Vvar__1__radd__24942,Vvar__2__rmul__24947,Vvar__3__ropp__24952,Vvar__4__req__24955,Vvar__2__rmul__24947)
=> ( c_24__type__25100___24t(Vvar__0__R__24941,Vvar__1__radd__24942,Vvar__2__rmul__24947,Vvar__3__ropp__24952,Vvar__4__req__24955,Vvar__3__ropp__24952)
=> ( c_24__type__25130___24t(Vvar__0__R__24941,Vvar__1__radd__24942,Vvar__2__rmul__24947,Vvar__3__ropp__24952,Vvar__4__req__24955,Vvar__4__req__24955)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__24941,Vvar__1__radd__24942,Vvar__2__rmul__24947,Vvar__3__ropp__24952,Vvar__4__req__24955)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__25160___24a5(Vvar__0__R__24941,Vvar__1__radd__24942,Vvar__2__rmul__24947,Vvar__3__ropp__24952,Vvar__4__req__24955),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__24941,c_24__type__25184___24a5(Vvar__0__R__24941,Vvar__1__radd__24942,Vvar__2__rmul__24947,Vvar__3__ropp__24952,Vvar__4__req__24955),Vvar__4__req__24955,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__24941,Vvar__0__R__24941,Vvar__4__req__24955,Vvar__4__req__24955)),Vvar__1__radd__24942)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__25217___24a5(Vvar__0__R__24941,Vvar__1__radd__24942,Vvar__2__rmul__24947,Vvar__3__ropp__24952,Vvar__4__req__24955),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__24941,c_24__type__25241___24a5(Vvar__0__R__24941,Vvar__1__radd__24942,Vvar__2__rmul__24947,Vvar__3__ropp__24952,Vvar__4__req__24955),Vvar__4__req__24955,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__24941,Vvar__0__R__24941,Vvar__4__req__24955,Vvar__4__req__24955)),Vvar__2__rmul__24947)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__25268___24a5(Vvar__0__R__24941,Vvar__1__radd__24942,Vvar__2__rmul__24947,Vvar__3__ropp__24952,Vvar__4__req__24955),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__24941,Vvar__0__R__24941,Vvar__4__req__24955,Vvar__4__req__24955),Vvar__3__ropp__24952)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX45357] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX45357)
=> ( VX45357 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__45358] :
( cType___24t(Vvar__0__R__45358)
& ? [Vvar__1__req__45359] :
( c_24__type__1173___24t(Vvar__0__R__45358,Vvar__1__req__45359)
& ? [Vvar__2__reqb__45364] :
( c_24__type__3122___24t(Vvar__0__R__45358,Vvar__2__reqb__45364)
& ! [Vvar__var__3__x__45370__45373] :
( t(Vvar__var__3__x__45370__45373,Vvar__0__R__45358)
=> ! [Vvar__var__4__y__45371__45374] :
( t(Vvar__var__4__y__45371__45374,Vvar__0__R__45358)
=> ( happ(happ(Vvar__2__reqb__45364,Vvar__var__3__x__45370__45373),Vvar__var__4__y__45371__45374) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__45359,Vvar__var__3__x__45370__45373),Vvar__var__4__y__45371__45374)) ) ) )
& VX45357 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__45358,Vvar__1__req__45359,Vvar__2__reqb__45364) ) ) )
| ? [Vvar__0__R__45376] :
( cType___24t(Vvar__0__R__45376)
& ? [Vvar__1__rO__45377] :
( t(Vvar__1__rO__45377,Vvar__0__R__45376)
& ? [Vvar__2__rI__45378] :
( t(Vvar__2__rI__45378,Vvar__0__R__45376)
& ? [Vvar__3__radd__45379] :
( c_24__type__3114___24t(Vvar__0__R__45376,Vvar__3__radd__45379)
& ? [Vvar__4__rmul__45384] :
( c_24__type__3114___24t(Vvar__0__R__45376,Vvar__4__rmul__45384)
& ? [Vvar__5__rsub__45389] :
( c_24__type__3114___24t(Vvar__0__R__45376,Vvar__5__rsub__45389)
& ? [Vvar__6__ropp__45394] :
( c_24__type__4409___24t(Vvar__0__R__45376,Vvar__6__ropp__45394)
& ? [Vvar__7__req__45397] :
( c_24__type__1173___24t(Vvar__0__R__45376,Vvar__7__req__45397)
& ? [Vvar__8__C__45402] :
( cType___24t(Vvar__8__C__45402)
& ? [Vvar__9__cO__45403] :
( t(Vvar__9__cO__45403,Vvar__8__C__45402)
& ? [Vvar__10__cI__45404] :
( t(Vvar__10__cI__45404,Vvar__8__C__45402)
& ? [Vvar__11__cadd__45405] :
( c_24__type__9090___24t(Vvar__0__R__45376,Vvar__8__C__45402,Vvar__11__cadd__45405)
& ? [Vvar__12__cmul__45410] :
( c_24__type__9090___24t(Vvar__0__R__45376,Vvar__8__C__45402,Vvar__12__cmul__45410)
& ? [Vvar__13__csub__45415] :
( c_24__type__9090___24t(Vvar__0__R__45376,Vvar__8__C__45402,Vvar__13__csub__45415)
& ? [Vvar__14__copp__45420] :
( c_24__type__9104___24t(Vvar__0__R__45376,Vvar__8__C__45402,Vvar__14__copp__45420)
& ? [Vvar__15__ceqb__45423] :
( c_24__type__9111___24t(Vvar__0__R__45376,Vvar__8__C__45402,Vvar__15__ceqb__45423)
& ? [Vvar__16__phi__45428] :
( c_24__type__3711___24t(Vvar__0__R__45376,Vvar__8__C__45402,Vvar__16__phi__45428)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__45376,Vvar__1__rO__45377,Vvar__2__rI__45378,Vvar__3__radd__45379,Vvar__4__rmul__45384,Vvar__5__rsub__45389,Vvar__6__ropp__45394,Vvar__7__req__45397,Vvar__8__C__45402,Vvar__9__cO__45403,Vvar__10__cI__45404,Vvar__11__cadd__45405,Vvar__12__cmul__45410,Vvar__13__csub__45415,Vvar__14__copp__45420,Vvar__15__ceqb__45423,Vvar__16__phi__45428)
& VX45357 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__45376,Vvar__1__rO__45377,Vvar__2__rI__45378,Vvar__3__radd__45379,Vvar__4__rmul__45384,Vvar__5__rsub__45389,Vvar__6__ropp__45394,Vvar__7__req__45397,Vvar__8__C__45402,Vvar__9__cO__45403,Vvar__10__cI__45404,Vvar__11__cadd__45405,Vvar__12__cmul__45410,Vvar__13__csub__45415,Vvar__14__copp__45420,Vvar__15__ceqb__45423,Vvar__16__phi__45428) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377] :
( cType___24t(Vvar__0__R__25325)
=> ( t(Vvar__1__rO__25326,Vvar__0__R__25325)
=> ( t(Vvar__2__rI__25327,Vvar__0__R__25325)
=> ( c_24__type__25721___24t(Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377,Vvar__3__radd__25328)
=> ( c_24__type__25934___24t(Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377,Vvar__4__rmul__25333)
=> ( c_24__type__26147___24t(Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377,Vvar__5__rsub__25338)
=> ( c_24__type__26342___24t(Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377,Vvar__6__ropp__25343)
=> ( c_24__type__26555___24t(Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377,Vvar__7__req__25346)
=> ( cType___24t(Vvar__8__C__25351)
=> ( t(Vvar__9__cO__25352,Vvar__8__C__25351)
=> ( t(Vvar__10__cI__25353,Vvar__8__C__25351)
=> ( c_24__type__26768___24t(Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377,Vvar__11__cadd__25354)
=> ( c_24__type__26981___24t(Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377,Vvar__12__cmul__25359)
=> ( c_24__type__27194___24t(Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377,Vvar__13__csub__25364)
=> ( c_24__type__27389___24t(Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377,Vvar__14__copp__25369)
=> ( c_24__type__27602___24t(Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377,Vvar__15__ceqb__25372)
=> ( c_24__type__27797___24t(Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377,Vvar__16__phi__25377)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__25325,Vvar__1__rO__25326,Vvar__2__rI__25327,Vvar__3__radd__25328,Vvar__4__rmul__25333,Vvar__5__rsub__25338,Vvar__6__ropp__25343,Vvar__7__req__25346,Vvar__8__C__25351,Vvar__9__cO__25352,Vvar__10__cI__25353,Vvar__11__cadd__25354,Vvar__12__cmul__25359,Vvar__13__csub__25364,Vvar__14__copp__25369,Vvar__15__ceqb__25372,Vvar__16__phi__25377)
=> ( p(happ(happ(Vvar__7__req__25346,happ(Vvar__16__phi__25377,Vvar__9__cO__25352)),Vvar__1__rO__25326))
& p(happ(happ(Vvar__7__req__25346,happ(Vvar__16__phi__25377,Vvar__10__cI__25353)),Vvar__2__rI__25327))
& ! [Vvar__var__var__var__var__var__var__19__x__25439__25441__25463__25465__25467__25469__25471] :
( t(Vvar__var__var__var__var__var__var__19__x__25439__25441__25463__25465__25467__25469__25471,Vvar__8__C__25351)
=> ! [Vvar__var__var__var__var__var__var__20__y__25440__25442__25464__25466__25468__25470__25472] :
( t(Vvar__var__var__var__var__var__var__20__y__25440__25442__25464__25466__25468__25470__25472,Vvar__8__C__25351)
=> p(happ(happ(Vvar__7__req__25346,happ(Vvar__16__phi__25377,happ(happ(Vvar__11__cadd__25354,Vvar__var__var__var__var__var__var__19__x__25439__25441__25463__25465__25467__25469__25471),Vvar__var__var__var__var__var__var__20__y__25440__25442__25464__25466__25468__25470__25472))),happ(happ(Vvar__3__radd__25328,happ(Vvar__16__phi__25377,Vvar__var__var__var__var__var__var__19__x__25439__25441__25463__25465__25467__25469__25471)),happ(Vvar__16__phi__25377,Vvar__var__var__var__var__var__var__20__y__25440__25442__25464__25466__25468__25470__25472)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__25444__25446__25473__25475__25477__25479__25481] :
( t(Vvar__var__var__var__var__var__var__20__x__25444__25446__25473__25475__25477__25479__25481,Vvar__8__C__25351)
=> ! [Vvar__var__var__var__var__var__var__21__y__25445__25447__25474__25476__25478__25480__25482] :
( t(Vvar__var__var__var__var__var__var__21__y__25445__25447__25474__25476__25478__25480__25482,Vvar__8__C__25351)
=> p(happ(happ(Vvar__7__req__25346,happ(Vvar__16__phi__25377,happ(happ(Vvar__13__csub__25364,Vvar__var__var__var__var__var__var__20__x__25444__25446__25473__25475__25477__25479__25481),Vvar__var__var__var__var__var__var__21__y__25445__25447__25474__25476__25478__25480__25482))),happ(happ(Vvar__5__rsub__25338,happ(Vvar__16__phi__25377,Vvar__var__var__var__var__var__var__20__x__25444__25446__25473__25475__25477__25479__25481)),happ(Vvar__16__phi__25377,Vvar__var__var__var__var__var__var__21__y__25445__25447__25474__25476__25478__25480__25482)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__25449__25451__25483__25485__25487__25489__25491] :
( t(Vvar__var__var__var__var__var__var__21__x__25449__25451__25483__25485__25487__25489__25491,Vvar__8__C__25351)
=> ! [Vvar__var__var__var__var__var__var__22__y__25450__25452__25484__25486__25488__25490__25492] :
( t(Vvar__var__var__var__var__var__var__22__y__25450__25452__25484__25486__25488__25490__25492,Vvar__8__C__25351)
=> p(happ(happ(Vvar__7__req__25346,happ(Vvar__16__phi__25377,happ(happ(Vvar__12__cmul__25359,Vvar__var__var__var__var__var__var__21__x__25449__25451__25483__25485__25487__25489__25491),Vvar__var__var__var__var__var__var__22__y__25450__25452__25484__25486__25488__25490__25492))),happ(happ(Vvar__4__rmul__25333,happ(Vvar__16__phi__25377,Vvar__var__var__var__var__var__var__21__x__25449__25451__25483__25485__25487__25489__25491)),happ(Vvar__16__phi__25377,Vvar__var__var__var__var__var__var__22__y__25450__25452__25484__25486__25488__25490__25492)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__25454__25455__25493__25494__25495__25496__25497] :
( t(Vvar__var__var__var__var__var__var__22__x__25454__25455__25493__25494__25495__25496__25497,Vvar__8__C__25351)
=> p(happ(happ(Vvar__7__req__25346,happ(Vvar__16__phi__25377,happ(Vvar__14__copp__25369,Vvar__var__var__var__var__var__var__22__x__25454__25455__25493__25494__25495__25496__25497))),happ(Vvar__6__ropp__25343,happ(Vvar__16__phi__25377,Vvar__var__var__var__var__var__var__22__x__25454__25455__25493__25494__25495__25496__25497)))) )
& ! [Vvar__var__var__var__var__var__23__x__25457__25460__25498__25501__25504__25507] :
( t(Vvar__var__var__var__var__var__23__x__25457__25460__25498__25501__25504__25507,Vvar__8__C__25351)
=> ! [Vvar__var__var__var__var__var__24__y__25458__25461__25499__25502__25505__25508] :
( t(Vvar__var__var__var__var__var__24__y__25458__25461__25499__25502__25505__25508,Vvar__8__C__25351)
=> ( happ(happ(Vvar__15__ceqb__25372,Vvar__var__var__var__var__var__23__x__25457__25460__25498__25501__25504__25507),Vvar__var__var__var__var__var__24__y__25458__25461__25499__25502__25505__25508) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__25346,happ(Vvar__16__phi__25377,Vvar__var__var__var__var__var__23__x__25457__25460__25498__25501__25504__25507)),happ(Vvar__16__phi__25377,Vvar__var__var__var__var__var__24__y__25458__25461__25499__25502__25505__25508))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__43629,Vvar__1__rO__43630,Vvar__2__rI__43631,Vvar__3__radd__43632,Vvar__4__rmul__43637,Vvar__5__rsub__43642,Vvar__6__ropp__43647,Vvar__7__req__43650] :
( cType___24t(Vvar__0__R__43629)
=> ( t(Vvar__1__rO__43630,Vvar__0__R__43629)
=> ( t(Vvar__2__rI__43631,Vvar__0__R__43629)
=> ( c_24__type__43853___24t(Vvar__0__R__43629,Vvar__1__rO__43630,Vvar__2__rI__43631,Vvar__3__radd__43632,Vvar__4__rmul__43637,Vvar__5__rsub__43642,Vvar__6__ropp__43647,Vvar__7__req__43650,Vvar__3__radd__43632)
=> ( c_24__type__43916___24t(Vvar__0__R__43629,Vvar__1__rO__43630,Vvar__2__rI__43631,Vvar__3__radd__43632,Vvar__4__rmul__43637,Vvar__5__rsub__43642,Vvar__6__ropp__43647,Vvar__7__req__43650,Vvar__4__rmul__43637)
=> ( c_24__type__43979___24t(Vvar__0__R__43629,Vvar__1__rO__43630,Vvar__2__rI__43631,Vvar__3__radd__43632,Vvar__4__rmul__43637,Vvar__5__rsub__43642,Vvar__6__ropp__43647,Vvar__7__req__43650,Vvar__5__rsub__43642)
=> ( c_24__type__44033___24t(Vvar__0__R__43629,Vvar__1__rO__43630,Vvar__2__rI__43631,Vvar__3__radd__43632,Vvar__4__rmul__43637,Vvar__5__rsub__43642,Vvar__6__ropp__43647,Vvar__7__req__43650,Vvar__6__ropp__43647)
=> ( c_24__type__44096___24t(Vvar__0__R__43629,Vvar__1__rO__43630,Vvar__2__rI__43631,Vvar__3__radd__43632,Vvar__4__rmul__43637,Vvar__5__rsub__43642,Vvar__6__ropp__43647,Vvar__7__req__43650,Vvar__7__req__43650)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__43629,Vvar__1__rO__43630,Vvar__2__rI__43631,Vvar__3__radd__43632,Vvar__4__rmul__43637,Vvar__5__rsub__43642,Vvar__6__ropp__43647,Vvar__7__req__43650)
=> ( ! [Vvar__var__var__var__var__var__8__x__43683__43684__43727__43728__43729__43730] :
( t(Vvar__var__var__var__var__var__8__x__43683__43684__43727__43728__43729__43730,Vvar__0__R__43629)
=> p(happ(happ(Vvar__7__req__43650,happ(happ(Vvar__3__radd__43632,Vvar__1__rO__43630),Vvar__var__var__var__var__var__8__x__43683__43684__43727__43728__43729__43730)),Vvar__var__var__var__var__var__8__x__43683__43684__43727__43728__43729__43730)) )
& ! [Vvar__var__var__var__var__9__x__43686__43688__43731__43733__43735] :
( t(Vvar__var__var__var__var__9__x__43686__43688__43731__43733__43735,Vvar__0__R__43629)
=> ! [Vvar__var__var__var__var__10__y__43687__43689__43732__43734__43736] :
( t(Vvar__var__var__var__var__10__y__43687__43689__43732__43734__43736,Vvar__0__R__43629)
=> p(happ(happ(Vvar__7__req__43650,happ(happ(Vvar__3__radd__43632,Vvar__var__var__var__var__9__x__43686__43688__43731__43733__43735),Vvar__var__var__var__var__10__y__43687__43689__43732__43734__43736)),happ(happ(Vvar__3__radd__43632,Vvar__var__var__var__var__10__y__43687__43689__43732__43734__43736),Vvar__var__var__var__var__9__x__43686__43688__43731__43733__43735))) ) )
& ! [Vvar__var__var__var__var__10__x__43691__43694__43737__43740__43743] :
( t(Vvar__var__var__var__var__10__x__43691__43694__43737__43740__43743,Vvar__0__R__43629)
=> ! [Vvar__var__var__var__var__11__y__43692__43695__43738__43741__43744] :
( t(Vvar__var__var__var__var__11__y__43692__43695__43738__43741__43744,Vvar__0__R__43629)
=> ! [Vvar__var__var__var__var__12__z__43693__43696__43739__43742__43745] :
( t(Vvar__var__var__var__var__12__z__43693__43696__43739__43742__43745,Vvar__0__R__43629)
=> p(happ(happ(Vvar__7__req__43650,happ(happ(Vvar__3__radd__43632,Vvar__var__var__var__var__10__x__43691__43694__43737__43740__43743),happ(happ(Vvar__3__radd__43632,Vvar__var__var__var__var__11__y__43692__43695__43738__43741__43744),Vvar__var__var__var__var__12__z__43693__43696__43739__43742__43745))),happ(happ(Vvar__3__radd__43632,happ(happ(Vvar__3__radd__43632,Vvar__var__var__var__var__10__x__43691__43694__43737__43740__43743),Vvar__var__var__var__var__11__y__43692__43695__43738__43741__43744)),Vvar__var__var__var__var__12__z__43693__43696__43739__43742__43745))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__43698__43699__43746__43747__43748__43749] :
( t(Vvar__var__var__var__var__var__11__x__43698__43699__43746__43747__43748__43749,Vvar__0__R__43629)
=> p(happ(happ(Vvar__7__req__43650,happ(happ(Vvar__4__rmul__43637,Vvar__2__rI__43631),Vvar__var__var__var__var__var__11__x__43698__43699__43746__43747__43748__43749)),Vvar__var__var__var__var__var__11__x__43698__43699__43746__43747__43748__43749)) )
& ! [Vvar__var__var__var__var__12__x__43701__43703__43750__43752__43754] :
( t(Vvar__var__var__var__var__12__x__43701__43703__43750__43752__43754,Vvar__0__R__43629)
=> ! [Vvar__var__var__var__var__13__y__43702__43704__43751__43753__43755] :
( t(Vvar__var__var__var__var__13__y__43702__43704__43751__43753__43755,Vvar__0__R__43629)
=> p(happ(happ(Vvar__7__req__43650,happ(happ(Vvar__4__rmul__43637,Vvar__var__var__var__var__12__x__43701__43703__43750__43752__43754),Vvar__var__var__var__var__13__y__43702__43704__43751__43753__43755)),happ(happ(Vvar__4__rmul__43637,Vvar__var__var__var__var__13__y__43702__43704__43751__43753__43755),Vvar__var__var__var__var__12__x__43701__43703__43750__43752__43754))) ) )
& ! [Vvar__var__var__var__var__13__x__43706__43709__43756__43759__43762] :
( t(Vvar__var__var__var__var__13__x__43706__43709__43756__43759__43762,Vvar__0__R__43629)
=> ! [Vvar__var__var__var__var__14__y__43707__43710__43757__43760__43763] :
( t(Vvar__var__var__var__var__14__y__43707__43710__43757__43760__43763,Vvar__0__R__43629)
=> ! [Vvar__var__var__var__var__15__z__43708__43711__43758__43761__43764] :
( t(Vvar__var__var__var__var__15__z__43708__43711__43758__43761__43764,Vvar__0__R__43629)
=> p(happ(happ(Vvar__7__req__43650,happ(happ(Vvar__4__rmul__43637,Vvar__var__var__var__var__13__x__43706__43709__43756__43759__43762),happ(happ(Vvar__4__rmul__43637,Vvar__var__var__var__var__14__y__43707__43710__43757__43760__43763),Vvar__var__var__var__var__15__z__43708__43711__43758__43761__43764))),happ(happ(Vvar__4__rmul__43637,happ(happ(Vvar__4__rmul__43637,Vvar__var__var__var__var__13__x__43706__43709__43756__43759__43762),Vvar__var__var__var__var__14__y__43707__43710__43757__43760__43763)),Vvar__var__var__var__var__15__z__43708__43711__43758__43761__43764))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__43713__43716__43765__43768__43771__43774] :
( t(Vvar__var__var__var__var__var__14__x__43713__43716__43765__43768__43771__43774,Vvar__0__R__43629)
=> ! [Vvar__var__var__var__var__var__15__y__43714__43717__43766__43769__43772__43775] :
( t(Vvar__var__var__var__var__var__15__y__43714__43717__43766__43769__43772__43775,Vvar__0__R__43629)
=> ! [Vvar__var__var__var__var__var__16__z__43715__43718__43767__43770__43773__43776] :
( t(Vvar__var__var__var__var__var__16__z__43715__43718__43767__43770__43773__43776,Vvar__0__R__43629)
=> p(happ(happ(Vvar__7__req__43650,happ(happ(Vvar__4__rmul__43637,happ(happ(Vvar__3__radd__43632,Vvar__var__var__var__var__var__14__x__43713__43716__43765__43768__43771__43774),Vvar__var__var__var__var__var__15__y__43714__43717__43766__43769__43772__43775)),Vvar__var__var__var__var__var__16__z__43715__43718__43767__43770__43773__43776)),happ(happ(Vvar__3__radd__43632,happ(happ(Vvar__4__rmul__43637,Vvar__var__var__var__var__var__14__x__43713__43716__43765__43768__43771__43774),Vvar__var__var__var__var__var__16__z__43715__43718__43767__43770__43773__43776)),happ(happ(Vvar__4__rmul__43637,Vvar__var__var__var__var__var__15__y__43714__43717__43766__43769__43772__43775),Vvar__var__var__var__var__var__16__z__43715__43718__43767__43770__43773__43776)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__43720__43722__43777__43779__43781__43783__43785] :
( t(Vvar__var__var__var__var__var__var__15__x__43720__43722__43777__43779__43781__43783__43785,Vvar__0__R__43629)
=> ! [Vvar__var__var__var__var__var__var__16__y__43721__43723__43778__43780__43782__43784__43786] :
( t(Vvar__var__var__var__var__var__var__16__y__43721__43723__43778__43780__43782__43784__43786,Vvar__0__R__43629)
=> p(happ(happ(Vvar__7__req__43650,happ(happ(Vvar__5__rsub__43642,Vvar__var__var__var__var__var__var__15__x__43720__43722__43777__43779__43781__43783__43785),Vvar__var__var__var__var__var__var__16__y__43721__43723__43778__43780__43782__43784__43786)),happ(happ(Vvar__3__radd__43632,Vvar__var__var__var__var__var__var__15__x__43720__43722__43777__43779__43781__43783__43785),happ(Vvar__6__ropp__43647,Vvar__var__var__var__var__var__var__16__y__43721__43723__43778__43780__43782__43784__43786)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__43725__43726__43787__43788__43789__43790__43791] :
( t(Vvar__var__var__var__var__var__var__16__x__43725__43726__43787__43788__43789__43790__43791,Vvar__0__R__43629)
=> p(happ(happ(Vvar__7__req__43650,happ(happ(Vvar__3__radd__43632,Vvar__var__var__var__var__var__var__16__x__43725__43726__43787__43788__43789__43790__43791),happ(Vvar__6__ropp__43647,Vvar__var__var__var__var__var__var__16__x__43725__43726__43787__43788__43789__43790__43791))),Vvar__1__rO__43630)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__44338,Vvar__1__rO__44339,Vvar__2__rI__44340,Vvar__3__radd__44341,Vvar__4__rmul__44346,Vvar__5__req__44351,Vvar__6__C__44356,Vvar__7__cO__44357,Vvar__8__cI__44358,Vvar__9__cadd__44359,Vvar__10__cmul__44364,Vvar__11__ceqb__44369,Vvar__12__phi__44374] :
( cType___24t(Vvar__0__R__44338)
=> ( t(Vvar__1__rO__44339,Vvar__0__R__44338)
=> ( t(Vvar__2__rI__44340,Vvar__0__R__44338)
=> ( c_24__type__44591___24t(Vvar__0__R__44338,Vvar__1__rO__44339,Vvar__2__rI__44340,Vvar__3__radd__44341,Vvar__4__rmul__44346,Vvar__5__req__44351,Vvar__6__C__44356,Vvar__7__cO__44357,Vvar__8__cI__44358,Vvar__9__cadd__44359,Vvar__10__cmul__44364,Vvar__11__ceqb__44369,Vvar__12__phi__44374,Vvar__3__radd__44341)
=> ( c_24__type__44716___24t(Vvar__0__R__44338,Vvar__1__rO__44339,Vvar__2__rI__44340,Vvar__3__radd__44341,Vvar__4__rmul__44346,Vvar__5__req__44351,Vvar__6__C__44356,Vvar__7__cO__44357,Vvar__8__cI__44358,Vvar__9__cadd__44359,Vvar__10__cmul__44364,Vvar__11__ceqb__44369,Vvar__12__phi__44374,Vvar__4__rmul__44346)
=> ( c_24__type__44841___24t(Vvar__0__R__44338,Vvar__1__rO__44339,Vvar__2__rI__44340,Vvar__3__radd__44341,Vvar__4__rmul__44346,Vvar__5__req__44351,Vvar__6__C__44356,Vvar__7__cO__44357,Vvar__8__cI__44358,Vvar__9__cadd__44359,Vvar__10__cmul__44364,Vvar__11__ceqb__44369,Vvar__12__phi__44374,Vvar__5__req__44351)
=> ( cType___24t(Vvar__6__C__44356)
=> ( t(Vvar__7__cO__44357,Vvar__6__C__44356)
=> ( t(Vvar__8__cI__44358,Vvar__6__C__44356)
=> ( c_24__type__44966___24t(Vvar__0__R__44338,Vvar__1__rO__44339,Vvar__2__rI__44340,Vvar__3__radd__44341,Vvar__4__rmul__44346,Vvar__5__req__44351,Vvar__6__C__44356,Vvar__7__cO__44357,Vvar__8__cI__44358,Vvar__9__cadd__44359,Vvar__10__cmul__44364,Vvar__11__ceqb__44369,Vvar__12__phi__44374,Vvar__9__cadd__44359)
=> ( c_24__type__45091___24t(Vvar__0__R__44338,Vvar__1__rO__44339,Vvar__2__rI__44340,Vvar__3__radd__44341,Vvar__4__rmul__44346,Vvar__5__req__44351,Vvar__6__C__44356,Vvar__7__cO__44357,Vvar__8__cI__44358,Vvar__9__cadd__44359,Vvar__10__cmul__44364,Vvar__11__ceqb__44369,Vvar__12__phi__44374,Vvar__10__cmul__44364)
=> ( c_24__type__45216___24t(Vvar__0__R__44338,Vvar__1__rO__44339,Vvar__2__rI__44340,Vvar__3__radd__44341,Vvar__4__rmul__44346,Vvar__5__req__44351,Vvar__6__C__44356,Vvar__7__cO__44357,Vvar__8__cI__44358,Vvar__9__cadd__44359,Vvar__10__cmul__44364,Vvar__11__ceqb__44369,Vvar__12__phi__44374,Vvar__11__ceqb__44369)
=> ( c_24__type__45327___24t(Vvar__0__R__44338,Vvar__1__rO__44339,Vvar__2__rI__44340,Vvar__3__radd__44341,Vvar__4__rmul__44346,Vvar__5__req__44351,Vvar__6__C__44356,Vvar__7__cO__44357,Vvar__8__cI__44358,Vvar__9__cadd__44359,Vvar__10__cmul__44364,Vvar__11__ceqb__44369,Vvar__12__phi__44374,Vvar__12__phi__44374)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__44338,Vvar__1__rO__44339,Vvar__2__rI__44340,Vvar__3__radd__44341,Vvar__4__rmul__44346,Vvar__5__req__44351,Vvar__6__C__44356,Vvar__7__cO__44357,Vvar__8__cI__44358,Vvar__9__cadd__44359,Vvar__10__cmul__44364,Vvar__11__ceqb__44369,Vvar__12__phi__44374)
=> ( p(happ(happ(Vvar__5__req__44351,happ(Vvar__12__phi__44374,Vvar__7__cO__44357)),Vvar__1__rO__44339))
& p(happ(happ(Vvar__5__req__44351,happ(Vvar__12__phi__44374,Vvar__8__cI__44358)),Vvar__2__rI__44340))
& ! [Vvar__var__var__var__var__var__var__15__x__44420__44422__44436__44438__44440__44442__44444] :
( t(Vvar__var__var__var__var__var__var__15__x__44420__44422__44436__44438__44440__44442__44444,Vvar__6__C__44356)
=> ! [Vvar__var__var__var__var__var__var__16__y__44421__44423__44437__44439__44441__44443__44445] :
( t(Vvar__var__var__var__var__var__var__16__y__44421__44423__44437__44439__44441__44443__44445,Vvar__6__C__44356)
=> p(happ(happ(Vvar__5__req__44351,happ(Vvar__12__phi__44374,happ(happ(Vvar__9__cadd__44359,Vvar__var__var__var__var__var__var__15__x__44420__44422__44436__44438__44440__44442__44444),Vvar__var__var__var__var__var__var__16__y__44421__44423__44437__44439__44441__44443__44445))),happ(happ(Vvar__3__radd__44341,happ(Vvar__12__phi__44374,Vvar__var__var__var__var__var__var__15__x__44420__44422__44436__44438__44440__44442__44444)),happ(Vvar__12__phi__44374,Vvar__var__var__var__var__var__var__16__y__44421__44423__44437__44439__44441__44443__44445)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__44425__44427__44446__44448__44450__44452__44454] :
( t(Vvar__var__var__var__var__var__var__16__x__44425__44427__44446__44448__44450__44452__44454,Vvar__6__C__44356)
=> ! [Vvar__var__var__var__var__var__var__17__y__44426__44428__44447__44449__44451__44453__44455] :
( t(Vvar__var__var__var__var__var__var__17__y__44426__44428__44447__44449__44451__44453__44455,Vvar__6__C__44356)
=> p(happ(happ(Vvar__5__req__44351,happ(Vvar__12__phi__44374,happ(happ(Vvar__10__cmul__44364,Vvar__var__var__var__var__var__var__16__x__44425__44427__44446__44448__44450__44452__44454),Vvar__var__var__var__var__var__var__17__y__44426__44428__44447__44449__44451__44453__44455))),happ(happ(Vvar__4__rmul__44346,happ(Vvar__12__phi__44374,Vvar__var__var__var__var__var__var__16__x__44425__44427__44446__44448__44450__44452__44454)),happ(Vvar__12__phi__44374,Vvar__var__var__var__var__var__var__17__y__44426__44428__44447__44449__44451__44453__44455)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__44430__44433__44456__44459__44462__44465] :
( t(Vvar__var__var__var__var__var__17__x__44430__44433__44456__44459__44462__44465,Vvar__6__C__44356)
=> ! [Vvar__var__var__var__var__var__18__y__44431__44434__44457__44460__44463__44466] :
( t(Vvar__var__var__var__var__var__18__y__44431__44434__44457__44460__44463__44466,Vvar__6__C__44356)
=> ( happ(happ(Vvar__11__ceqb__44369,Vvar__var__var__var__var__var__17__x__44430__44433__44456__44459__44462__44465),Vvar__var__var__var__var__var__18__y__44431__44434__44457__44460__44463__44466) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__44351,happ(Vvar__12__phi__44374,Vvar__var__var__var__var__var__17__x__44430__44433__44456__44459__44462__44465)),happ(Vvar__12__phi__44374,Vvar__var__var__var__var__var__18__y__44431__44434__44457__44460__44463__44466))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__43339,Vvar__1__rO__43340,Vvar__2__rI__43341,Vvar__3__radd__43342,Vvar__4__rmul__43347,Vvar__5__req__43352] :
( cType___24t(Vvar__0__R__43339)
=> ( t(Vvar__1__rO__43340,Vvar__0__R__43339)
=> ( t(Vvar__2__rI__43341,Vvar__0__R__43339)
=> ( c_24__type__43507___24t(Vvar__0__R__43339,Vvar__1__rO__43340,Vvar__2__rI__43341,Vvar__3__radd__43342,Vvar__4__rmul__43347,Vvar__5__req__43352,Vvar__3__radd__43342)
=> ( c_24__type__43546___24t(Vvar__0__R__43339,Vvar__1__rO__43340,Vvar__2__rI__43341,Vvar__3__radd__43342,Vvar__4__rmul__43347,Vvar__5__req__43352,Vvar__4__rmul__43347)
=> ( c_24__type__43585___24t(Vvar__0__R__43339,Vvar__1__rO__43340,Vvar__2__rI__43341,Vvar__3__radd__43342,Vvar__4__rmul__43347,Vvar__5__req__43352,Vvar__5__req__43352)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__43339,Vvar__1__rO__43340,Vvar__2__rI__43341,Vvar__3__radd__43342,Vvar__4__rmul__43347,Vvar__5__req__43352)
=> ( ! [Vvar__var__var__var__var__var__6__n__43377__43378__43416__43417__43418__43419] :
( t(Vvar__var__var__var__var__var__6__n__43377__43378__43416__43417__43418__43419,Vvar__0__R__43339)
=> p(happ(happ(Vvar__5__req__43352,happ(happ(Vvar__3__radd__43342,Vvar__1__rO__43340),Vvar__var__var__var__var__var__6__n__43377__43378__43416__43417__43418__43419)),Vvar__var__var__var__var__var__6__n__43377__43378__43416__43417__43418__43419)) )
& ! [Vvar__var__var__var__var__7__n__43380__43382__43420__43422__43424] :
( t(Vvar__var__var__var__var__7__n__43380__43382__43420__43422__43424,Vvar__0__R__43339)
=> ! [Vvar__var__var__var__var__8__m__43381__43383__43421__43423__43425] :
( t(Vvar__var__var__var__var__8__m__43381__43383__43421__43423__43425,Vvar__0__R__43339)
=> p(happ(happ(Vvar__5__req__43352,happ(happ(Vvar__3__radd__43342,Vvar__var__var__var__var__7__n__43380__43382__43420__43422__43424),Vvar__var__var__var__var__8__m__43381__43383__43421__43423__43425)),happ(happ(Vvar__3__radd__43342,Vvar__var__var__var__var__8__m__43381__43383__43421__43423__43425),Vvar__var__var__var__var__7__n__43380__43382__43420__43422__43424))) ) )
& ! [Vvar__var__var__var__var__8__n__43385__43388__43426__43429__43432] :
( t(Vvar__var__var__var__var__8__n__43385__43388__43426__43429__43432,Vvar__0__R__43339)
=> ! [Vvar__var__var__var__var__9__m__43386__43389__43427__43430__43433] :
( t(Vvar__var__var__var__var__9__m__43386__43389__43427__43430__43433,Vvar__0__R__43339)
=> ! [Vvar__var__var__var__var__10__p__43387__43390__43428__43431__43434] :
( t(Vvar__var__var__var__var__10__p__43387__43390__43428__43431__43434,Vvar__0__R__43339)
=> p(happ(happ(Vvar__5__req__43352,happ(happ(Vvar__3__radd__43342,Vvar__var__var__var__var__8__n__43385__43388__43426__43429__43432),happ(happ(Vvar__3__radd__43342,Vvar__var__var__var__var__9__m__43386__43389__43427__43430__43433),Vvar__var__var__var__var__10__p__43387__43390__43428__43431__43434))),happ(happ(Vvar__3__radd__43342,happ(happ(Vvar__3__radd__43342,Vvar__var__var__var__var__8__n__43385__43388__43426__43429__43432),Vvar__var__var__var__var__9__m__43386__43389__43427__43430__43433)),Vvar__var__var__var__var__10__p__43387__43390__43428__43431__43434))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__43392__43393__43435__43436__43437__43438] :
( t(Vvar__var__var__var__var__var__9__n__43392__43393__43435__43436__43437__43438,Vvar__0__R__43339)
=> p(happ(happ(Vvar__5__req__43352,happ(happ(Vvar__4__rmul__43347,Vvar__2__rI__43341),Vvar__var__var__var__var__var__9__n__43392__43393__43435__43436__43437__43438)),Vvar__var__var__var__var__var__9__n__43392__43393__43435__43436__43437__43438)) )
& ! [Vvar__var__var__var__var__var__10__n__43395__43396__43439__43440__43441__43442] :
( t(Vvar__var__var__var__var__var__10__n__43395__43396__43439__43440__43441__43442,Vvar__0__R__43339)
=> p(happ(happ(Vvar__5__req__43352,happ(happ(Vvar__4__rmul__43347,Vvar__1__rO__43340),Vvar__var__var__var__var__var__10__n__43395__43396__43439__43440__43441__43442)),Vvar__1__rO__43340)) )
& ! [Vvar__var__var__var__var__11__n__43398__43400__43443__43445__43447] :
( t(Vvar__var__var__var__var__11__n__43398__43400__43443__43445__43447,Vvar__0__R__43339)
=> ! [Vvar__var__var__var__var__12__m__43399__43401__43444__43446__43448] :
( t(Vvar__var__var__var__var__12__m__43399__43401__43444__43446__43448,Vvar__0__R__43339)
=> p(happ(happ(Vvar__5__req__43352,happ(happ(Vvar__4__rmul__43347,Vvar__var__var__var__var__11__n__43398__43400__43443__43445__43447),Vvar__var__var__var__var__12__m__43399__43401__43444__43446__43448)),happ(happ(Vvar__4__rmul__43347,Vvar__var__var__var__var__12__m__43399__43401__43444__43446__43448),Vvar__var__var__var__var__11__n__43398__43400__43443__43445__43447))) ) )
& ! [Vvar__var__var__var__var__12__n__43403__43406__43449__43452__43455] :
( t(Vvar__var__var__var__var__12__n__43403__43406__43449__43452__43455,Vvar__0__R__43339)
=> ! [Vvar__var__var__var__var__13__m__43404__43407__43450__43453__43456] :
( t(Vvar__var__var__var__var__13__m__43404__43407__43450__43453__43456,Vvar__0__R__43339)
=> ! [Vvar__var__var__var__var__14__p__43405__43408__43451__43454__43457] :
( t(Vvar__var__var__var__var__14__p__43405__43408__43451__43454__43457,Vvar__0__R__43339)
=> p(happ(happ(Vvar__5__req__43352,happ(happ(Vvar__4__rmul__43347,Vvar__var__var__var__var__12__n__43403__43406__43449__43452__43455),happ(happ(Vvar__4__rmul__43347,Vvar__var__var__var__var__13__m__43404__43407__43450__43453__43456),Vvar__var__var__var__var__14__p__43405__43408__43451__43454__43457))),happ(happ(Vvar__4__rmul__43347,happ(happ(Vvar__4__rmul__43347,Vvar__var__var__var__var__12__n__43403__43406__43449__43452__43455),Vvar__var__var__var__var__13__m__43404__43407__43450__43453__43456)),Vvar__var__var__var__var__14__p__43405__43408__43451__43454__43457))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__43410__43413__43458__43461__43464__43467] :
( t(Vvar__var__var__var__var__var__13__n__43410__43413__43458__43461__43464__43467,Vvar__0__R__43339)
=> ! [Vvar__var__var__var__var__var__14__m__43411__43414__43459__43462__43465__43468] :
( t(Vvar__var__var__var__var__var__14__m__43411__43414__43459__43462__43465__43468,Vvar__0__R__43339)
=> ! [Vvar__var__var__var__var__var__15__p__43412__43415__43460__43463__43466__43469] :
( t(Vvar__var__var__var__var__var__15__p__43412__43415__43460__43463__43466__43469,Vvar__0__R__43339)
=> p(happ(happ(Vvar__5__req__43352,happ(happ(Vvar__4__rmul__43347,happ(happ(Vvar__3__radd__43342,Vvar__var__var__var__var__var__13__n__43410__43413__43458__43461__43464__43467),Vvar__var__var__var__var__var__14__m__43411__43414__43459__43462__43465__43468)),Vvar__var__var__var__var__var__15__p__43412__43415__43460__43463__43466__43469)),happ(happ(Vvar__3__radd__43342,happ(happ(Vvar__4__rmul__43347,Vvar__var__var__var__var__var__13__n__43410__43413__43458__43461__43464__43467),Vvar__var__var__var__var__var__15__p__43412__43415__43460__43463__43466__43469)),happ(happ(Vvar__4__rmul__43347,Vvar__var__var__var__var__var__14__m__43411__43414__43459__43462__43465__43468),Vvar__var__var__var__var__var__15__p__43412__43415__43460__43463__43466__43469)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__27883,Vvar__1__copp__27884,Vvar__2__ceqb__27887,Vvar__3__get__sign__27892] :
( cType___24t(Vvar__0__C__27883)
=> ( c_24__type__27939___24t(Vvar__0__C__27883,Vvar__1__copp__27884,Vvar__2__ceqb__27887,Vvar__3__get__sign__27892,Vvar__1__copp__27884)
=> ( c_24__type__27958___24t(Vvar__0__C__27883,Vvar__1__copp__27884,Vvar__2__ceqb__27887,Vvar__3__get__sign__27892,Vvar__2__ceqb__27887)
=> ( c_24__type__27972___24t(Vvar__0__C__27883,Vvar__1__copp__27884,Vvar__2__ceqb__27887,Vvar__3__get__sign__27892,Vvar__3__get__sign__27892)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__27883,Vvar__1__copp__27884,Vvar__2__ceqb__27887,Vvar__3__get__sign__27892)
=> ( ! [Vvar__var__var__var__var__var__4__c__27909__27912__27915__27918__27921__27924] :
( t(Vvar__var__var__var__var__var__4__c__27909__27912__27915__27918__27921__27924,Vvar__0__C__27883)
=> ! [Vvar__var__var__var__var__var__5__c_27__27910__27913__27916__27919__27922__27925] :
( t(Vvar__var__var__var__var__var__5__c_27__27910__27913__27916__27919__27922__27925,Vvar__0__C__27883)
=> ( happ(Vvar__3__get__sign__27892,Vvar__var__var__var__var__var__4__c__27909__27912__27915__27918__27921__27924) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__27883,Vvar__var__var__var__var__var__5__c_27__27910__27913__27916__27919__27922__27925)
=> happ(happ(Vvar__2__ceqb__27887,Vvar__var__var__var__var__var__4__c__27909__27912__27915__27918__27921__27924),happ(Vvar__1__copp__27884,Vvar__var__var__var__var__var__5__c_27__27910__27913__27916__27919__27922__27925)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__44116,Vvar__1__radd__44117,Vvar__2__rmul__44122,Vvar__3__req__44127] :
( cType___24t(Vvar__0__R__44116)
=> ( c_24__type__44202___24t(Vvar__0__R__44116,Vvar__1__radd__44117,Vvar__2__rmul__44122,Vvar__3__req__44127,Vvar__1__radd__44117)
=> ( c_24__type__44225___24t(Vvar__0__R__44116,Vvar__1__radd__44117,Vvar__2__rmul__44122,Vvar__3__req__44127,Vvar__2__rmul__44122)
=> ( c_24__type__44248___24t(Vvar__0__R__44116,Vvar__1__radd__44117,Vvar__2__rmul__44122,Vvar__3__req__44127,Vvar__3__req__44127)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__44116,Vvar__1__radd__44117,Vvar__2__rmul__44122,Vvar__3__req__44127)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__44271___24a4(Vvar__0__R__44116,Vvar__1__radd__44117,Vvar__2__rmul__44122,Vvar__3__req__44127),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__44116,c_24__type__44289___24a4(Vvar__0__R__44116,Vvar__1__radd__44117,Vvar__2__rmul__44122,Vvar__3__req__44127),Vvar__3__req__44127,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__44116,Vvar__0__R__44116,Vvar__3__req__44127,Vvar__3__req__44127)),Vvar__1__radd__44117)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__44315___24a4(Vvar__0__R__44116,Vvar__1__radd__44117,Vvar__2__rmul__44122,Vvar__3__req__44127),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__44116,c_24__type__44333___24a4(Vvar__0__R__44116,Vvar__1__radd__44117,Vvar__2__rmul__44122,Vvar__3__req__44127),Vvar__3__req__44127,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__44116,Vvar__0__R__44116,Vvar__3__req__44127,Vvar__3__req__44127)),Vvar__2__rmul__44122)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Tait.Subst.substitution',axiom,
! [VX451] :
( cTait_2eSubst_2esubstitution___24t(VX451)
=> ? [Vvar__0__support__452] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__0__support__452)
& ? [Vvar__1__shift__453] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__shift__453)
& VX451 = cTait_2eSubst_2emk__sub___24a2(Vvar__0__support__452,Vvar__1__shift__453) ) ) ) ).
fof('$_inversion_Tait.Subst2.Joachimski.substitution',axiom,
! [VX2257] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(VX2257)
=> ( ? [Vvar__0___24Anonymous__2258] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__2258)
& ? [Vvar__1___24Anonymous__2259] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vvar__1___24Anonymous__2259)
& VX2257 = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__2258,Vvar__1___24Anonymous__2259) ) )
| ? [Vvar__0___24Anonymous__2260] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2260)
& VX2257 = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__2260) ) ) ) ).
fof('$_inversion_Tait.Term.term',axiom,
! [VX83] :
( cTait_2eTerm_2eterm___24t(VX83)
=> ( ? [Vvar__0___24Anonymous__84] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__84)
& VX83 = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__84) )
| ? [Vvar__0___24Anonymous__85] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__85)
& ? [Vvar__1___24Anonymous__86] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__86)
& VX83 = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__85,Vvar__1___24Anonymous__86) ) )
| ? [Vvar__0___24Anonymous__87] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__87)
& ? [Vvar__1___24Anonymous__88] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__88)
& VX83 = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__87,Vvar__1___24Anonymous__88) ) ) ) ) ).
fof('$_inversion_Tait.Term.type',axiom,
! [VX74] :
( cTait_2eTerm_2etype___24t(VX74)
=> ( VX74 = cTait_2eTerm_2eIota
| ? [Vvar__0___24Anonymous__75] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__75)
& ? [Vvar__1___24Anonymous__76] :
( cTait_2eTerm_2etype___24t(Vvar__1___24Anonymous__76)
& VX74 = cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__75,Vvar__1___24Anonymous__76) ) ) ) ) ).
fof('$_inversion_Tait.Typing.CorTyp',axiom,
! [Vvar__0___24Anonymous__313,Vvar__1___24Anonymous__314] :
( cTait_2eTyping_2econtext___24t(Vvar__0___24Anonymous__313)
=> ( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__314)
=> ( cTait_2eTyping_2eCorTyp___24a2(Vvar__0___24Anonymous__313,Vvar__1___24Anonymous__314)
=> ( ? [Vvar__0__rhos__316] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__0__rhos__316)
& ? [Vvar__1__n__317] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__317)
& p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__1__n__317,cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,Vvar__0__rhos__316)))
& Vvar__1___24Anonymous__314 = cTait_2eTerm_2eVar___24a1(Vvar__1__n__317)
& Vvar__0___24Anonymous__313 = Vvar__0__rhos__316 ) )
| ? [Vvar__0__rhos__319] :
( cTait_2eTyping_2econtext___24t(Vvar__0__rhos__319)
& ? [Vvar__1__r__320] :
( cTait_2eTerm_2eterm___24t(Vvar__1__r__320)
& ? [Vvar__2__s__321] :
( cTait_2eTerm_2eterm___24t(Vvar__2__s__321)
& cTait_2eTyping_2eCorTyp___24a2(Vvar__0__rhos__319,Vvar__1__r__320)
& cTait_2eTyping_2eCorTyp___24a2(Vvar__0__rhos__319,Vvar__2__s__321)
& ? [Vvar__5__sigma__324] :
( cTait_2eTerm_2etype___24t(Vvar__5__sigma__324)
& cTait_2eTyping_2etyp___24a2(Vvar__0__rhos__319,Vvar__1__r__320) = cTait_2eTerm_2eArrow___24a2(cTait_2eTyping_2etyp___24a2(Vvar__0__rhos__319,Vvar__2__s__321),Vvar__5__sigma__324)
& Vvar__1___24Anonymous__314 = cTait_2eTerm_2eApp___24a2(Vvar__1__r__320,Vvar__2__s__321)
& Vvar__0___24Anonymous__313 = Vvar__0__rhos__319 ) ) ) )
| ? [Vvar__0__rhos__326] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__0__rhos__326)
& ? [Vvar__1__rho__327] :
( cTait_2eTerm_2etype___24t(Vvar__1__rho__327)
& ? [Vvar__2__r__328] :
( cTait_2eTerm_2eterm___24t(Vvar__2__r__328)
& cTait_2eTyping_2eCorTyp___24a2(cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,Vvar__1__rho__327,Vvar__0__rhos__326),Vvar__2__r__328)
& Vvar__1___24Anonymous__314 = cTait_2eTerm_2eAbs___24a2(Vvar__1__rho__327,Vvar__2__r__328)
& Vvar__0___24Anonymous__313 = Vvar__0__rhos__326 ) ) ) ) ) ) ) ).
fof('$_inversion_Tait.nc.nc_type',axiom,
! [Vvar__0__A__115] :
( cType___24t(Vvar__0__A__115)
=> ( cTait_2enc_2enc__type___24a1(Vvar__0__A__115)
=> ? [Vvar__1___24Anonymous__118] :
( t(Vvar__1___24Anonymous__118,Vvar__0__A__115)
& p(c_24True) ) ) ) ).
fof('$_inversion_Tait.nc.test',axiom,
( p(cTait_2enc_2etest)
=> p(c_24True) ) ).
fof('$_lam_12554',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__12554___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esig___24a2(Vv__CANONICAL__0,c_24__lam__12558___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_12558',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__12558___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0))) ) ).
fof('$_lam_13460',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__13460___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_13480',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__13480___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__4,happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_lam_13789',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__13789___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_14587',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__14587___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__4,happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_lam_20498',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__20498___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__20426___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('$_lam_395',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__395___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0) ).
fof('$_lam_398',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__398___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ).
fof('$_lam_43214',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__43214___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_43222',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__43222___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_43230',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__43230___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_43238',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__43238___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_588',axiom,
! [Vv__CANONICAL__0] : c_24__lam__588___24a1(Vv__CANONICAL__0) = c_24__type__590___24a1(Vv__CANONICAL__0) ).
fof('$_lam_596',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__596___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24__prop__598,c_24__prop__599,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eO)) )
| ? [Vvar__0___24Anonymous__597] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__597)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__597)
& c_24__lam__596___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eSpecif_2eright___24a3(c_24__prop__600___24a1(Vvar__0___24Anonymous__597),c_24__prop__601___24a1(Vvar__0___24Anonymous__597),cCoq_2eInit_2ePeano_2eO__S___24a1(Vvar__0___24Anonymous__597)) ) ) ) ).
fof('$_lam_681',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__681___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__684___24a1(Vv__CANONICAL__0),c_24__prop__685___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__0___24Anonymous__682] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__682)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__682)
& c_24__lam__681___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(c_24__prop__688___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__682),c_24__prop__689___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__682)) ) ) ) ) ).
fof('$_prop_1153',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__1153___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_12433',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__12433___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__2 ) ).
fof('$_prop_12434',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__12434___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__2 ) ).
fof('$_prop_12610',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__12610___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_12611',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__12611___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_12612',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__12612___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_12613',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__12613___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_35583',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__35583___24a2(V0__A,V1__B))
<=> ( p(V0__A)
& p(V1__B) ) ) ).
fof('$_prop_45952',axiom,
! [Vvar__0___24Anonymous__45928,Vvar__0__S__45930,Vvar__1__x__45931,Vvar__2__y__45932] :
( p(c_24__prop__45952___24a4(Vvar__0___24Anonymous__45928,Vvar__0__S__45930,Vvar__1__x__45931,Vvar__2__y__45932))
<=> Vvar__1__x__45931 = Vvar__2__y__45932 ) ).
fof('$_prop_45953',axiom,
! [Vvar__0___24Anonymous__45928,Vvar__0__x__45933,Vvar__1__y__45934] :
( p(c_24__prop__45953___24a3(Vvar__0___24Anonymous__45928,Vvar__0__x__45933,Vvar__1__y__45934))
<=> Vvar__0__x__45933 = Vvar__1__y__45934 ) ).
fof('$_prop_45954',axiom,
! [Vvar__0___24Anonymous__45928,Vvar__0__x__45935,Vvar__1__s__45936] :
( p(c_24__prop__45954___24a3(Vvar__0___24Anonymous__45928,Vvar__0__x__45935,Vvar__1__s__45936))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__45935,Vvar__1__s__45936) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_45955',axiom,
! [Vvar__0___24Anonymous__45928,Vvar__0__P__45937,Vvar__1__Q__45938] :
( p(c_24__prop__45955___24a3(Vvar__0___24Anonymous__45928,Vvar__0__P__45937,Vvar__1__Q__45938))
<=> ( p(Vvar__0__P__45937)
& p(Vvar__1__Q__45938) ) ) ).
fof('$_prop_45956',axiom,
! [Vvar__0___24Anonymous__45928,Vvar__0__P__45941,Vvar__1__Q__45942] :
( p(c_24__prop__45956___24a3(Vvar__0___24Anonymous__45928,Vvar__0__P__45941,Vvar__1__Q__45942))
<=> ( p(Vvar__0__P__45941)
| p(Vvar__1__Q__45942) ) ) ).
fof('$_prop_45957',axiom,
! [Vvar__0___24Anonymous__45928,Vvar__0__P__45945,Vvar__1__Q__45946] :
( p(c_24__prop__45957___24a3(Vvar__0___24Anonymous__45928,Vvar__0__P__45945,Vvar__1__Q__45946))
<=> ( p(Vvar__0__P__45945)
=> p(Vvar__1__Q__45946) ) ) ).
fof('$_prop_45958',axiom,
! [Vvar__0___24Anonymous__45928,Vvar__0__P__45950] :
( p(c_24__prop__45958___24a2(Vvar__0___24Anonymous__45928,Vvar__0__P__45950))
<=> ~ p(Vvar__0__P__45950) ) ).
fof('$_prop_46129',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__46129___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_508',axiom,
! [V1__k,Vvar__0___24Anonymous__490] :
( p(c_24__prop__508___24a2(V1__k,Vvar__0___24Anonymous__490))
<=> Vvar__0___24Anonymous__490 = V1__k ) ).
fof('$_prop_509',axiom,
! [V1__k,Vvar__0___24Anonymous__490] :
( p(c_24__prop__509___24a2(V1__k,Vvar__0___24Anonymous__490))
<=> Vvar__0___24Anonymous__490 != V1__k ) ).
fof('$_prop_510',axiom,
! [V1__k,Vvar__0___24Anonymous__490] :
( p(c_24__prop__510___24a2(V1__k,Vvar__0___24Anonymous__490))
<=> Vvar__0___24Anonymous__490 = V1__k ) ).
fof('$_prop_511',axiom,
! [V1__k,Vvar__0___24Anonymous__490] :
( p(c_24__prop__511___24a2(V1__k,Vvar__0___24Anonymous__490))
<=> Vvar__0___24Anonymous__490 != V1__k ) ).
fof('$_prop_592',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__592___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_593',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__593___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_598',axiom,
( p(c_24__prop__598)
<=> cCoq_2eInit_2eDatatypes_2eO = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_599',axiom,
( p(c_24__prop__599)
<=> cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_600',axiom,
! [Vvar__0___24Anonymous__597] :
( p(c_24__prop__600___24a1(Vvar__0___24Anonymous__597))
<=> cCoq_2eInit_2eDatatypes_2eO = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__597) ) ).
fof('$_prop_601',axiom,
! [Vvar__0___24Anonymous__597] :
( p(c_24__prop__601___24a1(Vvar__0___24Anonymous__597))
<=> cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__597) ) ).
fof('$_prop_684',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__684___24a1(Vv__CANONICAL__0))
<=> cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_685',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__685___24a1(Vv__CANONICAL__0))
<=> cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0) != cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_688',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__682] :
( p(c_24__prop__688___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__682))
<=> Vv__CANONICAL__0 = Vvar__0___24Anonymous__682 ) ).
fof('$_prop_689',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__682] :
( p(c_24__prop__689___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__682))
<=> Vv__CANONICAL__0 != Vvar__0___24Anonymous__682 ) ).
fof('$_prop_693',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__693___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_694',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__694___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_type_1000',axiom,
! [Vvar__1001] :
( c_24__type__1000___24t(Vvar__1001)
<=> ! [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__1001,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1028',axiom,
! [Vvar__1029] :
( c_24__type__1028___24t(Vvar__1029)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__1029,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10424',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10425] :
( c_24__type__10424___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10425)
<=> ! [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__10425,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_1045',axiom,
! [Vvar__1046] :
( c_24__type__1045___24t(Vvar__1046)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__122___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__1046,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1061',axiom,
! [Vv__CANONICAL__0,Vvar__1062] :
( c_24__type__1061___24t(Vv__CANONICAL__0,Vvar__1062)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__1062,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1067',axiom,
! [Vvar__1068] :
( c_24__type__1067___24t(Vvar__1068)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1061___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1068,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_10760',axiom,
! [Vvar__10761] :
( c_24__type__10760___24t(Vvar__10761)
<=> ! [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__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__3114___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__9111___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__3711___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cType___24t(Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__5636___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__5645___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( c_24__type__10795___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__10761,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_10795',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10796] :
( c_24__type__10795___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10796)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__10796,Vv__CANONICAL__3)) ) ) ).
fof('$_type_1084',axiom,
! [Vvar__1085] :
( c_24__type__1084___24t(Vvar__1085)
<=> ! [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__1085,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1117',axiom,
! [Vv__CANONICAL__0,Vvar__1118] :
( c_24__type__1117___24t(Vv__CANONICAL__0,Vvar__1118)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__1118,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_11186',axiom,
! [Vvar__11187] :
( c_24__type__11186___24t(Vvar__11187)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__11191___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__11187,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_11191',axiom,
! [Vv__CANONICAL__0,Vvar__11192] :
( c_24__type__11191___24t(Vv__CANONICAL__0,Vvar__11192)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__11192,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_11290',axiom,
! [Vv__CANONICAL__0,Vvar__11291] :
( c_24__type__11290___24t(Vv__CANONICAL__0,Vvar__11291)
<=> ! [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__11291,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_113',axiom,
! [Vvar__114] :
( c_24__type__113___24t(Vvar__114)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTyping_2econtext___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__114,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_11412',axiom,
! [Vvar__11413] :
( c_24__type__11412___24t(Vvar__11413)
<=> ! [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__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__3122___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__11290___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__10)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__11413,Vv__CANONICAL__0),Vv__CANONICAL__1),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)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1147',axiom,
! [Vvar__1148] :
( c_24__type__1147___24t(Vvar__1148)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__1148,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_1151',axiom,
! [Vv__CANONICAL__0,Vvar__1152] :
( c_24__type__1151___24t(Vv__CANONICAL__0,Vvar__1152)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__1152,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_1173',axiom,
! [Vv__CANONICAL__0,Vvar__1174] :
( c_24__type__1173___24t(Vv__CANONICAL__0,Vvar__1174)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1174,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_11929',axiom,
! [Vvar__11930] :
( c_24__type__11929___24t(Vvar__11930)
<=> ! [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__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__4409___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__11930,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('$_type_11940',axiom,
! [Vvar__11941] :
( c_24__type__11940___24t(Vvar__11941)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__11941,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11956',axiom,
! [Vvar__11957] :
( c_24__type__11956___24t(Vvar__11957)
<=> ! [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__11957,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11958',axiom,
! [Vvar__11959] :
( c_24__type__11958___24t(Vvar__11959)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__11959,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11992',axiom,
! [Vvar__11993] :
( c_24__type__11992___24t(Vvar__11993)
<=> ! [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__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___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__11993,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_12069',axiom,
! [Vvar__12070] :
( c_24__type__12069___24t(Vvar__12070)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__12070,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12197',axiom,
! [Vvar__12198] :
( c_24__type__12197___24t(Vvar__12198)
<=> ! [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__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vv__CANONICAL__7)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__12198,Vv__CANONICAL__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('$_type_122',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__123] :
( c_24__type__122___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__123)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__123,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_12234',axiom,
! [Vvar__12235] :
( c_24__type__12234___24t(Vvar__12235)
<=> ! [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__3122___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__12235,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_12291',axiom,
! [Vvar__12292] :
( c_24__type__12291___24t(Vvar__12292)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__12292,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_12300',axiom,
! [Vvar__12301] :
( c_24__type__12300___24t(Vvar__12301)
<=> ! [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__12301,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12431',axiom,
! [Vv__CANONICAL__0,Vvar__12432] :
( c_24__type__12431___24t(Vv__CANONICAL__0,Vvar__12432)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__12433___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__12434___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(Vvar__12432,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_12459',axiom,
! [Vvar__12460] :
( c_24__type__12459___24t(Vvar__12460)
<=> ! [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__12460,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1247',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1248] :
( c_24__type__1247___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1248)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1248,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_12471',axiom,
! [Vvar__12472] :
( c_24__type__12471___24t(Vvar__12472)
<=> ! [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__12472,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_12547',axiom,
! [Vvar__12548] :
( c_24__type__12547___24t(Vvar__12548)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( Vv__CANONICAL__1 != cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esigT___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),c_24__lam__12554___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__12548,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_12623',axiom,
! [Vvar__12624] :
( c_24__type__12623___24t(Vvar__12624)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__12431___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__12624,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1282',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1283] :
( c_24__type__1282___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1283)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1283,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_1287',axiom,
! [Vvar__1288] :
( c_24__type__1287___24t(Vvar__1288)
<=> ! [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__1288,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_1292',axiom,
! [Vvar__1293] :
( c_24__type__1292___24t(Vvar__1293)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__1293,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_1296',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1297] :
( c_24__type__1296___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1297)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__1297,Vv__CANONICAL__2)) ) ) ).
fof('$_type_131',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__132] :
( c_24__type__131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__132)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__132,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_1324',axiom,
! [Vvar__1325] :
( c_24__type__1324___24t(Vvar__1325)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1328___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1335___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1342___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__1325,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('$_type_1328',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1329] :
( c_24__type__1328___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1329)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__1329,Vv__CANONICAL__2)) ) ) ).
fof('$_type_1335',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1336] :
( c_24__type__1335___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1336)
<=> ( p(Vv__CANONICAL__0)
=> t(Vvar__1336,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_1342',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1343] :
( c_24__type__1342___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1343)
<=> ( p(Vv__CANONICAL__1)
=> t(Vvar__1343,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_13449',axiom,
! [Vvar__13450] :
( c_24__type__13449___24t(Vvar__13450)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__13453___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__13450,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1345',axiom,
! [Vvar__1346] :
( c_24__type__1345___24t(Vvar__1346)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cTait_2eSubst_2esubstitution___24t(happ(happ(Vvar__1346,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13453',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13454] :
( c_24__type__13453___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13454)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(Vvar__13454,Vv__CANONICAL__2)) ) ) ).
fof('$_type_13466',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13467] :
( c_24__type__13466___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13467)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__13467,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_1347',axiom,
! [Vvar__1348] :
( c_24__type__1347___24t(Vvar__1348)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> cTait_2eSubst_2esubstitution___24t(happ(Vvar__1348,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1350',axiom,
! [Vvar__1351] :
( c_24__type__1350___24t(Vvar__1351)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__1351,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13522',axiom,
! [Vvar__13523] :
( c_24__type__13522___24t(Vvar__13523)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__13529___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__13523,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_13529',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13530] :
( c_24__type__13529___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13530)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__13530,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13558',axiom,
! [Vvar__13559] :
( c_24__type__13558___24t(Vvar__13559)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__13565___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__13559,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_13565',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13566] :
( c_24__type__13565___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13566)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13566,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1357',axiom,
! [Vv__CANONICAL__0,Vvar__1358] :
( c_24__type__1357___24t(Vv__CANONICAL__0,Vvar__1358)
<=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__1358,Vv__CANONICAL__1)) ) ) ).
fof('$_type_13572',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13573] :
( c_24__type__13572___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13573)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__13573,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_13619',axiom,
! [Vvar__13620] :
( c_24__type__13619___24t(Vvar__13620)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1061___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__13620,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_13649',axiom,
! [Vvar__13650] :
( c_24__type__13649___24t(Vvar__13650)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1061___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__13650,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_13757',axiom,
! [Vvar__13758] :
( c_24__type__13757___24t(Vvar__13758)
<=> ! [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__13758,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1379',axiom,
! [Vvar__1380] :
( c_24__type__1379___24t(Vvar__1380)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1381___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cTait_2eTerm_2eIota))
=> ! [Vv__CANONICAL__2] :
( c_24__type__1393___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__1380,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_13799',axiom,
! [Vvar__13800] :
( c_24__type__13799___24t(Vvar__13800)
<=> ! [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__13800,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1381',axiom,
! [Vvar__1382] :
( c_24__type__1381___24t(Vvar__1382)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__1382,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13886',axiom,
! [Vvar__13887] :
( c_24__type__13886___24t(Vvar__13887)
<=> ! [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_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,happ(happ(Vvar__13887,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13912',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13913] :
( c_24__type__13912___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13913)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__13913,Vv__CANONICAL__3)) ) ) ).
fof('$_type_1393',axiom,
! [Vv__CANONICAL__0,Vvar__1394] :
( c_24__type__1393___24t(Vv__CANONICAL__0,Vvar__1394)
<=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__3] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__3))
=> t(happ(happ(happ(happ(Vvar__1394,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,cTait_2eTerm_2eArrow___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ) ) ).
fof('$_type_1395',axiom,
! [Vvar__1396] :
( c_24__type__1395___24t(Vvar__1396)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1396,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14067',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14068] :
( c_24__type__14067___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14068)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__14068,Vv__CANONICAL__3)) ) ) ).
fof('$_type_14126',axiom,
! [Vvar__14127] :
( c_24__type__14126___24t(Vvar__14127)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2820___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__4] :
( c_24__type__14145___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__14127,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ) ).
fof('$_type_14145',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14146] :
( c_24__type__14145___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14146)
<=> ! [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__14146,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('$_type_1430',axiom,
! [Vv__CANONICAL__0,Vvar__1431] :
( c_24__type__1430___24t(Vv__CANONICAL__0,Vvar__1431)
<=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__1431,Vv__CANONICAL__1)) ) ) ).
fof('$_type_14414',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__14415] :
( c_24__type__14414___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__14415)
<=> ! [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__14415,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_14483',axiom,
! [Vvar__14484] :
( c_24__type__14483___24t(Vvar__14484)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1173___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__14484,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14521',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14522] :
( c_24__type__14521___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14522)
<=> ! [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__14522,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_14546',axiom,
! [Vvar__14547] :
( c_24__type__14546___24t(Vvar__14547)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__14547,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14668',axiom,
! [Vvar__14669] :
( c_24__type__14668___24t(Vvar__14669)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__14669,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14671',axiom,
! [Vvar__14672] :
( c_24__type__14671___24t(Vvar__14672)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__14672,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14674',axiom,
! [Vvar__14675] :
( c_24__type__14674___24t(Vvar__14675)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__14675,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14677',axiom,
! [Vvar__14678] :
( c_24__type__14677___24t(Vvar__14678)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__14678,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14680',axiom,
! [Vvar__14681] :
( c_24__type__14680___24t(Vvar__14681)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(Vvar__14681,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1469',axiom,
! [Vvar__1470] :
( c_24__type__1469___24t(Vvar__1470)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1471___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1474___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1486___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1494___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__1470,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_1471',axiom,
! [Vvar__1472] :
( c_24__type__1471___24t(Vvar__1472)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__1472,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1474',axiom,
! [Vv__CANONICAL__0,Vvar__1475] :
( c_24__type__1474___24t(Vv__CANONICAL__0,Vvar__1475)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__1475,Vv__CANONICAL__1),happ(Vv__CANONICAL__0,cTait_2eTerm_2eVar___24a1(Vv__CANONICAL__1))) ) ) ).
fof('$_type_148',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__149] :
( c_24__type__148___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__149)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__149,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__3) ) ) ) ) ).
fof('$_type_1486',axiom,
! [Vv__CANONICAL__0,Vvar__1487] :
( c_24__type__1486___24t(Vv__CANONICAL__0,Vvar__1487)
<=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__3] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__3))
=> t(happ(happ(happ(happ(Vvar__1487,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,cTait_2eTerm_2eApp___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ) ) ).
fof('$_type_14900',axiom,
! [Vvar__14901] :
( c_24__type__14900___24t(Vvar__14901)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__14901,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14903',axiom,
! [Vvar__14904] :
( c_24__type__14903___24t(Vvar__14904)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__14904,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14909',axiom,
! [Vvar__14910] :
( c_24__type__14909___24t(Vvar__14910)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__14910,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14927',axiom,
! [Vvar__14928] :
( c_24__type__14927___24t(Vvar__14928)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__14928,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1494',axiom,
! [Vv__CANONICAL__0,Vvar__1495] :
( c_24__type__1494___24t(Vv__CANONICAL__0,Vvar__1495)
<=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__2))
=> t(happ(happ(happ(Vvar__1495,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,cTait_2eTerm_2eAbs___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_type_14953',axiom,
! [Vvar__14954] :
( c_24__type__14953___24t(Vvar__14954)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__14954,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_15027',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15028] :
( c_24__type__15027___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15028)
<=> ! [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__15028,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_15161',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15162] :
( c_24__type__15161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15162)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__15162,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_154',axiom,
! [Vvar__155] :
( c_24__type__154___24t(Vvar__155)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cTait_2enc_2enc__type___24a1(Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__155,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_15683',axiom,
! [Vvar__15684] :
( c_24__type__15683___24t(Vvar__15684)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3122___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3122___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(happ(Vvar__15684,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_157',axiom,
! [Vv__CANONICAL__0,Vvar__158] :
( c_24__type__157___24t(Vv__CANONICAL__0,Vvar__158)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__158,Vv__CANONICAL__1)) ) ) ).
fof('$_type_15849',axiom,
! [Vvar__15850] :
( c_24__type__15849___24t(Vvar__15850)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__15853___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__15850,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_15853',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15854] :
( c_24__type__15853___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15854)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__15854,Vv__CANONICAL__2)) ) ) ).
fof('$_type_15887',axiom,
! [Vvar__15888] :
( c_24__type__15887___24t(Vvar__15888)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__15896___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(Vvar__15888,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_15896',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15897] :
( c_24__type__15896___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15897)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__2,happ(happ(Vvar__15897,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_16297',axiom,
! [Vvar__16298] :
( c_24__type__16297___24t(Vvar__16298)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__16298,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16351',axiom,
! [Vvar__16352] :
( c_24__type__16351___24t(Vvar__16352)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,happ(happ(Vvar__16352,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16681',axiom,
! [Vvar__16682] :
( c_24__type__16681___24t(Vvar__16682)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3122___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(Vvar__16682,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_17362',axiom,
! [Vvar__17363] :
( c_24__type__17362___24t(Vvar__17363)
<=> ! [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__17363,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17367',axiom,
! [Vvar__17368] :
( c_24__type__17367___24t(Vvar__17368)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__17368,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17375',axiom,
! [Vvar__17376] :
( c_24__type__17375___24t(Vvar__17376)
<=> ! [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__17376,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_174',axiom,
! [Vvar__175] :
( c_24__type__174___24t(Vvar__175)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ( cTait_2enc_2enc__type___24a1(Vv__CANONICAL__0)
=> ( cTait_2enc_2enc__type___24a1(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(happ(Vvar__175,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ).
fof('$_type_17517',axiom,
! [Vvar__17518] :
( c_24__type__17517___24t(Vvar__17518)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3122___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__17518,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_181',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__182] :
( c_24__type__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__182)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__182,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_18854',axiom,
! [Vvar__18855] :
( c_24__type__18854___24t(Vvar__18855)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3711___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__18855,Vv__CANONICAL__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('$_type_189',axiom,
! [Vvar__190] :
( c_24__type__189___24t(Vvar__190)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTyping_2econtext___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__190,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_18927',axiom,
! [Vvar__18928] :
( c_24__type__18927___24t(Vvar__18928)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1173___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3711___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__18928,Vv__CANONICAL__0),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('$_type_19506',axiom,
! [Vvar__19507] :
( c_24__type__19506___24t(Vvar__19507)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__19507,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19509',axiom,
! [Vvar__19510] :
( c_24__type__19509___24t(Vvar__19510)
<=> ! [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__19510,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19512',axiom,
! [Vvar__19513] :
( c_24__type__19512___24t(Vvar__19513)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__19513,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19517',axiom,
! [Vvar__19518] :
( c_24__type__19517___24t(Vvar__19518)
<=> ! [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__19518,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_19710',axiom,
! [Vvar__19711] :
( c_24__type__19710___24t(Vvar__19711)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__3711___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__5636___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__5645___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__19711,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_20630',axiom,
! [Vvar__20631] :
( c_24__type__20630___24t(Vvar__20631)
<=> ! [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__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__3122___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__11290___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__20631,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_20884',axiom,
! [Vvar__20885] :
( c_24__type__20884___24t(Vvar__20885)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1173___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__3711___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__5636___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__5645___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8)),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__20885,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_21169',axiom,
! [Vvar__21170] :
( c_24__type__21169___24t(Vvar__21170)
<=> ! [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__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__3122___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__11290___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__9)
=> 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)),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__21170,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_21329',axiom,
! [Vvar__21330] :
( c_24__type__21329___24t(Vvar__21330)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21337___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__21330,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_21337',axiom,
! [Vv__CANONICAL__0,Vvar__21338] :
( c_24__type__21337___24t(Vv__CANONICAL__0,Vvar__21338)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [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(Vvar__21338,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_223',axiom,
! [Vvar__224] :
( c_24__type__223___24t(Vvar__224)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__224,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2231',axiom,
! [Vvar__2232] :
( c_24__type__2231___24t(Vvar__2232)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__2)
=> cTait_2eTerm_2eterm___24t(happ(happ(happ(Vvar__2232,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2271',axiom,
! [Vvar__2272] :
( c_24__type__2271___24t(Vvar__2272)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__1)
=> cTait_2eSubst2_2eJoachimski_2esubstitution___24t(happ(happ(Vvar__2272,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2279',axiom,
! [Vvar__2280] :
( c_24__type__2279___24t(Vvar__2280)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cTait_2eSubst2_2eJoachimski_2esubstitution___24t(happ(happ(Vvar__2280,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_228',axiom,
! [Vvar__229] :
( c_24__type__228___24t(Vvar__229)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__229,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2296',axiom,
! [Vvar__2297] :
( c_24__type__2296___24t(Vvar__2297)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__2297,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2307',axiom,
! [Vvar__2308] :
( c_24__type__2307___24t(Vvar__2308)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__2308,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23454',axiom,
! [Vvar__23455] :
( c_24__type__23454___24t(Vvar__23455)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3114___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__23455,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_238',axiom,
! [Vvar__239] :
( c_24__type__238___24t(Vvar__239)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__239,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23841',axiom,
! [Vvar__23842] :
( c_24__type__23841___24t(Vvar__23842)
<=> ! [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__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__4409___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__9111___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__3711___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__5636___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__5645___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__10795___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__23842,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_24295',axiom,
! [Vvar__24296] :
( c_24__type__24295___24t(Vvar__24296)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__24296,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_24316',axiom,
! [Vvar__24317] :
( c_24__type__24316___24t(Vvar__24317)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3114___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__24317,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_24570',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__24571] :
( c_24__type__24570___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__24571)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24571,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24633',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__24634] :
( c_24__type__24633___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__24634)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24634,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24696',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__24697] :
( c_24__type__24696___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__24697)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24697,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24750',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__24751] :
( c_24__type__24750___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__24751)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__24751,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_24813',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__24814] :
( c_24__type__24813___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__24814)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24814,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_25046',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25047] :
( c_24__type__25046___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25047)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25047,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25076',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25077] :
( c_24__type__25076___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25077)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25077,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25100',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25101] :
( c_24__type__25100___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25101)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__25101,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_25130',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25131] :
( c_24__type__25130___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25131)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__25131,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_25160',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25161] :
( c_24__type__25160___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25161)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25161,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25184',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25185] :
( c_24__type__25184___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25185)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__25185,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_25217',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25218] :
( c_24__type__25217___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25218)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25218,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25241',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25242] :
( c_24__type__25241___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25242)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__25242,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_25268',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25269] :
( c_24__type__25268___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25269)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__25269,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_25721',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__25722] :
( c_24__type__25721___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__25722)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25722,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25934',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__25935] :
( c_24__type__25934___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__25935)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25935,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2601',axiom,
! [Vvar__2602] :
( c_24__type__2601___24t(Vvar__2602)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2602,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2612',axiom,
! [Vvar__2613] :
( c_24__type__2612___24t(Vvar__2613)
<=> ! [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__2613,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_2614',axiom,
! [Vvar__2615] :
( c_24__type__2614___24t(Vvar__2615)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2615,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26147',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__26148] :
( c_24__type__26147___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__26148)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26148,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2625',axiom,
! [Vvar__2626] :
( c_24__type__2625___24t(Vvar__2626)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__2626,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26342',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__26343] :
( c_24__type__26342___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__26343)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__26343,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_265',axiom,
! [Vvar__266] :
( c_24__type__265___24t(Vvar__266)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__266,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_26555',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__26556] :
( c_24__type__26555___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__26556)
<=> ! [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__26556,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_26768',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__26769] :
( c_24__type__26768___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__26769)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__26769,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_2698',axiom,
! [Vv__CANONICAL__0,Vvar__2699] :
( c_24__type__2698___24t(Vv__CANONICAL__0,Vvar__2699)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__2699,Vv__CANONICAL__1)) ) ) ).
fof('$_type_26981',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__26982] :
( c_24__type__26981___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__26982)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__26982,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_270',axiom,
! [Vvar__271] :
( c_24__type__270___24t(Vvar__271)
<=> ! [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__271,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2711',axiom,
! [Vvar__2712] :
( c_24__type__2711___24t(Vvar__2712)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__2713___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__2718___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__2712,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2713',axiom,
! [Vvar__2714] :
( c_24__type__2713___24t(Vvar__2714)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__2714,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2718',axiom,
! [Vv__CANONICAL__0,Vvar__2719] :
( c_24__type__2718___24t(Vv__CANONICAL__0,Vvar__2719)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__2719,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_27194',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__27195] :
( c_24__type__27194___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__27195)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__27195,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_273',axiom,
! [Vvar__274] :
( c_24__type__273___24t(Vvar__274)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__274,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27389',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__27390] :
( c_24__type__27389___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__27390)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__27390,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_2751',axiom,
! [Vvar__2752] :
( c_24__type__2751___24t(Vvar__2752)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__2752,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2756',axiom,
! [Vvar__2757] :
( c_24__type__2756___24t(Vvar__2757)
<=> ! [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__2757,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_27602',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__27603] :
( c_24__type__27602___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__27603)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__27603,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_2768',axiom,
! [Vvar__2769] :
( c_24__type__2768___24t(Vvar__2769)
<=> ! [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__2769,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_277',axiom,
! [Vvar__278] :
( c_24__type__277___24t(Vvar__278)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2etype___24t(happ(happ(Vvar__278,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27797',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__27798] :
( c_24__type__27797___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__27798)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__27798,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_2780',axiom,
! [Vvar__2781] :
( c_24__type__2780___24t(Vvar__2781)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__2781,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_279',axiom,
! [Vvar__280] :
( c_24__type__279___24t(Vvar__280)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cTait_2eTerm_2eterm___24t(happ(Vvar__280,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2792',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2793] :
( c_24__type__2792___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2793)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__2793,Vv__CANONICAL__2)) ) ) ).
fof('$_type_27939',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27940] :
( c_24__type__27939___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27940)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__27940,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_27958',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27959] :
( c_24__type__27958___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27959)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__27959,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_27972',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27973] :
( c_24__type__27972___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27973)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__27973,Vv__CANONICAL__4)) ) ) ).
fof('$_type_28122',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28123] :
( c_24__type__28122___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28123)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28123,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_2817',axiom,
! [Vvar__2818] :
( c_24__type__2817___24t(Vvar__2818)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2820___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__2832___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__2818,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_28172',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28173] :
( c_24__type__28172___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28173)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__28173,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_282',axiom,
! [Vvar__283] :
( c_24__type__282___24t(Vvar__283)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__283,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2820',axiom,
! [Vv__CANONICAL__0,Vvar__2821] :
( c_24__type__2820___24t(Vv__CANONICAL__0,Vvar__2821)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__2821,Vv__CANONICAL__1)) ) ) ).
fof('$_type_28222',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28223] :
( c_24__type__28222___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28223)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__28223,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_28264',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28265] :
( c_24__type__28264___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28265)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__28265,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_28314',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28315] :
( c_24__type__28314___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28315)
<=> ! [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__28315,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_2832',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2833] :
( c_24__type__2832___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2833)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(happ(Vvar__2833,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))) ) ) ) ) ).
fof('$_type_28390',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28391] :
( c_24__type__28390___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28391)
<=> ! [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__28391,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_28398',axiom,
! [Vvar__28399] :
( c_24__type__28398___24t(Vvar__28399)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28399,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_285',axiom,
! [Vvar__286] :
( c_24__type__285___24t(Vvar__286)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__286,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28521',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28522] :
( c_24__type__28521___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28522)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28522,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28565',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28566] :
( c_24__type__28565___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28566)
<=> ! [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__28566,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_28601',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28602] :
( c_24__type__28601___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28602)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__28602,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_2862',axiom,
! [Vv__CANONICAL__0,Vvar__2863] :
( c_24__type__2862___24t(Vv__CANONICAL__0,Vvar__2863)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__2863,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_28645',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28646] :
( c_24__type__28645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__28646)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__28646,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28657',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28658] :
( c_24__type__28657___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28658)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__28658,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_287',axiom,
! [Vvar__288] :
( c_24__type__287___24t(Vvar__288)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__288,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28778',axiom,
! [Vvar__28779] :
( c_24__type__28778___24t(Vvar__28779)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__28779,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28820',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28821] :
( c_24__type__28820___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28821)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28821,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_28889',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28890] :
( c_24__type__28889___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28890)
<=> ! [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__28890,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_28921',axiom,
! [Vvar__28922] :
( c_24__type__28921___24t(Vvar__28922)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1173___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__28922,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_28973',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28974] :
( c_24__type__28973___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28974)
<=> ! [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__28974,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_29031',axiom,
! [Vv__CANONICAL__0,Vvar__29032] :
( c_24__type__29031___24t(Vv__CANONICAL__0,Vvar__29032)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__29032,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_29070',axiom,
! [Vv__CANONICAL__0,Vvar__29071] :
( c_24__type__29070___24t(Vv__CANONICAL__0,Vvar__29071)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__29071,Vv__CANONICAL__1)) ) ) ).
fof('$_type_29078',axiom,
! [Vv__CANONICAL__0,Vvar__29079] :
( c_24__type__29078___24t(Vv__CANONICAL__0,Vvar__29079)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__29079,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_29111',axiom,
! [Vvar__29112] :
( c_24__type__29111___24t(Vvar__29112)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1173___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13572___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__29112,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_29152',axiom,
! [Vvar__29153] :
( c_24__type__29152___24t(Vvar__29153)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1173___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__29162___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13572___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__29153,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_29162',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29163] :
( c_24__type__29162___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29163)
<=> ! [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__29163,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_29177',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29178] :
( c_24__type__29177___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29178)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__29178,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_300',axiom,
! [Vvar__301] :
( c_24__type__300___24t(Vvar__301)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__0)
=> cTait_2eTerm_2etype___24t(happ(Vvar__301,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30172',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30173] :
( c_24__type__30172___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30173)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30173,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_30366',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30367] :
( c_24__type__30366___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30367)
<=> ! [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__30367,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_30695',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30696] :
( c_24__type__30695___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30696)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30696,Vv__CANONICAL__2)) ) ) ).
fof('$_type_30699',axiom,
! [Vvar__30700] :
( c_24__type__30699___24t(Vvar__30700)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__30700,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30717',axiom,
! [Vvar__30718] :
( c_24__type__30717___24t(Vvar__30718)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__30718,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_30734',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30735] :
( c_24__type__30734___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30735)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__30735,Vv__CANONICAL__2)) ) ) ).
fof('$_type_30738',axiom,
! [Vvar__30739] :
( c_24__type__30738___24t(Vvar__30739)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__30741___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__30739,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30741',axiom,
! [Vv__CANONICAL__0,Vvar__30742] :
( c_24__type__30741___24t(Vv__CANONICAL__0,Vvar__30742)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__30742,Vv__CANONICAL__1)) ) ) ).
fof('$_type_30758',axiom,
! [Vvar__30759] :
( c_24__type__30758___24t(Vvar__30759)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__30741___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__30759,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30775',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30776] :
( c_24__type__30775___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30776)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30776,Vv__CANONICAL__2)) ) ) ).
fof('$_type_30781',axiom,
! [Vvar__30782] :
( c_24__type__30781___24t(Vvar__30782)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__30782,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_30794',axiom,
! [Vvar__30795] :
( c_24__type__30794___24t(Vvar__30795)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__30795,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30817',axiom,
! [Vvar__30818] :
( c_24__type__30817___24t(Vvar__30818)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__30818,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30822',axiom,
! [Vvar__30823] :
( c_24__type__30822___24t(Vvar__30823)
<=> ! [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__30823,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_30834',axiom,
! [Vvar__30835] :
( c_24__type__30834___24t(Vvar__30835)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__30835,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30841',axiom,
! [Vvar__30842] :
( c_24__type__30841___24t(Vvar__30842)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__30842,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30872',axiom,
! [Vvar__30873] :
( c_24__type__30872___24t(Vvar__30873)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,Vv__CANONICAL__0)
=> cCoq_2eStrings_2eString_2estring___24t(happ(Vvar__30873,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30878',axiom,
! [Vvar__30879] :
( c_24__type__30878___24t(Vvar__30879)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,happ(Vvar__30879,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30941',axiom,
! [Vvar__30942] :
( c_24__type__30941___24t(Vvar__30942)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__30942,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_311',axiom,
! [Vvar__312] :
( c_24__type__311___24t(Vvar__312)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTyping_2econtext___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2etype___24t(happ(happ(Vvar__312,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3114',axiom,
! [Vv__CANONICAL__0,Vvar__3115] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vvar__3115)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3115,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3122',axiom,
! [Vv__CANONICAL__0,Vvar__3123] :
( c_24__type__3122___24t(Vv__CANONICAL__0,Vvar__3123)
<=> ! [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__3123,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_31337',axiom,
! [Vvar__31338] :
( c_24__type__31337___24t(Vvar__31338)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__31338,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31469',axiom,
! [Vvar__31470] :
( c_24__type__31469___24t(Vvar__31470)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__31470,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_31558',axiom,
! [Vvar__31559] :
( c_24__type__31558___24t(Vvar__31559)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__157___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__31563___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__31559,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_31563',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31564] :
( c_24__type__31563___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31564)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__31564,Vv__CANONICAL__2)) ) ) ).
fof('$_type_31676',axiom,
! [Vvar__31677] :
( c_24__type__31676___24t(Vvar__31677)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__31677,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31780',axiom,
! [Vv__CANONICAL__0,Vvar__31781] :
( c_24__type__31780___24t(Vv__CANONICAL__0,Vvar__31781)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__31781,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_31940',axiom,
! [Vvar__31941] :
( c_24__type__31940___24t(Vvar__31941)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1061___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__31780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(happ(happ(Vvar__31941,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_31952',axiom,
! [Vvar__31953] :
( c_24__type__31952___24t(Vvar__31953)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__31953,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33344',axiom,
! [Vvar__33345] :
( c_24__type__33344___24t(Vvar__33345)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__33345,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_33402',axiom,
! [Vvar__33403] :
( c_24__type__33402___24t(Vvar__33403)
<=> ! [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__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__33403,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_33873',axiom,
! [Vvar__33874] :
( c_24__type__33873___24t(Vvar__33874)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__33874,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_33884',axiom,
! [Vvar__33885] :
( c_24__type__33884___24t(Vvar__33885)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__33885,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33901',axiom,
! [Vvar__33902] :
( c_24__type__33901___24t(Vvar__33902)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__33902,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33909',axiom,
! [Vvar__33910] :
( c_24__type__33909___24t(Vvar__33910)
<=> ! [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__33910,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_34123',axiom,
! [Vvar__34124] :
( c_24__type__34123___24t(Vvar__34124)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(happ(happ(Vvar__34124,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34129',axiom,
! [Vvar__34130] :
( c_24__type__34129___24t(Vvar__34130)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(happ(happ(happ(Vvar__34130,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34416',axiom,
! [Vvar__34417] :
( c_24__type__34416___24t(Vvar__34417)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__34417,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34990',axiom,
! [Vvar__34991] :
( c_24__type__34990___24t(Vvar__34991)
<=> ! [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__34991,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35002',axiom,
! [Vvar__35003] :
( c_24__type__35002___24t(Vvar__35003)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(happ(Vvar__35003,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35005',axiom,
! [Vvar__35006] :
( c_24__type__35005___24t(Vvar__35006)
<=> ! [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__35006,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35015',axiom,
! [Vvar__35016] :
( c_24__type__35015___24t(Vvar__35016)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__1)
=> cTait_2eSubst2_2eJoachimski_2esubstitution___24t(happ(happ(Vvar__35016,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35019',axiom,
! [Vvar__35020] :
( c_24__type__35019___24t(Vvar__35020)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,happ(Vvar__35020,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35024',axiom,
! [Vv__CANONICAL__0,Vvar__35025] :
( c_24__type__35024___24t(Vv__CANONICAL__0,Vvar__35025)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__35025,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35046',axiom,
! [Vvar__35047] :
( c_24__type__35046___24t(Vvar__35047)
<=> ! [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__35047,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35053',axiom,
! [Vvar__35054] :
( c_24__type__35053___24t(Vvar__35054)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,happ(happ(Vvar__35054,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35056',axiom,
! [Vvar__35057] :
( c_24__type__35056___24t(Vvar__35057)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__35057,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35094',axiom,
! [Vvar__35095] :
( c_24__type__35094___24t(Vvar__35095)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__35095,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35135',axiom,
! [Vvar__35136] :
( c_24__type__35135___24t(Vvar__35136)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(happ(happ(Vvar__35136,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35137',axiom,
! [Vvar__35138] :
( c_24__type__35137___24t(Vvar__35138)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(happ(Vvar__35138,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35148',axiom,
! [Vvar__35149] :
( c_24__type__35148___24t(Vvar__35149)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__35024___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__35149,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_35178',axiom,
! [Vvar__35179] :
( c_24__type__35178___24t(Vvar__35179)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__35179,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35181',axiom,
! [Vvar__35182] :
( c_24__type__35181___24t(Vvar__35182)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__35182,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35183',axiom,
! [Vvar__35184] :
( c_24__type__35183___24t(Vvar__35184)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35184,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35227',axiom,
! [Vvar__35228] :
( c_24__type__35227___24t(Vvar__35228)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__35228,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35294',axiom,
! [Vvar__35295] :
( c_24__type__35294___24t(Vvar__35295)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(happ(Vvar__35295,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35456',axiom,
! [Vvar__35457] :
( c_24__type__35456___24t(Vvar__35457)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35457,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35467',axiom,
! [Vvar__35468] :
( c_24__type__35467___24t(Vvar__35468)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__35468,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35531',axiom,
! [Vvar__35532] :
( c_24__type__35531___24t(Vvar__35532)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cProp___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__35532,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_35581',axiom,
! [Vvar__35582] :
( c_24__type__35581___24t(Vvar__35582)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35582,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35614',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__35615] :
( c_24__type__35614___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__35615)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__35615,Vv__CANONICAL__6)) ) ) ).
fof('$_type_35642',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__35643] :
( c_24__type__35642___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__35643)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__35643,Vv__CANONICAL__6)) ) ) ).
fof('$_type_35653',axiom,
! [Vvar__35654] :
( c_24__type__35653___24t(Vvar__35654)
<=> ! [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__35654,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35656',axiom,
! [Vvar__35657] :
( c_24__type__35656___24t(Vvar__35657)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__35657,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35661',axiom,
! [Vvar__35662] :
( c_24__type__35661___24t(Vvar__35662)
<=> ! [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__35662,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35670',axiom,
! [Vvar__35671] :
( c_24__type__35670___24t(Vvar__35671)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__35671,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35870',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__35871] :
( c_24__type__35870___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__35871)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__35871,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35963',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__35964] :
( c_24__type__35963___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__35964)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__35964,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36056',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__36057] :
( c_24__type__36056___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__36057)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36057,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36138',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__36139] :
( c_24__type__36138___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__36139)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__36139,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_36231',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__36232] :
( c_24__type__36231___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__36232)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36232,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36313',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__36314] :
( c_24__type__36313___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__36314)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__36314,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_36406',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__36407] :
( c_24__type__36406___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__36407)
<=> ! [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__36407,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_36451',axiom,
! [Vvar__36452] :
( c_24__type__36451___24t(Vvar__36452)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__36452,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_36502',axiom,
! [Vvar__36503] :
( c_24__type__36502___24t(Vvar__36503)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__36503,Vv__CANONICAL__0)) ) ) ).
fof('$_type_36506',axiom,
! [Vvar__36507] :
( c_24__type__36506___24t(Vvar__36507)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__36502___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36502___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__36507,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36940',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__36941] :
( c_24__type__36940___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__36941)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36941,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_37041',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__37042] :
( c_24__type__37041___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__37042)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__37042,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3711',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3712] :
( c_24__type__3711___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3712)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__3712,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_37142',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__37143] :
( c_24__type__37142___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__37143)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__37143,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_37232',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__37233] :
( c_24__type__37232___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__37233)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__37233,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_37333',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__37334] :
( c_24__type__37333___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__37334)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__37334,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_37434',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__37435] :
( c_24__type__37434___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__37435)
<=> ! [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__37435,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_37535',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__37536] :
( c_24__type__37535___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__37536)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__37536,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_37678',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__37679] :
( c_24__type__37678___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__37679)
<=> ! [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__37679,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_37697',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__37698] :
( c_24__type__37697___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__37698)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__37698,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_37717',axiom,
! [Vvar__37718] :
( c_24__type__37717___24t(Vvar__37718)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1173___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1173___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__37718,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_37801',axiom,
! [Vvar__37802] :
( c_24__type__37801___24t(Vvar__37802)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__37802,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37806',axiom,
! [Vvar__37807] :
( c_24__type__37806___24t(Vvar__37807)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__37807,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37816',axiom,
! [Vvar__37817] :
( c_24__type__37816___24t(Vvar__37817)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__37817,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37818',axiom,
! [Vvar__37819] :
( c_24__type__37818___24t(Vvar__37819)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__37819,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37879',axiom,
! [Vvar__37880] :
( c_24__type__37879___24t(Vvar__37880)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__37880,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38',axiom,
! [Vvar__39] :
( c_24__type__38___24t(Vvar__39)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__39,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38447',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__38448] :
( c_24__type__38447___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__38448)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__38448,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_386',axiom,
! [Vvar__387] :
( c_24__type__386___24t(Vvar__387)
<=> ! [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__387,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38793',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__38794] :
( c_24__type__38793___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__38794)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__38794,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_388',axiom,
! [Vvar__389] :
( c_24__type__388___24t(Vvar__389)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__389,Vv__CANONICAL__0)) ) ) ).
fof('$_type_39139',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39140] :
( c_24__type__39139___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39140)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__39140,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_39462',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39463] :
( c_24__type__39462___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39463)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__39463,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_39808',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39809] :
( c_24__type__39808___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39809)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__39809,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_40154',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40155] :
( c_24__type__40154___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40155)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__40155,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_405',axiom,
! [Vvar__406] :
( c_24__type__405___24t(Vvar__406)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__406,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_40500',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40501] :
( c_24__type__40500___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40501)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__40501,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_40846',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40847] :
( c_24__type__40846___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40847)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__40847,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_41192',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__41193] :
( c_24__type__41192___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__41193)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__41193,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_41515',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__41516] :
( c_24__type__41515___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__41516)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__41516,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_41861',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__41862] :
( c_24__type__41861___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__41862)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__41862,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_42207',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__42208] :
( c_24__type__42207___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__42208)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__42208,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_42530',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__42531] :
( c_24__type__42530___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__42531)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__42531,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_42853',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__42854] :
( c_24__type__42853___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__42854)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__42854,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_431',axiom,
! [Vvar__432] :
( c_24__type__431___24t(Vvar__432)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__432,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43199',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__43200] :
( c_24__type__43199___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__43200)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__43200,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_43281',axiom,
! [Vvar__43282] :
( c_24__type__43281___24t(Vvar__43282)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1173___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1173___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1173___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__43282,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_43293',axiom,
! [Vvar__43294] :
( c_24__type__43293___24t(Vvar__43294)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__43294,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43296',axiom,
! [Vvar__43297] :
( c_24__type__43296___24t(Vvar__43297)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__43297,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43298',axiom,
! [Vvar__43299] :
( c_24__type__43298___24t(Vvar__43299)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(Vvar__43299,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43301',axiom,
! [Vvar__43302] :
( c_24__type__43301___24t(Vvar__43302)
<=> ! [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__43302,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43311',axiom,
! [Vvar__43312] :
( c_24__type__43311___24t(Vvar__43312)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__43312,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43316',axiom,
! [Vvar__43317] :
( c_24__type__43316___24t(Vvar__43317)
<=> ! [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__43317,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_43334',axiom,
! [Vvar__43335] :
( c_24__type__43334___24t(Vvar__43335)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__43335,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_43507',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__43508] :
( c_24__type__43507___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__43508)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__43508,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_43546',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__43547] :
( c_24__type__43546___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__43547)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__43547,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_43585',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__43586] :
( c_24__type__43585___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__43586)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__43586,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_43853',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__43854] :
( c_24__type__43853___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__43854)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__43854,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_43916',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__43917] :
( c_24__type__43916___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__43917)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__43917,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_43979',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__43980] :
( c_24__type__43979___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__43980)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__43980,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_44033',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__44034] :
( c_24__type__44033___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__44034)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__44034,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_4409',axiom,
! [Vv__CANONICAL__0,Vvar__4410] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vvar__4410)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__4410,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_44096',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__44097] :
( c_24__type__44096___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__44097)
<=> ! [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__44097,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_44202',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44203] :
( c_24__type__44202___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44203)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__44203,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_44225',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44226] :
( c_24__type__44225___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44226)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__44226,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_44248',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44249] :
( c_24__type__44248___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44249)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__44249,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_44271',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44272] :
( c_24__type__44271___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44272)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__44272,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_44289',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44290] :
( c_24__type__44289___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44290)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__44290,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_44315',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44316] :
( c_24__type__44315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44316)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__44316,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_44333',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44334] :
( c_24__type__44333___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__44334)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__44334,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_44591',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__44592] :
( c_24__type__44591___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__44592)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__44592,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_44716',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__44717] :
( c_24__type__44716___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__44717)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__44717,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_44841',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__44842] :
( c_24__type__44841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__44842)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__44842,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_44966',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__44967] :
( c_24__type__44966___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__44967)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__44967,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_45091',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__45092] :
( c_24__type__45091___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__45092)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__45092,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_45216',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__45217] :
( c_24__type__45216___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__45217)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__45217,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_45327',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__45328] :
( c_24__type__45327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__45328)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__45328,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_45352',axiom,
! [Vvar__45353] :
( c_24__type__45352___24t(Vvar__45353)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__45353,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_45567',axiom,
! [Vvar__45568] :
( c_24__type__45567___24t(Vvar__45568)
<=> ! [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__45568,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45593',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45594] :
( c_24__type__45593___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45594)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__45594,Vv__CANONICAL__3)) ) ) ).
fof('$_type_45601',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45602] :
( c_24__type__45601___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45602)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__45602,Vv__CANONICAL__3)) ) ) ).
fof('$_type_45609',axiom,
! [Vvar__45610] :
( c_24__type__45609___24t(Vvar__45610)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__157___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__45610,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_45649',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45650] :
( c_24__type__45649___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45650)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__45650,Vv__CANONICAL__3)) ) ) ).
fof('$_type_45657',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45658] :
( c_24__type__45657___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45658)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__45658,Vv__CANONICAL__3)) ) ) ).
fof('$_type_45665',axiom,
! [Vvar__45666] :
( c_24__type__45665___24t(Vvar__45666)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__30741___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__30741___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__45666,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_45716',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45717] :
( c_24__type__45716___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45717)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__45717,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_45727',axiom,
! [Vvar__45728] :
( c_24__type__45727___24t(Vvar__45728)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__45730___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__45728,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_45730',axiom,
! [Vv__CANONICAL__0,Vvar__45731] :
( c_24__type__45730___24t(Vv__CANONICAL__0,Vvar__45731)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__45731,Vv__CANONICAL__1)) ) ) ).
fof('$_type_45760',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__45761] :
( c_24__type__45760___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__45761)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__45761,Vv__CANONICAL__4)) ) ) ).
fof('$_type_45769',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__45770] :
( c_24__type__45769___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__45770)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__45770,Vv__CANONICAL__4)) ) ) ).
fof('$_type_45907',axiom,
! [Vvar__45908] :
( c_24__type__45907___24t(Vvar__45908)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__45908,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45925',axiom,
! [Vvar__45926] :
( c_24__type__45925___24t(Vvar__45926)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__45926,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45959',axiom,
! [Vvar__45960] :
( c_24__type__45959___24t(Vvar__45960)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cTait_2eSubst2_2eJoachimski_2esubstitution___24t(happ(Vvar__45960,Vv__CANONICAL__0)) ) ) ).
fof('$_type_45962',axiom,
! [Vvar__45963] :
( c_24__type__45962___24t(Vvar__45963)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__45963,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45968',axiom,
! [Vvar__45969] :
( c_24__type__45968___24t(Vvar__45969)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__45970___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__45970___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__45969,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45970',axiom,
! [Vvar__45971] :
( c_24__type__45970___24t(Vvar__45971)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__45971,Vv__CANONICAL__0)) ) ) ).
fof('$_type_46',axiom,
! [Vvar__47] :
( c_24__type__46___24t(Vvar__47)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__47,Vv__CANONICAL__0)) ) ) ).
fof('$_type_46041',axiom,
! [Vvar__46042] :
( c_24__type__46041___24t(Vvar__46042)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__46042,Vv__CANONICAL__0)) ) ) ).
fof('$_type_46055',axiom,
! [Vvar__46056] :
( c_24__type__46055___24t(Vvar__46056)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__46056,Vv__CANONICAL__0)) ) ) ).
fof('$_type_46069',axiom,
! [Vvar__46070] :
( c_24__type__46069___24t(Vvar__46070)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__46070,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_46084',axiom,
! [Vvar__46085] :
( c_24__type__46084___24t(Vvar__46085)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__46085,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_46094',axiom,
! [Vvar__46095] :
( c_24__type__46094___24t(Vvar__46095)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__46095,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_461',axiom,
! [Vvar__462] :
( c_24__type__461___24t(Vvar__462)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eSubst_2esubstitution___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,happ(Vvar__462,Vv__CANONICAL__0)) ) ) ).
fof('$_type_46115',axiom,
! [Vvar__46116] :
( c_24__type__46115___24t(Vvar__46116)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__46116,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46121',axiom,
! [Vvar__46122] :
( c_24__type__46121___24t(Vvar__46122)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(happ(happ(Vvar__46122,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46132',axiom,
! [Vvar__46133] :
( c_24__type__46132___24t(Vvar__46133)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__46134___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__46134___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__46133,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46134',axiom,
! [Vvar__46135] :
( c_24__type__46134___24t(Vvar__46135)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__46135,Vv__CANONICAL__0)) ) ) ).
fof('$_type_46145',axiom,
! [Vvar__46146] :
( c_24__type__46145___24t(Vvar__46146)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__46146,Vv__CANONICAL__0)) ) ) ).
fof('$_type_466',axiom,
! [Vvar__467] :
( c_24__type__466___24t(Vvar__467)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eSubst_2esubstitution___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__467,Vv__CANONICAL__0)) ) ) ).
fof('$_type_468',axiom,
! [Vvar__469] :
( c_24__type__468___24t(Vvar__469)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eSubst_2esubstitution___24t(Vv__CANONICAL__0)
=> cTait_2eSubst_2esubstitution___24t(happ(Vvar__469,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4784',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__4785] :
( c_24__type__4784___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__4785)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4785,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_479',axiom,
! [Vvar__480] :
( c_24__type__479___24t(Vvar__480)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst_2esubstitution___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__480,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_487',axiom,
! [Vvar__488] :
( c_24__type__487___24t(Vvar__488)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTyping_2econtext___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__488,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4877',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__4878] :
( c_24__type__4877___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__4878)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4878,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4970',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__4971] :
( c_24__type__4970___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__4971)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4971,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5052',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5053] :
( c_24__type__5052___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5053)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__5053,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_513',axiom,
! [Vvar__514] :
( c_24__type__513___24t(Vvar__514)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__514,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5145',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5146] :
( c_24__type__5145___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5146)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5146,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5227',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__5228] :
( c_24__type__5227___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__5228)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__5228,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_5320',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5321] :
( c_24__type__5320___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5321)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__5321,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_535',axiom,
! [Vvar__536] :
( c_24__type__535___24t(Vvar__536)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__536,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_560',axiom,
! [Vvar__561] :
( c_24__type__560___24t(Vvar__561)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTyping_2econtext___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,happ(happ(happ(Vvar__561,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5616',axiom,
! [Vvar__5617] :
( c_24__type__5616___24t(Vvar__5617)
<=> ! [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__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1173___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__3711___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__5636___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__5645___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__5617,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_5636',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__5637] :
( c_24__type__5636___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__5637)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__5637,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_5645',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__5646] :
( c_24__type__5645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__5646)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__5646,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_569',axiom,
! [Vvar__570] :
( c_24__type__569___24t(Vvar__570)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__2)
=> cTait_2eTerm_2eterm___24t(happ(happ(happ(Vvar__570,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_590',axiom,
! [Vv__CANONICAL__0,Vvar__591] :
( c_24__type__590___24t(Vv__CANONICAL__0,Vvar__591)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__592___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__593___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(Vvar__591,Vv__CANONICAL__1)) ) ) ).
fof('$_type_6666',axiom,
! [Vvar__6667] :
( c_24__type__6666___24t(Vvar__6667)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3122___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__6667,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_691',axiom,
! [Vvar__692] :
( c_24__type__691___24t(Vvar__692)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__693___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__694___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__692,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_696',axiom,
! [Vvar__697] :
( c_24__type__696___24t(Vvar__697)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__697,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_70',axiom,
! [Vvar__71] :
( c_24__type__70___24t(Vvar__71)
<=> ! [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__71,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_714',axiom,
! [Vvar__715] :
( c_24__type__714___24t(Vvar__715)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__715,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_718',axiom,
! [Vvar__719] :
( c_24__type__718___24t(Vvar__719)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__719,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7196',axiom,
! [Vvar__7197] :
( c_24__type__7196___24t(Vvar__7197)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__7197,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_72',axiom,
! [Vvar__73] :
( c_24__type__72___24t(Vvar__73)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__73,Vv__CANONICAL__0)) ) ) ).
fof('$_type_748',axiom,
! [Vvar__749] :
( c_24__type__748___24t(Vvar__749)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__749,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_751',axiom,
! [Vvar__752] :
( c_24__type__751___24t(Vvar__752)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__752,Vv__CANONICAL__0)) ) ) ).
fof('$_type_786',axiom,
! [Vvar__787] :
( c_24__type__786___24t(Vvar__787)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__787,Vv__CANONICAL__0)) ) ) ).
fof('$_type_837',axiom,
! [Vvar__838] :
( c_24__type__837___24t(Vvar__838)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2ePeano_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__838,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_839',axiom,
! [Vvar__840] :
( c_24__type__839___24t(Vvar__840)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__840,Vv__CANONICAL__0)) ) ) ).
fof('$_type_841',axiom,
! [Vvar__842] :
( c_24__type__841___24t(Vvar__842)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__842,Vv__CANONICAL__0)) ) ) ).
fof('$_type_860',axiom,
! [Vvar__861] :
( c_24__type__860___24t(Vvar__861)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__861,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8602',axiom,
! [Vvar__8603] :
( c_24__type__8602___24t(Vvar__8603)
<=> ! [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__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__3711___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__5636___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__5645___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__8603,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_862',axiom,
! [Vvar__863] :
( c_24__type__862___24t(Vvar__863)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__863,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8650',axiom,
! [Vvar__8651] :
( c_24__type__8650___24t(Vvar__8651)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__8651,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8661',axiom,
! [Vvar__8662] :
( c_24__type__8661___24t(Vvar__8662)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__8662,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8681',axiom,
! [Vvar__8682] :
( c_24__type__8681___24t(Vvar__8682)
<=> ! [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__8682,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_872',axiom,
! [Vvar__873] :
( c_24__type__872___24t(Vvar__873)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__873,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_888',axiom,
! [Vvar__889] :
( c_24__type__888___24t(Vvar__889)
<=> ! [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__889,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8900',axiom,
! [Vvar__8901] :
( c_24__type__8900___24t(Vvar__8901)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1173___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__3711___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__5636___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__5645___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__8901,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_891',axiom,
! [Vv__CANONICAL__0,Vvar__892] :
( c_24__type__891___24t(Vv__CANONICAL__0,Vvar__892)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__892,Vv__CANONICAL__1)) ) ) ).
fof('$_type_9003',axiom,
! [Vvar__9004] :
( c_24__type__9003___24t(Vvar__9004)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__9004,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9060',axiom,
! [Vvar__9061] :
( c_24__type__9060___24t(Vvar__9061)
<=> ! [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__3114___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3122___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(Vvar__9061,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_9090',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9091] :
( c_24__type__9090___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9091)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__9091,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_9104',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9105] :
( c_24__type__9104___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9105)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__9105,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_9111',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9112] :
( c_24__type__9111___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9112)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__9112,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_944',axiom,
! [Vvar__945] :
( c_24__type__944___24t(Vvar__945)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__945,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_956',axiom,
! [Vvar__957] :
( c_24__type__956___24t(Vvar__957)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__957,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_978',axiom,
! [Vvar__979] :
( c_24__type__978___24t(Vvar__979)
<=> ! [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__979,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_typeof_Coq.Arith.Compare_dec.le_gt_dec',axiom,
c_24__type__837___24t(cCoq_2eArith_2eCompare__dec_2ele__gt__dec) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__273___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
c_24__type__273___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq_dec',axiom,
c_24__type__691___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__36506___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
c_24__type__45727___24t(cCoq_2eArith_2eWf__nat_2eltof) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__35456___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__386___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__35467___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.E.eq',axiom,
c_24__type__45925___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
c_24__type__35183___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__35181___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
c_24__type__46094___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.add',axiom,
c_24__type__35135___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.cardinal',axiom,
c_24__type__35178___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elements',axiom,
c_24__type__35019___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.fold',axiom,
c_24__type__35148___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__46115___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev',axiom,
c_24__type__35137___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
c_24__type__46121___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Byte.x00',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex00) ).
fof('$_typeof_Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex01) ).
fof('$_typeof_Coq.Init.Byte.x02',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex02) ).
fof('$_typeof_Coq.Init.Byte.x03',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex03) ).
fof('$_typeof_Coq.Init.Byte.x04',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex04) ).
fof('$_typeof_Coq.Init.Byte.x05',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex05) ).
fof('$_typeof_Coq.Init.Byte.x06',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex06) ).
fof('$_typeof_Coq.Init.Byte.x07',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex07) ).
fof('$_typeof_Coq.Init.Byte.x08',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex08) ).
fof('$_typeof_Coq.Init.Byte.x09',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex09) ).
fof('$_typeof_Coq.Init.Byte.x0a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0a) ).
fof('$_typeof_Coq.Init.Byte.x0b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0b) ).
fof('$_typeof_Coq.Init.Byte.x0c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0c) ).
fof('$_typeof_Coq.Init.Byte.x0d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0d) ).
fof('$_typeof_Coq.Init.Byte.x0e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0e) ).
fof('$_typeof_Coq.Init.Byte.x0f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0f) ).
fof('$_typeof_Coq.Init.Byte.x10',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex10) ).
fof('$_typeof_Coq.Init.Byte.x11',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex11) ).
fof('$_typeof_Coq.Init.Byte.x12',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex12) ).
fof('$_typeof_Coq.Init.Byte.x13',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex13) ).
fof('$_typeof_Coq.Init.Byte.x14',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex14) ).
fof('$_typeof_Coq.Init.Byte.x15',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex15) ).
fof('$_typeof_Coq.Init.Byte.x16',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex16) ).
fof('$_typeof_Coq.Init.Byte.x17',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex17) ).
fof('$_typeof_Coq.Init.Byte.x18',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex18) ).
fof('$_typeof_Coq.Init.Byte.x19',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex19) ).
fof('$_typeof_Coq.Init.Byte.x1a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1a) ).
fof('$_typeof_Coq.Init.Byte.x1b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1b) ).
fof('$_typeof_Coq.Init.Byte.x1c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1c) ).
fof('$_typeof_Coq.Init.Byte.x1d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1d) ).
fof('$_typeof_Coq.Init.Byte.x1e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1e) ).
fof('$_typeof_Coq.Init.Byte.x1f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1f) ).
fof('$_typeof_Coq.Init.Byte.x20',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex20) ).
fof('$_typeof_Coq.Init.Byte.x21',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex21) ).
fof('$_typeof_Coq.Init.Byte.x22',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex22) ).
fof('$_typeof_Coq.Init.Byte.x23',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex23) ).
fof('$_typeof_Coq.Init.Byte.x24',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex24) ).
fof('$_typeof_Coq.Init.Byte.x25',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex25) ).
fof('$_typeof_Coq.Init.Byte.x26',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex26) ).
fof('$_typeof_Coq.Init.Byte.x27',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex27) ).
fof('$_typeof_Coq.Init.Byte.x28',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex28) ).
fof('$_typeof_Coq.Init.Byte.x29',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex29) ).
fof('$_typeof_Coq.Init.Byte.x2a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2a) ).
fof('$_typeof_Coq.Init.Byte.x2b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2b) ).
fof('$_typeof_Coq.Init.Byte.x2c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2c) ).
fof('$_typeof_Coq.Init.Byte.x2d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2d) ).
fof('$_typeof_Coq.Init.Byte.x2e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2e) ).
fof('$_typeof_Coq.Init.Byte.x2f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2f) ).
fof('$_typeof_Coq.Init.Byte.x30',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex30) ).
fof('$_typeof_Coq.Init.Byte.x31',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex31) ).
fof('$_typeof_Coq.Init.Byte.x32',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex32) ).
fof('$_typeof_Coq.Init.Byte.x33',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex33) ).
fof('$_typeof_Coq.Init.Byte.x34',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex34) ).
fof('$_typeof_Coq.Init.Byte.x35',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex35) ).
fof('$_typeof_Coq.Init.Byte.x36',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex36) ).
fof('$_typeof_Coq.Init.Byte.x37',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex37) ).
fof('$_typeof_Coq.Init.Byte.x38',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex38) ).
fof('$_typeof_Coq.Init.Byte.x39',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex39) ).
fof('$_typeof_Coq.Init.Byte.x3a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3a) ).
fof('$_typeof_Coq.Init.Byte.x3b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3b) ).
fof('$_typeof_Coq.Init.Byte.x3c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3c) ).
fof('$_typeof_Coq.Init.Byte.x3d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3d) ).
fof('$_typeof_Coq.Init.Byte.x3e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3e) ).
fof('$_typeof_Coq.Init.Byte.x3f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3f) ).
fof('$_typeof_Coq.Init.Byte.x40',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex40) ).
fof('$_typeof_Coq.Init.Byte.x41',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex41) ).
fof('$_typeof_Coq.Init.Byte.x42',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex42) ).
fof('$_typeof_Coq.Init.Byte.x43',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex43) ).
fof('$_typeof_Coq.Init.Byte.x44',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex44) ).
fof('$_typeof_Coq.Init.Byte.x45',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex45) ).
fof('$_typeof_Coq.Init.Byte.x46',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex46) ).
fof('$_typeof_Coq.Init.Byte.x47',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex47) ).
fof('$_typeof_Coq.Init.Byte.x48',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex48) ).
fof('$_typeof_Coq.Init.Byte.x49',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex49) ).
fof('$_typeof_Coq.Init.Byte.x4a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4a) ).
fof('$_typeof_Coq.Init.Byte.x4b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4b) ).
fof('$_typeof_Coq.Init.Byte.x4c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4c) ).
fof('$_typeof_Coq.Init.Byte.x4d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4d) ).
fof('$_typeof_Coq.Init.Byte.x4e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4e) ).
fof('$_typeof_Coq.Init.Byte.x4f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4f) ).
fof('$_typeof_Coq.Init.Byte.x50',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex50) ).
fof('$_typeof_Coq.Init.Byte.x51',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex51) ).
fof('$_typeof_Coq.Init.Byte.x52',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex52) ).
fof('$_typeof_Coq.Init.Byte.x53',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex53) ).
fof('$_typeof_Coq.Init.Byte.x54',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex54) ).
fof('$_typeof_Coq.Init.Byte.x55',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex55) ).
fof('$_typeof_Coq.Init.Byte.x56',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex56) ).
fof('$_typeof_Coq.Init.Byte.x57',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex57) ).
fof('$_typeof_Coq.Init.Byte.x58',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex58) ).
fof('$_typeof_Coq.Init.Byte.x59',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex59) ).
fof('$_typeof_Coq.Init.Byte.x5a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5a) ).
fof('$_typeof_Coq.Init.Byte.x5b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5b) ).
fof('$_typeof_Coq.Init.Byte.x5c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5c) ).
fof('$_typeof_Coq.Init.Byte.x5d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5d) ).
fof('$_typeof_Coq.Init.Byte.x5e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5e) ).
fof('$_typeof_Coq.Init.Byte.x5f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5f) ).
fof('$_typeof_Coq.Init.Byte.x60',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex60) ).
fof('$_typeof_Coq.Init.Byte.x61',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex61) ).
fof('$_typeof_Coq.Init.Byte.x62',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex62) ).
fof('$_typeof_Coq.Init.Byte.x63',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex63) ).
fof('$_typeof_Coq.Init.Byte.x64',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex64) ).
fof('$_typeof_Coq.Init.Byte.x65',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex65) ).
fof('$_typeof_Coq.Init.Byte.x66',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex66) ).
fof('$_typeof_Coq.Init.Byte.x67',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex67) ).
fof('$_typeof_Coq.Init.Byte.x68',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex68) ).
fof('$_typeof_Coq.Init.Byte.x69',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex69) ).
fof('$_typeof_Coq.Init.Byte.x6a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6a) ).
fof('$_typeof_Coq.Init.Byte.x6b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6b) ).
fof('$_typeof_Coq.Init.Byte.x6c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6c) ).
fof('$_typeof_Coq.Init.Byte.x6d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6d) ).
fof('$_typeof_Coq.Init.Byte.x6e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6e) ).
fof('$_typeof_Coq.Init.Byte.x6f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6f) ).
fof('$_typeof_Coq.Init.Byte.x70',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex70) ).
fof('$_typeof_Coq.Init.Byte.x71',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex71) ).
fof('$_typeof_Coq.Init.Byte.x72',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex72) ).
fof('$_typeof_Coq.Init.Byte.x73',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex73) ).
fof('$_typeof_Coq.Init.Byte.x74',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex74) ).
fof('$_typeof_Coq.Init.Byte.x75',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex75) ).
fof('$_typeof_Coq.Init.Byte.x76',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex76) ).
fof('$_typeof_Coq.Init.Byte.x77',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex77) ).
fof('$_typeof_Coq.Init.Byte.x78',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex78) ).
fof('$_typeof_Coq.Init.Byte.x79',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex79) ).
fof('$_typeof_Coq.Init.Byte.x7a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7a) ).
fof('$_typeof_Coq.Init.Byte.x7b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7b) ).
fof('$_typeof_Coq.Init.Byte.x7c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7c) ).
fof('$_typeof_Coq.Init.Byte.x7d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7d) ).
fof('$_typeof_Coq.Init.Byte.x7e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7e) ).
fof('$_typeof_Coq.Init.Byte.x7f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7f) ).
fof('$_typeof_Coq.Init.Byte.x80',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex80) ).
fof('$_typeof_Coq.Init.Byte.x81',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex81) ).
fof('$_typeof_Coq.Init.Byte.xcd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excd) ).
fof('$_typeof_Coq.Init.Byte.xce',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exce) ).
fof('$_typeof_Coq.Init.Byte.xcf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excf) ).
fof('$_typeof_Coq.Init.Byte.xd0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd0) ).
fof('$_typeof_Coq.Init.Byte.xd1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd1) ).
fof('$_typeof_Coq.Init.Byte.xd2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd2) ).
fof('$_typeof_Coq.Init.Byte.xd3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd3) ).
fof('$_typeof_Coq.Init.Byte.xd4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd4) ).
fof('$_typeof_Coq.Init.Byte.xd5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd5) ).
fof('$_typeof_Coq.Init.Byte.xd6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd6) ).
fof('$_typeof_Coq.Init.Byte.xd7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd7) ).
fof('$_typeof_Coq.Init.Byte.xd8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd8) ).
fof('$_typeof_Coq.Init.Byte.xd9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd9) ).
fof('$_typeof_Coq.Init.Byte.xda',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exda) ).
fof('$_typeof_Coq.Init.Byte.xdb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdb) ).
fof('$_typeof_Coq.Init.Byte.xdc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdc) ).
fof('$_typeof_Coq.Init.Byte.xdd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdd) ).
fof('$_typeof_Coq.Init.Byte.xde',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exde) ).
fof('$_typeof_Coq.Init.Byte.xdf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdf) ).
fof('$_typeof_Coq.Init.Byte.xe0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe0) ).
fof('$_typeof_Coq.Init.Byte.xe1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe1) ).
fof('$_typeof_Coq.Init.Byte.xe2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe2) ).
fof('$_typeof_Coq.Init.Byte.xe3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe3) ).
fof('$_typeof_Coq.Init.Byte.xe4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe4) ).
fof('$_typeof_Coq.Init.Byte.xe5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe5) ).
fof('$_typeof_Coq.Init.Byte.xe6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe6) ).
fof('$_typeof_Coq.Init.Byte.xe7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe7) ).
fof('$_typeof_Coq.Init.Byte.xe8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe8) ).
fof('$_typeof_Coq.Init.Byte.xe9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe9) ).
fof('$_typeof_Coq.Init.Byte.xea',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exea) ).
fof('$_typeof_Coq.Init.Byte.xeb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exeb) ).
fof('$_typeof_Coq.Init.Byte.xec',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exec) ).
fof('$_typeof_Coq.Init.Byte.xed',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exed) ).
fof('$_typeof_Coq.Init.Byte.xee',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exee) ).
fof('$_typeof_Coq.Init.Byte.xef',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exef) ).
fof('$_typeof_Coq.Init.Byte.xf0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf0) ).
fof('$_typeof_Coq.Init.Byte.xf1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf1) ).
fof('$_typeof_Coq.Init.Byte.xf2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf2) ).
fof('$_typeof_Coq.Init.Byte.xf3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf3) ).
fof('$_typeof_Coq.Init.Byte.xf4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf4) ).
fof('$_typeof_Coq.Init.Byte.xf5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf5) ).
fof('$_typeof_Coq.Init.Byte.xf6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf6) ).
fof('$_typeof_Coq.Init.Byte.xf7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf7) ).
fof('$_typeof_Coq.Init.Byte.xf8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf8) ).
fof('$_typeof_Coq.Init.Byte.xf9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf9) ).
fof('$_typeof_Coq.Init.Byte.xfa',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfa) ).
fof('$_typeof_Coq.Init.Byte.xfb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfb) ).
fof('$_typeof_Coq.Init.Byte.xfc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfc) ).
fof('$_typeof_Coq.Init.Byte.xfd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfd) ).
fof('$_typeof_Coq.Init.Byte.xfe',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfe) ).
fof('$_typeof_Coq.Init.Byte.xff',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exff) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__35531___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__862___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__38___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__860___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__386___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__70___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__228___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__2768___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__2751___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__2756___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__238___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__46___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.list_rec',axiom,
c_24__type__2817___24t(cCoq_2eInit_2eDatatypes_2elist__rec) ).
fof('$_typeof_Coq.Init.Datatypes.list_rect',axiom,
c_24__type__2817___24t(cCoq_2eInit_2eDatatypes_2elist__rect) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
c_24__type__2711___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__839___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__388___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__46___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__386___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__888___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__872___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__2780___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__872___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_typeof_Coq.Init.Datatypes.true',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2etrue) ).
fof('$_typeof_Coq.Init.Datatypes.tt',axiom,
cCoq_2eInit_2eDatatypes_2eunit___24t(cCoq_2eInit_2eDatatypes_2ett) ).
fof('$_typeof_Coq.Init.Datatypes.unit',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_typeof_Coq.Init.Datatypes.xorb',axiom,
c_24__type__386___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__270___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__36502___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__270___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__270___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__270___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__38___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__270___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__273___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__273___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__273___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__30717___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__30758___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__30817___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__30822___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__1287___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__30781___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__1292___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__30699___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__45609___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__30738___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__45665___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__431___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
c_24__type__1324___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__30794___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Lists.List.ForallPairs',axiom,
c_24__type__14483___24t(cCoq_2eLists_2eList_2eForallPairs) ).
fof('$_typeof_Coq.Lists.List.Forall_rect',axiom,
c_24__type__14126___24t(cCoq_2eLists_2eList_2eForall__rect) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__956___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.combine',axiom,
c_24__type__13757___24t(cCoq_2eLists_2eList_2ecombine) ).
fof('$_typeof_Coq.Lists.List.concat',axiom,
c_24__type__1028___24t(cCoq_2eLists_2eList_2econcat) ).
fof('$_typeof_Coq.Lists.List.count_occ',axiom,
c_24__type__12623___24t(cCoq_2eLists_2eList_2ecount__occ) ).
fof('$_typeof_Coq.Lists.List.exists_last',axiom,
c_24__type__12547___24t(cCoq_2eLists_2eList_2eexists__last) ).
fof('$_typeof_Coq.Lists.List.existsb',axiom,
c_24__type__13619___24t(cCoq_2eLists_2eList_2eexistsb) ).
fof('$_typeof_Coq.Lists.List.filter',axiom,
c_24__type__1067___24t(cCoq_2eLists_2eList_2efilter) ).
fof('$_typeof_Coq.Lists.List.find',axiom,
c_24__type__13649___24t(cCoq_2eLists_2eList_2efind) ).
fof('$_typeof_Coq.Lists.List.firstn',axiom,
c_24__type__1084___24t(cCoq_2eLists_2eList_2efirstn) ).
fof('$_typeof_Coq.Lists.List.flat_map',axiom,
c_24__type__13449___24t(cCoq_2eLists_2eList_2eflat__map) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__13522___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__13558___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.forallb',axiom,
c_24__type__13619___24t(cCoq_2eLists_2eList_2eforallb) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__12291___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.hd_error',axiom,
c_24__type__12300___24t(cCoq_2eLists_2eList_2ehd__error) ).
fof('$_typeof_Coq.Lists.List.incl',axiom,
c_24__type__13799___24t(cCoq_2eLists_2eList_2eincl) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__1147___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.lel',axiom,
c_24__type__13799___24t(cCoq_2eLists_2eList_2elel) ).
fof('$_typeof_Coq.Lists.List.list_prod',axiom,
c_24__type__13757___24t(cCoq_2eLists_2eList_2elist__prod) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__1045___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__265___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.nth_default',axiom,
c_24__type__12471___24t(cCoq_2eLists_2eList_2enth__default) ).
fof('$_typeof_Coq.Lists.List.nth_error',axiom,
c_24__type__978___24t(cCoq_2eLists_2eList_2enth__error) ).
fof('$_typeof_Coq.Lists.List.nth_ok',axiom,
c_24__type__12459___24t(cCoq_2eLists_2eList_2enth__ok) ).
fof('$_typeof_Coq.Lists.List.removelast',axiom,
c_24__type__1000___24t(cCoq_2eLists_2eList_2eremovelast) ).
fof('$_typeof_Coq.Lists.List.repeat',axiom,
c_24__type__14546___24t(cCoq_2eLists_2eList_2erepeat) ).
fof('$_typeof_Coq.Lists.List.rev',axiom,
c_24__type__1000___24t(cCoq_2eLists_2eList_2erev) ).
fof('$_typeof_Coq.Lists.List.rev\'',axiom,
c_24__type__1000___24t(cCoq_2eLists_2eList_2erev_27) ).
fof('$_typeof_Coq.Lists.List.rev_append',axiom,
c_24__type__70___24t(cCoq_2eLists_2eList_2erev__append) ).
fof('$_typeof_Coq.Lists.List.seq',axiom,
c_24__type__13886___24t(cCoq_2eLists_2eList_2eseq) ).
fof('$_typeof_Coq.Lists.List.skipn',axiom,
c_24__type__1084___24t(cCoq_2eLists_2eList_2eskipn) ).
fof('$_typeof_Coq.Lists.List.tl',axiom,
c_24__type__1000___24t(cCoq_2eLists_2eList_2etl) ).
fof('$_typeof_Coq.Lists.SetoidList.equivlistA',axiom,
c_24__type__28921___24t(cCoq_2eLists_2eSetoidList_2eequivlistA) ).
fof('$_typeof_Coq.Lists.SetoidList.inclA',axiom,
c_24__type__28921___24t(cCoq_2eLists_2eSetoidList_2einclA) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__29111___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__29111___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__29152___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__29152___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__35581___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
c_24__type__45962___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__45968___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__45962___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__45962___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__11956___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__35053___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__35046___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__11956___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__35056___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
c_24__type__36506___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).
fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__2625___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__223___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__223___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__786___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__786___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
c_24__type__46041___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
c_24__type__45925___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__45925___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNeg',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNul',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
c_24__type__46055___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__35094___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__46069___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__46084___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
c_24__type__786___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__35094___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__786___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
c_24__type__37806___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qdiv',axiom,
c_24__type__14677___24t(cCoq_2eQArith_2eQArith__base_2eQdiv) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq',axiom,
c_24__type__14671___24t(cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq_bool',axiom,
c_24__type__14674___24t(cCoq_2eQArith_2eQArith__base_2eQeq__bool) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__14668___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qminus',axiom,
c_24__type__14677___24t(cCoq_2eQArith_2eQArith__base_2eQminus) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmult',axiom,
c_24__type__14677___24t(cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__37801___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.QArith.QArith_base.Qopp',axiom,
c_24__type__14680___24t(cCoq_2eQArith_2eQArith__base_2eQopp) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__14909___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__14900___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__14903___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__37816___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__37816___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__14900___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__14900___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__14903___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__14900___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__37818___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__37879___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__28778___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__46___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__45567___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__46___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).
fof('$_typeof_Coq.Strings.String.String',axiom,
c_24__type__30834___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.append',axiom,
c_24__type__30841___24t(cCoq_2eStrings_2eString_2eappend) ).
fof('$_typeof_Coq.Strings.String.list_ascii_of_string',axiom,
c_24__type__30878___24t(cCoq_2eStrings_2eString_2elist__ascii__of__string) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Strings.String.string_of_list_ascii',axiom,
c_24__type__30872___24t(cCoq_2eStrings_2eString_2estring__of__list__ascii) ).
fof('$_typeof_Coq.Structures.DecidableTypeEx.N_as_DT.eq',axiom,
c_24__type__45962___24t(cCoq_2eStructures_2eDecidableTypeEx_2eN__as__DT_2eeq) ).
fof('$_typeof_Coq.Structures.DecidableTypeEx.Nat_as_DT.eq',axiom,
c_24__type__273___24t(cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2eeq) ).
fof('$_typeof_Coq.Structures.DecidableTypeEx.Positive_as_DT.eq',axiom,
c_24__type__45925___24t(cCoq_2eStructures_2eDecidableTypeEx_2ePositive__as__DT_2eeq) ).
fof('$_typeof_Coq.Structures.DecidableTypeEx.Z_as_DT.eq',axiom,
c_24__type__696___24t(cCoq_2eStructures_2eDecidableTypeEx_2eZ__as__DT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__37717___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__45962___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__273___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__273___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__45925___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
c_24__type__45925___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
c_24__type__696___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__2713___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.Vector.to_list',axiom,
c_24__type__33873___24t(cCoq_2eVectors_2eVector_2eto__list) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__33909___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__33901___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__33884___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.to_list',axiom,
c_24__type__33873___24t(cCoq_2eVectors_2eVectorDef_2eto__list) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__696___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
c_24__type__696___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__46132___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__696___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__696___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__696___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__696___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__696___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__718___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__714___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__748___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gtb',axiom,
c_24__type__34990___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egtb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__34990___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__714___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__714___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__46134___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__35227___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__751___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__718___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__714___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__35294___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__714___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__718___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__46145___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__34990___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength',axiom,
c_24__type__35005___24t(cCoq_2eZArith_2eZcomplements_2eZlength) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength_aux',axiom,
c_24__type__35002___24t(cCoq_2eZArith_2eZcomplements_2eZlength__aux) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__72___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__72___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__2614___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__37879___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__45907___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__46___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__46___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__944___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__46___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.QMicromega.QWitness',axiom,
cType___24t(cCoq_2emicromega_2eQMicromega_2eQWitness) ).
fof('$_typeof_Coq.micromega.RMicromega.RWitness',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRWitness) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__14953___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__14927___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__46___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__46___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__46___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__46___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__46___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
c_24__type__43296___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzIn',axiom,
c_24__type__43293___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzIn) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzZ',axiom,
c_24__type__43298___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzZ) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.cltb',axiom,
c_24__type__15683___24t(cCoq_2emicromega_2eRingMicromega_2ecltb) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
c_24__type__43281___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).
fof('$_typeof_Coq.micromega.RingMicromega.ge_bool',axiom,
c_24__type__16297___24t(cCoq_2emicromega_2eRingMicromega_2ege__bool) ).
fof('$_typeof_Coq.micromega.RingMicromega.map_option',axiom,
c_24__type__15849___24t(cCoq_2emicromega_2eRingMicromega_2emap__option) ).
fof('$_typeof_Coq.micromega.RingMicromega.map_option2',axiom,
c_24__type__15887___24t(cCoq_2emicromega_2eRingMicromega_2emap__option2) ).
fof('$_typeof_Coq.micromega.RingMicromega.nhyps_of_psatz',axiom,
c_24__type__16351___24t(cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.psub',axiom,
c_24__type__16681___24t(cCoq_2emicromega_2eRingMicromega_2epsub) ).
fof('$_typeof_Coq.micromega.Tauto.BFormula',axiom,
c_24__type__46___24t(cCoq_2emicromega_2eTauto_2eBFormula) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__30941___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.TFormula',axiom,
c_24__type__30941___24t(cCoq_2emicromega_2eTauto_2eTFormula) ).
fof('$_typeof_Coq.micromega.Tauto.and_cnf',axiom,
c_24__type__31952___24t(cCoq_2emicromega_2eTauto_2eand__cnf) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__872___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.Tauto.cnf',axiom,
c_24__type__872___24t(cCoq_2emicromega_2eTauto_2ecnf) ).
fof('$_typeof_Coq.micromega.Tauto.cnf_ff',axiom,
c_24__type__31676___24t(cCoq_2emicromega_2eTauto_2ecnf__ff) ).
fof('$_typeof_Coq.micromega.Tauto.cnf_tt',axiom,
c_24__type__31676___24t(cCoq_2emicromega_2eTauto_2ecnf__tt) ).
fof('$_typeof_Coq.micromega.Tauto.collect_annot',axiom,
c_24__type__31469___24t(cCoq_2emicromega_2eTauto_2ecollect__annot) ).
fof('$_typeof_Coq.micromega.Tauto.cons_id',axiom,
c_24__type__31337___24t(cCoq_2emicromega_2eTauto_2econs__id) ).
fof('$_typeof_Coq.micromega.Tauto.eval_cnf',axiom,
c_24__type__33402___24t(cCoq_2emicromega_2eTauto_2eeval__cnf) ).
fof('$_typeof_Coq.micromega.Tauto.eval_f',axiom,
c_24__type__31558___24t(cCoq_2emicromega_2eTauto_2eeval__f) ).
fof('$_typeof_Coq.micromega.Tauto.eval_tt',axiom,
c_24__type__33344___24t(cCoq_2emicromega_2eTauto_2eeval__tt) ).
fof('$_typeof_Coq.micromega.Tauto.or_cnf',axiom,
c_24__type__31940___24t(cCoq_2emicromega_2eTauto_2eor__cnf) ).
fof('$_typeof_Coq.micromega.ZMicromega.CutProof',axiom,
c_24__type__34123___24t(cCoq_2emicromega_2eZMicromega_2eCutProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.DoneProof',axiom,
cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(cCoq_2emicromega_2eZMicromega_2eDoneProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.EnumProof',axiom,
c_24__type__34129___24t(cCoq_2emicromega_2eZMicromega_2eEnumProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.RatProof',axiom,
c_24__type__34123___24t(cCoq_2emicromega_2eZMicromega_2eRatProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.E.eq',axiom,
c_24__type__45925___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eE_2eeq) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.MP.to_list',axiom,
c_24__type__35019___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eto__list) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZWitness',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZWitness) ).
fof('$_typeof_Coq.micromega.ZMicromega.make_conj',axiom,
c_24__type__14953___24t(cCoq_2emicromega_2eZMicromega_2emake__conj) ).
fof('$_typeof_Coq.micromega.ZMicromega.make_impl',axiom,
c_24__type__14927___24t(cCoq_2emicromega_2eZMicromega_2emake__impl) ).
fof('$_typeof_Coq.micromega.ZMicromega.valid_cut_sign',axiom,
c_24__type__34416___24t(cCoq_2emicromega_2eZMicromega_2evalid__cut__sign) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
c_24__type__751___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).
fof('$_typeof_Coq.setoid_ring.BinList.jump',axiom,
c_24__type__2601___24t(cCoq_2esetoid__ring_2eBinList_2ejump) ).
fof('$_typeof_Coq.setoid_ring.BinList.nth',axiom,
c_24__type__2612___24t(cCoq_2esetoid__ring_2eBinList_2enth) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__35656___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__35661___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__35653___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEdiv',axiom,
c_24__type__35661___24t(cCoq_2esetoid__ring_2eField__theory_2eFEdiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__8602___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__35670___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__35661___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEopp',axiom,
c_24__type__35670___24t(cCoq_2esetoid__ring_2eField__theory_2eFEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEsub',axiom,
c_24__type__35661___24t(cCoq_2esetoid__ring_2eField__theory_2eFEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__46___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__11186___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons2',axiom,
c_24__type__11412___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons2) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEadd',axiom,
c_24__type__6666___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
c_24__type__5616___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEopp',axiom,
c_24__type__7196___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEsub',axiom,
c_24__type__6666___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__8900___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__8681___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__8661___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.display_pow_linear',axiom,
c_24__type__10760___24t(cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__46___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__8650___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__8661___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__46___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_common',axiom,
c_24__type__9003___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__common) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
c_24__type__9003___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__left) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
c_24__type__9003___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__right) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.split',axiom,
c_24__type__9060___24t(cCoq_2esetoid__ring_2eField__theory_2esplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__11958___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nsub',axiom,
c_24__type__11956___24t(cCoq_2esetoid__ring_2eInitialRing_2eNsub) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nw_is0',axiom,
c_24__type__12069___24t(cCoq_2esetoid__ring_2eInitialRing_2eNw__is0) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__11992___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiNword',axiom,
c_24__type__12197___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__36451___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__36451___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__11929___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.get_signZ',axiom,
c_24__type__11940___24t(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.triv_div',axiom,
c_24__type__12234___24t(cCoq_2esetoid__ring_2eInitialRing_2etriv__div) ).
fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
c_24__type__386___24t(cCoq_2esetoid__ring_2eRing_2ebool__eq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.P0',axiom,
c_24__type__17362___24t(cCoq_2esetoid__ring_2eRing__polynom_2eP0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__19506___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__19506___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__19512___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__19517___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__19509___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__19710___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__19517___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__43311___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__43316___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__19517___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__46___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__17375___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__17362___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__17517___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pequiv',axiom,
c_24__type__18927___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePequiv) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__17367___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__46___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi',axiom,
c_24__type__18854___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__23841___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
c_24__type__20884___24t(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkPinj',axiom,
c_24__type__17367___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkPinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
c_24__type__21169___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__43334___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_rec',axiom,
c_24__type__21329___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec) ).
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__20630___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.r_list_pow',axiom,
c_24__type__23454___24t(cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.vmon',axiom,
c_24__type__43301___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
c_24__type__43301___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__28398___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__28398___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__45352___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
c_24__type__860___24t(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__11958___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__24316___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__24295___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).
fof('$_typeof_R.A',axiom,
c_24__type__189___24t(cR_2eA) ).
fof('$_typeof_R.H',axiom,
c_24__type__189___24t(cR_2eH) ).
fof('$_typeof_R.N',axiom,
c_24__type__189___24t(cR_2eN) ).
fof('$_typeof_R.abstr',axiom,
c_24__type__569___24t(cR_2eabstr) ).
fof('$_typeof_Tait.MoreList.consn',axiom,
c_24__type__405___24t(cTait_2eMoreList_2econsn) ).
fof('$_typeof_Tait.MoreList.exists_last',axiom,
c_24__type__12547___24t(cTait_2eMoreList_2eexists__last) ).
fof('$_typeof_Tait.MoreList.existsb',axiom,
c_24__type__13619___24t(cTait_2eMoreList_2eexistsb) ).
fof('$_typeof_Tait.MoreList.firstn',axiom,
c_24__type__1084___24t(cTait_2eMoreList_2efirstn) ).
fof('$_typeof_Tait.MoreList.last',axiom,
c_24__type__1147___24t(cTait_2eMoreList_2elast) ).
fof('$_typeof_Tait.MoreList.removelast',axiom,
c_24__type__1000___24t(cTait_2eMoreList_2eremovelast) ).
fof('$_typeof_Tait.MoreList.rev_acc',axiom,
c_24__type__70___24t(cTait_2eMoreList_2erev__acc) ).
fof('$_typeof_Tait.MoreList.seq',axiom,
c_24__type__13886___24t(cTait_2eMoreList_2eseq) ).
fof('$_typeof_Tait.Subst.mk_sub',axiom,
c_24__type__1345___24t(cTait_2eSubst_2emk__sub) ).
fof('$_typeof_Tait.Subst.shift',axiom,
c_24__type__466___24t(cTait_2eSubst_2eshift) ).
fof('$_typeof_Tait.Subst.sub',axiom,
c_24__type__479___24t(cTait_2eSubst_2esub) ).
fof('$_typeof_Tait.Subst.sub1',axiom,
c_24__type__1347___24t(cTait_2eSubst_2esub1) ).
fof('$_typeof_Tait.Subst.sublift',axiom,
c_24__type__468___24t(cTait_2eSubst_2esublift) ).
fof('$_typeof_Tait.Subst.substitution',axiom,
cType___24t(cTait_2eSubst_2esubstitution) ).
fof('$_typeof_Tait.Subst.support',axiom,
c_24__type__461___24t(cTait_2eSubst_2esupport) ).
fof('$_typeof_Tait.Subst2.Joachimski.Dot',axiom,
c_24__type__2271___24t(cTait_2eSubst2_2eJoachimski_2eDot) ).
fof('$_typeof_Tait.Subst2.Joachimski.PushList',axiom,
c_24__type__35015___24t(cTait_2eSubst2_2eJoachimski_2ePushList) ).
fof('$_typeof_Tait.Subst2.Joachimski.Up',axiom,
c_24__type__45959___24t(cTait_2eSubst2_2eJoachimski_2eUp) ).
fof('$_typeof_Tait.Subst2.Joachimski.sub',axiom,
c_24__type__2307___24t(cTait_2eSubst2_2eJoachimski_2esub) ).
fof('$_typeof_Tait.Subst2.Joachimski.sub\'',axiom,
c_24__type__2296___24t(cTait_2eSubst2_2eJoachimski_2esub_27) ).
fof('$_typeof_Tait.Subst2.Joachimski.sublift',axiom,
c_24__type__2279___24t(cTait_2eSubst2_2eJoachimski_2esublift) ).
fof('$_typeof_Tait.Subst2.Joachimski.substitution',axiom,
cType___24t(cTait_2eSubst2_2eJoachimski_2esubstitution) ).
fof('$_typeof_Tait.Subst2.above',axiom,
c_24__type__1350___24t(cTait_2eSubst2_2eabove) ).
fof('$_typeof_Tait.TaitCore.F',axiom,
c_24__type__487___24t(cTait_2eTaitCore_2eF) ).
fof('$_typeof_Tait.Term.Abs',axiom,
c_24__type__285___24t(cTait_2eTerm_2eAbs) ).
fof('$_typeof_Tait.Term.App',axiom,
c_24__type__282___24t(cTait_2eTerm_2eApp) ).
fof('$_typeof_Tait.Term.Arrow',axiom,
c_24__type__277___24t(cTait_2eTerm_2eArrow) ).
fof('$_typeof_Tait.Term.Iota',axiom,
cTait_2eTerm_2etype___24t(cTait_2eTerm_2eIota) ).
fof('$_typeof_Tait.Term.Var',axiom,
c_24__type__279___24t(cTait_2eTerm_2eVar) ).
fof('$_typeof_Tait.Term.arrow_left',axiom,
c_24__type__300___24t(cTait_2eTerm_2earrow__left) ).
fof('$_typeof_Tait.Term.arrow_right',axiom,
c_24__type__300___24t(cTait_2eTerm_2earrow__right) ).
fof('$_typeof_Tait.Term.down',axiom,
c_24__type__535___24t(cTait_2eTerm_2edown) ).
fof('$_typeof_Tait.Term.dterm',axiom,
cTait_2eTerm_2eterm___24t(cTait_2eTerm_2edterm) ).
fof('$_typeof_Tait.Term.dtype',axiom,
cTait_2eTerm_2etype___24t(cTait_2eTerm_2edtype) ).
fof('$_typeof_Tait.Term.lift',axiom,
c_24__type__2231___24t(cTait_2eTerm_2elift) ).
fof('$_typeof_Tait.Term.occurs',axiom,
c_24__type__513___24t(cTait_2eTerm_2eoccurs) ).
fof('$_typeof_Tait.Term.term',axiom,
cType___24t(cTait_2eTerm_2eterm) ).
fof('$_typeof_Tait.Term.term_rec',axiom,
c_24__type__1469___24t(cTait_2eTerm_2eterm__rec) ).
fof('$_typeof_Tait.Term.term_rect',axiom,
c_24__type__1469___24t(cTait_2eTerm_2eterm__rect) ).
fof('$_typeof_Tait.Term.type',axiom,
cType___24t(cTait_2eTerm_2etype) ).
fof('$_typeof_Tait.Term.type_rec',axiom,
c_24__type__1379___24t(cTait_2eTerm_2etype__rec) ).
fof('$_typeof_Tait.Term.type_rect',axiom,
c_24__type__1379___24t(cTait_2eTerm_2etype__rect) ).
fof('$_typeof_Tait.Term.up',axiom,
c_24__type__535___24t(cTait_2eTerm_2eup) ).
fof('$_typeof_Tait.Typing.TypJ',axiom,
c_24__type__113___24t(cTait_2eTyping_2eTypJ) ).
fof('$_typeof_Tait.Typing.context',axiom,
cType___24t(cTait_2eTyping_2econtext) ).
fof('$_typeof_Tait.Typing.ext_ctx',axiom,
c_24__type__560___24t(cTait_2eTyping_2eext__ctx) ).
fof('$_typeof_Tait.Typing.typ',axiom,
c_24__type__311___24t(cTait_2eTyping_2etyp) ).
fof('$_typeof_Tait.nc.ncP',axiom,
c_24__type__154___24t(cTait_2enc_2encP) ).
fof('$_typeof_Tait.nc.ncP2',axiom,
c_24__type__174___24t(cTait_2enc_2encP2) ).
fof('Coq.Arith.Compare_dec.dec_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.dec_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.dec_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.not_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Compare_dec.not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Compare_dec.not_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)) ) ) ) ).
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)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),V0__n))
=> p(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)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.gt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.Lt.S_pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n))
=> V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2epred___24a1(V0__n)) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(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)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(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)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('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)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
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.Minus.minus_n_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.Minus.minus_plus',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m),V0__n) = V1__m ) ) ).
fof('Coq.Arith.Minus.minus_plus_simpl_l_reverse',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m)) ) ) ) ).
fof('Coq.Arith.Minus.pred_of_minus',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2epred___24a1(V0__n) = cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_succ_r',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,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n))
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
| p(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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO)) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_0_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eO
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2esub___24a2(V1__m,V0__n),V0__n) = V1__m ) ) ) ).
fof('Coq.Arith.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.PeanoNat.Nat.sub_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__270,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__38,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat))),cCoq_2eInit_2eNat_2esub) ).
fof('Coq.Arith.Peano_dec.dec_eq_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__1153___24a2(V0__n,V1__m)) ) ) ).
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)
=> p(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)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m))) ) ) ).
fof('Coq.Bool.Bool.absurd_eq_bool',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ! [V1__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
=> ( p(c_24False)
=> V0__b = V1__b_27 ) ) ) ).
fof('Coq.Bool.Bool.orb_false_elim',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& V1__b2 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.empty_1',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__891___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__891___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__841___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__1151___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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Init.Peano.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(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)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.Init.Peano.plus_n_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Init.Peano.plus_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ).
fof('Coq.Init.Specif.sumbool_ind',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__1296___24t(V0__A,V1__B,V2__P)
=> ( ( p(V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.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_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__P] :
( c_24__type__1117___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)
=> ( 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_split',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__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l1)
& ? [V6__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2)
& V2__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V5__l1,V6__l2)
& V3__l_27 = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V5__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V6__l2)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__157___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_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__157___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__891___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__157___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__891___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.Forall2_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__181___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_app_inv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__181___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__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l_27)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l1,V4__l2),V5__l_27)
=> ? [V7__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V7__l1_27)
& ? [V8__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V8__l2_27)
& cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V3__l1,V7__l1_27)
& cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V4__l2,V8__l2_27)
& V5__l_27 = cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,V7__l1_27,V8__l2_27) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall2_app_inv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__181___24t(V0__A,V1__B,V2__R)
=> ! [V3__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l1_27)
=> ! [V4__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l2_27)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V5__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,V3__l1_27,V4__l2_27))
=> ? [V7__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l1)
& ? [V8__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V8__l2)
& cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V7__l1,V3__l1_27)
& cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V8__l2,V4__l2_27)
& V5__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l1,V8__l2) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall2_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__181___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_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__181___24t(V0__A,V1__B,V2__R)
=> cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)) ) ) ) ).
fof('Coq.Lists.List.Forall_forall',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__157___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)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l)
=> p(happ(V1__P,V3__x)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__157___24t(V0__A,V1__P)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.NoDup_remove_1',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_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V2__l_27)))
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_remove_2',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_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V2__l_27)))
=> ~ cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)) ) ) ) ) ) ).
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_cons_not_nil',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_2enil___24a1(V0__A) != cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V2__y)) ) ) ) ) ).
fof('Coq.Lists.List.app_eq_nil',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_2eapp___24a3(V0__A,V1__l,V2__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
=> ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& V2__l_27 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ) ) ).
fof('Coq.Lists.List.app_inj_tail',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)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__b,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( V1__x = V2__y
& V3__a = V4__b ) ) ) ) ) ) ) ).
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.app_nth1',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__d] :
( t(V3__d,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,V1__l,V3__d) ) ) ) ) ) ) ).
fof('Coq.Lists.List.concat_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V1__l1)
=> ! [V2__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V2__l2)
=> cCoq_2eLists_2eList_2econcat___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V1__l1,V2__l2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2econcat___24a2(V0__A,V1__l1),cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l2)) ) ) ) ).
fof('Coq.Lists.List.concat_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V2__l)
=> cCoq_2eLists_2eList_2econcat___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V1__x,V2__l)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l)) ) ) ) ).
fof('Coq.Lists.List.existsb_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1061___24t(V0__A,V1__f)
=> ! [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_2eexistsb___24a3(V0__A,V1__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V2__l1),cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l2)) ) ) ) ) ).
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__122___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__122___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)
=> ( 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_all2',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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),V1__n))
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l) = V2__l ) ) ) ) ).
fof('Coq.Lists.List.firstn_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [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_2efirstn___24a3(V0__A,V1__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l1),cCoq_2eLists_2eList_2efirstn___24a3(V0__A,cCoq_2eInit_2eNat_2esub___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l1)),V3__l2)) ) ) ) ) ).
fof('Coq.Lists.List.firstn_app_2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [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_2efirstn___24a3(V0__A,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l1),V1__n),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V3__l2)) ) ) ) ) ).
fof('Coq.Lists.List.firstn_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ).
fof('Coq.Lists.List.firstn_skipn',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_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l),cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,V2__l)) = V2__l ) ) ) ).
fof('Coq.Lists.List.fold_left_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__13529___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l_27)
=> ! [V5__i] :
( t(V5__i,V0__A)
=> cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,V3__l,V4__l_27),V5__i) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l_27,cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V3__l,V5__i)) ) ) ) ) ) ) ).
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__13572___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.forallb_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1061___24t(V0__A,V1__f)
=> ! [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_2eforallb___24a3(V0__A,V1__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V2__l1),cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l2)) ) ) ) ) ).
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)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27))
<=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
| 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)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m))
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m) ) ) ) ) ) ) ).
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)
=> ( ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m) )
=> 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)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V1__l)
<=> 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)
=> ( 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)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__m,V3__n)
=> 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)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n)
=> 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)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__m,V3__n)) ) ) ) ) ) ).
fof('Coq.Lists.List.map_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__122___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_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27)) = cCoq_2eInit_2eDatatypes_2eapp___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.Lists.List.map_ext',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__122___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__122___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__122___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__122___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)
=> ( 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__122___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__122___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)
=> ( 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__13460___24a1(V0__A),V1__l) = V1__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__122___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__13466___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__13480___24a5(V0__A,V1__B,V2__C,V3__f,V4__g),V5__l) ) ) ) ) ) ) ).
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_error_app1',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__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V3__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth__error___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V3__n) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_error_split',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__a] :
( t(V3__a,V0__A)
=> ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V2__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__a)
=> ? [V5__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l1)
& ? [V6__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2)
& V1__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V5__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V6__l2))
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V5__l1) = V2__n ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_split',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)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)))
=> ? [V5__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l1)
& ? [V6__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2)
& V2__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V5__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,cCoq_2eLists_2eList_2enth___24a4(V0__A,V1__n,V2__l,V3__d),V6__l2))
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V5__l1) = V1__n ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.removelast_app',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)
=> ( V2__l_27 != cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
=> cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l_27)) ) ) ) ) ).
fof('Coq.Lists.List.rev_app_distr',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)
=> cCoq_2eLists_2eList_2erev___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,V2__y)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__y),cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__x)) ) ) ) ).
fof('Coq.Lists.List.rev_append_rev',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_2eLists_2eList_2erev__append___24a3(V0__A,V1__l,V2__l_27) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l),V2__l_27) ) ) ) ).
fof('Coq.Lists.List.rev_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__891___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.rev_list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__891___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,cCoq_2eLists_2eList_2erev___24a2(V0__A,V4__l)))
=> p(happ(V1__P,cCoq_2eLists_2eList_2erev___24a2(V0__A,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,cCoq_2eLists_2eList_2erev___24a2(V0__A,V4__l))) ) ) ) ) ) ).
fof('Coq.Lists.List.rev_unit',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eLists_2eList_2erev___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l)) ) ) ) ).
fof('Coq.Lists.List.seq_app',axiom,
! [V0__len1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__len1)
=> ! [V1__len2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__len2)
=> ! [V2__start] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__start)
=> cCoq_2eLists_2eList_2eseq___24a2(V2__start,cCoq_2eInit_2eNat_2eadd___24a2(V0__len1,V1__len2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eLists_2eList_2eseq___24a2(V2__start,V0__len1),cCoq_2eLists_2eList_2eseq___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__start,V0__len1),V1__len2)) ) ) ) ).
fof('Coq.Lists.List.seq_length',axiom,
! [V0__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__len)
=> ! [V1__start] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__start)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eLists_2eList_2eseq___24a2(V1__start,V0__len)) = V0__len ) ) ).
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.List.skipn_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [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_2eskipn___24a3(V0__A,V1__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,V2__l1),cCoq_2eLists_2eList_2eskipn___24a3(V0__A,cCoq_2eInit_2eNat_2esub___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l1)),V3__l2)) ) ) ) ) ).
fof('Coq.Lists.List.skipn_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,c_24__cast__13804___24a1(V0__A)) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ).
fof('Coq.Lists.SetoidList.InA_alt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___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))
& cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__y,V3__l) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___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__1173___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__1173___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_compat',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__29031___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__891___24a1(V0__A),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cProp,cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA),c_3c_3d_3e)),cCoq_2eLists_2eSetoidList_2eInA___24a2(V0__A,V1__eqA)) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___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__1173___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__1173___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_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__891___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_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__891___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__1173___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__1173___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)
=> ( 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.InfA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__ltA] :
( c_24__type__1173___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.NoDupA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___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__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V4__l_27)
=> ( ! [V7__x] :
( t(V7__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V7__x,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V7__x,V4__l_27)
=> p(c_24False) ) ) )
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___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_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___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)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V3__l_27)))
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.SortA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__ltA] :
( c_24__type__1173___24t(V0__A,V3__ltA)
=> ! [V4__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
=> ! [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V3__ltA,V4__l1)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V3__ltA,V5__l2)
=> ( ! [V8__x] :
( t(V8__x,V0__A)
=> ! [V9__y] :
( t(V9__y,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V8__x,V4__l1)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V9__y,V5__l2)
=> p(happ(happ(V3__ltA,V8__x),V9__y)) ) ) ) )
=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V3__ltA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,V5__l2)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.app_eqlistA_compat',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___24t(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__29078___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),c_24__type__29070___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA))),cCoq_2eInit_2eDatatypes_2eapp___24a1(V0__A)) ) ) ).
fof('Coq.Lists.SetoidList.eqarefl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___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.eqasym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V1__eqA) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___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__1173___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__1173___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_equivlistA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eRelationClasses_2esubrelation___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA)) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___24t(V0__A,V1__eqA)
=> ! [V2__P] :
( c_24__type__1117___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_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___24t(V0__A,V1__eqA)
=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_rev_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___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)
=> ! [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,V5__l2,V6__l2_27)
=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l1),V5__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V3__l1_27),V6__l2_27)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_app_idem',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___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_app_proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__29078___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),c_24__type__29070___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA))),cCoq_2eInit_2eDatatypes_2eapp___24a1(V0__A)) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlist_equiv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___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_2eequivlistA___24a2(V0__A,V1__eqA)) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_eqlistA2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1173___24t(V0__A,V1__eqA)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__eqB] :
( c_24__type__29177___24t(V0__A,V2__B,V3__eqB)
=> ! [V4__f] :
( c_24__type__13572___24t(V0__A,V2__B,V4__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13572___24a2(V0__A,V2__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__9104___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.Logic.Decidable.dec_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__35583___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Decidable.imp_simp',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( p(V0__A)
=> p(V1__B) )
=> ( ~ p(V0__A)
| p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ~ ( p(V0__A)
| p(V1__B) )
=> ( ~ p(V0__A)
& ~ p(V1__B) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__2614___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.add_1_l',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2exH,V0__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V0__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__2614___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.QArith.QArith_base.Q_Setoid',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('Coq.QArith.QArith_base.Qeq_bool_eq',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.QArith.QArith_base.Qinv_comp',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__14680,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq,cCoq_2eQArith_2eQArith__base_2eQeq),cCoq_2eQArith_2eQArith__base_2eQinv) ).
fof('Coq.QArith.QArith_base.Qmult_comp',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__14677,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,c_24__type__14680,cCoq_2eQArith_2eQArith__base_2eQeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq,cCoq_2eQArith_2eQArith__base_2eQeq)),cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('Coq.QArith.QArith_base.Qopp_comp',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__14680,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq,cCoq_2eQArith_2eQArith__base_2eQeq),cCoq_2eQArith_2eQArith__base_2eQopp) ).
fof('Coq.QArith.QArith_base.Qplus_comp',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__14677,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,c_24__type__14680,cCoq_2eQArith_2eQArith__base_2eQeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq,cCoq_2eQArith_2eQArith__base_2eQeq)),cCoq_2eQArith_2eQArith__base_2eQplus) ).
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.Sorted.HdRel_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__1173___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_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__1173___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.Sorted_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__1173___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.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_refl',axiom,
! [V0__x] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.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__46129___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.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_2435204___24a2(V0__p,V1__q) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.Znat.Nat2Z.inj_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_iff',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)
<=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_sub',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n)) ) ).
fof('Coq.ZArith.Znat.inj_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__y) ) ) ) ).
fof('Coq.ZArith.Znat.inj_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_gt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Znat.inj_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Znat.inj_minus2',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.Znat.inj_neq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_le_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_lt_ge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zegal_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.auxiliary.Zge_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zgt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zle_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zlt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zne_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_square_nonneg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__3114___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__3114___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__3114___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1173___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1173___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_conj_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__157___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__157___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__157___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.RingMicromega.extract_hyps_app',axiom,
! [V0__C] :
( cType___24t(V0__C)
=> ! [V1__cO] :
( t(V1__cO,V0__C)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C),V2__l)
=> ! [V3__ln1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,V3__ln1)
=> ! [V4__ln2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,V4__ln2)
=> cCoq_2emicromega_2eRingMicromega_2eextract__hyps___24a4(V0__C,V1__cO,V2__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2enat,V3__ln1,V4__ln2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eextract__hyps___24a4(V0__C,V1__cO,V2__l,V3__ln1),cCoq_2emicromega_2eRingMicromega_2eextract__hyps___24a4(V0__C,V1__cO,V2__l,V4__ln2)) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.E_ST',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive)) ).
fof('Coq.omega.OmegaLemmas.OMEGA17',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA5',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA7',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ! [V3__t] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__t)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__z,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V3__t,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V3__t)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA8',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA10',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k1)
=> ! [V6__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__k2)
=> ! [V7__P] :
( c_24__type__72___24t(V7__P)
=> ( p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V6__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V6__k2)))))
=> p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V6__k2)))) ) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA11',axiom,
! [V0__v1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v1)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k1)
=> ! [V5__P] :
( c_24__type__72___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V4__k1)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l1,V4__k1),V3__l2))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,V1__c1),V2__l1),V4__k1),V3__l2))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA12',axiom,
! [V0__v2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v2)
=> ! [V1__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c2)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k2)
=> ! [V5__P] :
( c_24__type__72___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c2,V4__k2)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l2,V4__k2)))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,V1__c2),V3__l2),V4__k2)))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA13',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__72___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA14',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__72___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA15',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k2)
=> ! [V6__P] :
( c_24__type__72___24t(V6__P)
=> ( p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__c1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V5__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V5__k2)))))
=> p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V5__k2)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA16',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c)
=> ! [V2__l] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l)
=> ! [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__k)
=> ! [V4__P] :
( c_24__type__72___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c,V3__k)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l,V3__k))))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c),V2__l),V3__k))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__72___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x))) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_mult_distr_r',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__72___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_plus_distr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__72___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__72___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p)))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc_reverse',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__72___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_comm',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__72___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__y,V0__x)))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_permute',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__72___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__72___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__72___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor3',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__72___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y),V0__x))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor4',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ! [V3__P] :
( c_24__type__72___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__y,V2__z))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor5',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__72___24t(V2__P)
=> ( p(happ(V2__P,V1__y))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__72___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.intro_Z',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = V1__y
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.omega.OmegaLemmas.new_var',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& V0__x = V1__y ) ) ).
fof('Coq.setoid_ring.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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__3114___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__4409___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__3114___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__4409___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__3114___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__4409___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__3114___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__4409___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__1173___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V11__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V11__p)),V11__p)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.F_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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__3114___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__4409___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__1173___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.PCond_app',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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__3711___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__5636___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__5645___24t(V0__R,V8__C,V10__Cpow,V12__rpow)
=> ! [V13__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V13__l)
=> ! [V14__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V14__l1)
=> ! [V15__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__l2)
=> ( 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,V13__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V14__l1,V15__l2))
<=> ( 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,V13__l,V14__l1)
& 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,V13__l,V15__l2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv_r_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__3114___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__4409___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__1173___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V12__r] :
( t(V12__r,V0__R)
=> ( ~ p(happ(happ(V9__req,V12__r),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V12__r),V12__r)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3114___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3114___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__4409___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__1173___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__3114___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__4409___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_reg_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__3114___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__4409___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__1173___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q1] :
( t(V14__q1,V0__R)
=> ! [V15__q2] :
( t(V15__q2,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__p),V1__rO))
=> ( p(happ(happ(V9__req,happ(happ(V4__rmul,V13__p),V14__q1)),happ(happ(V4__rmul,V13__p),V15__q2)))
=> p(happ(happ(V9__req,V14__q1),V15__q2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.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__3114___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3114___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__4409___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__1173___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__3114___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__4409___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__3114___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3114___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__4409___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__1173___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__3114___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__4409___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.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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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_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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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_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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3114___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3114___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__4409___24t(V0__R,V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,c_3d___24a1(V0__R)) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_s_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3114___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3114___24t(V0__R,V2__rmul)
=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V0__R,V1__radd,V2__rmul,c_3d___24a1(V0__R)) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eqsth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).
fof('Coq.setoid_ring.Ring_theory.IDmorph',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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ! [V9__reqb] :
( c_24__type__3122___24t(V0__R,V9__reqb)
=> ( ! [V10__x] :
( t(V10__x,V0__R)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ( happ(happ(V9__reqb,V10__x),V11__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V7__req,V10__x),V11__y)) ) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__reqb,cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a1(V0__R)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Radd_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3114___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3114___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__4409___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__1173___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__3114___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__4409___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__3114___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3114___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__4409___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__1173___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__3114___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__4409___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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.get_sign_None_th',axiom,
! [V0__C] :
( cType___24t(V0__C)
=> ! [V1__copp] :
( c_24__type__4409___24t(V0__C,V1__copp)
=> ! [V2__ceqb] :
( c_24__type__3122___24t(V0__C,V2__ceqb)
=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V0__C,V1__copp,V2__ceqb,cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a1(V0__C)) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_reqe',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__3114___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__3114___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__4409___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__1173___24t(V0__R,V4__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3114___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__4409___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__3114___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__4409___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__4409___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__9090___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__9090___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__9090___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__9104___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__9111___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__3711___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__3114___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__3114___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__3114___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4409___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1173___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__9090___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__9090___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__9090___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__9104___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__9111___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__3711___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.rpow_pow_N',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__3114___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__1173___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__28657___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__13529___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('R.Ax2',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__r] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> ! [V2__s] :
( cTait_2eTerm_2eterm___24t(V2__s)
=> ( cR_2eA___24a4(V0__rhos,cTait_2eTerm_2eIota,V1__r,V2__s)
=> cR_2eN___24a4(V0__rhos,cTait_2eTerm_2eIota,V1__r,V2__s) ) ) ) ) ).
fof('R.Ax3',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eTerm_2eVar___24a1(V2__k),V1__rho)
=> cR_2eA___24a4(V0__rhos,V1__rho,cTait_2eTerm_2eVar___24a1(V2__k),cTait_2eTerm_2eVar___24a1(V2__k)) ) ) ) ) ).
fof('R.Ax4',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__r_27] :
( cTait_2eTerm_2eterm___24t(V4__r_27)
=> ! [V5__s] :
( cTait_2eTerm_2eterm___24t(V5__s)
=> ! [V6__s_27] :
( cTait_2eTerm_2eterm___24t(V6__s_27)
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,V5__s,V1__rho)
=> ( cR_2eA___24a4(V0__rhos,cTait_2eTerm_2eArrow___24a2(V1__rho,V2__sigma),V3__r,V4__r_27)
=> ( cR_2eN___24a4(V0__rhos,V1__rho,V5__s,V6__s_27)
=> cR_2eA___24a4(V0__rhos,V2__sigma,cTait_2eTerm_2eApp___24a2(V3__r,V5__s),cTait_2eTerm_2eApp___24a2(V4__r_27,V6__s_27)) ) ) ) ) ) ) ) ) ) ) ).
fof('R.Ax5',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__r] :
( cTait_2eTerm_2eterm___24t(V2__r)
=> ! [V3__s] :
( cTait_2eTerm_2eterm___24t(V3__s)
=> ! [V4__t] :
( cTait_2eTerm_2eterm___24t(V4__t)
=> ( cR_2eH___24a4(V0__rhos,V1__rho,V2__r,V3__s)
=> ( cR_2eN___24a4(V0__rhos,V1__rho,V3__s,V4__t)
=> cR_2eN___24a4(V0__rhos,V1__rho,V2__r,V4__t) ) ) ) ) ) ) ) ).
fof('R.Ax7',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__s] :
( cTait_2eTerm_2eterm___24t(V4__s)
=> ! [V5__t] :
( cTait_2eTerm_2eterm___24t(V5__t)
=> ( cR_2eH___24a4(V0__rhos,cTait_2eTerm_2eArrow___24a2(V1__rho,V2__sigma),V3__r,V4__s)
=> cR_2eH___24a4(V0__rhos,V2__sigma,cTait_2eTerm_2eApp___24a2(V3__r,V5__t),cTait_2eTerm_2eApp___24a2(V4__s,V5__t)) ) ) ) ) ) ) ) ).
fof('R.Ax_H_ext_ctx',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__sigmas)
=> ! [V2__rho] :
( cTait_2eTerm_2etype___24t(V2__rho)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__s] :
( cTait_2eTerm_2eterm___24t(V4__s)
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,V3__r,V2__rho)
=> ( cR_2eH___24a4(V0__rhos,V2__rho,V3__r,V4__s)
=> cR_2eH___24a4(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V0__rhos,V1__sigmas),V2__rho,V3__r,V4__s) ) ) ) ) ) ) ) ).
fof('Tait.MoreList.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('Tait.MoreList.app_nth1',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__d] :
( t(V3__d,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,V1__l,V3__d) ) ) ) ) ) ) ).
fof('Tait.MoreList.app_nth2',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__d] :
( t(V3__d,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( p(cCoq_2eInit_2ePeano_2ege___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,cCoq_2eInit_2eNat_2esub___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)),V2__l_27,V3__d) ) ) ) ) ) ) ).
fof('Tait.MoreList.consn_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cTait_2eMoreList_2econsn___24a4(V0__A,V1__n,V2__a,V3__l)) = cCoq_2eInit_2eNat_2eadd___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l)) ) ) ) ) ).
fof('Tait.MoreList.consn_nth1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__k)
=> ! [V5__d] :
( t(V5__d,V0__A)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V4__k,V1__n))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__k,cTait_2eMoreList_2econsn___24a4(V0__A,V1__n,V2__a,V3__l),V5__d) = V2__a ) ) ) ) ) ) ) ).
fof('Tait.MoreList.fold_left_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__13529___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l_27)
=> ! [V5__a] :
( t(V5__a,V0__A)
=> cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,V3__l,V4__l_27),V5__a) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l_27,cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V3__l,V5__a)) ) ) ) ) ) ) ).
fof('Tait.MoreList.map_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__122___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_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27)) = cCoq_2eInit_2eDatatypes_2eapp___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('Tait.MoreList.map_ext',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__122___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__122___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('Tait.MoreList.map_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__122___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('Tait.MoreList.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__122___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__13466___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__14587___24a5(V0__A,V1__B,V2__C,V3__f,V4__g),V5__l) ) ) ) ) ) ) ).
fof('Tait.MoreList.map_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__122___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('Tait.MoreList.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)
=> ( p(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('Tait.MoreList.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)
=> ( p(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('Tait.MoreList.rev_acc_rev',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)
=> cTait_2eMoreList_2erev__acc___24a3(V0__A,V1__l,V2__l_27) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l),V2__l_27) ) ) ) ).
fof('Tait.MoreList.seq_length',axiom,
! [V0__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__len)
=> ! [V1__start] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__start)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2enat,cTait_2eMoreList_2eseq___24a2(V1__start,V0__len)) = V0__len ) ) ).
fof('Tait.MoreList.seq_shift',axiom,
! [V0__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__len)
=> ! [V1__start] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__start)
=> cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eS,cTait_2eMoreList_2eseq___24a2(V1__start,V0__len)) = cTait_2eMoreList_2eseq___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__start),V0__len) ) ) ).
fof('Tait.TaitCore.F_occurs',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__rhos] :
( cTait_2eTyping_2econtext___24t(V1__rhos)
=> ! [V2__rho] :
( cTait_2eTerm_2etype___24t(V2__rho)
=> ! [V3__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__k)
=> ( cTait_2eTaitCore_2eF___24a4(V1__rhos,V2__rho,V0__r,V3__k)
=> cTait_2eTerm_2eoccurs___24a2(V3__k,V0__r) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).
fof('Tait.Term.term_ind',axiom,
! [V0__P] :
( c_24__type__287___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(V0__P,cTait_2eTerm_2eVar___24a1(V1__n))) )
=> ( ! [V2__t] :
( cTait_2eTerm_2eterm___24t(V2__t)
=> ( p(happ(V0__P,V2__t))
=> ! [V4__t] :
( cTait_2eTerm_2eterm___24t(V4__t)
=> ( p(happ(V0__P,V4__t))
=> p(happ(V0__P,cTait_2eTerm_2eApp___24a2(V2__t,V4__t))) ) ) ) )
=> ( ! [V3__t] :
( cTait_2eTerm_2etype___24t(V3__t)
=> ! [V4__t] :
( cTait_2eTerm_2eterm___24t(V4__t)
=> ( p(happ(V0__P,V4__t))
=> p(happ(V0__P,cTait_2eTerm_2eAbs___24a2(V3__t,V4__t))) ) ) )
=> ! [V4__t] :
( cTait_2eTerm_2eterm___24t(V4__t)
=> p(happ(V0__P,V4__t)) ) ) ) ) ) ).
fof('Tait.Term.type_ind',axiom,
! [V0__P] :
( c_24__type__1395___24t(V0__P)
=> ( p(happ(V0__P,cTait_2eTerm_2eIota))
=> ( ! [V2__t] :
( cTait_2eTerm_2etype___24t(V2__t)
=> ( p(happ(V0__P,V2__t))
=> ! [V4__t] :
( cTait_2eTerm_2etype___24t(V4__t)
=> ( p(happ(V0__P,V4__t))
=> p(happ(V0__P,cTait_2eTerm_2eArrow___24a2(V2__t,V4__t))) ) ) ) )
=> ! [V3__t] :
( cTait_2eTerm_2etype___24t(V3__t)
=> p(happ(V0__P,V3__t)) ) ) ) ) ).
fof('Tait.Typing.CorAbs',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__r] :
( cTait_2eTerm_2eterm___24t(V2__r)
=> ( cTait_2eTyping_2eCorTyp___24a2(cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V1__rho,V0__rhos),V2__r)
=> cTait_2eTyping_2eCorTyp___24a2(V0__rhos,cTait_2eTerm_2eAbs___24a2(V1__rho,V2__r)) ) ) ) ) ).
fof('Tait.Typing.CorApp',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__r] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> ! [V2__s] :
( cTait_2eTerm_2eterm___24t(V2__s)
=> ( cTait_2eTyping_2eCorTyp___24a2(V0__rhos,V1__r)
=> ( cTait_2eTyping_2eCorTyp___24a2(V0__rhos,V2__s)
=> ! [V5__sigma] :
( cTait_2eTerm_2etype___24t(V5__sigma)
=> ( cTait_2eTyping_2etyp___24a2(V0__rhos,V1__r) = cTait_2eTerm_2eArrow___24a2(cTait_2eTyping_2etyp___24a2(V0__rhos,V2__s),V5__sigma)
=> cTait_2eTyping_2eCorTyp___24a2(V0__rhos,cTait_2eTerm_2eApp___24a2(V1__r,V2__s)) ) ) ) ) ) ) ) ).
fof('Tait.Typing.CorVar',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V0__rhos)))
=> cTait_2eTyping_2eCorTyp___24a2(V0__rhos,cTait_2eTerm_2eVar___24a1(V1__n)) ) ) ) ).
fof('Tait.Typing.SubRed',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__s] :
( cTait_2eTerm_2eterm___24t(V4__s)
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eTerm_2eApp___24a2(cTait_2eTerm_2eAbs___24a2(V2__sigma,V3__r),V4__s),V1__rho)
=> cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eSubst_2esub___24a2(V3__r,cTait_2eSubst_2esub1___24a1(V4__s)),V1__rho) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_Abs',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__mu] :
( cTait_2eTerm_2etype___24t(V3__mu)
=> ! [V4__r] :
( cTait_2eTerm_2eterm___24t(V4__r)
=> ( V2__sigma = cTait_2eTerm_2eArrow___24a2(V1__rho,V3__mu)
=> ( cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V1__rho,V0__rhos),V4__r,V3__mu)
=> cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eTerm_2eAbs___24a2(V1__rho,V4__r),V2__sigma) ) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_App',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__s] :
( cTait_2eTerm_2eterm___24t(V4__s)
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,V3__r,cTait_2eTerm_2eArrow___24a2(V1__rho,V2__sigma))
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,V4__s,V1__rho)
=> cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eTerm_2eApp___24a2(V3__r,V4__s),V2__sigma) ) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_App_inv1',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__s] :
( cTait_2eTerm_2eterm___24t(V4__s)
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eTerm_2eApp___24a2(V3__r,V4__s),V1__rho)
=> ( V2__sigma = cTait_2eTyping_2etyp___24a2(V0__rhos,V4__s)
=> cTait_2eTyping_2eTypJ___24a3(V0__rhos,V3__r,cTait_2eTerm_2eArrow___24a2(V2__sigma,V1__rho)) ) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_App_inv2',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__s] :
( cTait_2eTerm_2eterm___24t(V4__s)
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eTerm_2eApp___24a2(V3__r,V4__s),V1__rho)
=> ( V2__sigma = cTait_2eTyping_2etyp___24a2(V0__rhos,V4__s)
=> cTait_2eTyping_2eTypJ___24a3(V0__rhos,V4__s,V2__sigma) ) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_ext_ctx',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__rhos] :
( cTait_2eTyping_2econtext___24t(V1__rhos)
=> ! [V2__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V2__sigmas)
=> ! [V3__rho] :
( cTait_2eTerm_2etype___24t(V3__rho)
=> ( cTait_2eTyping_2eTypJ___24a3(V1__rhos,V0__r,V3__rho)
=> cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__rhos,V2__sigmas),V0__r,V3__rho) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_up',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__sigmas)
=> ! [V2__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V2__rhos)
=> ! [V3__rho] :
( cTait_2eTerm_2etype___24t(V3__rho)
=> ! [V4__sigma] :
( cTait_2eTerm_2etype___24t(V4__sigma)
=> ! [V5__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__k)
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V1__sigmas) = V5__k
=> ( cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__sigmas,V2__rhos),V0__r,V3__rho)
=> cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V4__sigma,V2__rhos)),cTait_2eTerm_2eup___24a2(V5__k,V0__r),V3__rho) ) ) ) ) ) ) ) ) ).
fof('Tait.Typing.ext_ctx_TypJ',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__rho] :
( cTait_2eTerm_2etype___24t(V2__rho)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V0__rhos),V1__k))
=> cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V0__rhos,cTait_2eTyping_2eext__ctx___24a3(V0__rhos,V1__k,V2__rho)),cTait_2eTerm_2eVar___24a1(V1__k),V2__rho) ) ) ) ) ).
fof('Tait.Typing.ext_ctx_length',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__rho] :
( cTait_2eTerm_2etype___24t(V2__rho)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V0__rhos),V1__k))
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V0__rhos,cTait_2eTyping_2eext__ctx___24a3(V0__rhos,V1__k,V2__rho))) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__k) ) ) ) ) ).
fof('Tait.nc.ProofIrr_NoHope',axiom,
( ! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) )
<=> cTait_2enc_2enc___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eO) = cTait_2enc_2enc___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ) ).
fof('Tait.nc.ProofRelevance',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( cTait_2enc_2enc___24a2(V0__A,V1__a) = cTait_2enc_2enc___24a2(V0__A,V2__b)
=> V1__a = V2__b ) ) ) ) ).
fof('Tait.nc.nc',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> cTait_2enc_2enc__type___24a1(V0__A) ) ) ).
fof('Tait.nc.nc1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__122___24t(V0__A,V1__B,V2__f)
=> ( cTait_2enc_2enc__type___24a1(V0__A)
=> cTait_2enc_2enc__type___24a1(V1__B) ) ) ) ) ).
fof('Tait.nc.nc2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__131___24t(V0__A,V1__B,V2__C,V3__f)
=> ( cTait_2enc_2enc__type___24a1(V0__A)
=> ( cTait_2enc_2enc__type___24a1(V1__B)
=> cTait_2enc_2enc__type___24a1(V2__C) ) ) ) ) ) ) ).
fof('Tait.nc.nc3',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__D] :
( cType___24t(V3__D)
=> ! [V4__f] :
( c_24__type__148___24t(V0__A,V1__B,V2__C,V3__D,V4__f)
=> ( cTait_2enc_2enc__type___24a1(V0__A)
=> ( cTait_2enc_2enc__type___24a1(V1__B)
=> ( cTait_2enc_2enc__type___24a1(V2__C)
=> cTait_2enc_2enc__type___24a1(V3__D) ) ) ) ) ) ) ) ) ).
fof('Tait.nc.nc_ex',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( cTait_2enc_2enc__type___24a1(V0__A)
=> ? [V2__r] :
( t(V2__r,V0__A)
& c_24Proof = cTait_2enc_2enc___24a2(V0__A,V2__r) ) ) ) ).
fof('Tait.nc.nc_type_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( cProp___24t(V1__P)
=> ( ! [V2___24Anonymous] :
( t(V2___24Anonymous,V0__A)
=> p(V1__P) )
=> ( cTait_2enc_2enc__type___24a1(V0__A)
=> p(V1__P) ) ) ) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.xfold_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfold,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfold___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_12613_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__12613,V_24X1),V_24X2),V_24X3) = c_24__prop__12613___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.seq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2eseq,V_24X1),V_24X2) = cCoq_2eLists_2eList_2eseq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.Ndigits.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eNdigits_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eNdigits_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pequiv_$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('$adef_Coq.Init.Datatypes.BoolSpec_$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('$adef_Coq.Lists.List.repeat_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2erepeat,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2erepeat___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.Vector.to_list_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVector_2eto__list,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVector_2eto__list___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.rev_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev___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('$adef_Coq.setoid_ring.Ring_polynom.mk_monpol_list_$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(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEequiv_$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('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.nc.nc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2enc_2enc,V_24X1),V_24X2) = cTait_2enc_2enc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Tait.MoreList.consn_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTait_2eMoreList_2econsn,V_24X1),V_24X2),V_24X3),V_24X4) = cTait_2eMoreList_2econsn___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.get_sign_None_$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('$adef_Coq.Lists.List.count_occ_$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('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.Cj_$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('$adef_Coq.Relations.Relation_Operators.clos_refl_$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('$adef_Coq.setoid_ring.Ring_polynom.Pc_$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('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.Sorting.Sorted.LocallySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eLocallySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.inclA_$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('$adef_Coq.setoid_ring.BinList.nth_$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('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).
fof('$adef_Tait.MoreList.firstn_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTait_2eMoreList_2efirstn,V_24X1),V_24X2),V_24X3) = cTait_2eMoreList_2efirstn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Tait.MoreList.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTait_2eMoreList_2elast,V_24X1),V_24X2),V_24X3) = cTait_2eMoreList_2elast___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('$adef_$_prop_45953_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__45953,V_24X1),V_24X2),V_24X3) = c_24__prop__45953___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rec,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.collect_annot_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2ecollect__annot,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.Tauto.eval_f_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__f,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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.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_$_lam_43230_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__43230,V_24X1),V_24X2),V_24X3) = c_24__lam__43230___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_6_p_24283_24285_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__24283__24285,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__24283__24285___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_lam_43214_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__43214,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__43214___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$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('$adef_Coq.Init.Specif.sumbool_$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('$adef_$_lam_13789_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__13789,V_24X1),V_24X2),V_24X3) = c_24__lam__13789___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_510_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__510,V_24X1),V_24X2) = c_24__prop__510___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Term.up_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2eup,V_24X1) = cTait_2eTerm_2eup___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).
fof('$adef_Tait.MoreList.rev_acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTait_2eMoreList_2erev__acc,V_24X1),V_24X2),V_24X3) = cTait_2eMoreList_2erev__acc___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Tait.nc.ncP_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTait_2enc_2encP,V_24X1),V_24X2))
<=> cTait_2enc_2encP___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.Init.Specif.proj1_sig_$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('$adef_Coq.Init.Nat.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_35064_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__35064__1__add__carry,V_24X1),V_24X2) = c_24__fix__35064__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_600_$a1',axiom,
! [V_24X1] : happ(c_24__prop__600,V_24X1) = c_24__prop__600___24a1(V_24X1) ).
fof('$adef_$_lam_20498_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__20498,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__20498___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Lists.List.hd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2ehd,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2ehd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.cardinal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V_24X1) ).
fof('$adef_$_lam_43230_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__43230,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__43230___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.setoid_ring.Ring_polynom.Pphi_$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('$adef_$_fix_33859_v_CANONICAL_2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__fix__33859__v__CANONICAL__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__fix__33859__v__CANONICAL__2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_Coq.Structures.OrderedType.LT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_prop_509_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__509,V_24X1),V_24X2) = c_24__prop__509___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.rev_append_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$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('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_45952_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__45952,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__45952___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).
fof('$adef_$_prop_684_$a1',axiom,
! [V_24X1] : happ(c_24__prop__684,V_24X1) = c_24__prop__684___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Specif.sumbool$12598_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eSpecif_2esumbool_2412598,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_2412598___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$15446_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2415446,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2415446___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Tait.Term.Abs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2eAbs,V_24X1),V_24X2) = cTait_2eTerm_2eAbs___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_43222_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__43222,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__43222___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.BFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eTauto_2eBFormula,V_24X1) = cCoq_2emicromega_2eTauto_2eBFormula___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.or_clause_cnf_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eor__clause__cnf,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eor__clause__cnf___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.split_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esplit,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Tauto.and_cnf_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eand__cnf,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eand__cnf___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEadd_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEadd,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.Tauto.eval_cnf_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__cnf,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.micromega.Tauto.cnf_ff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf__ff,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf__ff___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.TFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_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_$_case_Coq.Init.Datatypes.nat$37872_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2437872,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2437872___24a1(V_24X1) ).
fof('$adef_Tait.nc.nc2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cTait_2enc_2enc2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cTait_2enc_2enc2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$28377_$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_2428377,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_2428377___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.elements_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkPinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkPinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$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('$adef_$_prop_694_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__694,V_24X1),V_24X2) = c_24__prop__694___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_14587_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__14587,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__14587___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.display_pow_linear_$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('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_17_mkopp_pow_23562_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__23562,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__23562___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$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.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.setoid_ring.Field_theory.Fcons2_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.micromega.RingMicromega.cltb_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecltb,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2ecltb___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_Coq.Strings.String.append_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eappend,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eappend___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.nc.nc2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTait_2enc_2enc2,V_24X1),V_24X2),V_24X3),V_24X4) = cTait_2enc_2enc2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring.bool_eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing_2ebool__eq,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.equivlistA_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eSetoidList_2eequivlistA,V_24X1),V_24X2) = cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V_24X1,V_24X2) ).
fof('$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.Reals.Rdefinitions.Rdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRdiv,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_lam_395_$a1',axiom,
! [V_24X1] : happ(c_24__lam__395,V_24X1) = c_24__lam__395___24a1(V_24X1) ).
fof('$adef_$_lam_20498_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__20498,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__20498___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Tait.Subst.mk_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst_2emk__sub,V_24X1),V_24X2) = cTait_2eSubst_2emk__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_12612_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__12612,V_24X1),V_24X2),V_24X3) = c_24__prop__12612___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$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('$adef_$_let_var_v_CANONICAL_4_683_687_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__var__v__CANONICAL__4__683__687,V_24X1),V_24X2),V_24X3) = c_24__let__var__v__CANONICAL__4__683__687___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Term.Var_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2eVar,V_24X1) = cTait_2eTerm_2eVar___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.list_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rec,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_681_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__681,V_24X1),V_24X2),V_24X3) = c_24__lam__681___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.cnf_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.Morphism_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eMorphism,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.PEsimp_$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_2eField__theory_2ePEsimp,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eField__theory_2ePEsimp___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons1_$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_2eField__theory_2eFcons1,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_2eField__theory_2eFcons1___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_lam_43238_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__43238,V_24X1),V_24X2),V_24X3) = c_24__lam__43238___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_case_Coq.Numbers.BinNums.Z$37867_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2437867,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2437867___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('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).
fof('$adef_$_lam_12554_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__12554,V_24X1),V_24X2) = c_24__lam__12554___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Term.lift_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTait_2eTerm_2elift,V_24X1),V_24X2),V_24X3) = cTait_2eTerm_2elift___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Term.type_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTait_2eTerm_2etype__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cTait_2eTerm_2etype__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a1(V_24X1) ).
fof('$adef_Tait.nc.ncP2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTait_2enc_2encP2,V_24X1),V_24X2),V_24X3))
<=> cTait_2enc_2encP2___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).
fof('$adef_$_prop_45956_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__45956,V_24X1),V_24X2),V_24X3) = c_24__prop__45956___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_511_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__511,V_24X1),V_24X2) = c_24__prop__511___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).
fof('$adef_$_prop_45954_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__45954,V_24X1),V_24X2),V_24X3) = c_24__prop__45954___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$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('$adef_Coq.Lists.List.combine_$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('$adef_Coq.Arith.Even.odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
<=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).
fof('$adef_Coq.Lists.List.ForallOrdPairs_$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('$adef_Coq.FSets.FSetPositive.PositiveSet.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_fix_15491_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__15491__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__15491__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_13460_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__13460,V_24X1),V_24X2) = c_24__lam__13460___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_13480_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__13480,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__13480___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_Tait.Term.App_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2eApp,V_24X1),V_24X2) = cTait_2eTerm_2eApp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRminus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_prop_688_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__688,V_24X1),V_24X2) = c_24__prop__688___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Init.Logic.eq_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eeq__refl,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_398_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__398,V_24X1),V_24X2),V_24X3) = c_24__lam__398___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.List.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_$_lam_14587_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__14587,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__14587___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRplus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Add_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eList_2eAdd,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eList_2eAdd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.rev_$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('$adef_Coq.setoid_ring.Field_theory.FEadd_$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('$adef_Tait.Term.term_rec_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2eterm__rec,V_24X1) = cTait_2eTerm_2eterm__rec___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_$_prop_35583_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35583,V_24X1),V_24X2) = c_24__prop__35583___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.cons_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2econs___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$a13',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).
fof('$adef_Coq.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.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_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_$_prop_45958_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__45958,V_24X1),V_24X2) = c_24__prop__45958___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_case_Coq.Numbers.BinNums.positive$46022_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2446022,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2446022___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_18_mkmult_pow_23563_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__23563,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__23563___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Strings.String.list_ascii_of_string_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eString_2elist__ascii__of__string,V_24X1) = cCoq_2eStrings_2eString_2elist__ascii__of__string___24a1(V_24X1) ).
fof('$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.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_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Operators.Ltl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eLtl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.EnvRing.Psub_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePsub,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eEnvRing_2ePsub___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Classes.RelationClasses.Symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eSymmetric,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.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_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_Tait.Typing.CorTyp_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTait_2eTyping_2eCorTyp,V_24X1),V_24X2))
<=> cTait_2eTyping_2eCorTyp___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRinv,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V_24X1) ).
fof('$adef_$_lam_395_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__395,V_24X1),V_24X2) = c_24__lam__395___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Subst.sub1_$a1',axiom,
! [V_24X1] : happ(cTait_2eSubst_2esub1,V_24X1) = cTait_2eSubst_2esub1___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.QArith.QArith_base.Qdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQdiv,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$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('$adef_Tait.Subst.sublift_$a1',axiom,
! [V_24X1] : happ(cTait_2eSubst_2esublift,V_24X1) = cTait_2eSubst_2esublift___24a1(V_24X1) ).
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('$adef_Tait.Term.arrow_left_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2earrow__left,V_24X1) = cTait_2eTerm_2earrow__left___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.eq_dec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.QArith.QArith_base.Qeq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$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('$adef_Coq.Init.Specif.sumbool_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$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('$adef_Tait.MoreList.seq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eMoreList_2eseq,V_24X1),V_24X2) = cTait_2eMoreList_2eseq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Init.Datatypes.sum_$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('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_aux_$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('$adef_Coq.setoid_ring.InitialRing.triv_div_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2etriv__div,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_common_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__common,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_398_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__398,V_24X1),V_24X2) = c_24__lam__398___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_593_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__593,V_24X1),V_24X2) = c_24__prop__593___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Empty_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty,V_24X1))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V_24X1) ) ).
fof('$adef_$_prop_12434_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__12434,V_24X1),V_24X2),V_24X3) = c_24__prop__12434___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_R.A_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cR_2eA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cR_2eA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_12433_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__12433,V_24X1),V_24X2),V_24X3) = c_24__prop__12433___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.eval_clause_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__clause,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eeval__clause___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Even.even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
<=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.QArith.QArith_base.Qeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq__bool,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmult,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmult___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('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.CompLtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompLtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_prop_45957_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__45957,V_24X1),V_24X2),V_24X3) = c_24__prop__45957___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.psub_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2epsub,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2epsub___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_let_20_lnum_10097_$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__10097,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),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__10097___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('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
<=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$35204_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2435204,V_24X1),V_24X2))
<=> c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2435204___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('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.list_prod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2elist__prod,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2elist__prod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_prop_1153_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1153,V_24X1),V_24X2) = c_24__prop__1153___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_588_$a1',axiom,
! [V_24X1] : happ(c_24__lam__588,V_24X1) = c_24__lam__588___24a1(V_24X1) ).
fof('$adef_$_lam_43222_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__43222,V_24X1),V_24X2),V_24X3) = c_24__lam__43222___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.Desc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eDesc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Tait.Term.type_rec_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2etype__rec,V_24X1) = cTait_2eTerm_2etype__rec___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.xelements_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_Tait.Subst.shift_$a1',axiom,
! [V_24X1] : happ(cTait_2eSubst_2eshift,V_24X1) = cTait_2eSubst_2eshift___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).
fof('$adef_Coq.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_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.Tauto.eval_tt_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__tt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.micromega.ZMicromega.valid_cut_sign_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2evalid__cut__sign,V_24X1) = cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V_24X1) ).
fof('$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_R.N_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cR_2eN,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cR_2eN___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_case_Coq.setoid_ring.Ring_polynom.Pol$10401_$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_2410401,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),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_2410401___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('$adef_$_lam_12558_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__12558,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__12558___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_13480_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__13480,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__13480___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Tait.Subst2.Joachimski.Dot_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2eDot,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2eDot___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.nc.nc_type_$a1',axiom,
! [V_24X1] :
( p(happ(cTait_2enc_2enc__type,V_24X1))
<=> cTait_2enc_2enc__type___24a1(V_24X1) ) ).
fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Compare_dec.le_lt_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eCompare__dec_2ele__lt__dec,V_24X1),V_24X2) = cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Term.term_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cTait_2eTerm_2eterm__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cTait_2eTerm_2eterm__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_fix_46038_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__46038__v__CANONICAL__0,V_24X1) = c_24__fix__46038__v__CANONICAL__0___24a1(V_24X1) ).
fof('$adef_$_lam_13460_$a1',axiom,
! [V_24X1] : happ(c_24__lam__13460,V_24X1) = c_24__lam__13460___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zlogarithm.Is_power_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZlogarithm_2eIs__power,V_24X1))
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V_24X1) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$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('$adef_Tait.Typing.TypJ_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTait_2eTyping_2eTypJ,V_24X1),V_24X2),V_24X3))
<=> cTait_2eTyping_2eTypJ___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('$adef_Tait.Subst2.above_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTait_2eSubst2_2eabove,V_24X1),V_24X2))
<=> cTait_2eSubst2_2eabove___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('$adef_Coq.micromega.RingMicromega.ge_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ege__bool,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQminus,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Typing.ext_ctx_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTait_2eTyping_2eext__ctx,V_24X1),V_24X2),V_24X3) = cTait_2eTyping_2eext__ctx___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_601_$a1',axiom,
! [V_24X1] : happ(c_24__prop__601,V_24X1) = c_24__prop__601___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).
fof('$adef_$_cast_13804_$a1',axiom,
! [V_24X1] : happ(c_24__cast__13804,V_24X1) = c_24__cast__13804___24a1(V_24X1) ).
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('$adef_Coq.setoid_ring.Ring_polynom.PX_$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('$adef_$_lam_43214_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__43214,V_24X1),V_24X2),V_24X3) = c_24__lam__43214___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_592_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__592,V_24X1),V_24X2) = c_24__prop__592___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_16_mkpow_23561_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__23561,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__23561___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEopp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEopp,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_Coq.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_Coq.ZArith.BinIntDef.Z.gtb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2egtb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_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_Coq.setoid_ring.Ring_theory.get_sign_None_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEsub_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEsub,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.eqlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.cneqb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecneqb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Specif.exist2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.map_option2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.String.String_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.split_aux_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esplit__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eField__theory_2esplit__aux___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.micromega.RingMicromega.extract_hyps_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eextract__hyps,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eextract__hyps___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.app_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1) = cCoq_2eInit_2eDatatypes_2eapp___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_$_let_var_6_p_24281_24284_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__24281__24284,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__24281__24284___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Tait.MoreList.removelast_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eMoreList_2eremovelast,V_24X1),V_24X2) = cTait_2eMoreList_2eremovelast___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sumbool_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.list_rect_$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('$adef_$_case_Coq.Init.Datatypes.nat$37850_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2437850,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2437850___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_12558_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__12558,V_24X1),V_24X2),V_24X3) = c_24__lam__12558___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Term.occurs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2eoccurs,V_24X1),V_24X2) = cTait_2eTerm_2eoccurs___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_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_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.String.string_of_list_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eString_2estring__of__list__ascii,V_24X1) = cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.nhyps_of_psatz_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Subst2.Joachimski.PushList_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2ePushList,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2ePushList___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.get_signZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ,V_24X1) = cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V_24X1) ).
fof('$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_Coq.micromega.RingMicromega.eval_op1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiNword_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$15359_$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_2415359,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2415359___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$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('$adef_Tait.MoreList.existsb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTait_2eMoreList_2eexistsb,V_24X1),V_24X2),V_24X3) = cTait_2eMoreList_2eexistsb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.Wf_nat.ltof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2eltof,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eArith_2eWf__nat_2eltof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_let_18_mkmult_pow_23563_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__23563,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__23563___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_prop_46129_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__46129,V_24X1),V_24X2) = c_24__prop__46129___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sorting.Sorted.Sorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eSorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
fof('$adef_Tait.Typing.typ_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTyping_2etyp,V_24X1),V_24X2) = cTait_2eTyping_2etyp___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('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.InA_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2) = cCoq_2eLists_2eSetoidList_2eInA___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.O_S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2ePeano_2eO__S,V_24X1) = cCoq_2eInit_2ePeano_2eO__S___24a1(V_24X1) ).
fof('$adef_$_prop_693_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__693,V_24X1),V_24X2) = c_24__prop__693___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rpow_def.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRpow__def_2epow,V_24X1),V_24X2) = cCoq_2eReals_2eRpow__def_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Subst2.Joachimski.sub\'_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2esub_27,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2esub_27___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_var_var_7_n_12567_12571_12580_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__var__7__n__12567__12571__12580,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__var__7__n__12567__12571__12580___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Tait.Term.term_rect_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2eterm__rect,V_24X1) = cTait_2eTerm_2eterm__rect___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.Computational_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eComputational,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$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('$adef_Tait.Term.type_rect_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2etype__rect,V_24X1) = cTait_2eTerm_2etype__rect___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.cnf_tt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf__tt,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_12611_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__12611,V_24X1),V_24X2),V_24X3) = c_24__prop__12611___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_R.H_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cR_2eH,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cR_2eH___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_rec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Tait.Term.Arrow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2eArrow,V_24X1),V_24X2) = cTait_2eTerm_2eArrow___24a2(V_24X1,V_24X2) ).
fof('$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_$_prop_689_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__689,V_24X1),V_24X2) = c_24__prop__689___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.subrelation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eRelationClasses_2esubrelation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eRelationClasses_2esubrelation___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Tait.Subst2.Joachimski.Up_$a1',axiom,
! [V_24X1] : happ(cTait_2eSubst2_2eJoachimski_2eUp,V_24X1) = cTait_2eSubst2_2eJoachimski_2eUp___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.eqlistA_$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('$adef_Coq.ZArith.BinInt.Z.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2edivide,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_11_subst_l_20426_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__11__subst__l__20426,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__11__subst__l__20426___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$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.QArith.QArith_base.Qinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQinv,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Compare_dec.le_gt_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eCompare__dec_2ele__gt__dec,V_24X1),V_24X2) = cCoq_2eArith_2eCompare__dec_2ele__gt__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_Coq.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_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Term.up_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2eup,V_24X1),V_24X2) = cTait_2eTerm_2eup___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_13789_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__13789,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__13789___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Tait.Subst2.Joachimski.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2esub,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQplus,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQplus___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.TaitCore.F_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cTait_2eTaitCore_2eF,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cTait_2eTaitCore_2eF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_16_mkpow_23561_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__let__16__mkpow__23561,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__23561___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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_$_prop_45955_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__45955,V_24X1),V_24X2),V_24X3) = c_24__prop__45955___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mon_of_pol_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.or_cnf_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eor__cnf,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eor__cnf___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.eq_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec,V_24X1),V_24X2) = cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPos.Pos.PeanoView_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView,V_24X1) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.ZArith.Znat.neq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnat_2eneq,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnat_2eneq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiN_$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('$adef_Coq.Lists.SetoidList.equivlistA_$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('$adef_Coq.Init.Specif.existT2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$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('$adef_Coq.Lists.List.filter_$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('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_$_prop_685_$a1',axiom,
! [V_24X1] : happ(c_24__prop__685,V_24X1) = c_24__prop__685___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.left_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
<=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).
fof('$adef_$_let_17_mkopp_pow_23562_$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__23562,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__23562___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.Lists.List.fold_right_$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('$adef_Coq.setoid_ring.InitialRing.Nw_is0_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eInitialRing_2eNw__is0,V_24X1) = cCoq_2esetoid__ring_2eInitialRing_2eNw__is0___24a1(V_24X1) ).
fof('$adef_Tait.Subst.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst_2esub,V_24X1),V_24X2) = cTait_2eSubst_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_12554_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__12554,V_24X1),V_24X2),V_24X3) = c_24__lam__12554___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
<=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Tait.Subst2.Joachimski.sublift_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2esublift,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2esublift___24a2(V_24X1,V_24X2) ).
fof('$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_Tait.Subst.support_$a1',axiom,
! [V_24X1] : happ(cTait_2eSubst_2esupport,V_24X1) = cTait_2eSubst_2esupport___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_12610_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__12610,V_24X1),V_24X2),V_24X3) = c_24__prop__12610___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Tait.Term.arrow_right_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2earrow__right,V_24X1) = cTait_2eTerm_2earrow__right___24a1(V_24X1) ).
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('$adef_Coq.micromega.RingMicromega.map_option_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2emap__option___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('$adef_Coq.FSets.FSetPositive.PositiveSet.fold_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.sig2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.right_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eright___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.denum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2edenum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Tait.Term.down_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2edown,V_24X1),V_24X2) = cTait_2eTerm_2edown___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.incl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(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('$adef_$_prop_508_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__508,V_24X1),V_24X2) = c_24__prop__508___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_596_$a1',axiom,
! [V_24X1] : happ(c_24__lam__596,V_24X1) = c_24__lam__596___24a1(V_24X1) ).
fof('$adef_$_lam_43238_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__43238,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__43238___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQopp,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQopp___24a1(V_24X1) ).
fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ).
fof('$tdef_$_type_10424',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__10424___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__10424___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_35019',axiom,
! [V_24Y] :
( c_24__type__35019___24t(V_24Y)
<=> t(V_24Y,c_24__type__35019) ) ).
fof('$tdef_$_type_21169',axiom,
! [V_24Y] :
( c_24__type__21169___24t(V_24Y)
<=> t(V_24Y,c_24__type__21169) ) ).
fof('$tdef_$_type_33402',axiom,
! [V_24Y] :
( c_24__type__33402___24t(V_24Y)
<=> t(V_24Y,c_24__type__33402) ) ).
fof('$tdef_$_type_714',axiom,
! [V_24Y] :
( c_24__type__714___24t(V_24Y)
<=> t(V_24Y,c_24__type__714) ) ).
fof('$tdef_$_type_26555',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__26555___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__26555___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_35015',axiom,
! [V_24Y] :
( c_24__type__35015___24t(V_24Y)
<=> t(V_24Y,c_24__type__35015) ) ).
fof('$tdef_$_type_33873',axiom,
! [V_24Y] :
( c_24__type__33873___24t(V_24Y)
<=> t(V_24Y,c_24__type__33873) ) ).
fof('$tdef_$_type_27602',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__27602___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__27602___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_15896',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__15896___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__15896___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_841',axiom,
! [V_24Y] :
( c_24__type__841___24t(V_24Y)
<=> t(V_24Y,c_24__type__841) ) ).
fof('$tdef_$_type_535',axiom,
! [V_24Y] :
( c_24__type__535___24t(V_24Y)
<=> t(V_24Y,c_24__type__535) ) ).
fof('$tdef_Coq.Init.Specif.sigT2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_45567',axiom,
! [V_24Y] :
( c_24__type__45567___24t(V_24Y)
<=> t(V_24Y,c_24__type__45567) ) ).
fof('$tdef_$_type_277',axiom,
! [V_24Y] :
( c_24__type__277___24t(V_24Y)
<=> t(V_24Y,c_24__type__277) ) ).
fof('$tdef_$_type_2612',axiom,
! [V_24Y] :
( c_24__type__2612___24t(V_24Y)
<=> t(V_24Y,c_24__type__2612) ) ).
fof('$tdef_Tait.Term.term',axiom,
! [V_24Y] :
( cTait_2eTerm_2eterm___24t(V_24Y)
<=> t(V_24Y,cTait_2eTerm_2eterm) ) ).
fof('$tdef_$_type_18854',axiom,
! [V_24Y] :
( c_24__type__18854___24t(V_24Y)
<=> t(V_24Y,c_24__type__18854) ) ).
fof('$tdef_$_type_44033',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__44033___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__44033___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_265',axiom,
! [V_24Y] :
( c_24__type__265___24t(V_24Y)
<=> t(V_24Y,c_24__type__265) ) ).
fof('$tdef_$_type_2307',axiom,
! [V_24Y] :
( c_24__type__2307___24t(V_24Y)
<=> t(V_24Y,c_24__type__2307) ) ).
fof('$tdef_$_type_26147',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__26147___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__26147___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_2862',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2862___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2862___24a1(V_24X1)) ) ).
fof('$tdef_$_type_37232',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__37232___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__37232___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_13757',axiom,
! [V_24Y] :
( c_24__type__13757___24t(V_24Y)
<=> t(V_24Y,c_24__type__13757) ) ).
fof('$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_24750',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__24750___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__24750___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_891',axiom,
! [V_24X1,V_24Y] :
( c_24__type__891___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__891___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1342',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1342___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1342___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_468',axiom,
! [V_24Y] :
( c_24__type__468___24t(V_24Y)
<=> t(V_24Y,c_24__type__468) ) ).
fof('$tdef_$_cast_35428',axiom,
! [V_24Y] :
( c_24__cast__35428___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35428) ) ).
fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
fof('$tdef_$_type_751',axiom,
! [V_24Y] :
( c_24__type__751___24t(V_24Y)
<=> t(V_24Y,c_24__type__751) ) ).
fof('$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('$tdef_$_cast_35432',axiom,
! [V_24Y] :
( c_24__cast__35432___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35432) ) ).
fof('$tdef_$_type_13565',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__13565___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__13565___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1173',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1173___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1173___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13912',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__13912___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__13912___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_45962',axiom,
! [V_24Y] :
( c_24__type__45962___24t(V_24Y)
<=> t(V_24Y,c_24__type__45962) ) ).
fof('$tdef_$_type_872',axiom,
! [V_24Y] :
( c_24__type__872___24t(V_24Y)
<=> t(V_24Y,c_24__type__872) ) ).
fof('$tdef_$_type_19509',axiom,
! [V_24Y] :
( c_24__type__19509___24t(V_24Y)
<=> t(V_24Y,c_24__type__19509) ) ).
fof('$tdef_$_type_1345',axiom,
! [V_24Y] :
( c_24__type__1345___24t(V_24Y)
<=> t(V_24Y,c_24__type__1345) ) ).
fof('$tdef_$_type_14953',axiom,
! [V_24Y] :
( c_24__type__14953___24t(V_24Y)
<=> t(V_24Y,c_24__type__14953) ) ).
fof('$tdef_$_type_35614',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__35614___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__35614___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_34129',axiom,
! [V_24Y] :
( c_24__type__34129___24t(V_24Y)
<=> t(V_24Y,c_24__type__34129) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ) ).
fof('$tdef_$_type_14145',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14145___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14145___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_45091',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__45091___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__45091___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_12623',axiom,
! [V_24Y] :
( c_24__type__12623___24t(V_24Y)
<=> t(V_24Y,c_24__type__12623) ) ).
fof('$tdef_$_type_4970',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__4970___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__4970___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_$_type_46121',axiom,
! [V_24Y] :
( c_24__type__46121___24t(V_24Y)
<=> t(V_24Y,c_24__type__46121) ) ).
fof('$tdef_$_type_35531',axiom,
! [V_24Y] :
( c_24__type__35531___24t(V_24Y)
<=> t(V_24Y,c_24__type__35531) ) ).
fof('$tdef_$_type_45925',axiom,
! [V_24Y] :
( c_24__type__45925___24t(V_24Y)
<=> t(V_24Y,c_24__type__45925) ) ).
fof('$tdef_$_type_1350',axiom,
! [V_24Y] :
( c_24__type__1350___24t(V_24Y)
<=> t(V_24Y,c_24__type__1350) ) ).
fof('$tdef_$_type_29070',axiom,
! [V_24X1,V_24Y] :
( c_24__type__29070___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__29070___24a1(V_24X1)) ) ).
fof('$tdef_$_cast_35442',axiom,
! [V_24Y] :
( c_24__cast__35442___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35442) ) ).
fof('$tdef_$_type_15887',axiom,
! [V_24Y] :
( c_24__type__15887___24t(V_24Y)
<=> t(V_24Y,c_24__type__15887) ) ).
fof('$tdef_$_type_40154',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__40154___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__40154___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.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('$tdef_$_type_44591',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__44591___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__44591___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_Coq.Init.Specif.sig2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_11290',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11290___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11290___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35653',axiom,
! [V_24Y] :
( c_24__type__35653___24t(V_24Y)
<=> t(V_24Y,c_24__type__35653) ) ).
fof('$tdef_$_type_1469',axiom,
! [V_24Y] :
( c_24__type__1469___24t(V_24Y)
<=> t(V_24Y,c_24__type__1469) ) ).
fof('$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_14671',axiom,
! [V_24Y] :
( c_24__type__14671___24t(V_24Y)
<=> t(V_24Y,c_24__type__14671) ) ).
fof('$tdef_$_type_1494',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1494___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1494___24a1(V_24X1)) ) ).
fof('$tdef_$_type_43916',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__43916___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__43916___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_8661',axiom,
! [V_24Y] :
( c_24__type__8661___24t(V_24Y)
<=> t(V_24Y,c_24__type__8661) ) ).
fof('$tdef_$_type_461',axiom,
! [V_24Y] :
( c_24__type__461___24t(V_24Y)
<=> t(V_24Y,c_24__type__461) ) ).
fof('$tdef_$_type_43301',axiom,
! [V_24Y] :
( c_24__type__43301___24t(V_24Y)
<=> t(V_24Y,c_24__type__43301) ) ).
fof('$tdef_$_type_1247',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__1247___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__1247___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_45727',axiom,
! [V_24Y] :
( c_24__type__45727___24t(V_24Y)
<=> t(V_24Y,c_24__type__45727) ) ).
fof('$tdef_$_type_29162',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__29162___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__29162___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_44315',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__44315___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__44315___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_14900',axiom,
! [V_24Y] :
( c_24__type__14900___24t(V_24Y)
<=> t(V_24Y,c_24__type__14900) ) ).
fof('$tdef_$_type_27194',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__27194___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__27194___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_786',axiom,
! [V_24Y] :
( c_24__type__786___24t(V_24Y)
<=> t(V_24Y,c_24__type__786) ) ).
fof('$tdef_$_type_27958',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__27958___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__27958___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
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_$_type_122',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__122___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__122___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35181',axiom,
! [V_24Y] :
( c_24__type__35181___24t(V_24Y)
<=> t(V_24Y,c_24__type__35181) ) ).
fof('$tdef_$_type_1151',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1151___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1151___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_466',axiom,
! [V_24Y] :
( c_24__type__466___24t(V_24Y)
<=> t(V_24Y,c_24__type__466) ) ).
fof('$tdef_$_type_388',axiom,
! [V_24Y] :
( c_24__type__388___24t(V_24Y)
<=> t(V_24Y,c_24__type__388) ) ).
fof('$tdef_$_type_37818',axiom,
! [V_24Y] :
( c_24__type__37818___24t(V_24Y)
<=> t(V_24Y,c_24__type__37818) ) ).
fof('$tdef_$_type_28889',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__28889___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__28889___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_2601',axiom,
! [V_24Y] :
( c_24__type__2601___24t(V_24Y)
<=> t(V_24Y,c_24__type__2601) ) ).
fof('$tdef_$_type_4877',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__4877___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__4877___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Tait.Subst.substitution',axiom,
! [V_24Y] :
( cTait_2eSubst_2esubstitution___24t(V_24Y)
<=> t(V_24Y,cTait_2eSubst_2esubstitution) ) ).
fof('$tdef_$_type_14067',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14067___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14067___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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('$tdef_$_cast_35446',axiom,
! [V_24Y] :
( c_24__cast__35446___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35446) ) ).
fof('$tdef_$_type_46084',axiom,
! [V_24Y] :
( c_24__type__46084___24t(V_24Y)
<=> t(V_24Y,c_24__type__46084) ) ).
fof('$tdef_$_type_40500',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__40500___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__40500___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_46055',axiom,
! [V_24Y] :
( c_24__type__46055___24t(V_24Y)
<=> t(V_24Y,c_24__type__46055) ) ).
fof('$tdef_$_type_44841',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__44841___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__44841___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_9111',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__9111___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__9111___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12069',axiom,
! [V_24Y] :
( c_24__type__12069___24t(V_24Y)
<=> t(V_24Y,c_24__type__12069) ) ).
fof('$tdef_Coq.Strings.Ascii.ascii',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).
fof('$tdef_$_type_8681',axiom,
! [V_24Y] :
( c_24__type__8681___24t(V_24Y)
<=> t(V_24Y,c_24__type__8681) ) ).
fof('$tdef_$_type_33901',axiom,
! [V_24Y] :
( c_24__type__33901___24t(V_24Y)
<=> t(V_24Y,c_24__type__33901) ) ).
fof('$tdef_$_type_33884',axiom,
! [V_24Y] :
( c_24__type__33884___24t(V_24Y)
<=> t(V_24Y,c_24__type__33884) ) ).
fof('$tdef_$_type_7196',axiom,
! [V_24Y] :
( c_24__type__7196___24t(V_24Y)
<=> t(V_24Y,c_24__type__7196) ) ).
fof('$tdef_$_type_5645',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__5645___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__5645___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_25076',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__25076___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__25076___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_270',axiom,
! [V_24Y] :
( c_24__type__270___24t(V_24Y)
<=> t(V_24Y,c_24__type__270) ) ).
fof('$tdef_$_type_35094',axiom,
! [V_24Y] :
( c_24__type__35094___24t(V_24Y)
<=> t(V_24Y,c_24__type__35094) ) ).
fof('$tdef_$_type_14677',axiom,
! [V_24Y] :
( c_24__type__14677___24t(V_24Y)
<=> t(V_24Y,c_24__type__14677) ) ).
fof('$tdef_$_type_1292',axiom,
! [V_24Y] :
( c_24__type__1292___24t(V_24Y)
<=> t(V_24Y,c_24__type__1292) ) ).
fof('$tdef_$_type_37041',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__37041___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__37041___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_223',axiom,
! [V_24Y] :
( c_24__type__223___24t(V_24Y)
<=> t(V_24Y,c_24__type__223) ) ).
fof('$tdef_$_type_35656',axiom,
! [V_24Y] :
( c_24__type__35656___24t(V_24Y)
<=> t(V_24Y,c_24__type__35656) ) ).
fof('$tdef_$_type_19512',axiom,
! [V_24Y] :
( c_24__type__19512___24t(V_24Y)
<=> t(V_24Y,c_24__type__19512) ) ).
fof('$tdef_$_type_38447',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__38447___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__38447___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_16681',axiom,
! [V_24Y] :
( c_24__type__16681___24t(V_24Y)
<=> t(V_24Y,c_24__type__16681) ) ).
fof('$tdef_$_type_10760',axiom,
! [V_24Y] :
( c_24__type__10760___24t(V_24Y)
<=> t(V_24Y,c_24__type__10760) ) ).
fof('$tdef_$_type_43298',axiom,
! [V_24Y] :
( c_24__type__43298___24t(V_24Y)
<=> t(V_24Y,c_24__type__43298) ) ).
fof('$tdef_$_type_31676',axiom,
! [V_24Y] :
( c_24__type__31676___24t(V_24Y)
<=> t(V_24Y,c_24__type__31676) ) ).
fof('$tdef_$_type_1045',axiom,
! [V_24Y] :
( c_24__type__1045___24t(V_24Y)
<=> t(V_24Y,c_24__type__1045) ) ).
fof('$tdef_$_type_2718',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2718___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2718___24a1(V_24X1)) ) ).
fof('$tdef_$_type_14674',axiom,
! [V_24Y] :
( c_24__type__14674___24t(V_24Y)
<=> t(V_24Y,c_24__type__14674) ) ).
fof('$tdef_$_type_1379',axiom,
! [V_24Y] :
( c_24__type__1379___24t(V_24Y)
<=> t(V_24Y,c_24__type__1379) ) ).
fof('$tdef_$_type_189',axiom,
! [V_24Y] :
( c_24__type__189___24t(V_24Y)
<=> t(V_24Y,c_24__type__189) ) ).
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_$_type_2832',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2832___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2832___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_40846',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__40846___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__40846___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_37697',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__37697___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__37697___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_43334',axiom,
! [V_24Y] :
( c_24__type__43334___24t(V_24Y)
<=> t(V_24Y,c_24__type__43334) ) ).
fof('$tdef_$_type_13453',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__13453___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__13453___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Byte.byte',axiom,
! [V_24Y] :
( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).
fof('$tdef_$_type_19710',axiom,
! [V_24Y] :
( c_24__type__19710___24t(V_24Y)
<=> t(V_24Y,c_24__type__19710) ) ).
fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_24316',axiom,
! [V_24Y] :
( c_24__type__24316___24t(V_24Y)
<=> t(V_24Y,c_24__type__24316) ) ).
fof('$tdef_$_type_27389',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__27389___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__27389___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_148',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__148___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__148___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_45601',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__45601___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__45601___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_31952',axiom,
! [V_24Y] :
( c_24__type__31952___24t(V_24Y)
<=> t(V_24Y,c_24__type__31952) ) ).
fof('$tdef_$_type_14668',axiom,
! [V_24Y] :
( c_24__type__14668___24t(V_24Y)
<=> t(V_24Y,c_24__type__14668) ) ).
fof('$tdef_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Strings.String.string',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eString_2estring___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eString_2estring) ) ).
fof('$tdef_$_type_24633',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__24633___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__24633___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_888',axiom,
! [V_24Y] :
( c_24__type__888___24t(V_24Y)
<=> t(V_24Y,c_24__type__888) ) ).
fof('$tdef_$_type_30872',axiom,
! [V_24Y] :
( c_24__type__30872___24t(V_24Y)
<=> t(V_24Y,c_24__type__30872) ) ).
fof('$tdef_$_type_5145',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5145___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5145___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_228',axiom,
! [V_24Y] :
( c_24__type__228___24t(V_24Y)
<=> t(V_24Y,c_24__type__228) ) ).
fof('$tdef_$_type_978',axiom,
! [V_24Y] :
( c_24__type__978___24t(V_24Y)
<=> t(V_24Y,c_24__type__978) ) ).
fof('$tdef_$_type_35581',axiom,
! [V_24Y] :
( c_24__type__35581___24t(V_24Y)
<=> t(V_24Y,c_24__type__35581) ) ).
fof('$tdef_$_type_20884',axiom,
! [V_24Y] :
( c_24__type__20884___24t(V_24Y)
<=> t(V_24Y,c_24__type__20884) ) ).
fof('$tdef_$_type_28222',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__28222___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__28222___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_30781',axiom,
! [V_24Y] :
( c_24__type__30781___24t(V_24Y)
<=> t(V_24Y,c_24__type__30781) ) ).
fof('$tdef_$_type_3114',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3114___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3114___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35870',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__35870___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__35870___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Specif.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('$tdef_$_cast_35448',axiom,
! [V_24Y] :
( c_24__cast__35448___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35448) ) ).
fof('$tdef_$_type_24813',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__24813___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__24813___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_8900',axiom,
! [V_24Y] :
( c_24__type__8900___24t(V_24Y)
<=> t(V_24Y,c_24__type__8900) ) ).
fof('$tdef_$_type_43316',axiom,
! [V_24Y] :
( c_24__type__43316___24t(V_24Y)
<=> t(V_24Y,c_24__type__43316) ) ).
fof('$tdef_$_type_28122',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__28122___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__28122___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_2768',axiom,
! [V_24Y] :
( c_24__type__2768___24t(V_24Y)
<=> t(V_24Y,c_24__type__2768) ) ).
fof('$tdef_$_type_1117',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1117___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1117___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28820',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28820___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28820___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Tait.Term.type',axiom,
! [V_24Y] :
( cTait_2eTerm_2etype___24t(V_24Y)
<=> t(V_24Y,cTait_2eTerm_2etype) ) ).
fof('$tdef_$_type_28645',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__28645___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__28645___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_36406',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__36406___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__36406___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_43293',axiom,
! [V_24Y] :
( c_24__type__43293___24t(V_24Y)
<=> t(V_24Y,c_24__type__43293) ) ).
fof('$tdef_$_type_1486',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1486___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1486___24a1(V_24X1)) ) ).
fof('$tdef_$_type_43311',axiom,
! [V_24Y] :
( c_24__type__43311___24t(V_24Y)
<=> t(V_24Y,c_24__type__43311) ) ).
fof('$tdef_$_type_25268',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__25268___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__25268___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_cast_35440',axiom,
! [V_24Y] :
( c_24__cast__35440___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35440) ) ).
fof('$tdef_$_type_44966',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__44966___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__44966___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_131',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__131___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__131___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_5052',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5052___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5052___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_12459',axiom,
! [V_24Y] :
( c_24__type__12459___24t(V_24Y)
<=> t(V_24Y,c_24__type__12459) ) ).
fof('$tdef_Coq.Structures.OrderedType.Compare',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( cCoq_2eStructures_2eOrderedType_2eCompare___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Init.Specif.sumor',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumor___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_691',axiom,
! [V_24Y] :
( c_24__type__691___24t(V_24Y)
<=> t(V_24Y,c_24__type__691) ) ).
fof('$tdef_$_type_1296',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1296___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1296___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11412',axiom,
! [V_24Y] :
( c_24__type__11412___24t(V_24Y)
<=> t(V_24Y,c_24__type__11412) ) ).
fof('$tdef_$_type_569',axiom,
! [V_24Y] :
( c_24__type__569___24t(V_24Y)
<=> t(V_24Y,c_24__type__569) ) ).
fof('$tdef_$_type_696',axiom,
! [V_24Y] :
( c_24__type__696___24t(V_24Y)
<=> t(V_24Y,c_24__type__696) ) ).
fof('$tdef_$_type_35183',axiom,
! [V_24Y] :
( c_24__type__35183___24t(V_24Y)
<=> t(V_24Y,c_24__type__35183) ) ).
fof('$tdef_$_type_287',axiom,
! [V_24Y] :
( c_24__type__287___24t(V_24Y)
<=> t(V_24Y,c_24__type__287) ) ).
fof('$tdef_$_type_27939',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__27939___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__27939___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_cast_35454',axiom,
! [V_24Y] :
( c_24__cast__35454___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35454) ) ).
fof('$tdef_$_type_2756',axiom,
! [V_24Y] :
( c_24__type__2756___24t(V_24Y)
<=> t(V_24Y,c_24__type__2756) ) ).
fof('$tdef_$_type_25241',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__25241___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__25241___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2711',axiom,
! [V_24Y] :
( c_24__type__2711___24t(V_24Y)
<=> t(V_24Y,c_24__type__2711) ) ).
fof('$tdef_$_type_157',axiom,
! [V_24X1,V_24Y] :
( c_24__type__157___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__157___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28172',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__28172___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__28172___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_35053',axiom,
! [V_24Y] :
( c_24__type__35053___24t(V_24Y)
<=> t(V_24Y,c_24__type__35053) ) ).
fof('$tdef_$_type_174',axiom,
! [V_24Y] :
( c_24__type__174___24t(V_24Y)
<=> t(V_24Y,c_24__type__174) ) ).
fof('$tdef_Tait.Typing.context',axiom,
! [V_24Y] :
( cTait_2eTyping_2econtext___24t(V_24Y)
<=> t(V_24Y,cTait_2eTyping_2econtext) ) ).
fof('$tdef_$_type_718',axiom,
! [V_24Y] :
( c_24__type__718___24t(V_24Y)
<=> t(V_24Y,c_24__type__718) ) ).
fof('$tdef_Coq.micromega.Tauto.cnf',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2817',axiom,
! [V_24Y] :
( c_24__type__2817___24t(V_24Y)
<=> t(V_24Y,c_24__type__2817) ) ).
fof('$tdef_$_type_15853',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15853___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15853___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_45327',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__45327___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__45327___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_11958',axiom,
! [V_24Y] :
( c_24__type__11958___24t(V_24Y)
<=> t(V_24Y,c_24__type__11958) ) ).
fof('$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_1324',axiom,
! [V_24Y] :
( c_24__type__1324___24t(V_24Y)
<=> t(V_24Y,c_24__type__1324) ) ).
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_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [V_24X1,V_24Y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_$_type_17517',axiom,
! [V_24Y] :
( c_24__type__17517___24t(V_24Y)
<=> t(V_24Y,c_24__type__17517) ) ).
fof('$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_35294',axiom,
! [V_24Y] :
( c_24__type__35294___24t(V_24Y)
<=> t(V_24Y,c_24__type__35294) ) ).
fof('$tdef_$_type_33909',axiom,
! [V_24Y] :
( c_24__type__33909___24t(V_24Y)
<=> t(V_24Y,c_24__type__33909) ) ).
fof('$tdef_$_type_30941',axiom,
! [V_24Y] :
( c_24__type__30941___24t(V_24Y)
<=> t(V_24Y,c_24__type__30941) ) ).
fof('$tdef_$_type_13529',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__13529___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__13529___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_44096',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__44096___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__44096___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_45769',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__45769___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__45769___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_21329',axiom,
! [V_24Y] :
( c_24__type__21329___24t(V_24Y)
<=> t(V_24Y,c_24__type__21329) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ) ).
fof('$tdef_$_type_41515',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__41515___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__41515___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_30775',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30775___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30775___24a2(V_24X1,V_24X2)) ) ).
fof('$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_14909',axiom,
! [V_24Y] :
( c_24__type__14909___24t(V_24Y)
<=> t(V_24Y,c_24__type__14909) ) ).
fof('$tdef_$_type_4784',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__4784___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__4784___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Formula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1028',axiom,
! [V_24Y] :
( c_24__type__1028___24t(V_24Y)
<=> t(V_24Y,c_24__type__1028) ) ).
fof('$tdef_$_type_46145',axiom,
! [V_24Y] :
( c_24__type__46145___24t(V_24Y)
<=> t(V_24Y,c_24__type__46145) ) ).
fof('$tdef_$_type_31563',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__31563___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__31563___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23841',axiom,
! [V_24Y] :
( c_24__type__23841___24t(V_24Y)
<=> t(V_24Y,c_24__type__23841) ) ).
fof('$tdef_$_type_35456',axiom,
! [V_24Y] :
( c_24__type__35456___24t(V_24Y)
<=> t(V_24Y,c_24__type__35456) ) ).
fof('$tdef_$_type_35178',axiom,
! [V_24Y] :
( c_24__type__35178___24t(V_24Y)
<=> t(V_24Y,c_24__type__35178) ) ).
fof('$tdef_$_type_300',axiom,
! [V_24Y] :
( c_24__type__300___24t(V_24Y)
<=> t(V_24Y,c_24__type__300) ) ).
fof('$tdef_$_type_25934',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__25934___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__25934___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ) ).
fof('$tdef_$_type_5227',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__5227___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__5227___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.Tauto.clause',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2emicromega_2eTauto_2eclause___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35467',axiom,
! [V_24Y] :
( c_24__type__35467___24t(V_24Y)
<=> t(V_24Y,c_24__type__35467) ) ).
fof('$tdef_$_type_14414',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__14414___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__14414___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2625',axiom,
! [V_24Y] :
( c_24__type__2625___24t(V_24Y)
<=> t(V_24Y,c_24__type__2625) ) ).
fof('$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_279',axiom,
! [V_24Y] :
( c_24__type__279___24t(V_24Y)
<=> t(V_24Y,c_24__type__279) ) ).
fof('$tdef_$_type_43853',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__43853___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__43853___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_31469',axiom,
! [V_24Y] :
( c_24__type__31469___24t(V_24Y)
<=> t(V_24Y,c_24__type__31469) ) ).
fof('$tdef_$_type_15683',axiom,
! [V_24Y] :
( c_24__type__15683___24t(V_24Y)
<=> t(V_24Y,c_24__type__15683) ) ).
fof('$tdef_$_type_25046',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__25046___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__25046___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_28521',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__28521___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__28521___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_38793',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__38793___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__38793___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_45593',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__45593___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__45593___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_44271',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__44271___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__44271___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_30734',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30734___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30734___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2792',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2792___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2792___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30878',axiom,
! [V_24Y] :
( c_24__type__30878___24t(V_24Y)
<=> t(V_24Y,c_24__type__30878) ) ).
fof('$tdef_$_type_1430',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1430___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1430___24a1(V_24X1)) ) ).
fof('$tdef_$_cast_35434',axiom,
! [V_24Y] :
( c_24__cast__35434___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35434) ) ).
fof('$tdef_$_type_35024',axiom,
! [V_24X1,V_24Y] :
( c_24__type__35024___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__35024___24a1(V_24X1)) ) ).
fof('$tdef_$_type_839',axiom,
! [V_24Y] :
( c_24__type__839___24t(V_24Y)
<=> t(V_24Y,c_24__type__839) ) ).
fof('$tdef_$_type_25721',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__25721___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__25721___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_30822',axiom,
! [V_24Y] :
( c_24__type__30822___24t(V_24Y)
<=> t(V_24Y,c_24__type__30822) ) ).
fof('$tdef_$_type_1474',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1474___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1474___24a1(V_24X1)) ) ).
fof('$tdef_$_type_560',axiom,
! [V_24Y] :
( c_24__type__560___24t(V_24Y)
<=> t(V_24Y,c_24__type__560) ) ).
fof('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$tdef_$_type_46115',axiom,
! [V_24Y] :
( c_24__type__46115___24t(V_24Y)
<=> t(V_24Y,c_24__type__46115) ) ).
fof('$tdef_$_type_34123',axiom,
! [V_24Y] :
( c_24__type__34123___24t(V_24Y)
<=> t(V_24Y,c_24__type__34123) ) ).
fof('$tdef_$_type_31780',axiom,
! [V_24X1,V_24Y] :
( c_24__type__31780___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__31780___24a1(V_24X1)) ) ).
fof('$tdef_$_type_29111',axiom,
! [V_24Y] :
( c_24__type__29111___24t(V_24Y)
<=> t(V_24Y,c_24__type__29111) ) ).
fof('$tdef_$_type_1381',axiom,
! [V_24Y] :
( c_24__type__1381___24t(V_24Y)
<=> t(V_24Y,c_24__type__1381) ) ).
fof('$tdef_$_type_45665',axiom,
! [V_24Y] :
( c_24__type__45665___24t(V_24Y)
<=> t(V_24Y,c_24__type__45665) ) ).
fof('$tdef_$_type_311',axiom,
! [V_24Y] :
( c_24__type__311___24t(V_24Y)
<=> t(V_24Y,c_24__type__311) ) ).
fof('$tdef_$_type_36502',axiom,
! [V_24Y] :
( c_24__type__36502___24t(V_24Y)
<=> t(V_24Y,c_24__type__36502) ) ).
fof('$tdef_$_type_14546',axiom,
! [V_24Y] :
( c_24__type__14546___24t(V_24Y)
<=> t(V_24Y,c_24__type__14546) ) ).
fof('$tdef_$_type_35135',axiom,
! [V_24Y] :
( c_24__type__35135___24t(V_24Y)
<=> t(V_24Y,c_24__type__35135) ) ).
fof('$tdef_$_type_45730',axiom,
! [V_24X1,V_24Y] :
( c_24__type__45730___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__45730___24a1(V_24X1)) ) ).
fof('$tdef_$_type_17375',axiom,
! [V_24Y] :
( c_24__type__17375___24t(V_24Y)
<=> t(V_24Y,c_24__type__17375) ) ).
fof('$tdef_$_type_13799',axiom,
! [V_24Y] :
( c_24__type__13799___24t(V_24Y)
<=> t(V_24Y,c_24__type__13799) ) ).
fof('$tdef_$_type_113',axiom,
! [V_24Y] :
( c_24__type__113___24t(V_24Y)
<=> t(V_24Y,c_24__type__113) ) ).
fof('$tdef_$_type_2296',axiom,
! [V_24Y] :
( c_24__type__2296___24t(V_24Y)
<=> t(V_24Y,c_24__type__2296) ) ).
fof('$tdef_$_type_1147',axiom,
! [V_24Y] :
( c_24__type__1147___24t(V_24Y)
<=> t(V_24Y,c_24__type__1147) ) ).
fof('$tdef_Coq.ZArith.Znumtheory.Euclid',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35148',axiom,
! [V_24Y] :
( c_24__type__35148___24t(V_24Y)
<=> t(V_24Y,c_24__type__35148) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).
fof('$tdef_$_type_9090',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__9090___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__9090___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_39808',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__39808___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__39808___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_19506',axiom,
! [V_24Y] :
( c_24__type__19506___24t(V_24Y)
<=> t(V_24Y,c_24__type__19506) ) ).
fof('$tdef_$_type_43296',axiom,
! [V_24Y] :
( c_24__type__43296___24t(V_24Y)
<=> t(V_24Y,c_24__type__43296) ) ).
fof('$tdef_$_type_1347',axiom,
! [V_24Y] :
( c_24__type__1347___24t(V_24Y)
<=> t(V_24Y,c_24__type__1347) ) ).
fof('$tdef_Coq.micromega.EnvRing.Mon',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2eMon) ) ).
fof('$tdef_$_type_35670',axiom,
! [V_24Y] :
( c_24__type__35670___24t(V_24Y)
<=> t(V_24Y,c_24__type__35670) ) ).
fof('$tdef_$_type_2614',axiom,
! [V_24Y] :
( c_24__type__2614___24t(V_24Y)
<=> t(V_24Y,c_24__type__2614) ) ).
fof('$tdef_$_type_44716',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__44716___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__44716___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_35642',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__35642___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__35642___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_862',axiom,
! [V_24Y] :
( c_24__type__862___24t(V_24Y)
<=> t(V_24Y,c_24__type__862) ) ).
fof('$tdef_$_type_45352',axiom,
! [V_24Y] :
( c_24__type__45352___24t(V_24Y)
<=> t(V_24Y,c_24__type__45352) ) ).
fof('$tdef_$_type_2820',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2820___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2820___24a1(V_24X1)) ) ).
fof('$tdef_$_type_43979',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__43979___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__43979___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_36451',axiom,
! [V_24Y] :
( c_24__type__36451___24t(V_24Y)
<=> t(V_24Y,c_24__type__36451) ) ).
fof('$tdef_$_cast_35426',axiom,
! [V_24Y] :
( c_24__cast__35426___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35426) ) ).
fof('$tdef_$_type_837',axiom,
! [V_24Y] :
( c_24__type__837___24t(V_24Y)
<=> t(V_24Y,c_24__type__837) ) ).
fof('$tdef_$_type_35046',axiom,
! [V_24Y] :
( c_24__type__35046___24t(V_24Y)
<=> t(V_24Y,c_24__type__35046) ) ).
fof('$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('$tdef_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ) ).
fof('$tdef_$_type_956',axiom,
! [V_24Y] :
( c_24__type__956___24t(V_24Y)
<=> t(V_24Y,c_24__type__956) ) ).
fof('$tdef_Coq.micromega.QMicromega.QWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eQMicromega_2eQWitness) ) ).
fof('$tdef_$_type_37806',axiom,
! [V_24Y] :
( c_24__type__37806___24t(V_24Y)
<=> t(V_24Y,c_24__type__37806) ) ).
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_$_type_28314',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__28314___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__28314___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_cast_35452',axiom,
! [V_24Y] :
( c_24__cast__35452___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35452) ) ).
fof('$tdef_$_type_21337',axiom,
! [V_24X1,V_24Y] :
( c_24__type__21337___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__21337___24a1(V_24X1)) ) ).
fof('$tdef_$_type_10795',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__10795___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__10795___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_cast_35444',axiom,
! [V_24Y] :
( c_24__cast__35444___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35444) ) ).
fof('$tdef_$_type_1067',axiom,
! [V_24Y] :
( c_24__type__1067___24t(V_24Y)
<=> t(V_24Y,c_24__type__1067) ) ).
fof('$tdef_$_type_37717',axiom,
! [V_24Y] :
( c_24__type__37717___24t(V_24Y)
<=> t(V_24Y,c_24__type__37717) ) ).
fof('$tdef_$_type_13449',axiom,
! [V_24Y] :
( c_24__type__13449___24t(V_24Y)
<=> t(V_24Y,c_24__type__13449) ) ).
fof('$tdef_$_type_1084',axiom,
! [V_24Y] :
( c_24__type__1084___24t(V_24Y)
<=> t(V_24Y,c_24__type__1084) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ) ).
fof('$tdef_$_type_273',axiom,
! [V_24Y] :
( c_24__type__273___24t(V_24Y)
<=> t(V_24Y,c_24__type__273) ) ).
fof('$tdef_$_type_46041',axiom,
! [V_24Y] :
( c_24__type__46041___24t(V_24Y)
<=> t(V_24Y,c_24__type__46041) ) ).
fof('$tdef_$_type_2271',axiom,
! [V_24Y] :
( c_24__type__2271___24t(V_24Y)
<=> t(V_24Y,c_24__type__2271) ) ).
fof('$tdef_$_cast_35424',axiom,
! [V_24Y] :
( c_24__cast__35424___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35424) ) ).
fof('$tdef_$_type_31337',axiom,
! [V_24Y] :
( c_24__type__31337___24t(V_24Y)
<=> t(V_24Y,c_24__type__31337) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ) ).
fof('$tdef_$_type_45716',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__45716___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__45716___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_39139',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__39139___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__39139___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_30695',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30695___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30695___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_405',axiom,
! [V_24Y] :
( c_24__type__405___24t(V_24Y)
<=> t(V_24Y,c_24__type__405) ) ).
fof('$tdef_$_type_154',axiom,
! [V_24Y] :
( c_24__type__154___24t(V_24Y)
<=> t(V_24Y,c_24__type__154) ) ).
fof('$tdef_$_type_45760',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__45760___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__45760___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_cast_35436',axiom,
! [V_24Y] :
( c_24__cast__35436___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35436) ) ).
fof('$tdef_$_cast_35450',axiom,
! [V_24Y] :
( c_24__cast__35450___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35450) ) ).
fof('$tdef_$_type_9104',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__9104___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__9104___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_33344',axiom,
! [V_24Y] :
( c_24__type__33344___24t(V_24Y)
<=> t(V_24Y,c_24__type__33344) ) ).
fof('$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_944',axiom,
! [V_24Y] :
( c_24__type__944___24t(V_24Y)
<=> t(V_24Y,c_24__type__944) ) ).
fof('$tdef_$_type_386',axiom,
! [V_24Y] :
( c_24__type__386___24t(V_24Y)
<=> t(V_24Y,c_24__type__386) ) ).
fof('$tdef_$_type_24295',axiom,
! [V_24Y] :
( c_24__type__24295___24t(V_24Y)
<=> t(V_24Y,c_24__type__24295) ) ).
fof('$tdef_$_type_16297',axiom,
! [V_24Y] :
( c_24__type__16297___24t(V_24Y)
<=> t(V_24Y,c_24__type__16297) ) ).
fof('$tdef_$_type_28390',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__28390___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__28390___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5616',axiom,
! [V_24Y] :
( c_24__type__5616___24t(V_24Y)
<=> t(V_24Y,c_24__type__5616) ) ).
fof('$tdef_$_type_30834',axiom,
! [V_24Y] :
( c_24__type__30834___24t(V_24Y)
<=> t(V_24Y,c_24__type__30834) ) ).
fof('$tdef_$_type_37434',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__37434___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__37434___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_487',axiom,
! [V_24Y] :
( c_24__type__487___24t(V_24Y)
<=> t(V_24Y,c_24__type__487) ) ).
fof('$tdef_$_type_19517',axiom,
! [V_24Y] :
( c_24__type__19517___24t(V_24Y)
<=> t(V_24Y,c_24__type__19517) ) ).
fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).
fof('$tdef_$_cast_35438',axiom,
! [V_24Y] :
( c_24__cast__35438___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35438) ) ).
fof('$tdef_$_type_46',axiom,
! [V_24Y] :
( c_24__type__46___24t(V_24Y)
<=> t(V_24Y,c_24__type__46) ) ).
fof('$tdef_$_type_42207',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__42207___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__42207___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_45970',axiom,
! [V_24Y] :
( c_24__type__45970___24t(V_24Y)
<=> t(V_24Y,c_24__type__45970) ) ).
fof('$tdef_$_type_37879',axiom,
! [V_24Y] :
( c_24__type__37879___24t(V_24Y)
<=> t(V_24Y,c_24__type__37879) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZWitness) ) ).
fof('$tdef_$_type_2231',axiom,
! [V_24Y] :
( c_24__type__2231___24t(V_24Y)
<=> t(V_24Y,c_24__type__2231) ) ).
fof('$tdef_$_type_513',axiom,
! [V_24Y] :
( c_24__type__513___24t(V_24Y)
<=> t(V_24Y,c_24__type__513) ) ).
fof('$tdef_$_type_748',axiom,
! [V_24Y] :
( c_24__type__748___24t(V_24Y)
<=> t(V_24Y,c_24__type__748) ) ).
fof('$tdef_$_type_11956',axiom,
! [V_24Y] :
( c_24__type__11956___24t(V_24Y)
<=> t(V_24Y,c_24__type__11956) ) ).
fof('$tdef_$_type_25160',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__25160___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__25160___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZArithProof) ) ).
fof('$tdef_$_type_24570',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__24570___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__24570___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_$_type_35661',axiom,
! [V_24Y] :
( c_24__type__35661___24t(V_24Y)
<=> t(V_24Y,c_24__type__35661) ) ).
fof('$tdef_$_type_20630',axiom,
! [V_24Y] :
( c_24__type__20630___24t(V_24Y)
<=> t(V_24Y,c_24__type__20630) ) ).
fof('$tdef_$_type_8602',axiom,
! [V_24Y] :
( c_24__type__8602___24t(V_24Y)
<=> t(V_24Y,c_24__type__8602) ) ).
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_$_type_27797',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__27797___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__27797___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_14521',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14521___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14521___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_41192',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__41192___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__41192___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Datatypes.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_2698',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2698___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2698___24a1(V_24X1)) ) ).
fof('$tdef_$_type_42853',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__42853___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__42853___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_37142',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__37142___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__37142___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_25130',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__25130___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__25130___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_282',axiom,
! [V_24Y] :
( c_24__type__282___24t(V_24Y)
<=> t(V_24Y,c_24__type__282) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).
fof('$tdef_$_type_12300',axiom,
! [V_24Y] :
( c_24__type__12300___24t(V_24Y)
<=> t(V_24Y,c_24__type__12300) ) ).
fof('$tdef_$_type_72',axiom,
! [V_24Y] :
( c_24__type__72___24t(V_24Y)
<=> t(V_24Y,c_24__type__72) ) ).
fof('$tdef_$_type_28657',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__28657___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__28657___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_70',axiom,
! [V_24Y] :
( c_24__type__70___24t(V_24Y)
<=> t(V_24Y,c_24__type__70) ) ).
fof('$tdef_$_type_30794',axiom,
! [V_24Y] :
( c_24__type__30794___24t(V_24Y)
<=> t(V_24Y,c_24__type__30794) ) ).
fof('$tdef_$_type_35056',axiom,
! [V_24Y] :
( c_24__type__35056___24t(V_24Y)
<=> t(V_24Y,c_24__type__35056) ) ).
fof('$tdef_$_type_3711',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3711___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3711___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30817',axiom,
! [V_24Y] :
( c_24__type__30817___24t(V_24Y)
<=> t(V_24Y,c_24__type__30817) ) ).
fof('$tdef_$_type_14903',axiom,
! [V_24Y] :
( c_24__type__14903___24t(V_24Y)
<=> t(V_24Y,c_24__type__14903) ) ).
fof('$tdef_$_type_15027',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__15027___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__15027___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_13649',axiom,
! [V_24Y] :
( c_24__type__13649___24t(V_24Y)
<=> t(V_24Y,c_24__type__13649) ) ).
fof('$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_25100',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__25100___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__25100___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_41861',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__41861___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__41861___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_45907',axiom,
! [V_24Y] :
( c_24__type__45907___24t(V_24Y)
<=> t(V_24Y,c_24__type__45907) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_35005',axiom,
! [V_24Y] :
( c_24__type__35005___24t(V_24Y)
<=> t(V_24Y,c_24__type__35005) ) ).
fof('$tdef_$_type_14126',axiom,
! [V_24Y] :
( c_24__type__14126___24t(V_24Y)
<=> t(V_24Y,c_24__type__14126) ) ).
fof('$tdef_$_type_43585',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__43585___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__43585___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_43507',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__43507___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__43507___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_36313',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__36313___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__36313___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_34990',axiom,
! [V_24Y] :
( c_24__type__34990___24t(V_24Y)
<=> t(V_24Y,c_24__type__34990) ) ).
fof('$tdef_$_type_30738',axiom,
! [V_24Y] :
( c_24__type__30738___24t(V_24Y)
<=> t(V_24Y,c_24__type__30738) ) ).
fof('$tdef_$_type_30758',axiom,
! [V_24Y] :
( c_24__type__30758___24t(V_24Y)
<=> t(V_24Y,c_24__type__30758) ) ).
fof('$tdef_$_type_1395',axiom,
! [V_24Y] :
( c_24__type__1395___24t(V_24Y)
<=> t(V_24Y,c_24__type__1395) ) ).
fof('$tdef_$_type_5636',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__5636___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__5636___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_35227',axiom,
! [V_24Y] :
( c_24__type__35227___24t(V_24Y)
<=> t(V_24Y,c_24__type__35227) ) ).
fof('$tdef_$_type_13619',axiom,
! [V_24Y] :
( c_24__type__13619___24t(V_24Y)
<=> t(V_24Y,c_24__type__13619) ) ).
fof('$tdef_$_type_37816',axiom,
! [V_24Y] :
( c_24__type__37816___24t(V_24Y)
<=> t(V_24Y,c_24__type__37816) ) ).
fof('$tdef_$_type_26768',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__26768___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__26768___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_31558',axiom,
! [V_24Y] :
( c_24__type__31558___24t(V_24Y)
<=> t(V_24Y,c_24__type__31558) ) ).
fof('$tdef_$_type_35963',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__35963___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__35963___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_1471',axiom,
! [V_24Y] :
( c_24__type__1471___24t(V_24Y)
<=> t(V_24Y,c_24__type__1471) ) ).
fof('$tdef_$_type_26981',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__26981___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__26981___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_28778',axiom,
! [V_24Y] :
( c_24__type__28778___24t(V_24Y)
<=> t(V_24Y,c_24__type__28778) ) ).
fof('$tdef_$_type_17362',axiom,
! [V_24Y] :
( c_24__type__17362___24t(V_24Y)
<=> t(V_24Y,c_24__type__17362) ) ).
fof('$tdef_$_type_1357',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1357___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1357___24a1(V_24X1)) ) ).
fof('$tdef_$_type_16351',axiom,
! [V_24Y] :
( c_24__type__16351___24t(V_24Y)
<=> t(V_24Y,c_24__type__16351) ) ).
fof('$tdef_$_type_11191',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11191___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11191___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1282',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1282___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1282___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_14680',axiom,
! [V_24Y] :
( c_24__type__14680___24t(V_24Y)
<=> t(V_24Y,c_24__type__14680) ) ).
fof('$tdef_$_type_45649',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__45649___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__45649___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_37678',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__37678___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__37678___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_13558',axiom,
! [V_24Y] :
( c_24__type__13558___24t(V_24Y)
<=> t(V_24Y,c_24__type__13558) ) ).
fof('$tdef_$_type_29152',axiom,
! [V_24Y] :
( c_24__type__29152___24t(V_24Y)
<=> t(V_24Y,c_24__type__29152) ) ).
fof('$tdef_$_type_43281',axiom,
! [V_24Y] :
( c_24__type__43281___24t(V_24Y)
<=> t(V_24Y,c_24__type__43281) ) ).
fof('$tdef_$_type_181',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__181___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__181___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_44225',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__44225___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__44225___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_30717',axiom,
! [V_24Y] :
( c_24__type__30717___24t(V_24Y)
<=> t(V_24Y,c_24__type__30717) ) ).
fof('$tdef_$_type_1393',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1393___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1393___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.CompareSpecT',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_$_type_1287',axiom,
! [V_24Y] :
( c_24__type__1287___24t(V_24Y)
<=> t(V_24Y,c_24__type__1287) ) ).
fof('$tdef_$_type_11992',axiom,
! [V_24Y] :
( c_24__type__11992___24t(V_24Y)
<=> t(V_24Y,c_24__type__11992) ) ).
fof('$tdef_$_type_36056',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__36056___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__36056___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_15849',axiom,
! [V_24Y] :
( c_24__type__15849___24t(V_24Y)
<=> t(V_24Y,c_24__type__15849) ) ).
fof('$tdef_$_type_9060',axiom,
! [V_24Y] :
( c_24__type__9060___24t(V_24Y)
<=> t(V_24Y,c_24__type__9060) ) ).
fof('$tdef_$_type_29031',axiom,
! [V_24X1,V_24Y] :
( c_24__type__29031___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__29031___24a1(V_24X1)) ) ).
fof('$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_28398',axiom,
! [V_24Y] :
( c_24__type__28398___24t(V_24Y)
<=> t(V_24Y,c_24__type__28398) ) ).
fof('$tdef_$_type_46134',axiom,
! [V_24Y] :
( c_24__type__46134___24t(V_24Y)
<=> t(V_24Y,c_24__type__46134) ) ).
fof('$tdef_$_type_31940',axiom,
! [V_24Y] :
( c_24__type__31940___24t(V_24Y)
<=> t(V_24Y,c_24__type__31940) ) ).
fof('$tdef_$_type_30741',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30741___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30741___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1000',axiom,
! [V_24Y] :
( c_24__type__1000___24t(V_24Y)
<=> t(V_24Y,c_24__type__1000) ) ).
fof('$tdef_Coq.micromega.EnvRing.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2713',axiom,
! [V_24Y] :
( c_24__type__2713___24t(V_24Y)
<=> t(V_24Y,c_24__type__2713) ) ).
fof('$tdef_$_type_30699',axiom,
! [V_24Y] :
( c_24__type__30699___24t(V_24Y)
<=> t(V_24Y,c_24__type__30699) ) ).
fof('$tdef_$_type_2279',axiom,
! [V_24Y] :
( c_24__type__2279___24t(V_24Y)
<=> t(V_24Y,c_24__type__2279) ) ).
fof('$tdef_$_type_14483',axiom,
! [V_24Y] :
( c_24__type__14483___24t(V_24Y)
<=> t(V_24Y,c_24__type__14483) ) ).
fof('$tdef_$_type_1328',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1328___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1328___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_13466',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__13466___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__13466___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_42530',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__42530___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__42530___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_35002',axiom,
! [V_24Y] :
( c_24__type__35002___24t(V_24Y)
<=> t(V_24Y,c_24__type__35002) ) ).
fof('$tdef_$_type_46094',axiom,
! [V_24Y] :
( c_24__type__46094___24t(V_24Y)
<=> t(V_24Y,c_24__type__46094) ) ).
fof('$tdef_$_type_29078',axiom,
! [V_24X1,V_24Y] :
( c_24__type__29078___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__29078___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28601',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__28601___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__28601___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ) ).
fof('$tdef_$_type_30841',axiom,
! [V_24Y] :
( c_24__type__30841___24t(V_24Y)
<=> t(V_24Y,c_24__type__30841) ) ).
fof('$tdef_$_type_27972',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__27972___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__27972___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_18927',axiom,
! [V_24Y] :
( c_24__type__18927___24t(V_24Y)
<=> t(V_24Y,c_24__type__18927) ) ).
fof('$tdef_$_type_12547',axiom,
! [V_24Y] :
( c_24__type__12547___24t(V_24Y)
<=> t(V_24Y,c_24__type__12547) ) ).
fof('$tdef_$_type_24696',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__24696___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__24696___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_26342',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__26342___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__26342___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_5320',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__5320___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__5320___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_45216',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__45216___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__45216___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_Coq.Bool.Bool.reflect',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_860',axiom,
! [V_24Y] :
( c_24__type__860___24t(V_24Y)
<=> t(V_24Y,c_24__type__860) ) ).
fof('$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_30366',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30366___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30366___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_30172',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30172___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30172___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_37333',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__37333___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__37333___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_38',axiom,
! [V_24Y] :
( c_24__type__38___24t(V_24Y)
<=> t(V_24Y,c_24__type__38) ) ).
fof('$tdef_$_type_44202',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__44202___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__44202___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_35137',axiom,
! [V_24Y] :
( c_24__type__35137___24t(V_24Y)
<=> t(V_24Y,c_24__type__35137) ) ).
fof('$tdef_$_type_44248',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__44248___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__44248___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_39462',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__39462___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__39462___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_45968',axiom,
! [V_24Y] :
( c_24__type__45968___24t(V_24Y)
<=> t(V_24Y,c_24__type__45968) ) ).
fof('$tdef_$_type_34416',axiom,
! [V_24Y] :
( c_24__type__34416___24t(V_24Y)
<=> t(V_24Y,c_24__type__34416) ) ).
fof('$tdef_$_type_46132',axiom,
! [V_24Y] :
( c_24__type__46132___24t(V_24Y)
<=> t(V_24Y,c_24__type__46132) ) ).
fof('$tdef_$_type_46069',axiom,
! [V_24Y] :
( c_24__type__46069___24t(V_24Y)
<=> t(V_24Y,c_24__type__46069) ) ).
fof('$tdef_$_type_36138',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__36138___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__36138___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_25217',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__25217___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__25217___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_1335',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1335___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1335___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_11940',axiom,
! [V_24Y] :
( c_24__type__11940___24t(V_24Y)
<=> t(V_24Y,c_24__type__11940) ) ).
fof('$tdef_$_type_3122',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3122___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3122___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13522',axiom,
! [V_24Y] :
( c_24__type__13522___24t(V_24Y)
<=> t(V_24Y,c_24__type__13522) ) ).
fof('$tdef_$_type_12291',axiom,
! [V_24Y] :
( c_24__type__12291___24t(V_24Y)
<=> t(V_24Y,c_24__type__12291) ) ).
fof('$tdef_$_type_28973',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28973___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28973___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_14927',axiom,
! [V_24Y] :
( c_24__type__14927___24t(V_24Y)
<=> t(V_24Y,c_24__type__14927) ) ).
fof('$tdef_$_type_11186',axiom,
! [V_24Y] :
( c_24__type__11186___24t(V_24Y)
<=> t(V_24Y,c_24__type__11186) ) ).
fof('$tdef_$_type_43546',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__43546___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__43546___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_37801',axiom,
! [V_24Y] :
( c_24__type__37801___24t(V_24Y)
<=> t(V_24Y,c_24__type__37801) ) ).
fof('$tdef_$_type_13886',axiom,
! [V_24Y] :
( c_24__type__13886___24t(V_24Y)
<=> t(V_24Y,c_24__type__13886) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolC',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28921',axiom,
! [V_24Y] :
( c_24__type__28921___24t(V_24Y)
<=> t(V_24Y,c_24__type__28921) ) ).
fof('$tdef_$_type_43199',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__43199___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__43199___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_12431',axiom,
! [V_24X1,V_24Y] :
( c_24__type__12431___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__12431___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8650',axiom,
! [V_24Y] :
( c_24__type__8650___24t(V_24Y)
<=> t(V_24Y,c_24__type__8650) ) ).
fof('$tdef_$_type_6666',axiom,
! [V_24Y] :
( c_24__type__6666___24t(V_24Y)
<=> t(V_24Y,c_24__type__6666) ) ).
fof('$tdef_$_type_36231',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__36231___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__36231___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_44289',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__44289___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__44289___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.micromega.RMicromega.RWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRWitness) ) ).
fof('$tdef_$_type_25184',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__25184___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__25184___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_238',axiom,
! [V_24Y] :
( c_24__type__238___24t(V_24Y)
<=> t(V_24Y,c_24__type__238) ) ).
fof('$tdef_$_type_13572',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__13572___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__13572___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12234',axiom,
! [V_24Y] :
( c_24__type__12234___24t(V_24Y)
<=> t(V_24Y,c_24__type__12234) ) ).
fof('$tdef_$_type_28264',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__28264___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__28264___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_45657',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__45657___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__45657___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_44333',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__44333___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__44333___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_15161',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__15161___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__15161___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_590',axiom,
! [V_24X1,V_24Y] :
( c_24__type__590___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__590___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28565',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__28565___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__28565___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_23454',axiom,
! [V_24Y] :
( c_24__type__23454___24t(V_24Y)
<=> t(V_24Y,c_24__type__23454) ) ).
fof('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).
fof('$tdef_$_type_479',axiom,
! [V_24Y] :
( c_24__type__479___24t(V_24Y)
<=> t(V_24Y,c_24__type__479) ) ).
fof('$tdef_$_type_12471',axiom,
! [V_24Y] :
( c_24__type__12471___24t(V_24Y)
<=> t(V_24Y,c_24__type__12471) ) ).
fof('$tdef_$_type_285',axiom,
! [V_24Y] :
( c_24__type__285___24t(V_24Y)
<=> t(V_24Y,c_24__type__285) ) ).
fof('$tdef_$_type_17367',axiom,
! [V_24Y] :
( c_24__type__17367___24t(V_24Y)
<=> t(V_24Y,c_24__type__17367) ) ).
fof('$tdef_$_type_2780',axiom,
! [V_24Y] :
( c_24__type__2780___24t(V_24Y)
<=> t(V_24Y,c_24__type__2780) ) ).
fof('$tdef_$_type_11929',axiom,
! [V_24Y] :
( c_24__type__11929___24t(V_24Y)
<=> t(V_24Y,c_24__type__11929) ) ).
fof('$tdef_$_type_37535',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__37535___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__37535___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_9003',axiom,
! [V_24Y] :
( c_24__type__9003___24t(V_24Y)
<=> t(V_24Y,c_24__type__9003) ) ).
fof('$tdef_$_type_2751',axiom,
! [V_24Y] :
( c_24__type__2751___24t(V_24Y)
<=> t(V_24Y,c_24__type__2751) ) ).
fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).
fof('$tdef_$_type_29177',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__29177___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__29177___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_36940',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__36940___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__36940___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Tait.Subst2.Joachimski.substitution',axiom,
! [V_24Y] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V_24Y)
<=> t(V_24Y,cTait_2eSubst2_2eJoachimski_2esubstitution) ) ).
fof('$tdef_$_type_36506',axiom,
! [V_24Y] :
( c_24__type__36506___24t(V_24Y)
<=> t(V_24Y,c_24__type__36506) ) ).
fof('$tdef_$_type_4409',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4409___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4409___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12197',axiom,
! [V_24Y] :
( c_24__type__12197___24t(V_24Y)
<=> t(V_24Y,c_24__type__12197) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.Nword',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2eNword) ) ).
fof('$tdef_$_type_1061',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1061___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1061___24a1(V_24X1)) ) ).
fof('$tdef_$_type_45959',axiom,
! [V_24Y] :
( c_24__type__45959___24t(V_24Y)
<=> t(V_24Y,c_24__type__45959) ) ).
fof('$tdef_$_type_431',axiom,
! [V_24Y] :
( c_24__type__431___24t(V_24Y)
<=> t(V_24Y,c_24__type__431) ) ).
fof('$tdef_$_cast_35430',axiom,
! [V_24Y] :
( c_24__cast__35430___24t(V_24Y)
<=> t(V_24Y,c_24__cast__35430) ) ).
fof('$tdef_$_type_45609',axiom,
! [V_24Y] :
( c_24__type__45609___24t(V_24Y)
<=> t(V_24Y,c_24__type__45609) ) ).
fof('_HAMMER_GOAL',conjecture,
( cTait_2enc_2enc__type___24a1(cTait_2eTyping_2econtext)
=> ( cTait_2enc_2enc__type___24a1(cTait_2eTyping_2econtext)
=> ( cTait_2enc_2enc__type___24a1(cTait_2eTyping_2econtext)
=> cTait_2enc_2enc2___24a5(cCoq_2eInit_2eDatatypes_2elist___24a1(c_24__cast__35424),cCoq_2eInit_2eDatatypes_2elist___24a1(c_24__cast__35426),cCoq_2eInit_2eDatatypes_2elist___24a1(c_24__cast__35428),cCoq_2eInit_2eDatatypes_2eapp___24a1(c_24__cast__35430),cTait_2enc_2enc2___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(c_24__cast__35432),cCoq_2eInit_2eDatatypes_2elist___24a1(c_24__cast__35434),cCoq_2eInit_2eDatatypes_2elist___24a1(c_24__cast__35436),cCoq_2eInit_2eDatatypes_2eapp___24a1(c_24__cast__35438))) = cTait_2enc_2enc2___24a5(cCoq_2eInit_2eDatatypes_2elist___24a1(c_24__cast__35440),cCoq_2eInit_2eDatatypes_2elist___24a1(c_24__cast__35442),cCoq_2eInit_2eDatatypes_2elist___24a1(c_24__cast__35444),cCoq_2eInit_2eDatatypes_2eapp___24a1(c_24__cast__35446),cTait_2enc_2enc2___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(c_24__cast__35448),cCoq_2eInit_2eDatatypes_2elist___24a1(c_24__cast__35450),cCoq_2eInit_2eDatatypes_2elist___24a1(c_24__cast__35452),cCoq_2eInit_2eDatatypes_2eapp___24a1(c_24__cast__35454))) ) ) ) ).
%------------------------------------------------------------------------------