TPTP Problem File: SEV631+1.p
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%------------------------------------------------------------------------------
% File : SEV631+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - HList Hcons inv
% 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 : HList.Hcons.inv.p [Kal26]
% Status : Theorem
% Rating : 0.39 v9.3.0
% Syntax : Number of formulae : 3118 (1030 unt; 0 def)
% Number of atoms : 13104 (3261 equ)
% Maximal formula atoms : 268 ( 4 avg)
% Number of connectives : 10201 ( 215 ~; 830 |;2012 &)
% (1214 <=>;5930 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 8 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 610 ( 609 usr; 0 prp; 1-23 aty)
% Number of functors : 1858 (1858 usr;1162 con; 0-22 aty)
% Number of variables : 12798 (11910 !; 888 ?)
% 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$17865',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2417865___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24__lam__17884___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) )
| ? [Vvar__1___24Anonymous__17869] :
( t(Vvar__1___24Anonymous__17869,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__17870] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__17870)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__17869,Vvar__2___24Anonymous__17870)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2417865___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24__lam__17912___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__17869,Vvar__2___24Anonymous__17870) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$35694',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__1) )
| ? [Vvar__1___24Anonymous__35698] :
( t(Vvar__1___24Anonymous__35698,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__35699] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__35699)
& Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__35698,Vvar__2___24Anonymous__35699)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vvar__1___24Anonymous__35698),cCoq_2eLists_2eList_2emap___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2___24Anonymous__35699)) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$418',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_24505___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24418___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__422] :
( t(Vvar__1___24Anonymous__422,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__423] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__423)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24505___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__422,Vvar__2___24Anonymous__423)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24418___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__422,c_24__fix__550__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__423,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$46502',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2enil___24a1(ciT)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a1(Vv__CANONICAL__0) = c_24__lam__46511 )
| ? [Vvar__1___24Anonymous__46506] :
( ciT___24t(Vvar__1___24Anonymous__46506)
& ? [Vvar__2___24Anonymous__46507] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vvar__2___24Anonymous__46507)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,Vvar__1___24Anonymous__46506,Vvar__2___24Anonymous__46507)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a1(Vv__CANONICAL__0) = c_24__lam__46514___24a2(Vvar__1___24Anonymous__46506,Vvar__2___24Anonymous__46507) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$505',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24505___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__509] :
( t(Vvar__1___24Anonymous__509,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__510] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__510)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__509,Vvar__2___24Anonymous__510)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24505___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__509,c_24__fix__550__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__510,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$120559',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24120559___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__120560] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120560)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120560)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24120559___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__120560)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$120581',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24120581___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__120582] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120582)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120582)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24120581___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__120582)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$33222',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__23647___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__33227] :
( t(Vvar__2___24Anonymous__33227,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__33228] :
( t(Vvar__3___24Anonymous__33228,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__33227,Vvar__3___24Anonymous__33228)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2433222___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__33227)),Vvar__3___24Anonymous__33228)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Specif.sumbool$15756',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( c_24__type__15621___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__3 = Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__15768___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__15769___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_2415756___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__let__var__var__7__n__15725__15729__15738___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)) )
| ( Vv__CANONICAL__3 != Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__15770___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__15771___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_2415756___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__let__var__var__7__n__15725__15729__15738___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$120576',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_24120581___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24120576___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__120577] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120577)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24120581___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__120577)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24120576___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__120577) )
| ? [Vvar__0___24Anonymous__120578] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120578)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24120581___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__120578)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24120576___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__120578) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$37861',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZ0
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2437861___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) )
| ? [Vvar__0___24Anonymous__37862] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37862)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37862)
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2437861___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__37862) ) )
| ? [Vvar__0___24Anonymous__37863] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37863)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37863)
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2437861___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__1 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__37863) ) ) ) ) ) ).
fof('$_case_Coq.setoid_ring.Ring_polynom.Pol$12167',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__16)
=> ( ? [Vvar__1___24Anonymous__12170] :
( t(Vvar__1___24Anonymous__12170,Vv__CANONICAL__8)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ( c_24__type__7767___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ( t(Vvar__1___24Anonymous__12170,Vv__CANONICAL__8)
=> ( Vv__CANONICAL__16 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vv__CANONICAL__8,Vvar__1___24Anonymous__12170)
& ( ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__12170),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2412167___24a17(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16) = c_24__let__17__lnum__11934___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15) )
| ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__12170),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2412167___24a17(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16) = happ(happ(Vv__CANONICAL__7,c_24__let__17__lnum__11934___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__16)) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__12173] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12173)
& ? [Vvar__2___24Anonymous__12174] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__2___24Anonymous__12174)
& Vv__CANONICAL__16 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vv__CANONICAL__8,Vvar__1___24Anonymous__12173,Vvar__2___24Anonymous__12174)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2412167___24a17(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16) = happ(happ(Vv__CANONICAL__7,c_24__let__17__lnum__11934___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__16)) ) )
| ? [Vvar__1___24Anonymous__12177] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__1___24Anonymous__12177)
& ? [Vvar__2___24Anonymous__12178] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12178)
& ? [Vvar__3___24Anonymous__12179] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__3___24Anonymous__12179)
& Vv__CANONICAL__16 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vv__CANONICAL__8,Vvar__1___24Anonymous__12177,Vvar__2___24Anonymous__12178,Vvar__3___24Anonymous__12179)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2412167___24a17(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16) = happ(happ(Vv__CANONICAL__7,c_24__let__17__lnum__11934___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a15(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__16)) ) ) ) ) ) ) ) ).
fof('$_case_Coq.setoid_ring.Ring_polynom.Pol$12766',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__12769] :
( t(Vvar__1___24Anonymous__12769,Vv__CANONICAL__8)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ( c_24__type__12789___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__11)
=> ( cType___24t(Vv__CANONICAL__13)
=> ( t(Vvar__1___24Anonymous__12769,Vv__CANONICAL__8)
=> ( Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vv__CANONICAL__8,Vvar__1___24Anonymous__12769)
& ( ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__12769),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2412766___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__12462___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__12769),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2412766___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__12462___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__12772] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12772)
& ? [Vvar__2___24Anonymous__12773] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__2___24Anonymous__12773)
& Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vv__CANONICAL__8,Vvar__1___24Anonymous__12772,Vvar__2___24Anonymous__12773)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2412766___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__12462___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__12776] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__1___24Anonymous__12776)
& ? [Vvar__2___24Anonymous__12777] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12777)
& ? [Vvar__3___24Anonymous__12778] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__3___24Anonymous__12778)
& Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vv__CANONICAL__8,Vvar__1___24Anonymous__12776,Vvar__2___24Anonymous__12777,Vvar__3___24Anonymous__12778)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2412766___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__12462___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('$_case_ExtLib.Data.Member.member$17801',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ( ? [Vvar__2__ls__17807] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2__ls__17807)
& Vv__CANONICAL__3 = cExtLib_2eData_2eMember_2eMZ___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2__ls__17807)
& c_24__case__ExtLib_2eData_2eMember_2emember_2417801___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cExtLib_2eData_2eMember_2eMZ___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2__ls__17807) )
| ? [Vvar__2__l__17810] :
( t(Vvar__2__l__17810,Vv__CANONICAL__0)
& ? [Vvar__3__ls__17811] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__3__ls__17811)
& ? [Vvar__4___24Anonymous__17812] :
( cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3__ls__17811,Vvar__4___24Anonymous__17812)
& Vv__CANONICAL__3 = cExtLib_2eData_2eMember_2eMN___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2__l__17810,Vvar__3__ls__17811,Vvar__4___24Anonymous__17812)
& c_24__case__ExtLib_2eData_2eMember_2emember_2417801___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cExtLib_2eData_2eMember_2eMN___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2__l__17810,Vvar__3__ls__17811,Vvar__4___24Anonymous__17812) ) ) ) ) ) ) ) ) ).
fof('$_def_$_let_11_subst_l_24915',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__24915___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_28087',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__28090] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28090)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28090)
& c_24__let__16__mkpow__28087___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__28091] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28091)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28091)
& c_24__let__16__mkpow__28087___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__28087___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_lnum_11934',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num] : c_24__let__17__lnum__11934___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num) ).
fof('$_def_$_let_17_mkopp_pow_28088',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__28088___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__28087___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_28089',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__28089___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__28087___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_20_lnum_12462',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num] : c_24__let__20__lnum__12462___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num) ).
fof('$_def_$_let_var_6_p_28807_28810',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28806] : c_24__let__var__6__p__28807__28810___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28806) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28806) ).
fof('$_def_$_let_var_6_p_28809_28811',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28808] : c_24__let__var__6__p__28809__28811___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28808) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28808) ).
fof('$_def_$_let_var_var_7_n_15725_15729_15738',axiom,
! [V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__15722] : c_24__let__var__var__7__n__15725__15729__15738___24a4(V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__15722) = cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,Vvar__2___24Anonymous__15722,V4__x) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
& V1__y = cCoq_2eInit_2eNat_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.Bool.Bool.Is_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24True) ) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24False) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V0__s)
<=> ! [V1__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__a)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__a,V0__s) ) ) ).
fof('$_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__37680] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37680)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37680)
& 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__37680,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf)) )
| ? [Vvar__0___24Anonymous__37681] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37681)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37681)
& 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__37681,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__37682] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__37682)
& ? [Vvar__1___24Anonymous__37683] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__37683)
& ? [Vvar__2___24Anonymous__37684] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__37684)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37682,Vvar__1___24Anonymous__37683,Vvar__2___24Anonymous__37684)
& ( ? [Vvar__0___24Anonymous__37697] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37697)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37697)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37682,Vvar__1___24Anonymous__37683,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__37697,Vvar__2___24Anonymous__37684)) )
| ? [Vvar__0___24Anonymous__37698] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37698)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37698)
& 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__37698,Vvar__0___24Anonymous__37682),Vvar__1___24Anonymous__37683,Vvar__2___24Anonymous__37684) )
| ( 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__37682,cCoq_2eInit_2eDatatypes_2etrue,Vvar__2___24Anonymous__37684) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__37664] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__37664)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__37664) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).
fof('$_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__45261] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__45261)
& ? [Vvar__1___24Anonymous__45262] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__45262)
& ? [Vvar__2___24Anonymous__45263] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__45263)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__45261,Vvar__1___24Anonymous__45262,Vvar__2___24Anonymous__45263)
& ( ? [Vvar__0___24Anonymous__45276] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45276)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45276)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__45276,Vvar__2___24Anonymous__45263) )
| ? [Vvar__0___24Anonymous__45277] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45277)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45277)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__45277,Vvar__0___24Anonymous__45261) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__45262 ) ) ) ) ) ) ) ) ) ).
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__45282] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45282)
& V1__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45282)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__45282,cCoq_2eNumbers_2eBinNums_2exI___24a1(V2__x)) )
| ? [Vvar__0___24Anonymous__45283] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45283)
& V1__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45283)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__45283,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('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__37678] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__37678)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__37678) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.xelements',axiom,
! [V1__m,V2__i,V3__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__m)
=> ( ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V1__m,V2__i,V3__a) = V3__a )
| ? [Vvar__0___24Anonymous__37705] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__37705)
& ? [Vvar__1___24Anonymous__37706] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__37706)
& ? [Vvar__2___24Anonymous__37707] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__37707)
& ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__37706)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37705,Vvar__1___24Anonymous__37706,Vvar__2___24Anonymous__37707)
& ( ( Vvar__1___24Anonymous__37706 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V1__m,V2__i,V3__a) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(Vvar__0___24Anonymous__37705,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__i),cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev___24a1(V2__i),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(Vvar__2___24Anonymous__37707,cCoq_2eNumbers_2eBinNums_2exI___24a1(V2__i),V3__a))) )
| ( Vvar__1___24Anonymous__37706 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V1__m,V2__i,V3__a) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(Vvar__0___24Anonymous__37705,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__i),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(Vvar__2___24Anonymous__37707,cCoq_2eNumbers_2eBinNums_2exI___24a1(V2__i),V3__a)) ) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__81] :
( t(Vvar__1___24Anonymous__81,V0__A)
& ? [Vvar__2___24Anonymous__82] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__82)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__81,Vvar__2___24Anonymous__82)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__81,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__82,V3__m)) ) ) ) ) ) ).
fof('$_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__5074] :
( t(Vvar__2___24Anonymous__5074,V0__A)
& ? [Vvar__3___24Anonymous__5075] :
( t(Vvar__3___24Anonymous__5075,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__5074,Vvar__3___24Anonymous__5075)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__5074 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__1972] :
( t(Vvar__1___24Anonymous__1972,V0__A)
& ? [Vvar__2___24Anonymous__1973] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1973)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1972,Vvar__2___24Anonymous__1973)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__1973)) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Datatypes.list_rect',axiom,
! [V0__A,V1__P,V2__f,V3__f,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__1926___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = V2__f )
| ? [Vvar__1___24Anonymous__1920] :
( t(Vvar__1___24Anonymous__1920,V0__A)
& ? [Vvar__2___24Anonymous__1921] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1921)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1920,Vvar__2___24Anonymous__1921)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = happ(happ(happ(V3__f,Vvar__1___24Anonymous__1920),Vvar__2___24Anonymous__1921),cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,Vvar__2___24Anonymous__1921)) ) ) ) ) ) ) ).
fof('$_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__5086] :
( t(Vvar__2___24Anonymous__5086,V0__A)
& ? [Vvar__3___24Anonymous__5087] :
( t(Vvar__3___24Anonymous__5087,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__5086,Vvar__3___24Anonymous__5087)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__5087 ) ) ) ) ) ).
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__2453] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2453)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2453)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__2453,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__38424] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__38424)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__38424)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__38427] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__38427)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__38427)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__38424,Vvar__0___24Anonymous__38427)) ) ) ) ) ) ) ) ).
fof('$_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__18125] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18125)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18125)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__18128] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18128)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18128)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__18125,Vvar__0___24Anonymous__18128)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__18122] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18122)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18122)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__18122,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pow',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__120157] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120157)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120157)
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__n,cCoq_2eInit_2eNat_2epow___24a2(V1__n,Vvar__0___24Anonymous__120157)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__38422] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__38422)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__38422)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__38422 ) ) ) ).
fof('$_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__2138] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2138)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2138)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__2141] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2141)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2141)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__2138,Vvar__0___24Anonymous__2141) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__35187___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__35181] :
( t(Vvar__2__x__35181,V0__A)
& p(happ(V1__P,Vvar__2__x__35181))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__35181)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__35181 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT1',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__35210___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__35204] :
( t(Vvar__2__x__35204,V0__A)
& ? [Vvar__3___24Anonymous__35205] :
( t(Vvar__3___24Anonymous__35205,happ(V1__P,Vvar__2__x__35204))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__35204,Vvar__3___24Anonymous__35205)
& cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__35204 ) ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT2',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__35233___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__35227] :
( t(Vvar__2__x__35227,V0__A)
& ? [Vvar__3___24Anonymous__35228] :
( t(Vvar__3___24Anonymous__35228,happ(V1__P,Vvar__2__x__35227))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__35227,Vvar__3___24Anonymous__35228)
& cCoq_2eInit_2eSpecif_2eprojT2___24a3(V0__A,V1__P,V2__x) = Vvar__3___24Anonymous__35228 ) ) ) ) ) ).
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)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__l))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__b,V2__l))
=> p(happ(happ(V1__R,V3__a),V4__b)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__93] :
( t(Vvar__1___24Anonymous__93,V0__A)
& ? [Vvar__2___24Anonymous__94] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__94)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__93,Vvar__2___24Anonymous__94)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> ( Vvar__1___24Anonymous__93 = V2__a
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__94)) ) ) ) ) ) ) ) ).
fof('$_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__16826] :
( t(Vvar__1___24Anonymous__16826,V0__A)
& ? [Vvar__2___24Anonymous__16827] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__16827)
& ( 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__16826,Vvar__2___24Anonymous__16827)
& ( ( 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__16838] :
( t(Vvar__1___24Anonymous__16838,V1__B)
& ? [Vvar__2___24Anonymous__16839] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__16839)
& V4__l_27 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__16838,Vvar__2___24Anonymous__16839)
& 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__16826,Vvar__1___24Anonymous__16838),cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,Vvar__2___24Anonymous__16827,Vvar__2___24Anonymous__16839)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.concat',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A))
& cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__2051] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__1___24Anonymous__2051)
& ? [Vvar__2___24Anonymous__2052] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__2052)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__1___24Anonymous__2051,Vvar__2___24Anonymous__2052)
& cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__1___24Anonymous__2051,cCoq_2eLists_2eList_2econcat___24a2(V0__A,Vvar__2___24Anonymous__2052)) ) ) ) ) ) ).
fof('$_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__15721] :
( t(Vvar__1___24Anonymous__15721,V0__A)
& ? [Vvar__2___24Anonymous__15722] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__15722)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__15721,Vvar__2___24Anonymous__15722)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_2415756___24a5(V0__A,V1__eq__dec,V4__x,Vvar__1___24Anonymous__15721,Vvar__2___24Anonymous__15722) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.existsb',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__3159] :
( t(Vvar__1___24Anonymous__3159,V0__A)
& ? [Vvar__2___24Anonymous__3160] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__3160)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3159,Vvar__2___24Anonymous__3160)
& cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(happ(V1__f,Vvar__1___24Anonymous__3159),cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__3160)) ) ) ) ) ) ).
fof('$_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__2369] :
( t(Vvar__1___24Anonymous__2369,V0__A)
& ? [Vvar__2___24Anonymous__2370] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2370)
& ( cType___24t(V0__A)
=> ( c_24__type__1217___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__2369,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2369,Vvar__2___24Anonymous__2370)
& ( ( happ(V1__f,Vvar__1___24Anonymous__2369) = 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__2369,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__2370)) )
| ( happ(V1__f,Vvar__1___24Anonymous__2369) = 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__2370) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.find',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__16725] :
( t(Vvar__1___24Anonymous__16725,V0__A)
& ? [Vvar__2___24Anonymous__16726] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__16726)
& ( cType___24t(V0__A)
=> ( c_24__type__1217___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__16725,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__16725,Vvar__2___24Anonymous__16726)
& ( ( happ(V1__f,Vvar__1___24Anonymous__16725) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__16725) )
| ( happ(V1__f,Vvar__1___24Anonymous__16725) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,Vvar__2___24Anonymous__16726) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__2058] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2058)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2058)
& ( ( 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__2065] :
( t(Vvar__1___24Anonymous__2065,V0__A)
& ? [Vvar__2___24Anonymous__2066] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2066)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2065,Vvar__2___24Anonymous__2066)
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2065,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,Vvar__0___24Anonymous__2058,Vvar__2___24Anonymous__2066)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.flat_map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__3053] :
( t(Vvar__1___24Anonymous__3053,V0__A)
& ? [Vvar__2___24Anonymous__3054] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__3054)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3053,Vvar__2___24Anonymous__3054)
& cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__3053),cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__3054)) ) ) ) ) ) ) ).
fof('$_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__3085] :
( t(Vvar__1___24Anonymous__3085,V1__B)
& ? [Vvar__2___24Anonymous__3086] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__3086)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__3085,Vvar__2___24Anonymous__3086)
& 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__3086,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__3085)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_right',axiom,
! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
| ? [Vvar__1___24Anonymous__3121] :
( t(Vvar__1___24Anonymous__3121,V1__B)
& ? [Vvar__2___24Anonymous__3122] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__3122)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__3121,Vvar__2___24Anonymous__3122)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__3121),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__3122)) ) ) ) ) ) ) ).
fof('$_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__3174] :
( t(Vvar__1___24Anonymous__3174,V0__A)
& ? [Vvar__2___24Anonymous__3175] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__3175)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3174,Vvar__2___24Anonymous__3175)
& cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eandb___24a2(happ(V1__f,Vvar__1___24Anonymous__3174),cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__3175)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd',axiom,
! [V0__A,V1__default,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = V1__default )
| ? [Vvar__1___24Anonymous__15482] :
( t(Vvar__1___24Anonymous__15482,V0__A)
& ? [Vvar__2___24Anonymous__15483] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__15483)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__15482,Vvar__2___24Anonymous__15483)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__15482 ) ) ) ) ) ).
fof('$_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__15493] :
( t(Vvar__1___24Anonymous__15493,V0__A)
& ? [Vvar__2___24Anonymous__15494] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__15494)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__15493,Vvar__2___24Anonymous__15494)
& cCoq_2eLists_2eList_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__15493) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.incl',axiom,
! [V0__A,V1__l,V2__m] :
( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m)) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__2292] :
( t(Vvar__1___24Anonymous__2292,V0__A)
& ? [Vvar__2___24Anonymous__2293] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2293)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2293)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2292,Vvar__2___24Anonymous__2293)
& ( ( Vvar__2___24Anonymous__2293 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__2292 )
| ? [Vvar__1___24Anonymous__2304] :
( t(Vvar__1___24Anonymous__2304,V0__A)
& ? [Vvar__2___24Anonymous__2305] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2305)
& Vvar__2___24Anonymous__2293 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2304,Vvar__2___24Anonymous__2305)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__2293,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.lel',axiom,
! [V0__A,V1__l,V2__m] :
( cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V2__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__m)) ) ).
fof('$_def_Coq.Lists.List.map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__2346] :
( t(Vvar__1___24Anonymous__2346,V0__A)
& ? [Vvar__2___24Anonymous__2347] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2347)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2346,Vvar__2___24Anonymous__2347)
& 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__2346),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__2347)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nodup',axiom,
! [V0__A,V1__decA,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_2enodup___24a3(V0__A,V1__decA,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__16894] :
( t(Vvar__1___24Anonymous__16894,V0__A)
& ? [Vvar__2___24Anonymous__16895] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__16895)
& ( cType___24t(V0__A)
=> ( c_24__type__15621___24t(V0__A,V1__decA)
=> ( t(Vvar__1___24Anonymous__16894,V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__16895)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895)
& ( ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895))
& cCoq_2eLists_2eList_2ein__dec___24a4(V0__A,V1__decA,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895),c_24__prop__16914___24a3(V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895))
& cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,V3__l) = cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,Vvar__2___24Anonymous__16895) )
| ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895))
& cCoq_2eLists_2eList_2ein__dec___24a4(V0__A,V1__decA,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895),c_24__prop__16926___24a3(V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895))
& cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__16894,cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,Vvar__2___24Anonymous__16895)) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__1982] :
( t(Vvar__1___24Anonymous__1982,V0__A)
& ? [Vvar__2___24Anonymous__1983] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1983)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1982,Vvar__2___24Anonymous__1983)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__1982 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__1985] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1985)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1985)
& ( ( 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__1992] :
( t(Vvar__1___24Anonymous__1992,V0__A)
& ? [Vvar__2___24Anonymous__1993] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1993)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1992,Vvar__2___24Anonymous__1993)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__1985,Vvar__2___24Anonymous__1993,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_default',axiom,
! [V0__A,V1__default,V2__l,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ? [Vvar__1___24Anonymous__15662] :
( t(Vvar__1___24Anonymous__15662,V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__15662)
& cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V1__default,V2__l,V3__n) = Vvar__1___24Anonymous__15662 )
| ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V1__default,V2__l,V3__n) = V1__default ) ) ) ) ) ).
fof('$_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__2007] :
( t(Vvar__1___24Anonymous__2007,V0__A)
& ? [Vvar__2___24Anonymous__2008] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2008)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2007,Vvar__2___24Anonymous__2008)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__2007) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2010] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2010)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2010)
& ( ( 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__2017] :
( t(Vvar__1___24Anonymous__2017,V0__A)
& ? [Vvar__2___24Anonymous__2018] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2018)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2017,Vvar__2___24Anonymous__2018)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,Vvar__2___24Anonymous__2018,Vvar__0___24Anonymous__2010) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_ok',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__15630] :
( t(Vvar__1___24Anonymous__15630,V0__A)
& ? [Vvar__2___24Anonymous__15631] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__15631)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__15630,Vvar__2___24Anonymous__15631)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__15633] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15633)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__15633)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__15640] :
( t(Vvar__1___24Anonymous__15640,V0__A)
& ? [Vvar__2___24Anonymous__15641] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__15641)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__15640,Vvar__2___24Anonymous__15641)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,Vvar__0___24Anonymous__15633,Vvar__2___24Anonymous__15641,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.partition',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_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) )
| ? [Vvar__1___24Anonymous__16744] :
( t(Vvar__1___24Anonymous__16744,V0__A)
& ? [Vvar__2___24Anonymous__16745] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__16745)
& ( cType___24t(V0__A)
=> ( c_24__type__1217___24t(V0__A,V1__f)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__16745)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__16744,Vvar__2___24Anonymous__16745)
& ? [Vvar__2___24Anonymous__16759] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__16759)
& ? [Vvar__3___24Anonymous__16760] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__3___24Anonymous__16760)
& ( cType___24t(V0__A)
=> ( c_24__type__1217___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__16744,V0__A)
=> ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,Vvar__2___24Anonymous__16745) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__16759,Vvar__3___24Anonymous__16760)
& ( ( happ(V1__f,Vvar__1___24Anonymous__16744) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__16744,Vvar__2___24Anonymous__16759),Vvar__3___24Anonymous__16760) )
| ( happ(V1__f,Vvar__1___24Anonymous__16744) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__16759,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__16744,Vvar__3___24Anonymous__16760)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.remove',axiom,
! [V0__A,V1__eq__dec,V3__x,V4__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__15676] :
( t(Vvar__1___24Anonymous__15676,V0__A)
& ? [Vvar__2___24Anonymous__15677] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__15677)
& ( cType___24t(V0__A)
=> ( c_24__type__15621___24t(V0__A,V1__eq__dec)
=> ( t(V3__x,V0__A)
=> ( t(Vvar__1___24Anonymous__15676,V0__A)
=> ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__15676,Vvar__2___24Anonymous__15677)
& ( ( V3__x = Vvar__1___24Anonymous__15676
& happ(happ(V1__eq__dec,V3__x),Vvar__1___24Anonymous__15676) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__15696___24a3(V0__A,V3__x,Vvar__1___24Anonymous__15676),c_24__prop__15697___24a3(V0__A,V3__x,Vvar__1___24Anonymous__15676))
& cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,V4__l) = cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,Vvar__2___24Anonymous__15677) )
| ( V3__x != Vvar__1___24Anonymous__15676
& happ(happ(V1__eq__dec,V3__x),Vvar__1___24Anonymous__15676) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__15698___24a3(V0__A,V3__x,Vvar__1___24Anonymous__15676),c_24__prop__15699___24a3(V0__A,V3__x,Vvar__1___24Anonymous__15676))
& cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__15676,cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,Vvar__2___24Anonymous__15677)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__2316] :
( t(Vvar__1___24Anonymous__2316,V0__A)
& ? [Vvar__2___24Anonymous__2317] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2317)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2317)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2316,Vvar__2___24Anonymous__2317)
& ( ( Vvar__2___24Anonymous__2317 = 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__2328] :
( t(Vvar__1___24Anonymous__2328,V0__A)
& ? [Vvar__2___24Anonymous__2329] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2329)
& Vvar__2___24Anonymous__2317 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2328,Vvar__2___24Anonymous__2329)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2316,cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,Vvar__2___24Anonymous__2317)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.repeat',axiom,
! [V0__A,V2__x,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,V3__n) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__0___24Anonymous__17481] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17481)
& V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17481)
& cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,V3__n) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,Vvar__0___24Anonymous__17481)) ) ) ) ) ).
fof('$_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__105] :
( t(Vvar__1___24Anonymous__105,V0__A)
& ? [Vvar__2___24Anonymous__106] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__106)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__105,Vvar__2___24Anonymous__106)
& 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__106),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__105,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__2336] :
( t(Vvar__1___24Anonymous__2336,V0__A)
& ? [Vvar__2___24Anonymous__2337] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2337)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2336,Vvar__2___24Anonymous__2337)
& cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V2__l,V3__l_27) = cCoq_2eLists_2eList_2erev__append___24a3(V0__A,Vvar__2___24Anonymous__2337,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2336,V3__l_27)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.seq',axiom,
! [V1__start,V2__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__len)
=> ( ( V2__len = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__0___24Anonymous__2443] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2443)
& V2__len = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2443)
& cCoq_2eLists_2eList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,V1__start,cCoq_2eLists_2eList_2eseq___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__start),Vvar__0___24Anonymous__2443)) ) ) ) ).
fof('$_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__2404] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2404)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2404)
& ( ( 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__2411] :
( t(Vvar__1___24Anonymous__2411,V0__A)
& ? [Vvar__2___24Anonymous__2412] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2412)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2411,Vvar__2___24Anonymous__2412)
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = cCoq_2eLists_2eList_2eskipn___24a3(V0__A,Vvar__0___24Anonymous__2404,Vvar__2___24Anonymous__2412) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.split',axiom,
! [V0__A,V1__B,V3__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B))
& cCoq_2eLists_2eList_2esplit___24a3(V0__A,V1__B,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)) )
| ? [Vvar__1___24Anonymous__16782] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,Vvar__1___24Anonymous__16782)
& ? [Vvar__2___24Anonymous__16783] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),Vvar__2___24Anonymous__16783)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,Vvar__1___24Anonymous__16782)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),Vvar__1___24Anonymous__16782,Vvar__2___24Anonymous__16783)
& ? [Vvar__2___24Anonymous__16801] :
( t(Vvar__2___24Anonymous__16801,V0__A)
& ? [Vvar__3___24Anonymous__16802] :
( t(Vvar__3___24Anonymous__16802,V1__B)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),Vvar__2___24Anonymous__16783)
=> ( Vvar__1___24Anonymous__16782 = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__16801,Vvar__3___24Anonymous__16802)
& ? [Vvar__2___24Anonymous__16814] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__16814)
& ? [Vvar__3___24Anonymous__16815] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__3___24Anonymous__16815)
& cCoq_2eLists_2eList_2esplit___24a3(V0__A,V1__B,Vvar__2___24Anonymous__16783) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),Vvar__2___24Anonymous__16814,Vvar__3___24Anonymous__16815)
& cCoq_2eLists_2eList_2esplit___24a3(V0__A,V1__B,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__2___24Anonymous__16801,Vvar__2___24Anonymous__16814),cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__3___24Anonymous__16802,Vvar__3___24Anonymous__16815)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__3037] :
( t(Vvar__1___24Anonymous__3037,V0__A)
& ? [Vvar__2___24Anonymous__3038] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__3038)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3037,Vvar__2___24Anonymous__3038)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__3038 ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.equivlistA',axiom,
! [V0__A,V1__eqA,V2__l,V3__l_27] :
( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l)
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l_27) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.inclA',axiom,
! [V0__A,V1__eqA,V2__l,V3__l_27] :
( cCoq_2eLists_2eSetoidList_2einclA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l_27) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.removeA',axiom,
! [V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__34438___24t(V0__A,V1__eqA,V1__eqA)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__34414] :
( t(Vvar__1___24Anonymous__34414,V0__A)
& ? [Vvar__2___24Anonymous__34415] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__34415)
& ( cType___24t(V0__A)
=> ( c_24__type__34447___24t(V0__A,V1__eqA,V1__eqA)
=> ( c_24__type__34456___24t(V0__A,V1__eqA,V2__eqA__dec)
=> ( t(V4__x,V0__A)
=> ( t(Vvar__1___24Anonymous__34414,V0__A)
=> ( V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__34414,Vvar__2___24Anonymous__34415)
& ( ( p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__34414))
& happ(happ(V2__eqA__dec,V4__x),Vvar__1___24Anonymous__34414) = cCoq_2eInit_2eSpecif_2eleft___24a2(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__34414),c_24__prop__34459___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__34414))
& cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l) = cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,Vvar__2___24Anonymous__34415) )
| ( ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__34414))
& happ(happ(V2__eqA__dec,V4__x),Vvar__1___24Anonymous__34414) = cCoq_2eInit_2eSpecif_2eright___24a2(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__34414),c_24__prop__34460___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__34414))
& cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__34414,cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,Vvar__2___24Anonymous__34415)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V6__z)))) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose2',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> ! [V7__z_27] :
( t(V7__z_27,V1__B)
=> ( p(happ(happ(V2__eqB,V6__z),V7__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V7__z_27)))) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V7__z)))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr2',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ! [V8__z_27] :
( t(V8__z_27,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> ( p(happ(happ(V2__eqB,V7__z),V8__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V8__z_27)))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
! [V0__U,V1__P,V2__p,V3__x] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V0__U,V1__P,V2__p,V3__x)
<=> ! [V4__y] :
( t(V4__y,happ(V1__P,V2__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
=> V3__x = V4__y ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Eq_rect_eq_on',axiom,
! [V0__U,V1__p,V2__Q,V3__x] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V0__U,V1__p,V2__Q,V3__x)
<=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
! [V0__U,V1__x,V2__P] :
( cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V0__U,V1__x,V2__P)
<=> ( p(happ(V2__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x)))
=> ( V1__x = V1__x
=> p(V2__P) ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.UIP_on_',axiom,
! [V0__U,V1__x,V2__y] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V0__U,V1__x,V2__y)
<=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ).
fof('$_def_Coq.NArith.BinNat.N.divide',axiom,
! [V0__p,V1__q] :
( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__p,V1__q)
<=> ? [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__r)
& V1__q = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__r,V0__p) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__37600] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37600)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37600)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__37603] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37603)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37603)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__37600,Vvar__0___24Anonymous__37603)) ) ) ) ) ) ) ) ).
fof('$_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__37619] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37619)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37619)
& ( ( 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__37622] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37622)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37622)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__37619,V1__b) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__37611] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37611)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37611)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__37612] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37612)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37612)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__37615] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37615)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37615)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__37612,Vvar__0___24Anonymous__37615) ) ) ) ) ) ) ) ).
fof('$_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__37605] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37605)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37605)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__37608] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37608)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37608)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__37605,Vvar__0___24Anonymous__37608)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__116350] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__116350)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__116350)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__116350)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__116414] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__116414)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__116414)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__116414,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__37626] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37626)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37626)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__37626) ) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
! [V0__x,V1__y] :
( p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y))
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__37631] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37631)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37631)
& ( ? [Vvar__0___24Anonymous__37635] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37635)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37635)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__37630__1__add__carry___24a2(Vvar__0___24Anonymous__37631,Vvar__0___24Anonymous__37635)) )
| ? [Vvar__0___24Anonymous__37636] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37636)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37636)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__37631,Vvar__0___24Anonymous__37636)) )
| ( 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__37631)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__37637] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37637)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37637)
& ( ? [Vvar__0___24Anonymous__37641] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37641)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37641)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__37637,Vvar__0___24Anonymous__37641)) )
| ? [Vvar__0___24Anonymous__37642] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37642)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37642)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__37637,Vvar__0___24Anonymous__37642)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37637) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__37643] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37643)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37643)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__37643)) )
| ? [Vvar__0___24Anonymous__37644] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37644)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37644)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37644) )
| ( 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__116529] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__116529)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__116529)
& 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__116529),Vvar__0___24Anonymous__116529)) )
| ? [Vvar__0___24Anonymous__116530] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__116530)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__116530)
& 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__116530),Vvar__0___24Anonymous__116530) )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__4739] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4739)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4739)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__4739)) )
| ? [Vvar__0___24Anonymous__4740] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4740)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__4740)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__4740)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_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__45251] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45251)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__45251)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__45251 )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__4736] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4736)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4736)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__4736)) )
| ? [Vvar__0___24Anonymous__4737] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4737)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__4737)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4737) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.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.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.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__19673] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19673)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19673)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__19673) )
| ? [Vvar__0___24Anonymous__19674] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19674)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19674)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__19674)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rdefinitions.Rge',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__33706] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33706)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33706)
& 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__33706)) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__646___24a1(V0__A) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Sets.Relations_1.Transitive',axiom,
! [V0__U,V1__R] :
( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__U,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ! [V4__z] :
( t(V4__z,V0__U)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Sorting.Sorted.StronglySorted_rect',axiom,
! [V0__A,V1__R,V2__P,V3__X,V4__X0,V5__l] : cCoq_2eSorting_2eSorted_2eStronglySorted__rect___24a6(V0__A,V1__R,V2__P,V3__X,V4__X0,V5__l) = cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,c_24__lam__34898___24a3(V0__A,V1__R,V2__P),c_24__lam__34917___24a4(V0__A,V1__R,V2__P,V3__X),c_24__lam__34982___24a4(V0__A,V1__R,V2__P,V4__X0),V5__l) ).
fof('$_def_Coq.Strings.String.list_ascii_of_string',axiom,
! [V1__s] :
( cCoq_2eStrings_2eString_2estring___24t(V1__s)
=> ( ( V1__s = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2elist__ascii__of__string___24a1(V1__s) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eStrings_2eAscii_2eascii) )
| ? [Vvar__0___24Anonymous__35417] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__35417)
& ? [Vvar__1___24Anonymous__35418] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__35418)
& V1__s = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__35417,Vvar__1___24Anonymous__35418)
& cCoq_2eStrings_2eString_2elist__ascii__of__string___24a1(V1__s) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eStrings_2eAscii_2eascii,Vvar__0___24Anonymous__35417,cCoq_2eStrings_2eString_2elist__ascii__of__string___24a1(Vvar__1___24Anonymous__35418)) ) ) ) ) ).
fof('$_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__35411] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1___24Anonymous__35411)
& ? [Vvar__2___24Anonymous__35412] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,Vvar__2___24Anonymous__35412)
& V1__s = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eStrings_2eAscii_2eascii,Vvar__1___24Anonymous__35411,Vvar__2___24Anonymous__35412)
& cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(V1__s) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1___24Anonymous__35411,cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(Vvar__2___24Anonymous__35412)) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [Vvar__48190] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__48190)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__48190) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__48191] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__48191)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__48191) ) ).
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__48189] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__48189)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__48189) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__48192] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__48192)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__48192) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__48193] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__48193)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__48193) ) ).
fof('$_def_Coq.Vectors.VectorDef.of_list',axiom,
! [V1__A,V2__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& cCoq_2eVectors_2eVectorDef_2eof__list___24a2(V1__A,V2__l) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A) )
| ? [Vvar__1___24Anonymous__36629] :
( t(Vvar__1___24Anonymous__36629,V1__A)
& ? [Vvar__2___24Anonymous__36630] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__36630)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__36629,Vvar__2___24Anonymous__36630)
& cCoq_2eVectors_2eVectorDef_2eof__list___24a2(V1__A,V2__l) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1___24Anonymous__36629,cCoq_2eInit_2eDatatypes_2elength___24a2(V1__A,Vvar__2___24Anonymous__36630),cCoq_2eVectors_2eVectorDef_2eof__list___24a2(V1__A,Vvar__2___24Anonymous__36630)) ) ) ) ) ) ).
fof('$_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__36692__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.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__117514] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__117514)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__117514)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__117514) )
| ? [Vvar__0___24Anonymous__117515] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__117515)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__117515)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__117515) ) ) ) ).
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__37744] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37744)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37744)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__37748] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37748)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37748)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__37744,Vvar__0___24Anonymous__37748)) )
| ? [Vvar__0___24Anonymous__37749] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37749)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37749)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__37744,Vvar__0___24Anonymous__37749) ) ) ) ) )
| ? [Vvar__0___24Anonymous__37750] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37750)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37750)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__37754] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37754)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37754)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__37754,Vvar__0___24Anonymous__37750) )
| ? [Vvar__0___24Anonymous__37755] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37755)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37755)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__37750,Vvar__0___24Anonymous__37755)) ) ) ) ) ) ) ) ).
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__45315] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45315)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45315)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__45316] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45316)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__45316)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__45317] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45317)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45317)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__45321] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45321)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45321)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__45317,Vvar__0___24Anonymous__45321) )
| ? [Vvar__0___24Anonymous__45322] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45322)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__45322)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__45323] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45323)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__45323)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__45327] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45327)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45327)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__45328] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45328)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__45328)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__45323,Vvar__0___24Anonymous__45328)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__117520] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__117520)
& ? [Vvar__3___24Anonymous__117521] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__117521)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__117520,Vvar__3___24Anonymous__117521)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__117520 ) ) ) ) ).
fof('$_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('$_def_Coq.ZArith.BinIntDef.Z.min',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__117528] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__117528)
& ? [Vvar__3___24Anonymous__117529] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__117529)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__117528,Vvar__3___24Anonymous__117529)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__117529 ) ) ) ) ).
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__37764] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37764)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37764)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__37768] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37768)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37768)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__37764,Vvar__0___24Anonymous__37768)) )
| ? [Vvar__0___24Anonymous__37769] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37769)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37769)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__37764,Vvar__0___24Anonymous__37769)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__37770] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37770)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37770)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__37774] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37774)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37774)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__37770,Vvar__0___24Anonymous__37774)) )
| ? [Vvar__0___24Anonymous__37775] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37775)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37775)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__37770,Vvar__0___24Anonymous__37775)) ) ) ) ) ) ) ) ).
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__37784] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37784)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37784)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37784) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__37781] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__37781)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__37781)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__37781)) ) ) ) ).
fof('$_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__37759] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37759)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37759)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37759) )
| ? [Vvar__0___24Anonymous__37760] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37760)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37760)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37760) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pos_sub',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__37727] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37727)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37727)
& ( ? [Vvar__0___24Anonymous__37731] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37731)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37731)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__37727,Vvar__0___24Anonymous__37731)) )
| ? [Vvar__0___24Anonymous__37732] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37732)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37732)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__37727,Vvar__0___24Anonymous__37732)) )
| ( V2__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37727)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__37733] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37733)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37733)
& ( ? [Vvar__0___24Anonymous__37737] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37737)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37737)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred__double___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__37733,Vvar__0___24Anonymous__37737)) )
| ? [Vvar__0___24Anonymous__37738] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37738)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37738)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__37733,Vvar__0___24Anonymous__37738)) )
| ( V2__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__37733)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__37739] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37739)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37739)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37739)) )
| ? [Vvar__0___24Anonymous__37740] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37740)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37740)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__37740)) )
| ( V2__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ) ).
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__37777] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37777)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37777)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__37777) )
| ? [Vvar__0___24Anonymous__37778] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37778)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37778)
& 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__37787] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37787)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37787)
& ( ( 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__37797] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37797)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37787)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37797)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37797)
& ? [Vvar__2___24Anonymous__37805] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__37805)
& ? [Vvar__3___24Anonymous__37806] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__37806)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__37787,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37797)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__37805,Vvar__3___24Anonymous__37806)
& 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__37805),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__37806)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__37808] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37808)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37787)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37808)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37808)
& ? [Vvar__2___24Anonymous__37816] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__37816)
& ? [Vvar__3___24Anonymous__37817] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__37817)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__37787,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37808)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__37816,Vvar__3___24Anonymous__37817)
& 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__37816)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__37817)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__37819] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37819)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37819)
& ( ( 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__37829] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37829)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37819)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37829)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37829)
& ? [Vvar__2___24Anonymous__37837] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__37837)
& ? [Vvar__3___24Anonymous__37838] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__37838)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__37819,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37829)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__37837,Vvar__3___24Anonymous__37838)
& 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__37837)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__37838))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__37840] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37840)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37819)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37840)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37840)
& ? [Vvar__2___24Anonymous__37848] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__37848)
& ? [Vvar__3___24Anonymous__37849] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__37849)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__37819,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37840)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__37848,Vvar__3___24Anonymous__37849)
& 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__37848),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__37849))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zcomplements.Zlength',axiom,
cCoq_2eZArith_2eZcomplements_2eZlength = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('$_def_Coq.ZArith.Zcomplements.Zlength_aux',axiom,
! [V1__acc,V2__A,V3__l] :
( cType___24t(V2__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V2__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__A)
& cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V1__acc,V2__A,V3__l) = V1__acc )
| ? [Vvar__1___24Anonymous__37587] :
( t(Vvar__1___24Anonymous__37587,V2__A)
& ? [Vvar__2___24Anonymous__37588] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V2__A,Vvar__2___24Anonymous__37588)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__A,Vvar__1___24Anonymous__37587,Vvar__2___24Anonymous__37588)
& 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__37588) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__5123___24a1(V0__D) ).
fof('$_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__3269] :
( t(Vvar__1___24Anonymous__3269,V1__A)
& ? [Vvar__2___24Anonymous__3270] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__3270)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__3270)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__3269,Vvar__2___24Anonymous__3270)
& ( ( Vvar__2___24Anonymous__3270 = 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__3269)) ) )
| ? [Vvar__1___24Anonymous__3281] :
( t(Vvar__1___24Anonymous__3281,V1__A)
& ? [Vvar__2___24Anonymous__3282] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__3282)
& Vvar__2___24Anonymous__3270 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__3281,Vvar__2___24Anonymous__3282)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__3269))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__3270) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__19681] :
( t(Vvar__1___24Anonymous__19681,V1__A)
& ? [Vvar__2___24Anonymous__19682] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__19682)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__19681,Vvar__2___24Anonymous__19682)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__19681))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__19682,V4__goal) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.micromega.RingMicromega.ge_bool',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__20445] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20445)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20445)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__20446] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20446)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20446)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__20449] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20449)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20449)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(Vvar__0___24Anonymous__20446,Vvar__0___24Anonymous__20449) ) ) ) ) ) ) ) ).
fof('$_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_checker',axiom,
! [V0__Term_27,V1__Annot,V2__Witness,V3__checker,V5__f,V6__l] :
( cType___24t(V0__Term_27)
=> ( cType___24t(V1__Annot)
=> ( cType___24t(V2__Witness)
=> ( 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_2ecnf__checker___24a6(V0__Term_27,V1__Annot,V2__Witness,V3__checker,V5__f,V6__l) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__1___24Anonymous__36293] :
( cCoq_2emicromega_2eTauto_2eclause___24t(V0__Term_27,V1__Annot,Vvar__1___24Anonymous__36293)
& ? [Vvar__2___24Anonymous__36294] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot),Vvar__2___24Anonymous__36294)
& ( cType___24t(V0__Term_27)
=> ( cType___24t(V1__Annot)
=> ( cType___24t(V2__Witness)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V2__Witness,V6__l)
=> ( V5__f = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot),Vvar__1___24Anonymous__36293,Vvar__2___24Anonymous__36294)
& ( ( V6__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__Witness)
& cCoq_2emicromega_2eTauto_2ecnf__checker___24a6(V0__Term_27,V1__Annot,V2__Witness,V3__checker,V5__f,V6__l) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__36307] :
( t(Vvar__1___24Anonymous__36307,V2__Witness)
& ? [Vvar__2___24Anonymous__36308] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V2__Witness,Vvar__2___24Anonymous__36308)
& ( cType___24t(V0__Term_27)
=> ( cType___24t(V1__Annot)
=> ( cType___24t(V2__Witness)
=> ( c_24__type__36319___24t(V0__Term_27,V1__Annot,V2__Witness,V3__checker)
=> ( cCoq_2emicromega_2eTauto_2eclause___24t(V0__Term_27,V1__Annot,Vvar__1___24Anonymous__36293)
=> ( t(Vvar__1___24Anonymous__36307,V2__Witness)
=> ( V6__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__Witness,Vvar__1___24Anonymous__36307,Vvar__2___24Anonymous__36308)
& ( ( happ(happ(V3__checker,Vvar__1___24Anonymous__36293),Vvar__1___24Anonymous__36307) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2emicromega_2eTauto_2ecnf__checker___24a6(V0__Term_27,V1__Annot,V2__Witness,V3__checker,V5__f,V6__l) = cCoq_2emicromega_2eTauto_2ecnf__checker___24a6(V0__Term_27,V1__Annot,V2__Witness,V3__checker,Vvar__2___24Anonymous__36294,Vvar__2___24Anonymous__36308) )
| ( happ(happ(V3__checker,Vvar__1___24Anonymous__36293),Vvar__1___24Anonymous__36307) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2emicromega_2eTauto_2ecnf__checker___24a6(V0__Term_27,V1__Annot,V2__Witness,V3__checker,V5__f,V6__l) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__4389] :
( t(Vvar__4___24Anonymous__4389,V1__TX)
& V5__f = cCoq_2emicromega_2eTauto_2eX___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__4389)
& 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__4394] :
( t(Vvar__4___24Anonymous__4394,V0__TA)
& ? [Vvar__5___24Anonymous__4395] :
( t(Vvar__5___24Anonymous__4395,V2__AA)
& V5__f = cCoq_2emicromega_2eTauto_2eA___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__4394,Vvar__5___24Anonymous__4395)
& 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__4395,cCoq_2eInit_2eDatatypes_2enil___24a1(V2__AA)) ) )
| ? [Vvar__4___24Anonymous__4401] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__4401)
& ? [Vvar__5___24Anonymous__4402] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__4402)
& V5__f = cCoq_2emicromega_2eTauto_2eCj___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__4401,Vvar__5___24Anonymous__4402)
& 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__4401),cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__4402)) ) )
| ? [Vvar__4___24Anonymous__4408] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__4408)
& ? [Vvar__5___24Anonymous__4409] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__4409)
& V5__f = cCoq_2emicromega_2eTauto_2eD___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__4408,Vvar__5___24Anonymous__4409)
& 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__4408),cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__4409)) ) )
| ? [Vvar__4___24Anonymous__4415] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__4415)
& V5__f = cCoq_2emicromega_2eTauto_2eN___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__4415)
& 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__4415) )
| ? [Vvar__4___24Anonymous__4420] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__4420)
& ? [Vvar__5___24Anonymous__4421] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V3__AF,Vvar__5___24Anonymous__4421)
& ? [Vvar__6___24Anonymous__4422] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__4422)
& V5__f = cCoq_2emicromega_2eTauto_2eI___24a7(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__4420,Vvar__5___24Anonymous__4421,Vvar__6___24Anonymous__4422)
& 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__4420),cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__4422)) ) ) ) ) ) ) ) ) ) ).
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__35428] :
( t(Vvar__1___24Anonymous__35428,V0__AF)
& V1__id = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__AF,Vvar__1___24Anonymous__35428)
& cCoq_2emicromega_2eTauto_2econs__id___24a3(V0__AF,V1__id,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__AF,Vvar__1___24Anonymous__35428,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('$_def_Coq.micromega.Tauto.eval_clause',axiom,
! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__cl] :
( cCoq_2emicromega_2eTauto_2eeval__clause___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__cl)
<=> ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V1__Term_27,V2__Annot),cCoq_2emicromega_2eTauto_2eeval__tt___24a5(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env),V5__cl) ) ).
fof('$_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__35518] :
( t(Vvar__4___24Anonymous__35518,V1__TX)
& V7__f = cCoq_2emicromega_2eTauto_2eX___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__35518)
& ( 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__35518)) ) )
| ? [Vvar__4___24Anonymous__35523] :
( t(Vvar__4___24Anonymous__35523,V0__TA)
& ? [Vvar__5___24Anonymous__35524] :
( t(Vvar__5___24Anonymous__35524,V2__AA)
& V7__f = cCoq_2emicromega_2eTauto_2eA___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__35523,Vvar__5___24Anonymous__35524)
& ( 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__35523)) ) ) )
| ? [Vvar__4___24Anonymous__35530] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__35530)
& ? [Vvar__5___24Anonymous__35531] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__35531)
& V7__f = cCoq_2emicromega_2eTauto_2eCj___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__35530,Vvar__5___24Anonymous__35531)
& ( 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__35530)
& cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__35531) ) ) ) )
| ? [Vvar__4___24Anonymous__35537] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__35537)
& ? [Vvar__5___24Anonymous__35538] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__35538)
& V7__f = cCoq_2emicromega_2eTauto_2eD___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__35537,Vvar__5___24Anonymous__35538)
& ( 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__35537)
| cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__35538) ) ) ) )
| ? [Vvar__4___24Anonymous__35544] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__35544)
& V7__f = cCoq_2emicromega_2eTauto_2eN___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__35544)
& ( 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__35544) ) )
| ? [Vvar__4___24Anonymous__35549] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__35549)
& ? [Vvar__5___24Anonymous__35550] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V3__AF,Vvar__5___24Anonymous__35550)
& ? [Vvar__6___24Anonymous__35551] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__35551)
& V7__f = cCoq_2emicromega_2eTauto_2eI___24a7(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__35549,Vvar__5___24Anonymous__35550,Vvar__6___24Anonymous__35551)
& ( 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__35549)
=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__6___24Anonymous__35551) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.eval_tt',axiom,
! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__tt] :
( cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__tt)
<=> p(happ(happ(V3__eval_27,V4__env),cCoq_2eInit_2eDatatypes_2efst___24a3(V1__Term_27,V2__Annot,V5__tt))) ) ).
fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
! [Vvar__36708] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__36708)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__36708) ) ).
fof('$_def_Coq.micromega.ZMicromega.Zunsat',axiom,
cCoq_2emicromega_2eZMicromega_2eZunsat = cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_def_Coq.micromega.ZMicromega.is_pol_Z0',axiom,
! [V0__p] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,V0__p)
=> ( ? [Vvar__1___24Anonymous__37010] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__37010)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__37010)
=> ( V0__p = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__37010)
& ( ( Vvar__1___24Anonymous__37010 = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2emicromega_2eZMicromega_2eis__pol__Z0___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__37014] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37014)
& Vvar__1___24Anonymous__37010 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37014)
& cCoq_2emicromega_2eZMicromega_2eis__pol__Z0___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__37015] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37015)
& Vvar__1___24Anonymous__37010 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37015)
& cCoq_2emicromega_2eZMicromega_2eis__pol__Z0___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__1___24Anonymous__37017] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__37017)
& ? [Vvar__2___24Anonymous__37018] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__37018)
& V0__p = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__37017,Vvar__2___24Anonymous__37018)
& cCoq_2emicromega_2eZMicromega_2eis__pol__Z0___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__37021] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__37021)
& ? [Vvar__2___24Anonymous__37022] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__37022)
& ? [Vvar__3___24Anonymous__37023] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3___24Anonymous__37023)
& V0__p = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__37021,Vvar__2___24Anonymous__37022,Vvar__3___24Anonymous__37023)
& cCoq_2emicromega_2eZMicromega_2eis__pol__Z0___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).
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('$_def_Coq.setoid_ring.BinList.jump',axiom,
! [V0__A,V2__p,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( ? [Vvar__0___24Anonymous__2666] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2666)
& V2__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2666)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__2666,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__2666,cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l))) )
| ? [Vvar__0___24Anonymous__2667] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2667)
& V2__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2667)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__2667,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__2667,V3__l)) )
| ( V2__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l) ) ) ) ) ).
fof('$_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__5001] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5001)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__5001)
& 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__5001,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__5001,cCoq_2eLists_2eList_2etl___24a2(V0__A,V4__l))) )
| ? [Vvar__0___24Anonymous__5002] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5002)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__5002)
& 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__5002,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__5002,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__10905] :
( t(Vvar__1___24Anonymous__10905,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__10905)
& 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__10905) )
| ? [Vvar__1___24Anonymous__10907] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10907)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__10907)
& 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__10907,V15__l) )
| ? [Vvar__1___24Anonymous__10909] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10909)
& ? [Vvar__2___24Anonymous__10910] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__10910)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__10909,Vvar__2___24Anonymous__10910)
& 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__10909)),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__10910)) ) )
| ? [Vvar__1___24Anonymous__10913] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10913)
& ? [Vvar__2___24Anonymous__10914] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__10914)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__10913,Vvar__2___24Anonymous__10914)
& 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__10913)),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__10914)) ) )
| ? [Vvar__1___24Anonymous__10917] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10917)
& ? [Vvar__2___24Anonymous__10918] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__10918)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__10917,Vvar__2___24Anonymous__10918)
& 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__10917)),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__10918)) ) )
| ? [Vvar__1___24Anonymous__10921] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10921)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__10921)
& 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__10921)) )
| ? [Vvar__1___24Anonymous__10923] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10923)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__10923)
& 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__10923)) )
| ? [Vvar__1___24Anonymous__10925] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10925)
& ? [Vvar__2___24Anonymous__10926] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__10926)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__10925,Vvar__2___24Anonymous__10926)
& 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__10925)),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__10926)) ) )
| ? [Vvar__1___24Anonymous__10929] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10929)
& ? [Vvar__2___24Anonymous__10930] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__10930)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__10929,Vvar__2___24Anonymous__10930)
& 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__10929)),happ(V12__Cp__phi,Vvar__2___24Anonymous__10930)) ) ) ) ) ) ) ) ).
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__13665] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13665)
& ? [Vvar__2___24Anonymous__13666] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__13666)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__13665,Vvar__2___24Anonymous__13666)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__13665),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__13666,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fcons',axiom,
! [V0__C,V1__ceqb,V3__e,V4__l] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFcons___24a4(V0__C,V1__ceqb,V3__e,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__e,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__13734] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13734)
& ? [Vvar__2___24Anonymous__13735] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__13735)
& ( cType___24t(V0__C)
=> ( c_24__type__5381___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V3__e)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13734)
=> ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__13734,Vvar__2___24Anonymous__13735)
& ( ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,Vvar__1___24Anonymous__13734) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eFcons___24a4(V0__C,V1__ceqb,V3__e,V4__l) = V4__l )
| ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,Vvar__1___24Anonymous__13734) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eFcons___24a4(V0__C,V1__ceqb,V3__e,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__13734,cCoq_2esetoid__ring_2eField__theory_2eFcons___24a4(V0__C,V1__ceqb,V3__e,Vvar__2___24Anonymous__13735)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fcons00',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V10__e)
=> ( ( V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) )
| ( V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) )
| ? [Vvar__1___24Anonymous__13984] :
( t(Vvar__1___24Anonymous__13984,V0__C)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13984)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) )
| ? [Vvar__1___24Anonymous__13986] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13986)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13986)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) )
| ? [Vvar__1___24Anonymous__13988] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13988)
& ? [Vvar__2___24Anonymous__13989] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13989)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13988,Vvar__2___24Anonymous__13989)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) ) )
| ? [Vvar__1___24Anonymous__13992] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13992)
& ? [Vvar__2___24Anonymous__13993] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13993)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13992,Vvar__2___24Anonymous__13993)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) ) )
| ? [Vvar__1___24Anonymous__13996] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13996)
& ? [Vvar__2___24Anonymous__13997] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13997)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13996,Vvar__2___24Anonymous__13997)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__1___24Anonymous__13996,cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__13997,V11__l)) ) )
| ? [Vvar__1___24Anonymous__14000] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14000)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14000)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) )
| ? [Vvar__1___24Anonymous__14002] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14002)
& ? [Vvar__2___24Anonymous__14003] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14003)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14002,Vvar__2___24Anonymous__14003)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__1___24Anonymous__14002,V11__l) ) ) ) ) ) ).
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.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__9675] :
( t(Vvar__1___24Anonymous__9675,V0__C)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__9675)
& 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__9675)) )
| ? [Vvar__1___24Anonymous__9677] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__9677)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__9677)
& 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__9679] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__9679)
& ? [Vvar__2___24Anonymous__9680] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__9680)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__9679,Vvar__2___24Anonymous__9680)
& 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__9683] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__9683)
& ? [Vvar__2___24Anonymous__9684] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__9684)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__9683,Vvar__2___24Anonymous__9684)
& 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__9687] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__9687)
& ? [Vvar__2___24Anonymous__9688] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__9688)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__9687,Vvar__2___24Anonymous__9688)
& 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__9691] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__9691)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__9691)
& 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__9693] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__9693)
& ? [Vvar__2___24Anonymous__9694] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__9694)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__9693,Vvar__2___24Anonymous__9694)
& 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.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__2734] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__2734)
& ? [Vvar__2___24Anonymous__2735] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__2735)
& ( 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__2735)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__2734,Vvar__2___24Anonymous__2735)
& ( ( Vvar__2___24Anonymous__2735 = 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__2734)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__2746] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__2746)
& ? [Vvar__2___24Anonymous__2747] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__2747)
& Vvar__2___24Anonymous__2735 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__2746,Vvar__2___24Anonymous__2747)
& ( 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__2734)),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__2735) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.PExpr_eq',axiom,
! [V0__C,V1__ceqb,V3__e,V4__e_27] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V3__e)
=> ( ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8310] :
( t(Vvar__1___24Anonymous__8310,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__8310)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8327] :
( t(Vvar__1___24Anonymous__8327,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__8327)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__8310),Vvar__1___24Anonymous__8327) )
| ? [Vvar__1___24Anonymous__8329] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8329)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__8329)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8331] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8331)
& ? [Vvar__2___24Anonymous__8332] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8332)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__8331,Vvar__2___24Anonymous__8332)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8335] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8335)
& ? [Vvar__2___24Anonymous__8336] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8336)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__8335,Vvar__2___24Anonymous__8336)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8339] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8339)
& ? [Vvar__2___24Anonymous__8340] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8340)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__8339,Vvar__2___24Anonymous__8340)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8343] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8343)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__8343)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8345] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8345)
& ? [Vvar__2___24Anonymous__8346] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8346)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__8345,Vvar__2___24Anonymous__8346)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__8349] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8349)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__8349)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8366] :
( t(Vvar__1___24Anonymous__8366,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__8366)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8368] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8368)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__8368)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__1___24Anonymous__8349,Vvar__1___24Anonymous__8368) )
| ? [Vvar__1___24Anonymous__8370] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8370)
& ? [Vvar__2___24Anonymous__8371] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8371)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__8370,Vvar__2___24Anonymous__8371)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8374] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8374)
& ? [Vvar__2___24Anonymous__8375] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8375)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__8374,Vvar__2___24Anonymous__8375)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8378] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8378)
& ? [Vvar__2___24Anonymous__8379] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8379)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__8378,Vvar__2___24Anonymous__8379)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8382] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8382)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__8382)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8384] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8384)
& ? [Vvar__2___24Anonymous__8385] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8385)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__8384,Vvar__2___24Anonymous__8385)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__8388] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8388)
& ? [Vvar__2___24Anonymous__8389] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8389)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__8388,Vvar__2___24Anonymous__8389)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8421] :
( t(Vvar__1___24Anonymous__8421,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__8421)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8423] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8423)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__8423)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8425] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8425)
& ? [Vvar__2___24Anonymous__8426] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8426)
& ( cType___24t(V0__C)
=> ( c_24__type__5381___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8388)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8425)
=> ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__8425,Vvar__2___24Anonymous__8426)
& ( ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__8388,Vvar__1___24Anonymous__8425) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__8389,Vvar__2___24Anonymous__8426) )
| ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__8388,Vvar__1___24Anonymous__8425) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__8431] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8431)
& ? [Vvar__2___24Anonymous__8432] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8432)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__8431,Vvar__2___24Anonymous__8432)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8435] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8435)
& ? [Vvar__2___24Anonymous__8436] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8436)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__8435,Vvar__2___24Anonymous__8436)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8439] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8439)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__8439)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8441] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8441)
& ? [Vvar__2___24Anonymous__8442] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8442)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__8441,Vvar__2___24Anonymous__8442)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__8445] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8445)
& ? [Vvar__2___24Anonymous__8446] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8446)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__8445,Vvar__2___24Anonymous__8446)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8478] :
( t(Vvar__1___24Anonymous__8478,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__8478)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8480] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8480)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__8480)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8482] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8482)
& ? [Vvar__2___24Anonymous__8483] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8483)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__8482,Vvar__2___24Anonymous__8483)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8486] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8486)
& ? [Vvar__2___24Anonymous__8487] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8487)
& ( cType___24t(V0__C)
=> ( c_24__type__5381___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8445)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8486)
=> ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__8486,Vvar__2___24Anonymous__8487)
& ( ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__8445,Vvar__1___24Anonymous__8486) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__8446,Vvar__2___24Anonymous__8487) )
| ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__8445,Vvar__1___24Anonymous__8486) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__8492] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8492)
& ? [Vvar__2___24Anonymous__8493] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8493)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__8492,Vvar__2___24Anonymous__8493)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8496] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8496)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__8496)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8498] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8498)
& ? [Vvar__2___24Anonymous__8499] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8499)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__8498,Vvar__2___24Anonymous__8499)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__8502] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8502)
& ? [Vvar__2___24Anonymous__8503] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8503)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__8502,Vvar__2___24Anonymous__8503)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8535] :
( t(Vvar__1___24Anonymous__8535,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__8535)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8537] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8537)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__8537)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8539] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8539)
& ? [Vvar__2___24Anonymous__8540] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8540)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__8539,Vvar__2___24Anonymous__8540)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8543] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8543)
& ? [Vvar__2___24Anonymous__8544] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8544)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__8543,Vvar__2___24Anonymous__8544)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8547] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8547)
& ? [Vvar__2___24Anonymous__8548] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8548)
& ( cType___24t(V0__C)
=> ( c_24__type__5381___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8502)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8547)
=> ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__8547,Vvar__2___24Anonymous__8548)
& ( ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__8502,Vvar__1___24Anonymous__8547) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__8503,Vvar__2___24Anonymous__8548) )
| ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__8502,Vvar__1___24Anonymous__8547) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__8553] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8553)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__8553)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8555] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8555)
& ? [Vvar__2___24Anonymous__8556] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8556)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__8555,Vvar__2___24Anonymous__8556)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__8559] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8559)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__8559)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8576] :
( t(Vvar__1___24Anonymous__8576,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__8576)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8578] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8578)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__8578)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8580] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8580)
& ? [Vvar__2___24Anonymous__8581] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8581)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__8580,Vvar__2___24Anonymous__8581)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8584] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8584)
& ? [Vvar__2___24Anonymous__8585] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8585)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__8584,Vvar__2___24Anonymous__8585)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8588] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8588)
& ? [Vvar__2___24Anonymous__8589] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8589)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__8588,Vvar__2___24Anonymous__8589)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8592] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8592)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__8592)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__8559,Vvar__1___24Anonymous__8592) )
| ? [Vvar__1___24Anonymous__8594] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8594)
& ? [Vvar__2___24Anonymous__8595] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8595)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__8594,Vvar__2___24Anonymous__8595)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__8598] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8598)
& ? [Vvar__2___24Anonymous__8599] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8599)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__8598,Vvar__2___24Anonymous__8599)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8631] :
( t(Vvar__1___24Anonymous__8631,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__8631)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8633] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8633)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__8633)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8635] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8635)
& ? [Vvar__2___24Anonymous__8636] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8636)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__8635,Vvar__2___24Anonymous__8636)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8639] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8639)
& ? [Vvar__2___24Anonymous__8640] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8640)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__8639,Vvar__2___24Anonymous__8640)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8643] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8643)
& ? [Vvar__2___24Anonymous__8644] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__8644)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__8643,Vvar__2___24Anonymous__8644)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8647] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8647)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__8647)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8649] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__8649)
& ? [Vvar__2___24Anonymous__8650] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8650)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8599)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8650)
=> ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__8649,Vvar__2___24Anonymous__8650)
& ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vvar__2___24Anonymous__8599,Vvar__2___24Anonymous__8650) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__8598,Vvar__1___24Anonymous__8649) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vvar__2___24Anonymous__8599,Vvar__2___24Anonymous__8650) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.absurd_PCond',axiom,
! [V0__C,V1__cO] : cCoq_2esetoid__ring_2eField__theory_2eabsurd__PCond___24a2(V0__C,V1__cO) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))) ).
fof('$_def_Coq.setoid_ring.Field_theory.condition',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__11229] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__11229)
& ? [Vvar__2__denum__11230] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__11230)
& ? [Vvar__3__condition__11231] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__11231)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__11229,Vvar__2__denum__11230,Vvar__3__condition__11231)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__11231 ) ) ) ) ) ).
fof('$_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__11220] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__11220)
& ? [Vvar__2__denum__11221] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__11221)
& ? [Vvar__3__condition__11222] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__11222)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__11220,Vvar__2__denum__11221,Vvar__3__condition__11222)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__11221 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.display_linear',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num,V16__den] : cCoq_2esetoid__ring_2eField__theory_2edisplay__linear___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num,V16__den) = c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2412167___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num,V16__den) ).
fof('$_def_Coq.setoid_ring.Field_theory.display_pow_linear',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den] : cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear___24a20(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den) = c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2412766___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('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__11209] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__11209)
& ? [Vvar__2__denum__11210] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__11210)
& ? [Vvar__3__condition__11211] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__11211)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__11209,Vvar__2__denum__11210,Vvar__3__condition__11211)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__11209 ) ) ) ) ) ).
fof('$_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__11315] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__11315)
& ? [Vvar__2__rsplit__common__11316] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__11316)
& ? [Vvar__3__rsplit__right__11317] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__11317)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__11315,Vvar__2__rsplit__common__11316,Vvar__3__rsplit__right__11317)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,V1__r) = Vvar__2__rsplit__common__11316 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__11304] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__11304)
& ? [Vvar__2__rsplit__common__11305] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__11305)
& ? [Vvar__3__rsplit__right__11306] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__11306)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__11304,Vvar__2__rsplit__common__11305,Vvar__3__rsplit__right__11306)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,V1__r) = Vvar__1__rsplit__left__11304 ) ) ) ) ) ).
fof('$_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__11324] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__11324)
& ? [Vvar__2__rsplit__common__11325] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__11325)
& ? [Vvar__3__rsplit__right__11326] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__11326)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__11324,Vvar__2__rsplit__common__11325,Vvar__3__rsplit__right__11326)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,V1__r) = Vvar__3__rsplit__right__11326 ) ) ) ) ) ).
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.Nwadd',axiom,
! [V1__w1,V2__w2] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V1__w1)
=> ( ( V1__w1 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2eNwadd___24a2(V1__w1,V2__w2) = V2__w2 )
| ? [Vvar__1___24Anonymous__46732] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__46732)
& ? [Vvar__2___24Anonymous__46733] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__46733)
& ( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V2__w2)
=> ( V1__w1 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__46732,Vvar__2___24Anonymous__46733)
& ( ( V2__w2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2eNwadd___24a2(V1__w1,V2__w2) = V1__w1 )
| ? [Vvar__1___24Anonymous__46744] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__46744)
& ? [Vvar__2___24Anonymous__46745] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__46745)
& V2__w2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__46744,Vvar__2___24Anonymous__46745)
& cCoq_2esetoid__ring_2eInitialRing_2eNwadd___24a2(V1__w1,V2__w2) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(Vvar__1___24Anonymous__46732,Vvar__1___24Anonymous__46744),cCoq_2esetoid__ring_2eInitialRing_2eNwadd___24a2(Vvar__2___24Anonymous__46733,Vvar__2___24Anonymous__46745)) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nwcons',axiom,
! [V0__n,V1__w] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V1__w)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V1__w = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2eNwcons___24a2(V0__n,V1__w) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN) )
| ? [Vvar__0___24Anonymous__45378] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45378)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__45378)
& cCoq_2esetoid__ring_2eInitialRing_2eNwcons___24a2(V0__n,V1__w) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,V0__n,V1__w) ) ) ) )
| ? [Vvar__1___24Anonymous__45380] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__45380)
& ? [Vvar__2___24Anonymous__45381] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__45381)
& V1__w = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__45380,Vvar__2___24Anonymous__45381)
& cCoq_2esetoid__ring_2eInitialRing_2eNwcons___24a2(V0__n,V1__w) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,V0__n,V1__w) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
! [Vvar__38251] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__38251)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__38251) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
=> ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
| ? [Vvar__0___24Anonymous__15313] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15313)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__15313)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__15313) ) ) ) ) ).
fof('$_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__38270] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__38270)
& ? [Vvar__2___24Anonymous__38271] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__38271)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__38270)
=> ( V8__w = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__38270,Vvar__2___24Anonymous__38271)
& ( ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__38271)
=> ( Vvar__1___24Anonymous__38270 = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( Vvar__2___24Anonymous__38271 = 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__38270) )
| ? [Vvar__1___24Anonymous__38292] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__38292)
& ? [Vvar__2___24Anonymous__38293] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__38293)
& Vvar__2___24Anonymous__38271 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__38292,Vvar__2___24Anonymous__38293)
& 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__38271)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__38295] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38295)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__38271)
=> ( Vvar__1___24Anonymous__38270 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__38295)
& ( ( Vvar__2___24Anonymous__38271 = 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__38270) )
| ? [Vvar__1___24Anonymous__38302] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__38302)
& ? [Vvar__2___24Anonymous__38303] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__38303)
& Vvar__2___24Anonymous__38271 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__38302,Vvar__2___24Anonymous__38303)
& 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__38270)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,Vvar__2___24Anonymous__38271)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__38209] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38209)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38209)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__38209)
& ( ? [Vvar__0___24Anonymous__38213] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38213)
& Vvar__0___24Anonymous__38209 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__38213)
& 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__38209))) )
| ? [Vvar__0___24Anonymous__38214] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38214)
& Vvar__0___24Anonymous__38209 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__38214)
& 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__38209))) )
| ( Vvar__0___24Anonymous__38209 = 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__38215] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38215)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38215)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__38215)
& ( ? [Vvar__0___24Anonymous__38219] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38219)
& Vvar__0___24Anonymous__38215 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__38219)
& 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__38215)) )
| ? [Vvar__0___24Anonymous__38220] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38220)
& Vvar__0___24Anonymous__38215 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__38220)
& 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__38215)) )
| ( Vvar__0___24Anonymous__38215 = 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_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__15238] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15238)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__15238)
& 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__15238) )
| ? [Vvar__0___24Anonymous__15239] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15239)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__15239)
& 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__15239)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.get_signZ',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__15291] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15291)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__15291)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__15292] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15292)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__15292)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__15292)) ) ) ) ).
fof('$_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__5381___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.Mphi',axiom,
! [V0__R,V1__rO,V2__rI,V3__rmul,V5__l,V6__M] :
( cType___24t(V0__R)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V6__M)
=> ( ( V6__M = cCoq_2esetoid__ring_2eRing__polynom_2emon0
& cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,V5__l,V6__M) = V2__rI )
| ? [Vvar__0___24Anonymous__23192] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23192)
& ? [Vvar__1___24Anonymous__23193] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__23193)
& V6__M = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__23192,Vvar__1___24Anonymous__23193)
& cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,V5__l,V6__M) = cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__R,Vvar__0___24Anonymous__23192,V5__l),Vvar__1___24Anonymous__23193) ) )
| ? [Vvar__0___24Anonymous__23195] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23195)
& ? [Vvar__1___24Anonymous__23196] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__23196)
& V6__M = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__23195,Vvar__1___24Anonymous__23196)
& cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,V5__l,V6__M) = happ(happ(V3__rmul,cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,cCoq_2eLists_2eList_2etl___24a2(V0__R,V5__l),Vvar__1___24Anonymous__23196)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V3__rmul,cCoq_2eLists_2eList_2ehd___24a3(V0__R,V1__rO,V5__l),Vvar__0___24Anonymous__23195)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.P0',axiom,
! [V0__C,V1__cO] : cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V0__C,V1__cO) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,V1__cO) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.P1',axiom,
! [V0__C,V1__cI] : cCoq_2esetoid__ring_2eRing__polynom_2eP1___24a2(V0__C,V1__cI) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,V1__cI) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V7__C)
=> ( cType___24t(V9__Cpow)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,V14__pe)
=> ( ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V1__rO )
| ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__3690] :
( t(Vvar__1___24Anonymous__3690,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__3690)
& 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__3690) )
| ? [Vvar__1___24Anonymous__3692] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3692)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__3692)
& 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__3692,V13__l) )
| ? [Vvar__1___24Anonymous__3694] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__3694)
& ? [Vvar__2___24Anonymous__3695] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__3695)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__3694,Vvar__2___24Anonymous__3695)
& 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__3694)),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__3695)) ) )
| ? [Vvar__1___24Anonymous__3698] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__3698)
& ? [Vvar__2___24Anonymous__3699] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__3699)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__3698,Vvar__2___24Anonymous__3699)
& 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__3698)),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__3699)) ) )
| ? [Vvar__1___24Anonymous__3702] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__3702)
& ? [Vvar__2___24Anonymous__3703] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__3703)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__3702,Vvar__2___24Anonymous__3703)
& 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__3702)),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__3703)) ) )
| ? [Vvar__1___24Anonymous__3706] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__3706)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__3706)
& 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__3706)) )
| ? [Vvar__1___24Anonymous__3708] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__3708)
& ? [Vvar__2___24Anonymous__3709] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__3709)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__3708,Vvar__2___24Anonymous__3709)
& 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__3708)),happ(V10__Cp__phi,Vvar__2___24Anonymous__3709)) ) ) ) ) ) ) ) ).
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__20838] :
( t(Vvar__1___24Anonymous__20838,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__20838)
& ( ? [Vvar__1___24Anonymous__20848] :
( t(Vvar__1___24Anonymous__20848,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__20848)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__20838),Vvar__1___24Anonymous__20848) )
| ? [Vvar__1___24Anonymous__20850] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20850)
& ? [Vvar__2___24Anonymous__20851] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__20851)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__20850,Vvar__2___24Anonymous__20851)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__20854] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20854)
& ? [Vvar__2___24Anonymous__20855] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20855)
& ? [Vvar__3___24Anonymous__20856] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__20856)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__20854,Vvar__2___24Anonymous__20855,Vvar__3___24Anonymous__20856)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__20861] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20861)
& ? [Vvar__2___24Anonymous__20862] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__20862)
& ( 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__20861,Vvar__2___24Anonymous__20862)
& ( ? [Vvar__1___24Anonymous__20882] :
( t(Vvar__1___24Anonymous__20882,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__20882)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__20884] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20884)
& ? [Vvar__2___24Anonymous__20885] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__20885)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20861)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20884)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__20884,Vvar__2___24Anonymous__20885)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__20861,Vvar__1___24Anonymous__20884) = 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__20862,Vvar__2___24Anonymous__20885) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__20861,Vvar__1___24Anonymous__20884) = 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__20861,Vvar__1___24Anonymous__20884) = 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__20890] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20890)
& ? [Vvar__2___24Anonymous__20891] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20891)
& ? [Vvar__3___24Anonymous__20892] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__20892)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__20890,Vvar__2___24Anonymous__20891,Vvar__3___24Anonymous__20892)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__20897] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20897)
& ? [Vvar__2___24Anonymous__20898] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20898)
& ? [Vvar__3___24Anonymous__20899] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__20899)
& ( 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__20897,Vvar__2___24Anonymous__20898,Vvar__3___24Anonymous__20899)
& ( ? [Vvar__1___24Anonymous__20932] :
( t(Vvar__1___24Anonymous__20932,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__20932)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__20934] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20934)
& ? [Vvar__2___24Anonymous__20935] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__20935)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__20934,Vvar__2___24Anonymous__20935)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__20938] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20938)
& ? [Vvar__2___24Anonymous__20939] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20939)
& ? [Vvar__3___24Anonymous__20940] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__20940)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20898)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20939)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__20938,Vvar__2___24Anonymous__20939,Vvar__3___24Anonymous__20940)
& ( ( cType___24t(V0__C)
=> ( c_24__type__5381___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20897)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20938)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__20898,Vvar__2___24Anonymous__20939) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__20897,Vvar__1___24Anonymous__20938) = 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__20899,Vvar__3___24Anonymous__20940) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__20897,Vvar__1___24Anonymous__20938) = 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__20898,Vvar__2___24Anonymous__20939) = 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__20898,Vvar__2___24Anonymous__20939) = 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__23026] :
( t(Vvar__1___24Anonymous__23026,V4__C)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V4__C,Vvar__1___24Anonymous__23026)
& 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__23026) )
| ? [Vvar__1___24Anonymous__23028] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23028)
& ? [Vvar__2___24Anonymous__23029] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__2___24Anonymous__23029)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V4__C,Vvar__1___24Anonymous__23028,Vvar__2___24Anonymous__23029)
& 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__23028,V7__l),Vvar__2___24Anonymous__23029) ) )
| ? [Vvar__1___24Anonymous__23032] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__1___24Anonymous__23032)
& ? [Vvar__2___24Anonymous__23033] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23033)
& ? [Vvar__3___24Anonymous__23034] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__3___24Anonymous__23034)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V4__C,Vvar__1___24Anonymous__23032,Vvar__2___24Anonymous__23033,Vvar__3___24Anonymous__23034)
& 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__23032)),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__23033))),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__23034)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V15__get__sign,c_24__let__16__mkpow__28087___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__28088___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__28089___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.add_pow_list',axiom,
! [V0__R,V1__r,V2__n,V3__l] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( ( V2__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list___24a4(V0__R,V1__r,V2__n,V3__l) = V3__l )
| ? [Vvar__0___24Anonymous__26558] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26558)
& V2__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26558)
& cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list___24a4(V0__R,V1__r,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,V1__r,Vvar__0___24Anonymous__26558),V3__l) ) ) ) ) ).
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__25141] :
( 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__25141)
& ? [Vvar__2___24Anonymous__25142] :
( 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__25142)
& ( 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__25141)
=> ( 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__25141,Vvar__2___24Anonymous__25142)
& ? [Vvar__2___24Anonymous__25160] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__2___24Anonymous__25160)
& ? [Vvar__3___24Anonymous__25161] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__3___24Anonymous__25161)
& ( 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__25142)
=> ( Vvar__1___24Anonymous__25141 = 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__25160,Vvar__3___24Anonymous__25161)
& ( ( Vvar__2___24Anonymous__25142 = 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__25160)),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__25161))) ) )
| ? [Vvar__1___24Anonymous__25172] :
( 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__25172)
& ? [Vvar__2___24Anonymous__25173] :
( 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__25173)
& Vvar__2___24Anonymous__25142 = 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__25172,Vvar__2___24Anonymous__25173)
& ( 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__25160)),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__25161)))
& 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__25142) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__20969] :
( t(Vvar__1___24Anonymous__20969,V0__C)
& V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__20969)
& cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = V2__P )
| ? [Vvar__1___24Anonymous__20971] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20971)
& ? [Vvar__2___24Anonymous__20972] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__20972)
& V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__20971,Vvar__2___24Anonymous__20972)
& 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__20971),Vvar__2___24Anonymous__20972) ) )
| ? [Vvar__1___24Anonymous__20975] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20975)
& ? [Vvar__2___24Anonymous__20976] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20976)
& ? [Vvar__3___24Anonymous__20977] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__20977)
& V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__20975,Vvar__2___24Anonymous__20976,Vvar__3___24Anonymous__20977)
& 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('$_def_Coq.setoid_ring.Ring_polynom.mkZmon',axiom,
! [V0__j,V1__M] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V1__M)
=> ( ( V1__M = cCoq_2esetoid__ring_2eRing__polynom_2emon0
& cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2emon0 )
| ? [Vvar__0___24Anonymous__21738] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21738)
& ? [Vvar__1___24Anonymous__21739] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__21739)
& V1__M = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__21738,Vvar__1___24Anonymous__21739)
& cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V0__j,V1__M) ) )
| ? [Vvar__0___24Anonymous__21741] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21741)
& ? [Vvar__1___24Anonymous__21742] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__21742)
& V1__M = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__21741,Vvar__1___24Anonymous__21742)
& cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V0__j,V1__M) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.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__25504] :
( 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__25504)
& ? [Vvar__2___24Anonymous__25505] :
( 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__25505)
& ( 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__25504)
=> ( 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__25504,Vvar__2___24Anonymous__25505)
& ? [Vvar__2___24Anonymous__25521] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__25521)
& ? [Vvar__3___24Anonymous__25522] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__25522)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__2952___24t(V0__C,V3__cadd)
=> ( c_24__type__2952___24t(V0__C,V4__cmul)
=> ( c_24__type__2952___24t(V0__C,V5__csub)
=> ( c_24__type__2961___24t(V0__C,V6__copp)
=> ( c_24__type__5381___24t(V0__C,V7__ceqb)
=> ( c_24__type__13781___24t(V0__C,V8__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__25521)
=> ( Vvar__1___24Anonymous__25504 = 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__25521,Vvar__3___24Anonymous__25522)
& ( ? [Vvar__1___24Anonymous__25530] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__25530)
& 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__25521)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__25530)
& 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__25530,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__25522)),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__25505)) )
| ( 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__25521)) = 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__25505) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__44189] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44189)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44189)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(happ(V1__rmul,V3__r),V4__x),V4__x,Vvar__0___24Anonymous__44189),V4__x,Vvar__0___24Anonymous__44189) )
| ? [Vvar__0___24Anonymous__44190] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44190)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44190)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,Vvar__0___24Anonymous__44190),V4__x,Vvar__0___24Anonymous__44190) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__24987___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.r_list_pow',axiom,
! [V0__R,V1__rI,V2__rmul,V4__l] :
( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive))
& cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,V4__l) = V1__rI )
| ? [Vvar__1___24Anonymous__27953] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__27953)
& ? [Vvar__2___24Anonymous__27954] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__2___24Anonymous__27954)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__27953)
=> ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__1___24Anonymous__27953,Vvar__2___24Anonymous__27954)
& ? [Vvar__2___24Anonymous__27966] :
( t(Vvar__2___24Anonymous__27966,V0__R)
& ? [Vvar__3___24Anonymous__27967] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3___24Anonymous__27967)
& Vvar__1___24Anonymous__27953 = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__2___24Anonymous__27966,Vvar__3___24Anonymous__27967)
& cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,V4__l) = happ(happ(V2__rmul,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,Vvar__2___24Anonymous__27966,Vvar__3___24Anonymous__27967)),cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,Vvar__2___24Anonymous__27954)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__28826] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28826)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28826)
& 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__28826) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__28806] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28806)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28806)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__28807__28810___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28806)),c_24__let__var__6__p__28807__28810___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28806))) )
| ? [Vvar__0___24Anonymous__28808] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28808)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28808)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__28809__28811___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28808)),c_24__let__var__6__p__28809__28811___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28808)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_ExtLib.Data.Member.get_next',axiom,
! [V0__T,V1__ls,V2__y,V3__x,V4__m] :
( cType___24t(V0__T)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__ls)
=> ( t(V2__y,V0__T)
=> ( t(V3__x,V0__T)
=> ( cExtLib_2eData_2eMember_2emember___24t(V0__T,V3__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V2__y,V1__ls),V4__m)
=> ( ? [Vvar__2__ls__18057] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,Vvar__2__ls__18057)
& V4__m = cExtLib_2eData_2eMember_2eMZ___24a3(V0__T,V3__x,Vvar__2__ls__18057)
& cExtLib_2eData_2eMember_2eget__next___24a5(V0__T,V1__ls,V2__y,V3__x,V4__m) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cExtLib_2eData_2eMember_2emember___24a3(V0__T,V3__x,Vvar__2__ls__18057)) )
| ? [Vvar__2__l__18060] :
( t(Vvar__2__l__18060,V0__T)
& ? [Vvar__3__ls__18061] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,Vvar__3__ls__18061)
& ? [Vvar__4___24Anonymous__18062] :
( cExtLib_2eData_2eMember_2emember___24t(V0__T,V3__x,Vvar__3__ls__18061,Vvar__4___24Anonymous__18062)
& V4__m = cExtLib_2eData_2eMember_2eMN___24a5(V0__T,V3__x,Vvar__2__l__18060,Vvar__3__ls__18061,Vvar__4___24Anonymous__18062)
& cExtLib_2eData_2eMember_2eget__next___24a5(V0__T,V1__ls,V2__y,V3__x,V4__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cExtLib_2eData_2eMember_2emember___24a3(V0__T,V3__x,Vvar__3__ls__18061),Vvar__4___24Anonymous__18062) ) ) ) ) ) ) ) ) ) ).
fof('$_def_ExtLib.Data.Member.member_rec',axiom,
! [V0__T,V1__a,V2__P] : cExtLib_2eData_2eMember_2emember__rec___24a3(V0__T,V1__a,V2__P) = cExtLib_2eData_2eMember_2emember__rect___24a3(V0__T,V1__a,V2__P) ).
fof('$_def_ExtLib.Data.Member.member_rect',axiom,
! [V0__T,V1__a,V2__P,V3__f,V4__f,V6__l,V7__m] :
( cType___24t(V0__T)
=> ( t(V1__a,V0__T)
=> ( c_24__type__17592___24t(V0__T,V1__a,V2__P,V6__l,V2__P)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V6__l)
=> ( cExtLib_2eData_2eMember_2emember___24t(V0__T,V1__a,V6__l,V7__m)
=> ( ? [Vvar__2__ls__17570] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,Vvar__2__ls__17570)
& V7__m = cExtLib_2eData_2eMember_2eMZ___24a3(V0__T,V1__a,Vvar__2__ls__17570)
& cExtLib_2eData_2eMember_2emember__rect___24a7(V0__T,V1__a,V2__P,V3__f,V4__f,V6__l,V7__m) = happ(V3__f,Vvar__2__ls__17570) )
| ? [Vvar__2__l__17573] :
( t(Vvar__2__l__17573,V0__T)
& ? [Vvar__3__ls__17574] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,Vvar__3__ls__17574)
& ? [Vvar__4___24Anonymous__17575] :
( cExtLib_2eData_2eMember_2emember___24t(V0__T,V1__a,Vvar__3__ls__17574,Vvar__4___24Anonymous__17575)
& V7__m = cExtLib_2eData_2eMember_2eMN___24a5(V0__T,V1__a,Vvar__2__l__17573,Vvar__3__ls__17574,Vvar__4___24Anonymous__17575)
& cExtLib_2eData_2eMember_2emember__rect___24a7(V0__T,V1__a,V2__P,V3__f,V4__f,V6__l,V7__m) = happ(happ(happ(happ(V4__f,Vvar__2__l__17573),Vvar__3__ls__17574),Vvar__4___24Anonymous__17575),cExtLib_2eData_2eMember_2emember__rect___24a7(V0__T,V1__a,V2__P,V3__f,V4__f,Vvar__3__ls__17574,Vvar__4___24Anonymous__17575)) ) ) ) ) ) ) ) ) ) ).
fof('$_def_ExtLib.Data.Member.to_nat',axiom,
! [V0__T,V1__a,V3__ls,V4__m] :
( cType___24t(V0__T)
=> ( t(V1__a,V0__T)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V3__ls)
=> ( cExtLib_2eData_2eMember_2emember___24t(V0__T,V1__a,V3__ls,V4__m)
=> ( ? [Vvar__2__ls__17756] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,Vvar__2__ls__17756)
& V4__m = cExtLib_2eData_2eMember_2eMZ___24a3(V0__T,V1__a,Vvar__2__ls__17756)
& cExtLib_2eData_2eMember_2eto__nat___24a4(V0__T,V1__a,V3__ls,V4__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__2__l__17759] :
( t(Vvar__2__l__17759,V0__T)
& ? [Vvar__3__ls__17760] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,Vvar__3__ls__17760)
& ? [Vvar__4___24Anonymous__17761] :
( cExtLib_2eData_2eMember_2emember___24t(V0__T,V1__a,Vvar__3__ls__17760,Vvar__4___24Anonymous__17761)
& V4__m = cExtLib_2eData_2eMember_2eMN___24a5(V0__T,V1__a,Vvar__2__l__17759,Vvar__3__ls__17760,Vvar__4___24Anonymous__17761)
& cExtLib_2eData_2eMember_2eto__nat___24a4(V0__T,V1__a,V3__ls,V4__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cExtLib_2eData_2eMember_2eto__nat___24a4(V0__T,V1__a,Vvar__3__ls__17760,Vvar__4___24Anonymous__17761)) ) ) ) ) ) ) ) ) ).
fof('$_def_ExtLib.Structures.Functor.ID',axiom,
! [V0__T,V1__f] :
( cExtLib_2eStructures_2eFunctor_2eID___24a2(V0__T,V1__f)
<=> ! [V2__x] :
( t(V2__x,V0__T)
=> happ(V1__f,V2__x) = V2__x ) ) ).
fof('$_def_ExtLib.Tactics.Injection.result',axiom,
! [V0__P,V1__Injective] :
( cProp___24t(V0__P)
=> ( cExtLib_2eTactics_2eInjection_2eInjective___24t(V0__P,V1__Injective)
=> ? [Vvar__1__result__15468] :
( cProp___24t(Vvar__1__result__15468)
& ( p(V0__P)
=> p(Vvar__1__result__15468) )
& V1__Injective = cExtLib_2eTactics_2eInjection_2eBuild__Injective___24a2(V0__P,Vvar__1__result__15468)
& ( cExtLib_2eTactics_2eInjection_2eresult___24a2(V0__P,V1__Injective)
<=> p(Vvar__1__result__15468) ) ) ) ) ).
fof('$_def_HList.hlist.Injection_equiv_hlist_app',axiom,
! [V0__eqv,V1__a,V2__b,V3__c,V4__c_27,V5__d,V6__d_27] : cHList_2ehlist_2eInjection__equiv__hlist__app___24a7(V0__eqv,V1__a,V2__b,V3__c,V4__c_27,V5__d,V6__d_27) = cExtLib_2eTactics_2eInjection_2eBuild__Injective___24a3(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,cCoq_2eInit_2eDatatypes_2eapp___24a3(ciT,V1__a,V2__b),cHList_2ehlist_2ehlist__app___24a4(V1__a,V2__b,V3__c,V5__d),cHList_2ehlist_2ehlist__app___24a4(V1__a,V2__b,V4__c_27,V6__d_27)),c_24__prop__126634___24a7(V0__eqv,V1__a,V2__b,V3__c,V4__c_27,V5__d,V6__d_27),c_24__lam__126658___24a7(V0__eqv,V1__a,V2__b,V3__c,V4__c_27,V5__d,V6__d_27)) ).
fof('$_def_HList.hlist.Injection_equiv_hlist_cons',axiom,
! [V0__eqv,V1__ls,V2__i,V3__a,V4__b,V5__c,V6__d] : cHList_2ehlist_2eInjection__equiv__hlist__cons___24a7(V0__eqv,V1__ls,V2__i,V3__a,V4__b,V5__c,V6__d) = cExtLib_2eTactics_2eInjection_2eBuild__Injective___24a3(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,V2__i,V1__ls),cHList_2ehlist_2eHcons___24a4(V2__i,V1__ls,V3__a,V5__c),cHList_2ehlist_2eHcons___24a4(V2__i,V1__ls,V4__b,V6__d)),c_24__prop__126684___24a7(V0__eqv,V1__ls,V2__i,V3__a,V4__b,V5__c,V6__d),cHList_2ehlist_2eequiv__hlist__Hcons___24a7(V0__eqv,V1__ls,V2__i,V3__a,V4__b,V5__c,V6__d)) ).
fof('$_def_HList.hlist.hlist_app',axiom,
! [V1__ll,V2__lr,V3__h] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V1__ll)
=> ( cHList_2ehlist_2ehlist___24t(V1__ll,V3__h)
=> ( ( V3__h = cHList_2ehlist_2eHnil
& cHList_2ehlist_2ehlist__app___24a3(V1__ll,V2__lr,V3__h) = c_24__lam__47639___24a2(V1__ll,V2__lr) )
| ? [Vvar__0__l__47623] :
( ciT___24t(Vvar__0__l__47623)
& ? [Vvar__1__ls__47624] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vvar__1__ls__47624)
& ? [Vvar__2___24Anonymous__47625] :
( cF___24t(Vvar__0__l__47623,Vvar__2___24Anonymous__47625)
& ? [Vvar__3___24Anonymous__47626] :
( cHList_2ehlist_2ehlist___24t(Vvar__1__ls__47624,Vvar__3___24Anonymous__47626)
& V3__h = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__47623,Vvar__1__ls__47624,Vvar__2___24Anonymous__47625,Vvar__3___24Anonymous__47626)
& cHList_2ehlist_2ehlist__app___24a3(V1__ll,V2__lr,V3__h) = c_24__lam__47646___24a6(V1__ll,V2__lr,Vvar__0__l__47623,Vvar__1__ls__47624,Vvar__2___24Anonymous__47625,Vvar__3___24Anonymous__47626) ) ) ) ) ) ) ) ).
fof('$_def_HList.hlist.hlist_hd',axiom,
! [V0__a,V1__b,V2__hl] :
( ciT___24t(V0__a)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V1__b)
=> ( cHList_2ehlist_2ehlist___24t(cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,V0__a,V1__b),V2__hl)
=> ( ( V2__hl = cHList_2ehlist_2eHnil
& cHList_2ehlist_2ehlist__hd___24a3(V0__a,V1__b,V2__hl) = cCoq_2eInit_2eDatatypes_2ett )
| ? [Vvar__0__l__46534] :
( ciT___24t(Vvar__0__l__46534)
& ? [Vvar__1__ls__46535] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vvar__1__ls__46535)
& ? [Vvar__2___24Anonymous__46536] :
( cF___24t(Vvar__0__l__46534,Vvar__2___24Anonymous__46536)
& ? [Vvar__3___24Anonymous__46537] :
( cHList_2ehlist_2ehlist___24t(Vvar__1__ls__46535,Vvar__3___24Anonymous__46537)
& V2__hl = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46534,Vvar__1__ls__46535,Vvar__2___24Anonymous__46536,Vvar__3___24Anonymous__46537)
& cHList_2ehlist_2ehlist__hd___24a3(V0__a,V1__b,V2__hl) = Vvar__2___24Anonymous__46536 ) ) ) ) ) ) ) ) ).
fof('$_def_HList.hlist.hlist_rec',axiom,
! [V0__P] : cHList_2ehlist_2ehlist__rec___24a1(V0__P) = cHList_2ehlist_2ehlist__rect___24a1(V0__P) ).
fof('$_def_HList.hlist.hlist_rect',axiom,
! [V0__P,V1__f,V2__f,V4__l,V5__h] :
( c_24__type__46627___24t(V0__P,V4__l,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V4__l)
=> ( cHList_2ehlist_2ehlist___24t(V4__l,V5__h)
=> ( ( V5__h = cHList_2ehlist_2eHnil
& cHList_2ehlist_2ehlist__rect___24a5(V0__P,V1__f,V2__f,V4__l,V5__h) = V1__f )
| ? [Vvar__0__l__46612] :
( ciT___24t(Vvar__0__l__46612)
& ? [Vvar__1__ls__46613] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vvar__1__ls__46613)
& ? [Vvar__2___24Anonymous__46614] :
( cF___24t(Vvar__0__l__46612,Vvar__2___24Anonymous__46614)
& ? [Vvar__3___24Anonymous__46615] :
( cHList_2ehlist_2ehlist___24t(Vvar__1__ls__46613,Vvar__3___24Anonymous__46615)
& V5__h = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46612,Vvar__1__ls__46613,Vvar__2___24Anonymous__46614,Vvar__3___24Anonymous__46615)
& cHList_2ehlist_2ehlist__rect___24a5(V0__P,V1__f,V2__f,V4__l,V5__h) = happ(happ(happ(happ(happ(V2__f,Vvar__0__l__46612),Vvar__1__ls__46613),Vvar__2___24Anonymous__46614),Vvar__3___24Anonymous__46615),cHList_2ehlist_2ehlist__rect___24a5(V0__P,V1__f,V2__f,Vvar__1__ls__46613,Vvar__3___24Anonymous__46615)) ) ) ) ) ) ) ) ) ).
fof('$_def_HList.hlist.hlist_rev\'',axiom,
! [V1__ls,V2__ls_27,V3__h] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V1__ls)
=> ( cHList_2ehlist_2ehlist___24t(V1__ls,V3__h)
=> ( ( V3__h = cHList_2ehlist_2eHnil
& cHList_2ehlist_2ehlist__rev_27___24a3(V1__ls,V2__ls_27,V3__h) = c_24__lam__47639___24a2(V1__ls,V2__ls_27) )
| ? [Vvar__0__l__48241] :
( ciT___24t(Vvar__0__l__48241)
& ? [Vvar__1__ls__48242] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vvar__1__ls__48242)
& ? [Vvar__2___24Anonymous__48243] :
( cF___24t(Vvar__0__l__48241,Vvar__2___24Anonymous__48243)
& ? [Vvar__3___24Anonymous__48244] :
( cHList_2ehlist_2ehlist___24t(Vvar__1__ls__48242,Vvar__3___24Anonymous__48244)
& V3__h = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__48241,Vvar__1__ls__48242,Vvar__2___24Anonymous__48243,Vvar__3___24Anonymous__48244)
& cHList_2ehlist_2ehlist__rev_27___24a3(V1__ls,V2__ls_27,V3__h) = c_24__lam__48310___24a6(V1__ls,V2__ls_27,Vvar__0__l__48241,Vvar__1__ls__48242,Vvar__2___24Anonymous__48243,Vvar__3___24Anonymous__48244) ) ) ) ) ) ) ) ).
fof('$_def_HList.hlist.hlist_tl',axiom,
! [V0__a,V1__b,V2__hl] :
( ciT___24t(V0__a)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V1__b)
=> ( cHList_2ehlist_2ehlist___24t(cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,V0__a,V1__b),V2__hl)
=> ( ( V2__hl = cHList_2ehlist_2eHnil
& cHList_2ehlist_2ehlist__tl___24a3(V0__a,V1__b,V2__hl) = cCoq_2eInit_2eDatatypes_2ett )
| ? [Vvar__0__l__46518] :
( ciT___24t(Vvar__0__l__46518)
& ? [Vvar__1__ls__46519] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vvar__1__ls__46519)
& ? [Vvar__2___24Anonymous__46520] :
( cF___24t(Vvar__0__l__46518,Vvar__2___24Anonymous__46520)
& ? [Vvar__3___24Anonymous__46521] :
( cHList_2ehlist_2ehlist___24t(Vvar__1__ls__46519,Vvar__3___24Anonymous__46521)
& V2__hl = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46518,Vvar__1__ls__46519,Vvar__2___24Anonymous__46520,Vvar__3___24Anonymous__46521)
& cHList_2ehlist_2ehlist__tl___24a3(V0__a,V1__b,V2__hl) = Vvar__3___24Anonymous__46521 ) ) ) ) ) ) ) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__5036,Vvar__1___24Anonymous__5037,Vvar__0__P__5038,Vvar__1___24Anonymous__5039] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5036) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5038) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__37669,Vvar__1___24Anonymous__37670,Vvar__2___24Anonymous__37671] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37669,Vvar__1___24Anonymous__37670,Vvar__2___24Anonymous__37671) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__113965,Vvar__1__Plt__113966,Vvar__2__Pgt__113967,Vvar__3___24Anonymous__113968,Vvar__0__Peq__113969,Vvar__1__Plt__113970,Vvar__2__Pgt__113971,Vvar__3___24Anonymous__113972] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__113965,Vvar__1__Plt__113966,Vvar__2__Pgt__113967) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__113969,Vvar__1__Plt__113970,Vvar__2__Pgt__113971) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__1902] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1902) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__11,Vvar__1___24Anonymous__12,Vvar__0__A__13] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__11,Vvar__1___24Anonymous__12) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__13) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__2712,Vvar__1__B__2713,Vvar__2___24Anonymous__2714,Vvar__0__A__2715,Vvar__1__B__2716,Vvar__2___24Anonymous__2717] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__2712,Vvar__1__B__2713,Vvar__2___24Anonymous__2714) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__2715,Vvar__1__B__2716,Vvar__2___24Anonymous__2717) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__52,Vvar__0__A__53,Vvar__1___24Anonymous__54,Vvar__2___24Anonymous__55] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__52) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__53,Vvar__1___24Anonymous__54,Vvar__2___24Anonymous__55) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__35338,Vvar__1__B__35339,Vvar__2___24Anonymous__35340,Vvar__0__A__35341,Vvar__1__B__35342,Vvar__2___24Anonymous__35343] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__35338,Vvar__1__B__35339,Vvar__2___24Anonymous__35340) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__35341,Vvar__1__B__35342) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__35254,Vvar__1__B__35255,Vvar__2___24Anonymous__35256,Vvar__0__A__35257,Vvar__1__B__35258,Vvar__2___24Anonymous__35259] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__35254,Vvar__1__B__35255) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__35257,Vvar__1__B__35258) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__2694] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2694) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__5019] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5019) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__2678,Vvar__0___24Anonymous__2679] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2678) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2679) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__45248] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__45248) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__120601,Vvar__1___24Anonymous__120602,Vvar__0__x__120603,Vvar__1__n__120604,Vvar__2___24Anonymous__120605] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__120601) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__120603,Vvar__1__n__120604) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__35369,Vvar__1___24Anonymous__35370] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__35369,Vvar__1___24Anonymous__35370) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__120311,Vvar__1__lt__120312,Vvar__2__eq__120313,Vvar__3__x__120314,Vvar__4__y__120315,Vvar__5___24Anonymous__120316,Vvar__0__X__120317,Vvar__1__lt__120318,Vvar__2__eq__120319,Vvar__3__x__120320,Vvar__4__y__120321,Vvar__5___24Anonymous__120322] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__120311,Vvar__1__lt__120312,Vvar__2__eq__120313,Vvar__3__x__120314,Vvar__4__y__120315) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__120317,Vvar__1__lt__120318,Vvar__2__eq__120319,Vvar__3__x__120320,Vvar__4__y__120321) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__47677,Vvar__0__n__47678,Vvar__1___24Anonymous__47679] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__47677) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__47678,Vvar__1___24Anonymous__47679) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__36600,Vvar__0__A__36601,Vvar__1__h__36602,Vvar__2__n__36603,Vvar__3___24Anonymous__36604] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__36600) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__36601,Vvar__1__h__36602,Vvar__2__n__36603,Vvar__3___24Anonymous__36604) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__5249,Vvar__1___24Anonymous__5250,Vvar__0__C__5251,Vvar__1___24Anonymous__5252] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__5249,Vvar__1___24Anonymous__5250) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__5251,Vvar__1___24Anonymous__5252) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__2262,Vvar__1___24Anonymous__2263,Vvar__0__C__2264,Vvar__1___24Anonymous__2265,Vvar__2___24Anonymous__2266] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__2262,Vvar__1___24Anonymous__2263) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__2264,Vvar__1___24Anonymous__2265,Vvar__2___24Anonymous__2266) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__5394,Vvar__1___24Anonymous__5395] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__5394,Vvar__1___24Anonymous__5395) ).
fof('$_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$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__3403,Vvar__1___24Anonymous__3404,Vvar__0__C__3405,Vvar__1___24Anonymous__3406] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__3403,Vvar__1___24Anonymous__3404) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__3405,Vvar__1___24Anonymous__3406) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__1019,Vvar__1__TX__1020,Vvar__2__AA__1021,Vvar__3__AF__1022,Vvar__0__TA__1023,Vvar__1__TX__1024,Vvar__2__AA__1025,Vvar__3__AF__1026] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__1019,Vvar__1__TX__1020,Vvar__2__AA__1021,Vvar__3__AF__1022) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__1023,Vvar__1__TX__1024,Vvar__2__AA__1025,Vvar__3__AF__1026) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__36773,Vvar__1___24Anonymous__36774] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__36773,Vvar__1___24Anonymous__36774) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__10848,Vvar__0__C__10849] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__10848) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__10849) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__3643,Vvar__0__C__3644] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__3643) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__3644) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__20783,Vvar__1___24Anonymous__20784,Vvar__0__C__20785,Vvar__1___24Anonymous__20786,Vvar__2___24Anonymous__20787] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__20783,Vvar__1___24Anonymous__20784) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__20785,Vvar__1___24Anonymous__20786,Vvar__2___24Anonymous__20787) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__21725,Vvar__1___24Anonymous__21726] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__21725,Vvar__1___24Anonymous__21726) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__122045,Vvar__1__req__122046,Vvar__2__reqb__122047,Vvar__3___24Anonymous__122048] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__122045,Vvar__1__req__122046,Vvar__2__reqb__122047) ).
fof('$_discrim_ExtLib.Data.Member.MZ$ExtLib.Data.Member.MN',axiom,
! [Vvar__0__T__17523,Vvar__1__a__17524,Vvar__2__ls__17525,Vvar__0__T__17526,Vvar__1__a__17527,Vvar__2__l__17528,Vvar__3__ls__17529,Vvar__4___24Anonymous__17530] : cExtLib_2eData_2eMember_2eMZ___24a3(Vvar__0__T__17523,Vvar__1__a__17524,Vvar__2__ls__17525) != cExtLib_2eData_2eMember_2eMN___24a5(Vvar__0__T__17526,Vvar__1__a__17527,Vvar__2__l__17528,Vvar__3__ls__17529,Vvar__4___24Anonymous__17530) ).
fof('$_discrim_HList.hlist.Hnil$HList.hlist.Hcons',axiom,
! [Vvar__0__l__46668,Vvar__1__ls__46669,Vvar__2___24Anonymous__46670,Vvar__3___24Anonymous__46671] : cHList_2ehlist_2eHnil != cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46668,Vvar__1__ls__46669,Vvar__2___24Anonymous__46670,Vvar__3___24Anonymous__46671) ).
fof('$_fix_36692_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__36692__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__36697] :
( t(Vvar__1__h__36697,Vv__CANONICAL__0)
& ? [Vvar__2__n__36698] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__36698)
& ? [Vvar__3___24Anonymous__36699] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vvar__2__n__36698,Vvar__3___24Anonymous__36699)
& Vv__CANONICAL__4 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vvar__1__h__36697,Vvar__2__n__36698,Vvar__3___24Anonymous__36699)
& c_24__fix__36692__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__36697,c_24__fix__36692__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2__n__36698,Vvar__3___24Anonymous__36699,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_fix_37630_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__37645] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37645)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37645)
& ( ? [Vvar__0___24Anonymous__37649] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37649)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37649)
& c_24__fix__37630__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__37630__1__add__carry___24a2(Vvar__0___24Anonymous__37645,Vvar__0___24Anonymous__37649)) )
| ? [Vvar__0___24Anonymous__37650] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37650)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37650)
& c_24__fix__37630__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__37630__1__add__carry___24a2(Vvar__0___24Anonymous__37645,Vvar__0___24Anonymous__37650)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__37630__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__37645)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__37651] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37651)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37651)
& ( ? [Vvar__0___24Anonymous__37655] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37655)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37655)
& c_24__fix__37630__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__37630__1__add__carry___24a2(Vvar__0___24Anonymous__37651,Vvar__0___24Anonymous__37655)) )
| ? [Vvar__0___24Anonymous__37656] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37656)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37656)
& c_24__fix__37630__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__37651,Vvar__0___24Anonymous__37656)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__37630__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__37651)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__37657] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37657)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37657)
& c_24__fix__37630__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__37657)) )
| ? [Vvar__0___24Anonymous__37658] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37658)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37658)
& c_24__fix__37630__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__37658)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__37630__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_fix_550_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__550__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__554] :
( t(Vvar__1___24Anonymous__554,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__555] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__555)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__554,Vvar__2___24Anonymous__555)
& c_24__fix__550__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__554,c_24__fix__550__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__555,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__5044,Vvar__0__P__5045,Vvar__1___24Anonymous__5046,Vvar__1___24Anonymous__5047] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5044) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5045)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__5044 = Vvar__0__P__5045 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__5040,Vvar__0__P__5041,Vvar__1___24Anonymous__5042,Vvar__1___24Anonymous__5043] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5040) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5041)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__5040 = Vvar__0__P__5041 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__37672,Vvar__0___24Anonymous__37673,Vvar__1___24Anonymous__37674,Vvar__1___24Anonymous__37675,Vvar__2___24Anonymous__37676,Vvar__2___24Anonymous__37677] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37672,Vvar__1___24Anonymous__37674,Vvar__2___24Anonymous__37676) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37673,Vvar__1___24Anonymous__37675,Vvar__2___24Anonymous__37677)
=> ( Vvar__2___24Anonymous__37676 = Vvar__2___24Anonymous__37677
& Vvar__1___24Anonymous__37674 = Vvar__1___24Anonymous__37675
& Vvar__0___24Anonymous__37672 = Vvar__0___24Anonymous__37673 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__113973,Vvar__0__Peq__113974,Vvar__1__Plt__113975,Vvar__1__Plt__113976,Vvar__2__Pgt__113977,Vvar__2__Pgt__113978,Vvar__3___24Anonymous__113979,Vvar__3___24Anonymous__113980] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__113973,Vvar__1__Plt__113975,Vvar__2__Pgt__113977) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__113974,Vvar__1__Plt__113976,Vvar__2__Pgt__113978)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__113977 = Vvar__2__Pgt__113978
& Vvar__1__Plt__113975 = Vvar__1__Plt__113976
& Vvar__0__Peq__113973 = Vvar__0__Peq__113974 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__113989,Vvar__0__Peq__113990,Vvar__1__Plt__113991,Vvar__1__Plt__113992,Vvar__2__Pgt__113993,Vvar__2__Pgt__113994,Vvar__3___24Anonymous__113995,Vvar__3___24Anonymous__113996] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__113989,Vvar__1__Plt__113991,Vvar__2__Pgt__113993) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__113990,Vvar__1__Plt__113992,Vvar__2__Pgt__113994)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__113993 = Vvar__2__Pgt__113994
& Vvar__1__Plt__113991 = Vvar__1__Plt__113992
& Vvar__0__Peq__113989 = Vvar__0__Peq__113990 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__113981,Vvar__0__Peq__113982,Vvar__1__Plt__113983,Vvar__1__Plt__113984,Vvar__2__Pgt__113985,Vvar__2__Pgt__113986,Vvar__3___24Anonymous__113987,Vvar__3___24Anonymous__113988] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__113981,Vvar__1__Plt__113983,Vvar__2__Pgt__113985) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__113982,Vvar__1__Plt__113984,Vvar__2__Pgt__113986)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__113985 = Vvar__2__Pgt__113986
& Vvar__1__Plt__113983 = Vvar__1__Plt__113984
& Vvar__0__Peq__113981 = Vvar__0__Peq__113982 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__18,Vvar__0__A__19] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__18) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__19)
=> Vvar__0__A__18 = Vvar__0__A__19 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__1903,Vvar__0___24Anonymous__1904] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1903) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1904)
=> Vvar__0___24Anonymous__1903 = Vvar__0___24Anonymous__1904 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__14,Vvar__0__A__15,Vvar__1___24Anonymous__16,Vvar__1___24Anonymous__17] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__14,Vvar__1___24Anonymous__16) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__15,Vvar__1___24Anonymous__17)
=> ( Vvar__1___24Anonymous__16 = Vvar__1___24Anonymous__17
& Vvar__0__A__14 = Vvar__0__A__15 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__58,Vvar__0__A__59,Vvar__1___24Anonymous__60,Vvar__1___24Anonymous__61,Vvar__2___24Anonymous__62,Vvar__2___24Anonymous__63] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__58,Vvar__1___24Anonymous__60,Vvar__2___24Anonymous__62) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__59,Vvar__1___24Anonymous__61,Vvar__2___24Anonymous__63)
=> ( Vvar__2___24Anonymous__62 = Vvar__2___24Anonymous__63
& Vvar__1___24Anonymous__60 = Vvar__1___24Anonymous__61
& Vvar__0__A__58 = Vvar__0__A__59 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__2718,Vvar__0__A__2719,Vvar__1__B__2720,Vvar__1__B__2721,Vvar__2___24Anonymous__2722,Vvar__2___24Anonymous__2723] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__2718,Vvar__1__B__2720,Vvar__2___24Anonymous__2722) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__2719,Vvar__1__B__2721,Vvar__2___24Anonymous__2723)
=> ( Vvar__2___24Anonymous__2722 = Vvar__2___24Anonymous__2723
& Vvar__1__B__2720 = Vvar__1__B__2721
& Vvar__0__A__2718 = Vvar__0__A__2719 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__2724,Vvar__0__A__2725,Vvar__1__B__2726,Vvar__1__B__2727,Vvar__2___24Anonymous__2728,Vvar__2___24Anonymous__2729] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__2724,Vvar__1__B__2726,Vvar__2___24Anonymous__2728) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__2725,Vvar__1__B__2727,Vvar__2___24Anonymous__2729)
=> ( Vvar__2___24Anonymous__2728 = Vvar__2___24Anonymous__2729
& Vvar__1__B__2726 = Vvar__1__B__2727
& Vvar__0__A__2724 = Vvar__0__A__2725 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__56,Vvar__0__A__57] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__56) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__57)
=> Vvar__0__A__56 = Vvar__0__A__57 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__30,Vvar__0__A__31,Vvar__1__B__32,Vvar__1__B__33,Vvar__2___24Anonymous__34,Vvar__2___24Anonymous__35,Vvar__3___24Anonymous__36,Vvar__3___24Anonymous__37] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__30,Vvar__1__B__32,Vvar__2___24Anonymous__34,Vvar__3___24Anonymous__36) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__31,Vvar__1__B__33,Vvar__2___24Anonymous__35,Vvar__3___24Anonymous__37)
=> ( Vvar__3___24Anonymous__36 = Vvar__3___24Anonymous__37
& Vvar__2___24Anonymous__34 = Vvar__2___24Anonymous__35
& Vvar__1__B__32 = Vvar__1__B__33
& Vvar__0__A__30 = Vvar__0__A__31 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__2179,Vvar__0__A__2180,Vvar__1__P__2181,Vvar__1__P__2182,Vvar__2__x__2183,Vvar__2__x__2184,Vvar__3___24Anonymous__2185,Vvar__3___24Anonymous__2186] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2179,Vvar__1__P__2181,Vvar__2__x__2183) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2180,Vvar__1__P__2182,Vvar__2__x__2184)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__2183 = Vvar__2__x__2184
& Vvar__1__P__2181 = Vvar__1__P__2182
& Vvar__0__A__2179 = Vvar__0__A__2180 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__46463,Vvar__0__A__46464,Vvar__1__P__46465,Vvar__1__P__46466,Vvar__2__Q__46467,Vvar__2__Q__46468,Vvar__3__x__46469,Vvar__3__x__46470,Vvar__4___24Anonymous__46471,Vvar__4___24Anonymous__46472,Vvar__5___24Anonymous__46473,Vvar__5___24Anonymous__46474] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__46463,Vvar__1__P__46465,Vvar__2__Q__46467,Vvar__3__x__46469) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__46464,Vvar__1__P__46466,Vvar__2__Q__46468,Vvar__3__x__46470)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__46469 = Vvar__3__x__46470
& Vvar__2__Q__46467 = Vvar__2__Q__46468
& Vvar__1__P__46465 = Vvar__1__P__46466
& Vvar__0__A__46463 = Vvar__0__A__46464 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__2220,Vvar__0__A__2221,Vvar__1__P__2222,Vvar__1__P__2223,Vvar__2__x__2224,Vvar__2__x__2225,Vvar__3___24Anonymous__2226,Vvar__3___24Anonymous__2227] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__2220,Vvar__1__P__2222,Vvar__2__x__2224,Vvar__3___24Anonymous__2226) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__2221,Vvar__1__P__2223,Vvar__2__x__2225,Vvar__3___24Anonymous__2227)
=> ( Vvar__3___24Anonymous__2226 = Vvar__3___24Anonymous__2227
& Vvar__2__x__2224 = Vvar__2__x__2225
& Vvar__1__P__2222 = Vvar__1__P__2223
& Vvar__0__A__2220 = Vvar__0__A__2221 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__45176,Vvar__0__A__45177,Vvar__1__P__45178,Vvar__1__P__45179,Vvar__2__Q__45180,Vvar__2__Q__45181,Vvar__3__x__45182,Vvar__3__x__45183,Vvar__4___24Anonymous__45184,Vvar__4___24Anonymous__45185,Vvar__5___24Anonymous__45186,Vvar__5___24Anonymous__45187] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__45176,Vvar__1__P__45178,Vvar__2__Q__45180,Vvar__3__x__45182,Vvar__4___24Anonymous__45184,Vvar__5___24Anonymous__45186) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__45177,Vvar__1__P__45179,Vvar__2__Q__45181,Vvar__3__x__45183,Vvar__4___24Anonymous__45185,Vvar__5___24Anonymous__45187)
=> ( Vvar__5___24Anonymous__45186 = Vvar__5___24Anonymous__45187
& Vvar__4___24Anonymous__45184 = Vvar__4___24Anonymous__45185
& Vvar__3__x__45182 = Vvar__3__x__45183
& Vvar__2__Q__45180 = Vvar__2__Q__45181
& Vvar__1__P__45178 = Vvar__1__P__45179
& Vvar__0__A__45176 = Vvar__0__A__45177 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__35344,Vvar__0__A__35345,Vvar__1__B__35346,Vvar__1__B__35347,Vvar__2___24Anonymous__35348,Vvar__2___24Anonymous__35349] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__35344,Vvar__1__B__35346,Vvar__2___24Anonymous__35348) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__35345,Vvar__1__B__35347,Vvar__2___24Anonymous__35349)
=> ( Vvar__2___24Anonymous__35348 = Vvar__2___24Anonymous__35349
& Vvar__1__B__35346 = Vvar__1__B__35347
& Vvar__0__A__35344 = Vvar__0__A__35345 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__35350,Vvar__0__A__35351,Vvar__1__B__35352,Vvar__1__B__35353,Vvar__2___24Anonymous__35354,Vvar__2___24Anonymous__35355] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__35350,Vvar__1__B__35352) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__35351,Vvar__1__B__35353)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__35352 = Vvar__1__B__35353
& Vvar__0__A__35350 = Vvar__0__A__35351 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__35260,Vvar__0__A__35261,Vvar__1__B__35262,Vvar__1__B__35263,Vvar__2___24Anonymous__35264,Vvar__2___24Anonymous__35265] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__35260,Vvar__1__B__35262) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__35261,Vvar__1__B__35263)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__35262 = Vvar__1__B__35263
& Vvar__0__A__35260 = Vvar__0__A__35261 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__35266,Vvar__0__A__35267,Vvar__1__B__35268,Vvar__1__B__35269,Vvar__2___24Anonymous__35270,Vvar__2___24Anonymous__35271] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__35266,Vvar__1__B__35268) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__35267,Vvar__1__B__35269)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__35268 = Vvar__1__B__35269
& Vvar__0__A__35266 = Vvar__0__A__35267 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__2695,Vvar__0___24Anonymous__2696] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2695) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2696)
=> Vvar__0___24Anonymous__2695 = Vvar__0___24Anonymous__2696 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__5022,Vvar__0___24Anonymous__5023] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5022) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5023)
=> Vvar__0___24Anonymous__5022 = Vvar__0___24Anonymous__5023 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__5020,Vvar__0___24Anonymous__5021] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5020) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5021)
=> Vvar__0___24Anonymous__5020 = Vvar__0___24Anonymous__5021 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__2680,Vvar__0___24Anonymous__2681] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2680) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2681)
=> Vvar__0___24Anonymous__2680 = Vvar__0___24Anonymous__2681 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__2682,Vvar__0___24Anonymous__2683] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2682) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2683)
=> Vvar__0___24Anonymous__2682 = Vvar__0___24Anonymous__2683 ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__45249,Vvar__0___24Anonymous__45250] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__45249) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__45250)
=> Vvar__0___24Anonymous__45249 = Vvar__0___24Anonymous__45250 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__19429,Vvar__0__Qnum__19430,Vvar__1__Qden__19431,Vvar__1__Qden__19432] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__19429,Vvar__1__Qden__19431) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__19430,Vvar__1__Qden__19432)
=> ( Vvar__1__Qden__19431 = Vvar__1__Qden__19432
& Vvar__0__Qnum__19429 = Vvar__0__Qnum__19430 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__120616,Vvar__0__x__120617,Vvar__1__n__120618,Vvar__1__n__120619,Vvar__2___24Anonymous__120620,Vvar__2___24Anonymous__120621] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__120616,Vvar__1__n__120618) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__120617,Vvar__1__n__120619)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__120618 = Vvar__1__n__120619
& Vvar__0__x__120616 = Vvar__0__x__120617 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__120606,Vvar__0__x__120607,Vvar__1___24Anonymous__120608,Vvar__1___24Anonymous__120609] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__120606) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__120607)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__120606 = Vvar__0__x__120607 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__120610,Vvar__0__x__120611,Vvar__1__n__120612,Vvar__1__n__120613,Vvar__2___24Anonymous__120614,Vvar__2___24Anonymous__120615] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__120610,Vvar__1__n__120612) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__120611,Vvar__1__n__120613)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__120612 = Vvar__1__n__120613
& Vvar__0__x__120610 = Vvar__0__x__120611 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__4753,Vvar__0___24Anonymous__4754,Vvar__1___24Anonymous__4755,Vvar__1___24Anonymous__4756,Vvar__2___24Anonymous__4757,Vvar__2___24Anonymous__4758,Vvar__3___24Anonymous__4759,Vvar__3___24Anonymous__4760,Vvar__4___24Anonymous__4761,Vvar__4___24Anonymous__4762,Vvar__5___24Anonymous__4763,Vvar__5___24Anonymous__4764,Vvar__6___24Anonymous__4765,Vvar__6___24Anonymous__4766,Vvar__7___24Anonymous__4767,Vvar__7___24Anonymous__4768] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4753,Vvar__1___24Anonymous__4755,Vvar__2___24Anonymous__4757,Vvar__3___24Anonymous__4759,Vvar__4___24Anonymous__4761,Vvar__5___24Anonymous__4763,Vvar__6___24Anonymous__4765,Vvar__7___24Anonymous__4767) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4754,Vvar__1___24Anonymous__4756,Vvar__2___24Anonymous__4758,Vvar__3___24Anonymous__4760,Vvar__4___24Anonymous__4762,Vvar__5___24Anonymous__4764,Vvar__6___24Anonymous__4766,Vvar__7___24Anonymous__4768)
=> ( Vvar__7___24Anonymous__4767 = Vvar__7___24Anonymous__4768
& Vvar__6___24Anonymous__4765 = Vvar__6___24Anonymous__4766
& Vvar__5___24Anonymous__4763 = Vvar__5___24Anonymous__4764
& Vvar__4___24Anonymous__4761 = Vvar__4___24Anonymous__4762
& Vvar__3___24Anonymous__4759 = Vvar__3___24Anonymous__4760
& Vvar__2___24Anonymous__4757 = Vvar__2___24Anonymous__4758
& Vvar__1___24Anonymous__4755 = Vvar__1___24Anonymous__4756
& Vvar__0___24Anonymous__4753 = Vvar__0___24Anonymous__4754 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__35371,Vvar__0___24Anonymous__35372,Vvar__1___24Anonymous__35373,Vvar__1___24Anonymous__35374] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__35371,Vvar__1___24Anonymous__35373) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__35372,Vvar__1___24Anonymous__35374)
=> ( Vvar__1___24Anonymous__35373 = Vvar__1___24Anonymous__35374
& Vvar__0___24Anonymous__35371 = Vvar__0___24Anonymous__35372 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__120335,Vvar__0__X__120336,Vvar__1__lt__120337,Vvar__1__lt__120338,Vvar__2__eq__120339,Vvar__2__eq__120340,Vvar__3__x__120341,Vvar__3__x__120342,Vvar__4__y__120343,Vvar__4__y__120344,Vvar__5___24Anonymous__120345,Vvar__5___24Anonymous__120346] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__120335,Vvar__1__lt__120337,Vvar__2__eq__120339,Vvar__3__x__120341,Vvar__4__y__120343) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__120336,Vvar__1__lt__120338,Vvar__2__eq__120340,Vvar__3__x__120342,Vvar__4__y__120344)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__120343 = Vvar__4__y__120344
& Vvar__3__x__120341 = Vvar__3__x__120342
& Vvar__2__eq__120339 = Vvar__2__eq__120340
& Vvar__1__lt__120337 = Vvar__1__lt__120338
& Vvar__0__X__120335 = Vvar__0__X__120336 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__120347,Vvar__0__X__120348,Vvar__1__lt__120349,Vvar__1__lt__120350,Vvar__2__eq__120351,Vvar__2__eq__120352,Vvar__3__x__120353,Vvar__3__x__120354,Vvar__4__y__120355,Vvar__4__y__120356,Vvar__5___24Anonymous__120357,Vvar__5___24Anonymous__120358] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__120347,Vvar__1__lt__120349,Vvar__2__eq__120351,Vvar__3__x__120353,Vvar__4__y__120355) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__120348,Vvar__1__lt__120350,Vvar__2__eq__120352,Vvar__3__x__120354,Vvar__4__y__120356)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__120355 = Vvar__4__y__120356
& Vvar__3__x__120353 = Vvar__3__x__120354
& Vvar__2__eq__120351 = Vvar__2__eq__120352
& Vvar__1__lt__120349 = Vvar__1__lt__120350
& Vvar__0__X__120347 = Vvar__0__X__120348 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__120323,Vvar__0__X__120324,Vvar__1__lt__120325,Vvar__1__lt__120326,Vvar__2__eq__120327,Vvar__2__eq__120328,Vvar__3__x__120329,Vvar__3__x__120330,Vvar__4__y__120331,Vvar__4__y__120332,Vvar__5___24Anonymous__120333,Vvar__5___24Anonymous__120334] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__120323,Vvar__1__lt__120325,Vvar__2__eq__120327,Vvar__3__x__120329,Vvar__4__y__120331) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__120324,Vvar__1__lt__120326,Vvar__2__eq__120328,Vvar__3__x__120330,Vvar__4__y__120332)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__120331 = Vvar__4__y__120332
& Vvar__3__x__120329 = Vvar__3__x__120330
& Vvar__2__eq__120327 = Vvar__2__eq__120328
& Vvar__1__lt__120325 = Vvar__1__lt__120326
& Vvar__0__X__120323 = Vvar__0__X__120324 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__47680,Vvar__0__n__47681] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__47680) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__47681)
=> Vvar__0__n__47680 = Vvar__0__n__47681 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__47682,Vvar__0__n__47683,Vvar__1___24Anonymous__47684,Vvar__1___24Anonymous__47685] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__47682,Vvar__1___24Anonymous__47684) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__47683,Vvar__1___24Anonymous__47685)
=> ( Vvar__1___24Anonymous__47684 = Vvar__1___24Anonymous__47685
& Vvar__0__n__47682 = Vvar__0__n__47683 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__36607,Vvar__0__A__36608,Vvar__1__h__36609,Vvar__1__h__36610,Vvar__2__n__36611,Vvar__2__n__36612,Vvar__3___24Anonymous__36613,Vvar__3___24Anonymous__36614] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__36607,Vvar__1__h__36609,Vvar__2__n__36611,Vvar__3___24Anonymous__36613) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__36608,Vvar__1__h__36610,Vvar__2__n__36612,Vvar__3___24Anonymous__36614)
=> ( Vvar__3___24Anonymous__36613 = Vvar__3___24Anonymous__36614
& Vvar__2__n__36611 = Vvar__2__n__36612
& Vvar__1__h__36609 = Vvar__1__h__36610
& Vvar__0__A__36607 = Vvar__0__A__36608 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__36605,Vvar__0__A__36606] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__36605) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__36606)
=> Vvar__0__A__36605 = Vvar__0__A__36606 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__122357,Vvar__0__a__122358,Vvar__1__b__122359,Vvar__1__b__122360,Vvar__2__u__122361,Vvar__2__u__122362,Vvar__3__v__122363,Vvar__3__v__122364,Vvar__4__d__122365,Vvar__4__d__122366,Vvar__5___24Anonymous__122367,Vvar__5___24Anonymous__122368,Vvar__6___24Anonymous__122369,Vvar__6___24Anonymous__122370] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__122357,Vvar__1__b__122359,Vvar__2__u__122361,Vvar__3__v__122363,Vvar__4__d__122365) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__122358,Vvar__1__b__122360,Vvar__2__u__122362,Vvar__3__v__122364,Vvar__4__d__122366)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__122365 = Vvar__4__d__122366
& Vvar__3__v__122363 = Vvar__3__v__122364
& Vvar__2__u__122361 = Vvar__2__u__122362
& Vvar__1__b__122359 = Vvar__1__b__122360
& Vvar__0__a__122357 = Vvar__0__a__122358 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__122418,Vvar__0__x__122419,Vvar__1__p__122420,Vvar__1__p__122421,Vvar__2__q__122422,Vvar__2__q__122423,Vvar__3__r__122424,Vvar__3__r__122425,Vvar__4___24Anonymous__122426,Vvar__4___24Anonymous__122427,Vvar__5___24Anonymous__122428,Vvar__5___24Anonymous__122429,Vvar__6___24Anonymous__122430,Vvar__6___24Anonymous__122431] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__122418,Vvar__1__p__122420,Vvar__2__q__122422,Vvar__3__r__122424) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__122419,Vvar__1__p__122421,Vvar__2__q__122423,Vvar__3__r__122425)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__122424 = Vvar__3__r__122425
& Vvar__2__q__122422 = Vvar__2__q__122423
& Vvar__1__p__122420 = Vvar__1__p__122421
& Vvar__0__x__122418 = Vvar__0__x__122419 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__5257,Vvar__0__C__5258,Vvar__1___24Anonymous__5259,Vvar__1___24Anonymous__5260] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__5257,Vvar__1___24Anonymous__5259) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__5258,Vvar__1___24Anonymous__5260)
=> ( Vvar__1___24Anonymous__5259 = Vvar__1___24Anonymous__5260
& Vvar__0__C__5257 = Vvar__0__C__5258 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__5261,Vvar__0__C__5262,Vvar__1___24Anonymous__5263,Vvar__1___24Anonymous__5264,Vvar__2___24Anonymous__5265,Vvar__2___24Anonymous__5266] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__5261,Vvar__1___24Anonymous__5263,Vvar__2___24Anonymous__5265) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__5262,Vvar__1___24Anonymous__5264,Vvar__2___24Anonymous__5266)
=> ( Vvar__2___24Anonymous__5265 = Vvar__2___24Anonymous__5266
& Vvar__1___24Anonymous__5263 = Vvar__1___24Anonymous__5264
& Vvar__0__C__5261 = Vvar__0__C__5262 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__5253,Vvar__0__C__5254,Vvar__1___24Anonymous__5255,Vvar__1___24Anonymous__5256] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__5253,Vvar__1___24Anonymous__5255) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__5254,Vvar__1___24Anonymous__5256)
=> ( Vvar__1___24Anonymous__5255 = Vvar__1___24Anonymous__5256
& Vvar__0__C__5253 = Vvar__0__C__5254 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__5273,Vvar__0__C__5274,Vvar__1___24Anonymous__5275,Vvar__1___24Anonymous__5276,Vvar__2___24Anonymous__5277,Vvar__2___24Anonymous__5278] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__5273,Vvar__1___24Anonymous__5275,Vvar__2___24Anonymous__5277) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__5274,Vvar__1___24Anonymous__5276,Vvar__2___24Anonymous__5278)
=> ( Vvar__2___24Anonymous__5277 = Vvar__2___24Anonymous__5278
& Vvar__1___24Anonymous__5275 = Vvar__1___24Anonymous__5276
& Vvar__0__C__5273 = Vvar__0__C__5274 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__5279,Vvar__0__C__5280,Vvar__1___24Anonymous__5281,Vvar__1___24Anonymous__5282] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__5279,Vvar__1___24Anonymous__5281) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__5280,Vvar__1___24Anonymous__5282)
=> ( Vvar__1___24Anonymous__5281 = Vvar__1___24Anonymous__5282
& Vvar__0__C__5279 = Vvar__0__C__5280 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__5283,Vvar__0__C__5284,Vvar__1___24Anonymous__5285,Vvar__1___24Anonymous__5286,Vvar__2___24Anonymous__5287,Vvar__2___24Anonymous__5288] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__5283,Vvar__1___24Anonymous__5285,Vvar__2___24Anonymous__5287) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__5284,Vvar__1___24Anonymous__5286,Vvar__2___24Anonymous__5288)
=> ( Vvar__2___24Anonymous__5287 = Vvar__2___24Anonymous__5288
& Vvar__1___24Anonymous__5285 = Vvar__1___24Anonymous__5286
& Vvar__0__C__5283 = Vvar__0__C__5284 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__5267,Vvar__0__C__5268,Vvar__1___24Anonymous__5269,Vvar__1___24Anonymous__5270,Vvar__2___24Anonymous__5271,Vvar__2___24Anonymous__5272] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__5267,Vvar__1___24Anonymous__5269,Vvar__2___24Anonymous__5271) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__5268,Vvar__1___24Anonymous__5270,Vvar__2___24Anonymous__5272)
=> ( Vvar__2___24Anonymous__5271 = Vvar__2___24Anonymous__5272
& Vvar__1___24Anonymous__5269 = Vvar__1___24Anonymous__5270
& Vvar__0__C__5267 = Vvar__0__C__5268 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__2277,Vvar__0__C__2278,Vvar__1___24Anonymous__2279,Vvar__1___24Anonymous__2280,Vvar__2___24Anonymous__2281,Vvar__2___24Anonymous__2282,Vvar__3___24Anonymous__2283,Vvar__3___24Anonymous__2284] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__2277,Vvar__1___24Anonymous__2279,Vvar__2___24Anonymous__2281,Vvar__3___24Anonymous__2283) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__2278,Vvar__1___24Anonymous__2280,Vvar__2___24Anonymous__2282,Vvar__3___24Anonymous__2284)
=> ( Vvar__3___24Anonymous__2283 = Vvar__3___24Anonymous__2284
& Vvar__2___24Anonymous__2281 = Vvar__2___24Anonymous__2282
& Vvar__1___24Anonymous__2279 = Vvar__1___24Anonymous__2280
& Vvar__0__C__2277 = Vvar__0__C__2278 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__2267,Vvar__0__C__2268,Vvar__1___24Anonymous__2269,Vvar__1___24Anonymous__2270] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__2267,Vvar__1___24Anonymous__2269) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__2268,Vvar__1___24Anonymous__2270)
=> ( Vvar__1___24Anonymous__2269 = Vvar__1___24Anonymous__2270
& Vvar__0__C__2267 = Vvar__0__C__2268 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__2271,Vvar__0__C__2272,Vvar__1___24Anonymous__2273,Vvar__1___24Anonymous__2274,Vvar__2___24Anonymous__2275,Vvar__2___24Anonymous__2276] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__2271,Vvar__1___24Anonymous__2273,Vvar__2___24Anonymous__2275) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__2272,Vvar__1___24Anonymous__2274,Vvar__2___24Anonymous__2276)
=> ( Vvar__2___24Anonymous__2275 = Vvar__2___24Anonymous__2276
& Vvar__1___24Anonymous__2273 = Vvar__1___24Anonymous__2274
& Vvar__0__C__2271 = Vvar__0__C__2272 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__5400,Vvar__0___24Anonymous__5401,Vvar__1___24Anonymous__5402,Vvar__1___24Anonymous__5403] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__5400,Vvar__1___24Anonymous__5402) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__5401,Vvar__1___24Anonymous__5403)
=> ( Vvar__1___24Anonymous__5402 = Vvar__1___24Anonymous__5403
& Vvar__0___24Anonymous__5400 = Vvar__0___24Anonymous__5401 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__5396,Vvar__0___24Anonymous__5397,Vvar__1___24Anonymous__5398,Vvar__1___24Anonymous__5399] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__5396,Vvar__1___24Anonymous__5398) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__5397,Vvar__1___24Anonymous__5399)
=> ( Vvar__1___24Anonymous__5398 = Vvar__1___24Anonymous__5399
& Vvar__0___24Anonymous__5396 = Vvar__0___24Anonymous__5397 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__19629,Vvar__0__r__19630] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__19629) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__19630)
=> Vvar__0__r__19629 = Vvar__0__r__19630 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__19617,Vvar__0__r1__19618,Vvar__1__r2__19619,Vvar__1__r2__19620] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__19617,Vvar__1__r2__19619) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__19618,Vvar__1__r2__19620)
=> ( Vvar__1__r2__19619 = Vvar__1__r2__19620
& Vvar__0__r1__19617 = Vvar__0__r1__19618 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__19621,Vvar__0__r1__19622,Vvar__1__r2__19623,Vvar__1__r2__19624] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__19621,Vvar__1__r2__19623) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__19622,Vvar__1__r2__19624)
=> ( Vvar__1__r2__19623 = Vvar__1__r2__19624
& Vvar__0__r1__19621 = Vvar__0__r1__19622 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__19631,Vvar__0__r__19632] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__19631) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__19632)
=> Vvar__0__r__19631 = Vvar__0__r__19632 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__19613,Vvar__0__r1__19614,Vvar__1__r2__19615,Vvar__1__r2__19616] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__19613,Vvar__1__r2__19615) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__19614,Vvar__1__r2__19616)
=> ( Vvar__1__r2__19615 = Vvar__1__r2__19616
& Vvar__0__r1__19613 = Vvar__0__r1__19614 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__19625,Vvar__0__r1__19626,Vvar__1__z__19627,Vvar__1__z__19628] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__19625,Vvar__1__z__19627) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__19626,Vvar__1__z__19628)
=> ( Vvar__1__z__19627 = Vvar__1__z__19628
& Vvar__0__r1__19625 = Vvar__0__r1__19626 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__19609,Vvar__0__r__19610] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__19609) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__19610)
=> Vvar__0__r__19609 = Vvar__0__r__19610 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__19611,Vvar__0__r__19612] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__19611) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__19612)
=> Vvar__0__r__19611 = Vvar__0__r__19612 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__20663,Vvar__0__T__20664,Vvar__1__Flhs__20665,Vvar__1__Flhs__20666,Vvar__2__Fop__20667,Vvar__2__Fop__20668,Vvar__3__Frhs__20669,Vvar__3__Frhs__20670] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__20663,Vvar__1__Flhs__20665,Vvar__2__Fop__20667,Vvar__3__Frhs__20669) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__20664,Vvar__1__Flhs__20666,Vvar__2__Fop__20668,Vvar__3__Frhs__20670)
=> ( Vvar__3__Frhs__20669 = Vvar__3__Frhs__20670
& Vvar__2__Fop__20667 = Vvar__2__Fop__20668
& Vvar__1__Flhs__20665 = Vvar__1__Flhs__20666
& Vvar__0__T__20663 = Vvar__0__T__20664 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__3427,Vvar__0__C__3428,Vvar__1___24Anonymous__3429,Vvar__1___24Anonymous__3430,Vvar__2___24Anonymous__3431,Vvar__2___24Anonymous__3432] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__3427,Vvar__1___24Anonymous__3429,Vvar__2___24Anonymous__3431) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__3428,Vvar__1___24Anonymous__3430,Vvar__2___24Anonymous__3432)
=> ( Vvar__2___24Anonymous__3431 = Vvar__2___24Anonymous__3432
& Vvar__1___24Anonymous__3429 = Vvar__1___24Anonymous__3430
& Vvar__0__C__3427 = Vvar__0__C__3428 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__3433,Vvar__0__C__3434,Vvar__1___24Anonymous__3435,Vvar__1___24Anonymous__3436] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__3433,Vvar__1___24Anonymous__3435) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__3434,Vvar__1___24Anonymous__3436)
=> ( Vvar__1___24Anonymous__3435 = Vvar__1___24Anonymous__3436
& Vvar__0__C__3433 = Vvar__0__C__3434 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__3407,Vvar__0__C__3408,Vvar__1___24Anonymous__3409,Vvar__1___24Anonymous__3410] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__3407,Vvar__1___24Anonymous__3409) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__3408,Vvar__1___24Anonymous__3410)
=> ( Vvar__1___24Anonymous__3409 = Vvar__1___24Anonymous__3410
& Vvar__0__C__3407 = Vvar__0__C__3408 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__3415,Vvar__0__C__3416,Vvar__1___24Anonymous__3417,Vvar__1___24Anonymous__3418,Vvar__2___24Anonymous__3419,Vvar__2___24Anonymous__3420] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__3415,Vvar__1___24Anonymous__3417,Vvar__2___24Anonymous__3419) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__3416,Vvar__1___24Anonymous__3418,Vvar__2___24Anonymous__3420)
=> ( Vvar__2___24Anonymous__3419 = Vvar__2___24Anonymous__3420
& Vvar__1___24Anonymous__3417 = Vvar__1___24Anonymous__3418
& Vvar__0__C__3415 = Vvar__0__C__3416 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__3421,Vvar__0__C__3422,Vvar__1___24Anonymous__3423,Vvar__1___24Anonymous__3424,Vvar__2___24Anonymous__3425,Vvar__2___24Anonymous__3426] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__3421,Vvar__1___24Anonymous__3423,Vvar__2___24Anonymous__3425) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__3422,Vvar__1___24Anonymous__3424,Vvar__2___24Anonymous__3426)
=> ( Vvar__2___24Anonymous__3425 = Vvar__2___24Anonymous__3426
& Vvar__1___24Anonymous__3423 = Vvar__1___24Anonymous__3424
& Vvar__0__C__3421 = Vvar__0__C__3422 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__3411,Vvar__0__C__3412,Vvar__1___24Anonymous__3413,Vvar__1___24Anonymous__3414] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__3411,Vvar__1___24Anonymous__3413) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__3412,Vvar__1___24Anonymous__3414)
=> ( Vvar__1___24Anonymous__3413 = Vvar__1___24Anonymous__3414
& Vvar__0__C__3411 = Vvar__0__C__3412 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__3437,Vvar__0__C__3438] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__3437) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__3438)
=> Vvar__0__C__3437 = Vvar__0__C__3438 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__1053,Vvar__0__TA__1054,Vvar__1__TX__1055,Vvar__1__TX__1056,Vvar__2__AA__1057,Vvar__2__AA__1058,Vvar__3__AF__1059,Vvar__3__AF__1060,Vvar__4___24Anonymous__1061,Vvar__4___24Anonymous__1062,Vvar__5___24Anonymous__1063,Vvar__5___24Anonymous__1064] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__1053,Vvar__1__TX__1055,Vvar__2__AA__1057,Vvar__3__AF__1059,Vvar__4___24Anonymous__1061,Vvar__5___24Anonymous__1063) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__1054,Vvar__1__TX__1056,Vvar__2__AA__1058,Vvar__3__AF__1060,Vvar__4___24Anonymous__1062,Vvar__5___24Anonymous__1064)
=> ( Vvar__5___24Anonymous__1063 = Vvar__5___24Anonymous__1064
& Vvar__4___24Anonymous__1061 = Vvar__4___24Anonymous__1062
& Vvar__3__AF__1059 = Vvar__3__AF__1060
& Vvar__2__AA__1057 = Vvar__2__AA__1058
& Vvar__1__TX__1055 = Vvar__1__TX__1056
& Vvar__0__TA__1053 = Vvar__0__TA__1054 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__1065,Vvar__0__TA__1066,Vvar__1__TX__1067,Vvar__1__TX__1068,Vvar__2__AA__1069,Vvar__2__AA__1070,Vvar__3__AF__1071,Vvar__3__AF__1072,Vvar__4___24Anonymous__1073,Vvar__4___24Anonymous__1074,Vvar__5___24Anonymous__1075,Vvar__5___24Anonymous__1076] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__1065,Vvar__1__TX__1067,Vvar__2__AA__1069,Vvar__3__AF__1071,Vvar__4___24Anonymous__1073,Vvar__5___24Anonymous__1075) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__1066,Vvar__1__TX__1068,Vvar__2__AA__1070,Vvar__3__AF__1072,Vvar__4___24Anonymous__1074,Vvar__5___24Anonymous__1076)
=> ( Vvar__5___24Anonymous__1075 = Vvar__5___24Anonymous__1076
& Vvar__4___24Anonymous__1073 = Vvar__4___24Anonymous__1074
& Vvar__3__AF__1071 = Vvar__3__AF__1072
& Vvar__2__AA__1069 = Vvar__2__AA__1070
& Vvar__1__TX__1067 = Vvar__1__TX__1068
& Vvar__0__TA__1065 = Vvar__0__TA__1066 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__1077,Vvar__0__TA__1078,Vvar__1__TX__1079,Vvar__1__TX__1080,Vvar__2__AA__1081,Vvar__2__AA__1082,Vvar__3__AF__1083,Vvar__3__AF__1084,Vvar__4___24Anonymous__1085,Vvar__4___24Anonymous__1086,Vvar__5___24Anonymous__1087,Vvar__5___24Anonymous__1088] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__1077,Vvar__1__TX__1079,Vvar__2__AA__1081,Vvar__3__AF__1083,Vvar__4___24Anonymous__1085,Vvar__5___24Anonymous__1087) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__1078,Vvar__1__TX__1080,Vvar__2__AA__1082,Vvar__3__AF__1084,Vvar__4___24Anonymous__1086,Vvar__5___24Anonymous__1088)
=> ( Vvar__5___24Anonymous__1087 = Vvar__5___24Anonymous__1088
& Vvar__4___24Anonymous__1085 = Vvar__4___24Anonymous__1086
& Vvar__3__AF__1083 = Vvar__3__AF__1084
& Vvar__2__AA__1081 = Vvar__2__AA__1082
& Vvar__1__TX__1079 = Vvar__1__TX__1080
& Vvar__0__TA__1077 = Vvar__0__TA__1078 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__1035,Vvar__0__TA__1036,Vvar__1__TX__1037,Vvar__1__TX__1038,Vvar__2__AA__1039,Vvar__2__AA__1040,Vvar__3__AF__1041,Vvar__3__AF__1042] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__1035,Vvar__1__TX__1037,Vvar__2__AA__1039,Vvar__3__AF__1041) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__1036,Vvar__1__TX__1038,Vvar__2__AA__1040,Vvar__3__AF__1042)
=> ( Vvar__3__AF__1041 = Vvar__3__AF__1042
& Vvar__2__AA__1039 = Vvar__2__AA__1040
& Vvar__1__TX__1037 = Vvar__1__TX__1038
& Vvar__0__TA__1035 = Vvar__0__TA__1036 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__1099,Vvar__0__TA__1100,Vvar__1__TX__1101,Vvar__1__TX__1102,Vvar__2__AA__1103,Vvar__2__AA__1104,Vvar__3__AF__1105,Vvar__3__AF__1106,Vvar__4___24Anonymous__1107,Vvar__4___24Anonymous__1108,Vvar__5___24Anonymous__1109,Vvar__5___24Anonymous__1110,Vvar__6___24Anonymous__1111,Vvar__6___24Anonymous__1112] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__1099,Vvar__1__TX__1101,Vvar__2__AA__1103,Vvar__3__AF__1105,Vvar__4___24Anonymous__1107,Vvar__5___24Anonymous__1109,Vvar__6___24Anonymous__1111) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__1100,Vvar__1__TX__1102,Vvar__2__AA__1104,Vvar__3__AF__1106,Vvar__4___24Anonymous__1108,Vvar__5___24Anonymous__1110,Vvar__6___24Anonymous__1112)
=> ( Vvar__6___24Anonymous__1111 = Vvar__6___24Anonymous__1112
& Vvar__5___24Anonymous__1109 = Vvar__5___24Anonymous__1110
& Vvar__4___24Anonymous__1107 = Vvar__4___24Anonymous__1108
& Vvar__3__AF__1105 = Vvar__3__AF__1106
& Vvar__2__AA__1103 = Vvar__2__AA__1104
& Vvar__1__TX__1101 = Vvar__1__TX__1102
& Vvar__0__TA__1099 = Vvar__0__TA__1100 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__1089,Vvar__0__TA__1090,Vvar__1__TX__1091,Vvar__1__TX__1092,Vvar__2__AA__1093,Vvar__2__AA__1094,Vvar__3__AF__1095,Vvar__3__AF__1096,Vvar__4___24Anonymous__1097,Vvar__4___24Anonymous__1098] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__1089,Vvar__1__TX__1091,Vvar__2__AA__1093,Vvar__3__AF__1095,Vvar__4___24Anonymous__1097) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__1090,Vvar__1__TX__1092,Vvar__2__AA__1094,Vvar__3__AF__1096,Vvar__4___24Anonymous__1098)
=> ( Vvar__4___24Anonymous__1097 = Vvar__4___24Anonymous__1098
& Vvar__3__AF__1095 = Vvar__3__AF__1096
& Vvar__2__AA__1093 = Vvar__2__AA__1094
& Vvar__1__TX__1091 = Vvar__1__TX__1092
& Vvar__0__TA__1089 = Vvar__0__TA__1090 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__1027,Vvar__0__TA__1028,Vvar__1__TX__1029,Vvar__1__TX__1030,Vvar__2__AA__1031,Vvar__2__AA__1032,Vvar__3__AF__1033,Vvar__3__AF__1034] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__1027,Vvar__1__TX__1029,Vvar__2__AA__1031,Vvar__3__AF__1033) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__1028,Vvar__1__TX__1030,Vvar__2__AA__1032,Vvar__3__AF__1034)
=> ( Vvar__3__AF__1033 = Vvar__3__AF__1034
& Vvar__2__AA__1031 = Vvar__2__AA__1032
& Vvar__1__TX__1029 = Vvar__1__TX__1030
& Vvar__0__TA__1027 = Vvar__0__TA__1028 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__1043,Vvar__0__TA__1044,Vvar__1__TX__1045,Vvar__1__TX__1046,Vvar__2__AA__1047,Vvar__2__AA__1048,Vvar__3__AF__1049,Vvar__3__AF__1050,Vvar__4___24Anonymous__1051,Vvar__4___24Anonymous__1052] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__1043,Vvar__1__TX__1045,Vvar__2__AA__1047,Vvar__3__AF__1049,Vvar__4___24Anonymous__1051) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__1044,Vvar__1__TX__1046,Vvar__2__AA__1048,Vvar__3__AF__1050,Vvar__4___24Anonymous__1052)
=> ( Vvar__4___24Anonymous__1051 = Vvar__4___24Anonymous__1052
& Vvar__3__AF__1049 = Vvar__3__AF__1050
& Vvar__2__AA__1047 = Vvar__2__AA__1048
& Vvar__1__TX__1045 = Vvar__1__TX__1046
& Vvar__0__TA__1043 = Vvar__0__TA__1044 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__36779,Vvar__0___24Anonymous__36780,Vvar__1___24Anonymous__36781,Vvar__1___24Anonymous__36782] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__36779,Vvar__1___24Anonymous__36781) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__36780,Vvar__1___24Anonymous__36782)
=> ( Vvar__1___24Anonymous__36781 = Vvar__1___24Anonymous__36782
& Vvar__0___24Anonymous__36779 = Vvar__0___24Anonymous__36780 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__36783,Vvar__0___24Anonymous__36784,Vvar__1___24Anonymous__36785,Vvar__1___24Anonymous__36786,Vvar__2___24Anonymous__36787,Vvar__2___24Anonymous__36788] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__36783,Vvar__1___24Anonymous__36785,Vvar__2___24Anonymous__36787) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__36784,Vvar__1___24Anonymous__36786,Vvar__2___24Anonymous__36788)
=> ( Vvar__2___24Anonymous__36787 = Vvar__2___24Anonymous__36788
& Vvar__1___24Anonymous__36785 = Vvar__1___24Anonymous__36786
& Vvar__0___24Anonymous__36783 = Vvar__0___24Anonymous__36784 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__36775,Vvar__0___24Anonymous__36776,Vvar__1___24Anonymous__36777,Vvar__1___24Anonymous__36778] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__36775,Vvar__1___24Anonymous__36777) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__36776,Vvar__1___24Anonymous__36778)
=> ( Vvar__1___24Anonymous__36777 = Vvar__1___24Anonymous__36778
& Vvar__0___24Anonymous__36775 = Vvar__0___24Anonymous__36776 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__10852,Vvar__0__C__10853] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__10852) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__10853)
=> Vvar__0__C__10852 = Vvar__0__C__10853 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__10850,Vvar__0__C__10851] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__10850) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__10851)
=> Vvar__0__C__10850 = Vvar__0__C__10851 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__10858,Vvar__0__C__10859,Vvar__1___24Anonymous__10860,Vvar__1___24Anonymous__10861] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__10858,Vvar__1___24Anonymous__10860) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__10859,Vvar__1___24Anonymous__10861)
=> ( Vvar__1___24Anonymous__10860 = Vvar__1___24Anonymous__10861
& Vvar__0__C__10858 = Vvar__0__C__10859 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__10862,Vvar__0__C__10863,Vvar__1___24Anonymous__10864,Vvar__1___24Anonymous__10865,Vvar__2___24Anonymous__10866,Vvar__2___24Anonymous__10867] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__10862,Vvar__1___24Anonymous__10864,Vvar__2___24Anonymous__10866) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__10863,Vvar__1___24Anonymous__10865,Vvar__2___24Anonymous__10867)
=> ( Vvar__2___24Anonymous__10866 = Vvar__2___24Anonymous__10867
& Vvar__1___24Anonymous__10864 = Vvar__1___24Anonymous__10865
& Vvar__0__C__10862 = Vvar__0__C__10863 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__10854,Vvar__0__C__10855,Vvar__1___24Anonymous__10856,Vvar__1___24Anonymous__10857] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__10854,Vvar__1___24Anonymous__10856) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__10855,Vvar__1___24Anonymous__10857)
=> ( Vvar__1___24Anonymous__10856 = Vvar__1___24Anonymous__10857
& Vvar__0__C__10854 = Vvar__0__C__10855 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__10888,Vvar__0__C__10889,Vvar__1___24Anonymous__10890,Vvar__1___24Anonymous__10891,Vvar__2___24Anonymous__10892,Vvar__2___24Anonymous__10893] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__10888,Vvar__1___24Anonymous__10890,Vvar__2___24Anonymous__10892) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__10889,Vvar__1___24Anonymous__10891,Vvar__2___24Anonymous__10893)
=> ( Vvar__2___24Anonymous__10892 = Vvar__2___24Anonymous__10893
& Vvar__1___24Anonymous__10890 = Vvar__1___24Anonymous__10891
& Vvar__0__C__10888 = Vvar__0__C__10889 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__10884,Vvar__0__C__10885,Vvar__1___24Anonymous__10886,Vvar__1___24Anonymous__10887] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__10884,Vvar__1___24Anonymous__10886) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__10885,Vvar__1___24Anonymous__10887)
=> ( Vvar__1___24Anonymous__10886 = Vvar__1___24Anonymous__10887
& Vvar__0__C__10884 = Vvar__0__C__10885 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__10874,Vvar__0__C__10875,Vvar__1___24Anonymous__10876,Vvar__1___24Anonymous__10877,Vvar__2___24Anonymous__10878,Vvar__2___24Anonymous__10879] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__10874,Vvar__1___24Anonymous__10876,Vvar__2___24Anonymous__10878) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__10875,Vvar__1___24Anonymous__10877,Vvar__2___24Anonymous__10879)
=> ( Vvar__2___24Anonymous__10878 = Vvar__2___24Anonymous__10879
& Vvar__1___24Anonymous__10876 = Vvar__1___24Anonymous__10877
& Vvar__0__C__10874 = Vvar__0__C__10875 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__10880,Vvar__0__C__10881,Vvar__1___24Anonymous__10882,Vvar__1___24Anonymous__10883] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__10880,Vvar__1___24Anonymous__10882) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__10881,Vvar__1___24Anonymous__10883)
=> ( Vvar__1___24Anonymous__10882 = Vvar__1___24Anonymous__10883
& Vvar__0__C__10880 = Vvar__0__C__10881 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__10894,Vvar__0__C__10895,Vvar__1___24Anonymous__10896,Vvar__1___24Anonymous__10897,Vvar__2___24Anonymous__10898,Vvar__2___24Anonymous__10899] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__10894,Vvar__1___24Anonymous__10896,Vvar__2___24Anonymous__10898) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__10895,Vvar__1___24Anonymous__10897,Vvar__2___24Anonymous__10899)
=> ( Vvar__2___24Anonymous__10898 = Vvar__2___24Anonymous__10899
& Vvar__1___24Anonymous__10896 = Vvar__1___24Anonymous__10897
& Vvar__0__C__10894 = Vvar__0__C__10895 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__10868,Vvar__0__C__10869,Vvar__1___24Anonymous__10870,Vvar__1___24Anonymous__10871,Vvar__2___24Anonymous__10872,Vvar__2___24Anonymous__10873] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__10868,Vvar__1___24Anonymous__10870,Vvar__2___24Anonymous__10872) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__10869,Vvar__1___24Anonymous__10871,Vvar__2___24Anonymous__10873)
=> ( Vvar__2___24Anonymous__10872 = Vvar__2___24Anonymous__10873
& Vvar__1___24Anonymous__10870 = Vvar__1___24Anonymous__10871
& Vvar__0__C__10868 = Vvar__0__C__10869 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__11191,Vvar__0__C__11192,Vvar__1__num__11193,Vvar__1__num__11194,Vvar__2__denum__11195,Vvar__2__denum__11196,Vvar__3__condition__11197,Vvar__3__condition__11198] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__11191,Vvar__1__num__11193,Vvar__2__denum__11195,Vvar__3__condition__11197) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__11192,Vvar__1__num__11194,Vvar__2__denum__11196,Vvar__3__condition__11198)
=> ( Vvar__3__condition__11197 = Vvar__3__condition__11198
& Vvar__2__denum__11195 = Vvar__2__denum__11196
& Vvar__1__num__11193 = Vvar__1__num__11194
& Vvar__0__C__11191 = Vvar__0__C__11192 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__11294,Vvar__0__C__11295,Vvar__1__rsplit__left__11296,Vvar__1__rsplit__left__11297,Vvar__2__rsplit__common__11298,Vvar__2__rsplit__common__11299,Vvar__3__rsplit__right__11300,Vvar__3__rsplit__right__11301] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__11294,Vvar__1__rsplit__left__11296,Vvar__2__rsplit__common__11298,Vvar__3__rsplit__right__11300) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__11295,Vvar__1__rsplit__left__11297,Vvar__2__rsplit__common__11299,Vvar__3__rsplit__right__11301)
=> ( Vvar__3__rsplit__right__11300 = Vvar__3__rsplit__right__11301
& Vvar__2__rsplit__common__11298 = Vvar__2__rsplit__common__11299
& Vvar__1__rsplit__left__11296 = Vvar__1__rsplit__left__11297
& Vvar__0__C__11294 = Vvar__0__C__11295 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__3647,Vvar__0__C__3648] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__3647) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__3648)
=> Vvar__0__C__3647 = Vvar__0__C__3648 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__3645,Vvar__0__C__3646] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__3645) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__3646)
=> Vvar__0__C__3645 = Vvar__0__C__3646 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__3653,Vvar__0__C__3654,Vvar__1___24Anonymous__3655,Vvar__1___24Anonymous__3656] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__3653,Vvar__1___24Anonymous__3655) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__3654,Vvar__1___24Anonymous__3656)
=> ( Vvar__1___24Anonymous__3655 = Vvar__1___24Anonymous__3656
& Vvar__0__C__3653 = Vvar__0__C__3654 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__3657,Vvar__0__C__3658,Vvar__1___24Anonymous__3659,Vvar__1___24Anonymous__3660,Vvar__2___24Anonymous__3661,Vvar__2___24Anonymous__3662] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__3657,Vvar__1___24Anonymous__3659,Vvar__2___24Anonymous__3661) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__3658,Vvar__1___24Anonymous__3660,Vvar__2___24Anonymous__3662)
=> ( Vvar__2___24Anonymous__3661 = Vvar__2___24Anonymous__3662
& Vvar__1___24Anonymous__3659 = Vvar__1___24Anonymous__3660
& Vvar__0__C__3657 = Vvar__0__C__3658 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__3649,Vvar__0__C__3650,Vvar__1___24Anonymous__3651,Vvar__1___24Anonymous__3652] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__3649,Vvar__1___24Anonymous__3651) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__3650,Vvar__1___24Anonymous__3652)
=> ( Vvar__1___24Anonymous__3651 = Vvar__1___24Anonymous__3652
& Vvar__0__C__3649 = Vvar__0__C__3650 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__3669,Vvar__0__C__3670,Vvar__1___24Anonymous__3671,Vvar__1___24Anonymous__3672,Vvar__2___24Anonymous__3673,Vvar__2___24Anonymous__3674] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__3669,Vvar__1___24Anonymous__3671,Vvar__2___24Anonymous__3673) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__3670,Vvar__1___24Anonymous__3672,Vvar__2___24Anonymous__3674)
=> ( Vvar__2___24Anonymous__3673 = Vvar__2___24Anonymous__3674
& Vvar__1___24Anonymous__3671 = Vvar__1___24Anonymous__3672
& Vvar__0__C__3669 = Vvar__0__C__3670 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__3675,Vvar__0__C__3676,Vvar__1___24Anonymous__3677,Vvar__1___24Anonymous__3678] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__3675,Vvar__1___24Anonymous__3677) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__3676,Vvar__1___24Anonymous__3678)
=> ( Vvar__1___24Anonymous__3677 = Vvar__1___24Anonymous__3678
& Vvar__0__C__3675 = Vvar__0__C__3676 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__3679,Vvar__0__C__3680,Vvar__1___24Anonymous__3681,Vvar__1___24Anonymous__3682,Vvar__2___24Anonymous__3683,Vvar__2___24Anonymous__3684] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__3679,Vvar__1___24Anonymous__3681,Vvar__2___24Anonymous__3683) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__3680,Vvar__1___24Anonymous__3682,Vvar__2___24Anonymous__3684)
=> ( Vvar__2___24Anonymous__3683 = Vvar__2___24Anonymous__3684
& Vvar__1___24Anonymous__3681 = Vvar__1___24Anonymous__3682
& Vvar__0__C__3679 = Vvar__0__C__3680 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__3663,Vvar__0__C__3664,Vvar__1___24Anonymous__3665,Vvar__1___24Anonymous__3666,Vvar__2___24Anonymous__3667,Vvar__2___24Anonymous__3668] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__3663,Vvar__1___24Anonymous__3665,Vvar__2___24Anonymous__3667) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__3664,Vvar__1___24Anonymous__3666,Vvar__2___24Anonymous__3668)
=> ( Vvar__2___24Anonymous__3667 = Vvar__2___24Anonymous__3668
& Vvar__1___24Anonymous__3665 = Vvar__1___24Anonymous__3666
& Vvar__0__C__3663 = Vvar__0__C__3664 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__20798,Vvar__0__C__20799,Vvar__1___24Anonymous__20800,Vvar__1___24Anonymous__20801,Vvar__2___24Anonymous__20802,Vvar__2___24Anonymous__20803,Vvar__3___24Anonymous__20804,Vvar__3___24Anonymous__20805] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__20798,Vvar__1___24Anonymous__20800,Vvar__2___24Anonymous__20802,Vvar__3___24Anonymous__20804) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__20799,Vvar__1___24Anonymous__20801,Vvar__2___24Anonymous__20803,Vvar__3___24Anonymous__20805)
=> ( Vvar__3___24Anonymous__20804 = Vvar__3___24Anonymous__20805
& Vvar__2___24Anonymous__20802 = Vvar__2___24Anonymous__20803
& Vvar__1___24Anonymous__20800 = Vvar__1___24Anonymous__20801
& Vvar__0__C__20798 = Vvar__0__C__20799 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__20788,Vvar__0__C__20789,Vvar__1___24Anonymous__20790,Vvar__1___24Anonymous__20791] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__20788,Vvar__1___24Anonymous__20790) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__20789,Vvar__1___24Anonymous__20791)
=> ( Vvar__1___24Anonymous__20790 = Vvar__1___24Anonymous__20791
& Vvar__0__C__20788 = Vvar__0__C__20789 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__20792,Vvar__0__C__20793,Vvar__1___24Anonymous__20794,Vvar__1___24Anonymous__20795,Vvar__2___24Anonymous__20796,Vvar__2___24Anonymous__20797] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__20792,Vvar__1___24Anonymous__20794,Vvar__2___24Anonymous__20796) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__20793,Vvar__1___24Anonymous__20795,Vvar__2___24Anonymous__20797)
=> ( Vvar__2___24Anonymous__20796 = Vvar__2___24Anonymous__20797
& Vvar__1___24Anonymous__20794 = Vvar__1___24Anonymous__20795
& Vvar__0__C__20792 = Vvar__0__C__20793 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__21731,Vvar__0___24Anonymous__21732,Vvar__1___24Anonymous__21733,Vvar__1___24Anonymous__21734] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__21731,Vvar__1___24Anonymous__21733) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__21732,Vvar__1___24Anonymous__21734)
=> ( Vvar__1___24Anonymous__21733 = Vvar__1___24Anonymous__21734
& Vvar__0___24Anonymous__21731 = Vvar__0___24Anonymous__21732 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__21727,Vvar__0___24Anonymous__21728,Vvar__1___24Anonymous__21729,Vvar__1___24Anonymous__21730] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__21727,Vvar__1___24Anonymous__21729) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__21728,Vvar__1___24Anonymous__21730)
=> ( Vvar__1___24Anonymous__21729 = Vvar__1___24Anonymous__21730
& Vvar__0___24Anonymous__21727 = Vvar__0___24Anonymous__21728 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__122049,Vvar__0__R__122050,Vvar__1__req__122051,Vvar__1__req__122052,Vvar__2__reqb__122053,Vvar__2__reqb__122054,Vvar__3___24Anonymous__122055,Vvar__3___24Anonymous__122056] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__122049,Vvar__1__req__122051,Vvar__2__reqb__122053) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__122050,Vvar__1__req__122052,Vvar__2__reqb__122054)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__122053 = Vvar__2__reqb__122054
& Vvar__1__req__122051 = Vvar__1__req__122052
& Vvar__0__R__122049 = Vvar__0__R__122050 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__122057,Vvar__0__R__122058,Vvar__1__rO__122059,Vvar__1__rO__122060,Vvar__2__rI__122061,Vvar__2__rI__122062,Vvar__3__radd__122063,Vvar__3__radd__122064,Vvar__4__rmul__122065,Vvar__4__rmul__122066,Vvar__5__rsub__122067,Vvar__5__rsub__122068,Vvar__6__ropp__122069,Vvar__6__ropp__122070,Vvar__7__req__122071,Vvar__7__req__122072,Vvar__8__C__122073,Vvar__8__C__122074,Vvar__9__cO__122075,Vvar__9__cO__122076,Vvar__10__cI__122077,Vvar__10__cI__122078,Vvar__11__cadd__122079,Vvar__11__cadd__122080,Vvar__12__cmul__122081,Vvar__12__cmul__122082,Vvar__13__csub__122083,Vvar__13__csub__122084,Vvar__14__copp__122085,Vvar__14__copp__122086,Vvar__15__ceqb__122087,Vvar__15__ceqb__122088,Vvar__16__phi__122089,Vvar__16__phi__122090,Vvar__17___24Anonymous__122091,Vvar__17___24Anonymous__122092] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__122057,Vvar__1__rO__122059,Vvar__2__rI__122061,Vvar__3__radd__122063,Vvar__4__rmul__122065,Vvar__5__rsub__122067,Vvar__6__ropp__122069,Vvar__7__req__122071,Vvar__8__C__122073,Vvar__9__cO__122075,Vvar__10__cI__122077,Vvar__11__cadd__122079,Vvar__12__cmul__122081,Vvar__13__csub__122083,Vvar__14__copp__122085,Vvar__15__ceqb__122087,Vvar__16__phi__122089) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__122058,Vvar__1__rO__122060,Vvar__2__rI__122062,Vvar__3__radd__122064,Vvar__4__rmul__122066,Vvar__5__rsub__122068,Vvar__6__ropp__122070,Vvar__7__req__122072,Vvar__8__C__122074,Vvar__9__cO__122076,Vvar__10__cI__122078,Vvar__11__cadd__122080,Vvar__12__cmul__122082,Vvar__13__csub__122084,Vvar__14__copp__122086,Vvar__15__ceqb__122088,Vvar__16__phi__122090)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__122089 = Vvar__16__phi__122090
& Vvar__15__ceqb__122087 = Vvar__15__ceqb__122088
& Vvar__14__copp__122085 = Vvar__14__copp__122086
& Vvar__13__csub__122083 = Vvar__13__csub__122084
& Vvar__12__cmul__122081 = Vvar__12__cmul__122082
& Vvar__11__cadd__122079 = Vvar__11__cadd__122080
& Vvar__10__cI__122077 = Vvar__10__cI__122078
& Vvar__9__cO__122075 = Vvar__9__cO__122076
& Vvar__8__C__122073 = Vvar__8__C__122074
& Vvar__7__req__122071 = Vvar__7__req__122072
& Vvar__6__ropp__122069 = Vvar__6__ropp__122070
& Vvar__5__rsub__122067 = Vvar__5__rsub__122068
& Vvar__4__rmul__122065 = Vvar__4__rmul__122066
& Vvar__3__radd__122063 = Vvar__3__radd__122064
& Vvar__2__rI__122061 = Vvar__2__rI__122062
& Vvar__1__rO__122059 = Vvar__1__rO__122060
& Vvar__0__R__122057 = Vvar__0__R__122058 ) ) ).
fof('$_inj_ExtLib.Core.RelDec.Build_RelDec',axiom,
! [Vvar__0__T__120516,Vvar__0__T__120517,Vvar__1__equ__120518,Vvar__1__equ__120519,Vvar__2__rel__dec__120520,Vvar__2__rel__dec__120521] :
( cExtLib_2eCore_2eRelDec_2eBuild__RelDec___24a3(Vvar__0__T__120516,Vvar__1__equ__120518,Vvar__2__rel__dec__120520) = cExtLib_2eCore_2eRelDec_2eBuild__RelDec___24a3(Vvar__0__T__120517,Vvar__1__equ__120519,Vvar__2__rel__dec__120521)
=> ( Vvar__2__rel__dec__120520 = Vvar__2__rel__dec__120521
& Vvar__1__equ__120518 = Vvar__1__equ__120519
& Vvar__0__T__120516 = Vvar__0__T__120517 ) ) ).
fof('$_inj_ExtLib.Data.Member.MN',axiom,
! [Vvar__0__T__17537,Vvar__0__T__17538,Vvar__1__a__17539,Vvar__1__a__17540,Vvar__2__l__17541,Vvar__2__l__17542,Vvar__3__ls__17543,Vvar__3__ls__17544,Vvar__4___24Anonymous__17545,Vvar__4___24Anonymous__17546] :
( cExtLib_2eData_2eMember_2eMN___24a5(Vvar__0__T__17537,Vvar__1__a__17539,Vvar__2__l__17541,Vvar__3__ls__17543,Vvar__4___24Anonymous__17545) = cExtLib_2eData_2eMember_2eMN___24a5(Vvar__0__T__17538,Vvar__1__a__17540,Vvar__2__l__17542,Vvar__3__ls__17544,Vvar__4___24Anonymous__17546)
=> ( Vvar__4___24Anonymous__17545 = Vvar__4___24Anonymous__17546
& Vvar__3__ls__17543 = Vvar__3__ls__17544
& Vvar__2__l__17541 = Vvar__2__l__17542
& Vvar__1__a__17539 = Vvar__1__a__17540
& Vvar__0__T__17537 = Vvar__0__T__17538 ) ) ).
fof('$_inj_ExtLib.Data.Member.MZ',axiom,
! [Vvar__0__T__17531,Vvar__0__T__17532,Vvar__1__a__17533,Vvar__1__a__17534,Vvar__2__ls__17535,Vvar__2__ls__17536] :
( cExtLib_2eData_2eMember_2eMZ___24a3(Vvar__0__T__17531,Vvar__1__a__17533,Vvar__2__ls__17535) = cExtLib_2eData_2eMember_2eMZ___24a3(Vvar__0__T__17532,Vvar__1__a__17534,Vvar__2__ls__17536)
=> ( Vvar__2__ls__17535 = Vvar__2__ls__17536
& Vvar__1__a__17533 = Vvar__1__a__17534
& Vvar__0__T__17531 = Vvar__0__T__17532 ) ) ).
fof('$_inj_ExtLib.Tactics.Injection.Build_Injective',axiom,
! [Vvar__0__P__15452,Vvar__0__P__15453,Vvar__1__result__15454,Vvar__1__result__15455,Vvar__2__injection__15456,Vvar__2__injection__15457] :
( cExtLib_2eTactics_2eInjection_2eBuild__Injective___24a2(Vvar__0__P__15452,Vvar__1__result__15454) = cExtLib_2eTactics_2eInjection_2eBuild__Injective___24a2(Vvar__0__P__15453,Vvar__1__result__15455)
=> ( c_24Proof = c_24Proof
& Vvar__1__result__15454 = Vvar__1__result__15455
& Vvar__0__P__15452 = Vvar__0__P__15453 ) ) ).
fof('$_inj_HList.hlist.Hcons',axiom,
! [Vvar__0__l__46672,Vvar__0__l__46673,Vvar__1__ls__46674,Vvar__1__ls__46675,Vvar__2___24Anonymous__46676,Vvar__2___24Anonymous__46677,Vvar__3___24Anonymous__46678,Vvar__3___24Anonymous__46679] :
( cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672,Vvar__1__ls__46674,Vvar__2___24Anonymous__46676,Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673,Vvar__1__ls__46675,Vvar__2___24Anonymous__46677,Vvar__3___24Anonymous__46679)
=> ( Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679
& Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677
& Vvar__1__ls__46674 = Vvar__1__ls__46675
& Vvar__0__l__46672 = Vvar__0__l__46673 ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__118676] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__118676)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__118676)
=> ( Vvar__0___24Anonymous__118676 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__118678] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__118678)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__118678)
& Vvar__0___24Anonymous__118676 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__118678) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__118680] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__118680)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__118680)
=> ? [Vvar__0__n__118682] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__118682)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__118682)
& Vvar__0___24Anonymous__118680 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__118682) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__5026,Vvar__1___24Anonymous__5027,VX5028] :
( cProp___24t(Vvar__0__P__5026)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__5027)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__5026,Vvar__1___24Anonymous__5027,VX5028)
=> ( ( p(Vvar__0__P__5026)
& Vvar__1___24Anonymous__5027 = cCoq_2eInit_2eDatatypes_2etrue
& VX5028 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5026) )
| ( ~ p(Vvar__0__P__5026)
& Vvar__1___24Anonymous__5027 = cCoq_2eInit_2eDatatypes_2efalse
& VX5028 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5026) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX37665] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX37665)
=> ( VX37665 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__37666] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__37666)
& ? [Vvar__1___24Anonymous__37667] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__37667)
& ? [Vvar__2___24Anonymous__37668] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__37668)
& VX37665 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37666,Vvar__1___24Anonymous__37667,Vvar__2___24Anonymous__37668) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX5048] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX5048)
=> ( VX5048 = cCoq_2eInit_2eByte_2ex00
| VX5048 = cCoq_2eInit_2eByte_2ex01
| VX5048 = cCoq_2eInit_2eByte_2ex02
| VX5048 = cCoq_2eInit_2eByte_2ex03
| VX5048 = cCoq_2eInit_2eByte_2ex04
| VX5048 = cCoq_2eInit_2eByte_2ex05
| VX5048 = cCoq_2eInit_2eByte_2ex06
| VX5048 = cCoq_2eInit_2eByte_2ex07
| VX5048 = cCoq_2eInit_2eByte_2ex08
| VX5048 = cCoq_2eInit_2eByte_2ex09
| VX5048 = cCoq_2eInit_2eByte_2ex0a
| VX5048 = cCoq_2eInit_2eByte_2ex0b
| VX5048 = cCoq_2eInit_2eByte_2ex0c
| VX5048 = cCoq_2eInit_2eByte_2ex0d
| VX5048 = cCoq_2eInit_2eByte_2ex0e
| VX5048 = cCoq_2eInit_2eByte_2ex0f
| VX5048 = cCoq_2eInit_2eByte_2ex10
| VX5048 = cCoq_2eInit_2eByte_2ex11
| VX5048 = cCoq_2eInit_2eByte_2ex12
| VX5048 = cCoq_2eInit_2eByte_2ex13
| VX5048 = cCoq_2eInit_2eByte_2ex14
| VX5048 = cCoq_2eInit_2eByte_2ex15
| VX5048 = cCoq_2eInit_2eByte_2ex16
| VX5048 = cCoq_2eInit_2eByte_2ex17
| VX5048 = cCoq_2eInit_2eByte_2ex18
| VX5048 = cCoq_2eInit_2eByte_2ex19
| VX5048 = cCoq_2eInit_2eByte_2ex1a
| VX5048 = cCoq_2eInit_2eByte_2ex1b
| VX5048 = cCoq_2eInit_2eByte_2ex1c
| VX5048 = cCoq_2eInit_2eByte_2ex1d
| VX5048 = cCoq_2eInit_2eByte_2ex1e
| VX5048 = cCoq_2eInit_2eByte_2ex1f
| VX5048 = cCoq_2eInit_2eByte_2ex20
| VX5048 = cCoq_2eInit_2eByte_2ex21
| VX5048 = cCoq_2eInit_2eByte_2ex22
| VX5048 = cCoq_2eInit_2eByte_2ex23
| VX5048 = cCoq_2eInit_2eByte_2ex24
| VX5048 = cCoq_2eInit_2eByte_2ex25
| VX5048 = cCoq_2eInit_2eByte_2ex26
| VX5048 = cCoq_2eInit_2eByte_2ex27
| VX5048 = cCoq_2eInit_2eByte_2ex28
| VX5048 = cCoq_2eInit_2eByte_2ex29
| VX5048 = cCoq_2eInit_2eByte_2ex2a
| VX5048 = cCoq_2eInit_2eByte_2ex2b
| VX5048 = cCoq_2eInit_2eByte_2ex2c
| VX5048 = cCoq_2eInit_2eByte_2ex2d
| VX5048 = cCoq_2eInit_2eByte_2ex2e
| VX5048 = cCoq_2eInit_2eByte_2ex2f
| VX5048 = cCoq_2eInit_2eByte_2ex30
| VX5048 = cCoq_2eInit_2eByte_2ex31
| VX5048 = cCoq_2eInit_2eByte_2ex32
| VX5048 = cCoq_2eInit_2eByte_2ex33
| VX5048 = cCoq_2eInit_2eByte_2ex34
| VX5048 = cCoq_2eInit_2eByte_2ex35
| VX5048 = cCoq_2eInit_2eByte_2ex36
| VX5048 = cCoq_2eInit_2eByte_2ex37
| VX5048 = cCoq_2eInit_2eByte_2ex38
| VX5048 = cCoq_2eInit_2eByte_2ex39
| VX5048 = cCoq_2eInit_2eByte_2ex3a
| VX5048 = cCoq_2eInit_2eByte_2ex3b
| VX5048 = cCoq_2eInit_2eByte_2ex3c
| VX5048 = cCoq_2eInit_2eByte_2ex3d
| VX5048 = cCoq_2eInit_2eByte_2ex3e
| VX5048 = cCoq_2eInit_2eByte_2ex3f
| VX5048 = cCoq_2eInit_2eByte_2ex40
| VX5048 = cCoq_2eInit_2eByte_2ex41
| VX5048 = cCoq_2eInit_2eByte_2ex42
| VX5048 = cCoq_2eInit_2eByte_2ex43
| VX5048 = cCoq_2eInit_2eByte_2ex44
| VX5048 = cCoq_2eInit_2eByte_2ex45
| VX5048 = cCoq_2eInit_2eByte_2ex46
| VX5048 = cCoq_2eInit_2eByte_2ex47
| VX5048 = cCoq_2eInit_2eByte_2ex48
| VX5048 = cCoq_2eInit_2eByte_2ex49
| VX5048 = cCoq_2eInit_2eByte_2ex4a
| VX5048 = cCoq_2eInit_2eByte_2ex4b
| VX5048 = cCoq_2eInit_2eByte_2ex4c
| VX5048 = cCoq_2eInit_2eByte_2ex4d
| VX5048 = cCoq_2eInit_2eByte_2ex4e
| VX5048 = cCoq_2eInit_2eByte_2ex4f
| VX5048 = cCoq_2eInit_2eByte_2ex50
| VX5048 = cCoq_2eInit_2eByte_2ex51
| VX5048 = cCoq_2eInit_2eByte_2ex52
| VX5048 = cCoq_2eInit_2eByte_2ex53
| VX5048 = cCoq_2eInit_2eByte_2ex54
| VX5048 = cCoq_2eInit_2eByte_2ex55
| VX5048 = cCoq_2eInit_2eByte_2ex56
| VX5048 = cCoq_2eInit_2eByte_2ex57
| VX5048 = cCoq_2eInit_2eByte_2ex58
| VX5048 = cCoq_2eInit_2eByte_2ex59
| VX5048 = cCoq_2eInit_2eByte_2ex5a
| VX5048 = cCoq_2eInit_2eByte_2ex5b
| VX5048 = cCoq_2eInit_2eByte_2ex5c
| VX5048 = cCoq_2eInit_2eByte_2ex5d
| VX5048 = cCoq_2eInit_2eByte_2ex5e
| VX5048 = cCoq_2eInit_2eByte_2ex5f
| VX5048 = cCoq_2eInit_2eByte_2ex60
| VX5048 = cCoq_2eInit_2eByte_2ex61
| VX5048 = cCoq_2eInit_2eByte_2ex62
| VX5048 = cCoq_2eInit_2eByte_2ex63
| VX5048 = cCoq_2eInit_2eByte_2ex64
| VX5048 = cCoq_2eInit_2eByte_2ex65
| VX5048 = cCoq_2eInit_2eByte_2ex66
| VX5048 = cCoq_2eInit_2eByte_2ex67
| VX5048 = cCoq_2eInit_2eByte_2ex68
| VX5048 = cCoq_2eInit_2eByte_2ex69
| VX5048 = cCoq_2eInit_2eByte_2ex6a
| VX5048 = cCoq_2eInit_2eByte_2ex6b
| VX5048 = cCoq_2eInit_2eByte_2ex6c
| VX5048 = cCoq_2eInit_2eByte_2ex6d
| VX5048 = cCoq_2eInit_2eByte_2ex6e
| VX5048 = cCoq_2eInit_2eByte_2ex6f
| VX5048 = cCoq_2eInit_2eByte_2ex70
| VX5048 = cCoq_2eInit_2eByte_2ex71
| VX5048 = cCoq_2eInit_2eByte_2ex72
| VX5048 = cCoq_2eInit_2eByte_2ex73
| VX5048 = cCoq_2eInit_2eByte_2ex74
| VX5048 = cCoq_2eInit_2eByte_2ex75
| VX5048 = cCoq_2eInit_2eByte_2ex76
| VX5048 = cCoq_2eInit_2eByte_2ex77
| VX5048 = cCoq_2eInit_2eByte_2ex78
| VX5048 = cCoq_2eInit_2eByte_2ex79
| VX5048 = cCoq_2eInit_2eByte_2ex7a
| VX5048 = cCoq_2eInit_2eByte_2ex7b
| VX5048 = cCoq_2eInit_2eByte_2ex7c
| VX5048 = cCoq_2eInit_2eByte_2ex7d
| VX5048 = cCoq_2eInit_2eByte_2ex7e
| VX5048 = cCoq_2eInit_2eByte_2ex7f
| VX5048 = cCoq_2eInit_2eByte_2ex80
| VX5048 = cCoq_2eInit_2eByte_2ex81
| VX5048 = cCoq_2eInit_2eByte_2ex82
| VX5048 = cCoq_2eInit_2eByte_2ex83
| VX5048 = cCoq_2eInit_2eByte_2ex84
| VX5048 = cCoq_2eInit_2eByte_2ex85
| VX5048 = cCoq_2eInit_2eByte_2ex86
| VX5048 = cCoq_2eInit_2eByte_2ex87
| VX5048 = cCoq_2eInit_2eByte_2ex88
| VX5048 = cCoq_2eInit_2eByte_2ex89
| VX5048 = cCoq_2eInit_2eByte_2ex8a
| VX5048 = cCoq_2eInit_2eByte_2ex8b
| VX5048 = cCoq_2eInit_2eByte_2ex8c
| VX5048 = cCoq_2eInit_2eByte_2ex8d
| VX5048 = cCoq_2eInit_2eByte_2ex8e
| VX5048 = cCoq_2eInit_2eByte_2ex8f
| VX5048 = cCoq_2eInit_2eByte_2ex90
| VX5048 = cCoq_2eInit_2eByte_2ex91
| VX5048 = cCoq_2eInit_2eByte_2ex92
| VX5048 = cCoq_2eInit_2eByte_2ex93
| VX5048 = cCoq_2eInit_2eByte_2ex94
| VX5048 = cCoq_2eInit_2eByte_2ex95
| VX5048 = cCoq_2eInit_2eByte_2ex96
| VX5048 = cCoq_2eInit_2eByte_2ex97
| VX5048 = cCoq_2eInit_2eByte_2ex98
| VX5048 = cCoq_2eInit_2eByte_2ex99
| VX5048 = cCoq_2eInit_2eByte_2ex9a
| VX5048 = cCoq_2eInit_2eByte_2ex9b
| VX5048 = cCoq_2eInit_2eByte_2ex9c
| VX5048 = cCoq_2eInit_2eByte_2ex9d
| VX5048 = cCoq_2eInit_2eByte_2ex9e
| VX5048 = cCoq_2eInit_2eByte_2ex9f
| VX5048 = cCoq_2eInit_2eByte_2exa0
| VX5048 = cCoq_2eInit_2eByte_2exa1
| VX5048 = cCoq_2eInit_2eByte_2exa2
| VX5048 = cCoq_2eInit_2eByte_2exa3
| VX5048 = cCoq_2eInit_2eByte_2exa4
| VX5048 = cCoq_2eInit_2eByte_2exa5
| VX5048 = cCoq_2eInit_2eByte_2exa6
| VX5048 = cCoq_2eInit_2eByte_2exa7
| VX5048 = cCoq_2eInit_2eByte_2exa8
| VX5048 = cCoq_2eInit_2eByte_2exa9
| VX5048 = cCoq_2eInit_2eByte_2exaa
| VX5048 = cCoq_2eInit_2eByte_2exab
| VX5048 = cCoq_2eInit_2eByte_2exac
| VX5048 = cCoq_2eInit_2eByte_2exad
| VX5048 = cCoq_2eInit_2eByte_2exae
| VX5048 = cCoq_2eInit_2eByte_2exaf
| VX5048 = cCoq_2eInit_2eByte_2exb0
| VX5048 = cCoq_2eInit_2eByte_2exb1
| VX5048 = cCoq_2eInit_2eByte_2exb2
| VX5048 = cCoq_2eInit_2eByte_2exb3
| VX5048 = cCoq_2eInit_2eByte_2exb4
| VX5048 = cCoq_2eInit_2eByte_2exb5
| VX5048 = cCoq_2eInit_2eByte_2exb6
| VX5048 = cCoq_2eInit_2eByte_2exb7
| VX5048 = cCoq_2eInit_2eByte_2exb8
| VX5048 = cCoq_2eInit_2eByte_2exb9
| VX5048 = cCoq_2eInit_2eByte_2exba
| VX5048 = cCoq_2eInit_2eByte_2exbb
| VX5048 = cCoq_2eInit_2eByte_2exbc
| VX5048 = cCoq_2eInit_2eByte_2exbd
| VX5048 = cCoq_2eInit_2eByte_2exbe
| VX5048 = cCoq_2eInit_2eByte_2exbf
| VX5048 = cCoq_2eInit_2eByte_2exc0
| VX5048 = cCoq_2eInit_2eByte_2exc1
| VX5048 = cCoq_2eInit_2eByte_2exc2
| VX5048 = cCoq_2eInit_2eByte_2exc3
| VX5048 = cCoq_2eInit_2eByte_2exc4
| VX5048 = cCoq_2eInit_2eByte_2exc5
| VX5048 = cCoq_2eInit_2eByte_2exc6
| VX5048 = cCoq_2eInit_2eByte_2exc7
| VX5048 = cCoq_2eInit_2eByte_2exc8
| VX5048 = cCoq_2eInit_2eByte_2exc9
| VX5048 = cCoq_2eInit_2eByte_2exca
| VX5048 = cCoq_2eInit_2eByte_2excb
| VX5048 = cCoq_2eInit_2eByte_2excc
| VX5048 = cCoq_2eInit_2eByte_2excd
| VX5048 = cCoq_2eInit_2eByte_2exce
| VX5048 = cCoq_2eInit_2eByte_2excf
| VX5048 = cCoq_2eInit_2eByte_2exd0
| VX5048 = cCoq_2eInit_2eByte_2exd1
| VX5048 = cCoq_2eInit_2eByte_2exd2
| VX5048 = cCoq_2eInit_2eByte_2exd3
| VX5048 = cCoq_2eInit_2eByte_2exd4
| VX5048 = cCoq_2eInit_2eByte_2exd5
| VX5048 = cCoq_2eInit_2eByte_2exd6
| VX5048 = cCoq_2eInit_2eByte_2exd7
| VX5048 = cCoq_2eInit_2eByte_2exd8
| VX5048 = cCoq_2eInit_2eByte_2exd9
| VX5048 = cCoq_2eInit_2eByte_2exda
| VX5048 = cCoq_2eInit_2eByte_2exdb
| VX5048 = cCoq_2eInit_2eByte_2exdc
| VX5048 = cCoq_2eInit_2eByte_2exdd
| VX5048 = cCoq_2eInit_2eByte_2exde
| VX5048 = cCoq_2eInit_2eByte_2exdf
| VX5048 = cCoq_2eInit_2eByte_2exe0
| VX5048 = cCoq_2eInit_2eByte_2exe1
| VX5048 = cCoq_2eInit_2eByte_2exe2
| VX5048 = cCoq_2eInit_2eByte_2exe3
| VX5048 = cCoq_2eInit_2eByte_2exe4
| VX5048 = cCoq_2eInit_2eByte_2exe5
| VX5048 = cCoq_2eInit_2eByte_2exe6
| VX5048 = cCoq_2eInit_2eByte_2exe7
| VX5048 = cCoq_2eInit_2eByte_2exe8
| VX5048 = cCoq_2eInit_2eByte_2exe9
| VX5048 = cCoq_2eInit_2eByte_2exea
| VX5048 = cCoq_2eInit_2eByte_2exeb
| VX5048 = cCoq_2eInit_2eByte_2exec
| VX5048 = cCoq_2eInit_2eByte_2exed
| VX5048 = cCoq_2eInit_2eByte_2exee
| VX5048 = cCoq_2eInit_2eByte_2exef
| VX5048 = cCoq_2eInit_2eByte_2exf0
| VX5048 = cCoq_2eInit_2eByte_2exf1
| VX5048 = cCoq_2eInit_2eByte_2exf2
| VX5048 = cCoq_2eInit_2eByte_2exf3
| VX5048 = cCoq_2eInit_2eByte_2exf4
| VX5048 = cCoq_2eInit_2eByte_2exf5
| VX5048 = cCoq_2eInit_2eByte_2exf6
| VX5048 = cCoq_2eInit_2eByte_2exf7
| VX5048 = cCoq_2eInit_2eByte_2exf8
| VX5048 = cCoq_2eInit_2eByte_2exf9
| VX5048 = cCoq_2eInit_2eByte_2exfa
| VX5048 = cCoq_2eInit_2eByte_2exfb
| VX5048 = cCoq_2eInit_2eByte_2exfc
| VX5048 = cCoq_2eInit_2eByte_2exfd
| VX5048 = cCoq_2eInit_2eByte_2exfe
| VX5048 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__5050,Vvar__1__Q__5051,Vvar__2___24Anonymous__5052] :
( cProp___24t(Vvar__0__P__5050)
=> ( cProp___24t(Vvar__1__Q__5051)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__5052)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__5050,Vvar__1__Q__5051,Vvar__2___24Anonymous__5052)
=> ( ( p(Vvar__0__P__5050)
& Vvar__2___24Anonymous__5052 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__5051)
& Vvar__2___24Anonymous__5052 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__37872,Vvar__1__Plt__37873,Vvar__2__Pgt__37874,Vvar__3___24Anonymous__37875] :
( cProp___24t(Vvar__0__Peq__37872)
=> ( cProp___24t(Vvar__1__Plt__37873)
=> ( cProp___24t(Vvar__2__Pgt__37874)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__37875)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__37872,Vvar__1__Plt__37873,Vvar__2__Pgt__37874,Vvar__3___24Anonymous__37875)
=> ( ( p(Vvar__0__Peq__37872)
& Vvar__3___24Anonymous__37875 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__37873)
& Vvar__3___24Anonymous__37875 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__37874)
& Vvar__3___24Anonymous__37875 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__113924,Vvar__1__Plt__113925,Vvar__2__Pgt__113926,Vvar__3___24Anonymous__113927,VX113928] :
( cProp___24t(Vvar__0__Peq__113924)
=> ( cProp___24t(Vvar__1__Plt__113925)
=> ( cProp___24t(Vvar__2__Pgt__113926)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__113927)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__113924,Vvar__1__Plt__113925,Vvar__2__Pgt__113926,Vvar__3___24Anonymous__113927,VX113928)
=> ( ( p(Vvar__0__Peq__113924)
& Vvar__3___24Anonymous__113927 = cCoq_2eInit_2eDatatypes_2eEq
& VX113928 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__113924,Vvar__1__Plt__113925,Vvar__2__Pgt__113926) )
| ( p(Vvar__1__Plt__113925)
& Vvar__3___24Anonymous__113927 = cCoq_2eInit_2eDatatypes_2eLt
& VX113928 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__113924,Vvar__1__Plt__113925,Vvar__2__Pgt__113926) )
| ( p(Vvar__2__Pgt__113926)
& Vvar__3___24Anonymous__113927 = cCoq_2eInit_2eDatatypes_2eGt
& VX113928 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__113924,Vvar__1__Plt__113925,Vvar__2__Pgt__113926) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX1)
=> ( VX1 = cCoq_2eInit_2eDatatypes_2etrue
| VX1 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX37871] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX37871)
=> ( VX37871 = cCoq_2eInit_2eDatatypes_2eEq
| VX37871 = cCoq_2eInit_2eDatatypes_2eLt
| VX37871 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__46,VX47] :
( cType___24t(Vvar__0__A__46)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__46,VX47)
=> ( VX47 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__46)
| ? [Vvar__1___24Anonymous__50] :
( t(Vvar__1___24Anonymous__50,Vvar__0__A__46)
& ? [Vvar__2___24Anonymous__51] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__46,Vvar__2___24Anonymous__51)
& VX47 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__46,Vvar__1___24Anonymous__50,Vvar__2___24Anonymous__51) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX1900] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX1900)
=> ( VX1900 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__1901] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1901)
& VX1900 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1901) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__4,VX5] :
( cType___24t(Vvar__0__A__4)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__4,VX5)
=> ( ? [Vvar__1___24Anonymous__7] :
( t(Vvar__1___24Anonymous__7,Vvar__0__A__4)
& VX5 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__4,Vvar__1___24Anonymous__7) )
| VX5 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__4) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__20,Vvar__1__B__21,VX22] :
( cType___24t(Vvar__0__A__20)
=> ( cType___24t(Vvar__1__B__21)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__20,Vvar__1__B__21,VX22)
=> ? [Vvar__2___24Anonymous__25] :
( t(Vvar__2___24Anonymous__25,Vvar__0__A__20)
& ? [Vvar__3___24Anonymous__26] :
( t(Vvar__3___24Anonymous__26,Vvar__1__B__21)
& VX22 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__20,Vvar__1__B__21,Vvar__2___24Anonymous__25,Vvar__3___24Anonymous__26) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__2702,Vvar__1__B__2703,VX2704] :
( cType___24t(Vvar__0__A__2702)
=> ( cType___24t(Vvar__1__B__2703)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__2702,Vvar__1__B__2703,VX2704)
=> ( ? [Vvar__2___24Anonymous__2707] :
( t(Vvar__2___24Anonymous__2707,Vvar__0__A__2702)
& VX2704 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__2702,Vvar__1__B__2703,Vvar__2___24Anonymous__2707) )
| ? [Vvar__2___24Anonymous__2710] :
( t(Vvar__2___24Anonymous__2710,Vvar__1__B__2703)
& VX2704 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__2702,Vvar__1__B__2703,Vvar__2___24Anonymous__2710) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX2697] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX2697)
=> VX2697 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__2145,Vvar__1___24Anonymous__2146] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__2145)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__2146)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__2145,Vvar__1___24Anonymous__2146)
=> ( Vvar__1___24Anonymous__2146 = Vvar__0__n__2145
| ? [Vvar__1__m__2150] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__2150)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__2145,Vvar__1__m__2150)
& Vvar__1___24Anonymous__2146 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__2150) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__2156,Vvar__1__P__2157,VX2160] :
( cType___24t(Vvar__0__A__2156)
=> ( c_24__type__2170___24t(Vvar__0__A__2156,Vvar__1__P__2157,Vvar__1__P__2157)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__2156,Vvar__1__P__2157,VX2160)
=> ? [Vvar__2__x__2165] :
( t(Vvar__2__x__2165,Vvar__0__A__2156)
& p(happ(Vvar__1__P__2157,Vvar__2__x__2165))
& VX2160 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2156,Vvar__1__P__2157,Vvar__2__x__2165) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__46419,Vvar__1__P__46420,Vvar__2__Q__46423,VX46426] :
( cType___24t(Vvar__0__A__46419)
=> ( c_24__type__46443___24t(Vvar__0__A__46419,Vvar__1__P__46420,Vvar__2__Q__46423,Vvar__1__P__46420)
=> ( c_24__type__46451___24t(Vvar__0__A__46419,Vvar__1__P__46420,Vvar__2__Q__46423,Vvar__2__Q__46423)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__46419,Vvar__1__P__46420,Vvar__2__Q__46423,VX46426)
=> ? [Vvar__3__x__46434] :
( t(Vvar__3__x__46434,Vvar__0__A__46419)
& p(happ(Vvar__1__P__46420,Vvar__3__x__46434))
& p(happ(Vvar__2__Q__46423,Vvar__3__x__46434))
& VX46426 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__46419,Vvar__1__P__46420,Vvar__2__Q__46423,Vvar__3__x__46434) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__2197,Vvar__1__P__2198,VX2201] :
( cType___24t(Vvar__0__A__2197)
=> ( c_24__type__2211___24t(Vvar__0__A__2197,Vvar__1__P__2198,Vvar__1__P__2198)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__2197,Vvar__1__P__2198,VX2201)
=> ? [Vvar__2__x__2206] :
( t(Vvar__2__x__2206,Vvar__0__A__2197)
& ? [Vvar__3___24Anonymous__2207] :
( t(Vvar__3___24Anonymous__2207,happ(Vvar__1__P__2198,Vvar__2__x__2206))
& VX2201 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__2197,Vvar__1__P__2198,Vvar__2__x__2206,Vvar__3___24Anonymous__2207) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__45132,Vvar__1__P__45133,Vvar__2__Q__45136,VX45139] :
( cType___24t(Vvar__0__A__45132)
=> ( c_24__type__45156___24t(Vvar__0__A__45132,Vvar__1__P__45133,Vvar__2__Q__45136,Vvar__1__P__45133)
=> ( c_24__type__45164___24t(Vvar__0__A__45132,Vvar__1__P__45133,Vvar__2__Q__45136,Vvar__2__Q__45136)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__45132,Vvar__1__P__45133,Vvar__2__Q__45136,VX45139)
=> ? [Vvar__3__x__45147] :
( t(Vvar__3__x__45147,Vvar__0__A__45132)
& ? [Vvar__4___24Anonymous__45148] :
( t(Vvar__4___24Anonymous__45148,happ(Vvar__1__P__45133,Vvar__3__x__45147))
& ? [Vvar__5___24Anonymous__45149] :
( t(Vvar__5___24Anonymous__45149,happ(Vvar__2__Q__45136,Vvar__3__x__45147))
& VX45139 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__45132,Vvar__1__P__45133,Vvar__2__Q__45136,Vvar__3__x__45147,Vvar__4___24Anonymous__45148,Vvar__5___24Anonymous__45149) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__35242,Vvar__1__B__35243,VX35244] :
( cProp___24t(Vvar__0__A__35242)
=> ( cProp___24t(Vvar__1__B__35243)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__35242,Vvar__1__B__35243,VX35244)
=> ( ( p(Vvar__0__A__35242)
& VX35244 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__35242,Vvar__1__B__35243) )
| ( p(Vvar__1__B__35243)
& VX35244 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__35242,Vvar__1__B__35243) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__35326,Vvar__1__B__35327,VX35328] :
( cType___24t(Vvar__0__A__35326)
=> ( cProp___24t(Vvar__1__B__35327)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__35326,Vvar__1__B__35327,VX35328)
=> ( ? [Vvar__2___24Anonymous__35331] :
( t(Vvar__2___24Anonymous__35331,Vvar__0__A__35326)
& VX35328 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__35326,Vvar__1__B__35327,Vvar__2___24Anonymous__35331) )
| ( p(Vvar__1__B__35327)
& VX35328 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__35326,Vvar__1__B__35327) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__2417,Vvar__1__a__2418,Vvar__2___24Anonymous__2419,Vvar__3___24Anonymous__2420] :
( cType___24t(Vvar__0__A__2417)
=> ( t(Vvar__1__a__2418,Vvar__0__A__2417)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2417,Vvar__2___24Anonymous__2419)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2417,Vvar__3___24Anonymous__2420)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__2417,Vvar__1__a__2418,Vvar__2___24Anonymous__2419,Vvar__3___24Anonymous__2420)
=> ( ? [Vvar__2__l__2424] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2417,Vvar__2__l__2424)
& Vvar__3___24Anonymous__2420 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2417,Vvar__1__a__2418,Vvar__2__l__2424)
& Vvar__2___24Anonymous__2419 = Vvar__2__l__2424 )
| ? [Vvar__2__x__2427] :
( t(Vvar__2__x__2427,Vvar__0__A__2417)
& ? [Vvar__3__l__2428] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2417,Vvar__3__l__2428)
& ? [Vvar__4__l_27__2429] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2417,Vvar__4__l_27__2429)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__2417,Vvar__1__a__2418,Vvar__3__l__2428,Vvar__4__l_27__2429)
& Vvar__3___24Anonymous__2420 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2417,Vvar__2__x__2427,Vvar__4__l_27__2429)
& Vvar__2___24Anonymous__2419 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2417,Vvar__2__x__2427,Vvar__3__l__2428) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__16953,Vvar__1__P__16954,Vvar__2___24Anonymous__16957] :
( cType___24t(Vvar__0__A__16953)
=> ( c_24__type__16977___24t(Vvar__0__A__16953,Vvar__1__P__16954,Vvar__2___24Anonymous__16957,Vvar__1__P__16954)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__16953,Vvar__2___24Anonymous__16957)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__16953,Vvar__1__P__16954,Vvar__2___24Anonymous__16957)
=> ( ? [Vvar__2__x__16963] :
( t(Vvar__2__x__16963,Vvar__0__A__16953)
& ? [Vvar__3__l__16964] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__16953,Vvar__3__l__16964)
& p(happ(Vvar__1__P__16954,Vvar__2__x__16963))
& Vvar__2___24Anonymous__16957 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__16953,Vvar__2__x__16963,Vvar__3__l__16964) ) )
| ? [Vvar__2__x__16970] :
( t(Vvar__2__x__16970,Vvar__0__A__16953)
& ? [Vvar__3__l__16971] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__16953,Vvar__3__l__16971)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__16953,Vvar__1__P__16954,Vvar__3__l__16971)
& Vvar__2___24Anonymous__16957 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__16953,Vvar__2__x__16970,Vvar__3__l__16971) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__3196,Vvar__1__P__3197,Vvar__2___24Anonymous__3200] :
( cType___24t(Vvar__0__A__3196)
=> ( c_24__type__3218___24t(Vvar__0__A__3196,Vvar__1__P__3197,Vvar__2___24Anonymous__3200,Vvar__1__P__3197)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3196,Vvar__2___24Anonymous__3200)
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__3196,Vvar__1__P__3197,Vvar__2___24Anonymous__3200))
=> ( Vvar__2___24Anonymous__3200 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3196)
| ? [Vvar__2__x__3210] :
( t(Vvar__2__x__3210,Vvar__0__A__3196)
& ? [Vvar__3__l__3211] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3196,Vvar__3__l__3211)
& p(happ(Vvar__1__P__3197,Vvar__2__x__3210))
& p(cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__3196,Vvar__1__P__3197,Vvar__3__l__3211))
& Vvar__2___24Anonymous__3200 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3196,Vvar__2__x__3210,Vvar__3__l__3211) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__2073,Vvar__1__B__2074,Vvar__2__R__2075,Vvar__3___24Anonymous__2080,Vvar__4___24Anonymous__2081] :
( cType___24t(Vvar__0__A__2073)
=> ( cType___24t(Vvar__1__B__2074)
=> ( c_24__type__2118___24t(Vvar__0__A__2073,Vvar__1__B__2074,Vvar__2__R__2075,Vvar__3___24Anonymous__2080,Vvar__4___24Anonymous__2081,Vvar__2__R__2075)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2073,Vvar__3___24Anonymous__2080)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__2074,Vvar__4___24Anonymous__2081)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__2073,Vvar__1__B__2074,Vvar__2__R__2075,Vvar__3___24Anonymous__2080,Vvar__4___24Anonymous__2081)
=> ( ( Vvar__4___24Anonymous__2081 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__2074)
& Vvar__3___24Anonymous__2080 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2073) )
| ? [Vvar__3__x__2097] :
( t(Vvar__3__x__2097,Vvar__0__A__2073)
& ? [Vvar__4__y__2098] :
( t(Vvar__4__y__2098,Vvar__1__B__2074)
& ? [Vvar__5__l__2099] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2073,Vvar__5__l__2099)
& ? [Vvar__6__l_27__2100] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__2074,Vvar__6__l_27__2100)
& p(happ(happ(Vvar__2__R__2075,Vvar__3__x__2097),Vvar__4__y__2098))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__2073,Vvar__1__B__2074,Vvar__2__R__2075,Vvar__5__l__2099,Vvar__6__l_27__2100)
& Vvar__4___24Anonymous__2081 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__2074,Vvar__4__y__2098,Vvar__6__l_27__2100)
& Vvar__3___24Anonymous__2080 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2073,Vvar__3__x__2097,Vvar__5__l__2099) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__3226,Vvar__1__R__3227,Vvar__2___24Anonymous__3232] :
( cType___24t(Vvar__0__A__3226)
=> ( c_24__type__3259___24t(Vvar__0__A__3226,Vvar__1__R__3227,Vvar__2___24Anonymous__3232,Vvar__1__R__3227)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3226,Vvar__2___24Anonymous__3232)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__3226,Vvar__1__R__3227,Vvar__2___24Anonymous__3232)
=> ( Vvar__2___24Anonymous__3232 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3226)
| ? [Vvar__2__a__3246] :
( t(Vvar__2__a__3246,Vvar__0__A__3226)
& ? [Vvar__3__l__3247] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3226,Vvar__3__l__3247)
& p(cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__3226,happ(Vvar__1__R__3227,Vvar__2__a__3246),Vvar__3__l__3247))
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__3226,Vvar__1__R__3227,Vvar__3__l__3247)
& Vvar__2___24Anonymous__3232 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3226,Vvar__2__a__3246,Vvar__3__l__3247) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__3187,Vvar__1___24Anonymous__3188] :
( cType___24t(Vvar__0__A__3187)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3187,Vvar__1___24Anonymous__3188)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__3187,Vvar__1___24Anonymous__3188)
=> ( Vvar__1___24Anonymous__3188 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3187)
| ? [Vvar__1__x__3192] :
( t(Vvar__1__x__3192,Vvar__0__A__3187)
& ? [Vvar__2__l__3193] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3187,Vvar__2__l__3193)
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__3187,Vvar__1__x__3192,Vvar__2__l__3193))
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__3187,Vvar__2__l__3193)
& Vvar__1___24Anonymous__3188 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3187,Vvar__1__x__3192,Vvar__2__l__3193) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__2471,Vvar__1__eqA__2472,Vvar__2__x__2477,Vvar__3___24Anonymous__2478] :
( cType___24t(Vvar__0__A__2471)
=> ( c_24__type__2511___24t(Vvar__0__A__2471,Vvar__1__eqA__2472,Vvar__2__x__2477,Vvar__3___24Anonymous__2478,Vvar__1__eqA__2472)
=> ( t(Vvar__2__x__2477,Vvar__0__A__2471)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2471,Vvar__3___24Anonymous__2478)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__2471,Vvar__1__eqA__2472,Vvar__2__x__2477,Vvar__3___24Anonymous__2478)
=> ( ? [Vvar__3__y__2487] :
( t(Vvar__3__y__2487,Vvar__0__A__2471)
& ? [Vvar__4__l__2488] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2471,Vvar__4__l__2488)
& p(happ(happ(Vvar__1__eqA__2472,Vvar__2__x__2477),Vvar__3__y__2487))
& Vvar__3___24Anonymous__2478 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2471,Vvar__3__y__2487,Vvar__4__l__2488) ) )
| ? [Vvar__3__y__2497] :
( t(Vvar__3__y__2497,Vvar__0__A__2471)
& ? [Vvar__4__l__2498] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2471,Vvar__4__l__2498)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__2471,Vvar__1__eqA__2472,Vvar__2__x__2477,Vvar__4__l__2498)
& Vvar__3___24Anonymous__2478 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2471,Vvar__3__y__2497,Vvar__4__l__2498) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__3912,Vvar__1__eqA__3913,Vvar__2___24Anonymous__3918] :
( cType___24t(Vvar__0__A__3912)
=> ( c_24__type__3945___24t(Vvar__0__A__3912,Vvar__1__eqA__3913,Vvar__2___24Anonymous__3918,Vvar__1__eqA__3913)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3912,Vvar__2___24Anonymous__3918)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__3912,Vvar__1__eqA__3913,Vvar__2___24Anonymous__3918)
=> ( Vvar__2___24Anonymous__3918 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3912)
| ? [Vvar__2__x__3932] :
( t(Vvar__2__x__3932,Vvar__0__A__3912)
& ? [Vvar__3__l__3933] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3912,Vvar__3__l__3933)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__3912,Vvar__1__eqA__3913,Vvar__2__x__3932,Vvar__3__l__3933)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__3912,Vvar__1__eqA__3913,Vvar__3__l__3933)
& Vvar__2___24Anonymous__3918 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3912,Vvar__2__x__3932,Vvar__3__l__3933) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__3950,Vvar__1__eqA__3951,Vvar__2___24Anonymous__3956,Vvar__3___24Anonymous__3957] :
( cType___24t(Vvar__0__A__3950)
=> ( c_24__type__3988___24t(Vvar__0__A__3950,Vvar__1__eqA__3951,Vvar__2___24Anonymous__3956,Vvar__3___24Anonymous__3957,Vvar__1__eqA__3951)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3950,Vvar__2___24Anonymous__3956)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3950,Vvar__3___24Anonymous__3957)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__3950,Vvar__1__eqA__3951,Vvar__2___24Anonymous__3956,Vvar__3___24Anonymous__3957)
=> ( ( Vvar__3___24Anonymous__3957 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3950)
& Vvar__2___24Anonymous__3956 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3950) )
| ? [Vvar__2__x__3971] :
( t(Vvar__2__x__3971,Vvar__0__A__3950)
& ? [Vvar__3__x_27__3972] :
( t(Vvar__3__x_27__3972,Vvar__0__A__3950)
& ? [Vvar__4__l__3973] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3950,Vvar__4__l__3973)
& ? [Vvar__5__l_27__3974] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3950,Vvar__5__l_27__3974)
& p(happ(happ(Vvar__1__eqA__3951,Vvar__2__x__3971),Vvar__3__x_27__3972))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__3950,Vvar__1__eqA__3951,Vvar__4__l__3973,Vvar__5__l_27__3974)
& Vvar__3___24Anonymous__3957 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3950,Vvar__3__x_27__3972,Vvar__5__l_27__3974)
& Vvar__2___24Anonymous__3956 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3950,Vvar__2__x__3971,Vvar__4__l__3973) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__37892,Vvar__1__P__37893,Vvar__2__p__37896,Vvar__3__x__37897,Vvar__4__q__37898,Vvar__5___24Anonymous__37899] :
( cType___24t(Vvar__0__U__37892)
=> ( c_24__type__37914___24t(Vvar__0__U__37892,Vvar__1__P__37893,Vvar__2__p__37896,Vvar__3__x__37897,Vvar__4__q__37898,Vvar__5___24Anonymous__37899,Vvar__1__P__37893)
=> ( t(Vvar__2__p__37896,Vvar__0__U__37892)
=> ( t(Vvar__3__x__37897,happ(Vvar__1__P__37893,Vvar__2__p__37896))
=> ( t(Vvar__4__q__37898,Vvar__0__U__37892)
=> ( t(Vvar__5___24Anonymous__37899,happ(Vvar__1__P__37893,Vvar__4__q__37898))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__37892,Vvar__1__P__37893,Vvar__2__p__37896,Vvar__3__x__37897,Vvar__4__q__37898,Vvar__5___24Anonymous__37899)
=> ( Vvar__5___24Anonymous__37899 = Vvar__3__x__37897
& Vvar__4__q__37898 = Vvar__2__p__37896 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__114092,Vvar__1__P__114093,Vvar__2__p__114096,Vvar__3__x__114097,Vvar__4__q__114098,Vvar__5__y__114099] :
( cType___24t(Vvar__0__U__114092)
=> ( c_24__type__114118___24t(Vvar__0__U__114092,Vvar__1__P__114093,Vvar__2__p__114096,Vvar__3__x__114097,Vvar__4__q__114098,Vvar__5__y__114099,Vvar__1__P__114093)
=> ( t(Vvar__2__p__114096,Vvar__0__U__114092)
=> ( t(Vvar__3__x__114097,happ(Vvar__1__P__114093,Vvar__2__p__114096))
=> ( t(Vvar__4__q__114098,Vvar__0__U__114092)
=> ( t(Vvar__5__y__114099,happ(Vvar__1__P__114093,Vvar__4__q__114098))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__114092,Vvar__1__P__114093,Vvar__2__p__114096,Vvar__3__x__114097,Vvar__4__q__114098,Vvar__5__y__114099)
=> ( Vvar__4__q__114098 = Vvar__2__p__114096
& Vvar__3__x__114097 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__114092,Vvar__4__q__114098,Vvar__1__P__114093,Vvar__5__y__114099,Vvar__2__p__114096)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.JMeq.JMeq',axiom,
! [Vvar__0__A__119957,Vvar__1__x__119958,Vvar__2__B__119959,Vvar__3___24Anonymous__119960] :
( cType___24t(Vvar__0__A__119957)
=> ( t(Vvar__1__x__119958,Vvar__0__A__119957)
=> ( cType___24t(Vvar__2__B__119959)
=> ( t(Vvar__3___24Anonymous__119960,Vvar__2__B__119959)
=> ( cCoq_2eLogic_2eJMeq_2eJMeq___24a4(Vvar__0__A__119957,Vvar__1__x__119958,Vvar__2__B__119959,Vvar__3___24Anonymous__119960)
=> ( Vvar__3___24Anonymous__119960 = Vvar__1__x__119958
& Vvar__2__B__119959 = Vvar__0__A__119957 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX2692] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX2692)
=> ( VX2692 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__2693] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2693)
& VX2692 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2693) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX5013] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX5013)
=> ( VX5013 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__5014] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5014)
& VX5013 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5014) )
| ? [Vvar__0___24Anonymous__5015] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5015)
& VX5013 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5015) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX2673] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX2673)
=> ( ? [Vvar__0___24Anonymous__2674] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2674)
& VX2673 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2674) )
| ? [Vvar__0___24Anonymous__2675] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2675)
& VX2673 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2675) )
| VX2673 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX45245] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX45245)
=> ( VX45245 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__45246] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45246)
& VX45245 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__45246) )
| VX45245 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX19426] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX19426)
=> ? [Vvar__0__Qnum__19427] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__19427)
& ? [Vvar__1__Qden__19428] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__19428)
& VX19426 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__19427,Vvar__1__Qden__19428) ) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__120533,Vvar__1___24Anonymous__120534,VX120535] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__120533)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__120534)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__120533,Vvar__1___24Anonymous__120534,VX120535)
=> ( ( Vvar__0__x__120533 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__120534 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX120535 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__120533) )
| ? [Vvar__1__n__120539] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__120539)
& Vvar__0__x__120533 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__120539)
& Vvar__1___24Anonymous__120534 = c_24__case__Coq_2eInit_2eDatatypes_2enat_24120559___24a3(Vvar__0__x__120533,Vvar__1___24Anonymous__120534,Vvar__1__n__120539)
& VX120535 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__120533,Vvar__1__n__120539) )
| ? [Vvar__1__n__120544] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__120544)
& Vvar__0__x__120533 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__120544))
& Vvar__1___24Anonymous__120534 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24120576___24a3(Vvar__0__x__120533,Vvar__1___24Anonymous__120534,Vvar__1__n__120544)
& VX120535 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__120533,Vvar__1__n__120544) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__124,Vvar__1__leA__125,Vvar__2___24Anonymous__130] :
( cType___24t(Vvar__0__A__124)
=> ( c_24__type__220___24t(Vvar__0__A__124,Vvar__1__leA__125,Vvar__2___24Anonymous__130,Vvar__1__leA__125)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__124,Vvar__2___24Anonymous__130)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__124,Vvar__1__leA__125,Vvar__2___24Anonymous__130)
=> ( Vvar__2___24Anonymous__130 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__124)
| ? [Vvar__2__x__144] :
( t(Vvar__2__x__144,Vvar__0__A__124)
& Vvar__2___24Anonymous__130 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__124,Vvar__2__x__144,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__124)) )
| ? [Vvar__2__x__151] :
( t(Vvar__2__x__151,Vvar__0__A__124)
& ? [Vvar__3__y__152] :
( t(Vvar__3__y__152,Vvar__0__A__124)
& ? [Vvar__4__l__153] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__124,Vvar__4__l__153)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__124,Vvar__1__leA__125,Vvar__2__x__151,Vvar__3__y__152)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__124,Vvar__1__leA__125,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__124,Vvar__4__l__153,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__124,Vvar__3__y__152,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__124))))
& Vvar__2___24Anonymous__130 = c_24__case__Coq_2eInit_2eDatatypes_2elist_24418___24a6(Vvar__0__A__124,Vvar__1__leA__125,Vvar__2___24Anonymous__130,Vvar__2__x__151,Vvar__3__y__152,Vvar__4__l__153) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__19703,Vvar__1__leA__19704,Vvar__2___24Anonymous__19709,Vvar__3___24Anonymous__19710] :
( cType___24t(Vvar__0__A__19703)
=> ( c_24__type__19752___24t(Vvar__0__A__19703,Vvar__1__leA__19704,Vvar__2___24Anonymous__19709,Vvar__3___24Anonymous__19710,Vvar__1__leA__19704)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__19703,Vvar__2___24Anonymous__19709)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__19703,Vvar__3___24Anonymous__19710)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__19703,Vvar__1__leA__19704,Vvar__2___24Anonymous__19709,Vvar__3___24Anonymous__19710)
=> ( ? [Vvar__2__a__19718] :
( t(Vvar__2__a__19718,Vvar__0__A__19703)
& ? [Vvar__3__x__19719] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__19703,Vvar__3__x__19719)
& Vvar__3___24Anonymous__19710 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__19703,Vvar__2__a__19718,Vvar__3__x__19719)
& Vvar__2___24Anonymous__19709 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__19703) ) )
| ? [Vvar__2__a__19726] :
( t(Vvar__2__a__19726,Vvar__0__A__19703)
& ? [Vvar__3__b__19727] :
( t(Vvar__3__b__19727,Vvar__0__A__19703)
& p(happ(happ(Vvar__1__leA__19704,Vvar__2__a__19726),Vvar__3__b__19727))
& ? [Vvar__5__x__19729] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__19703,Vvar__5__x__19729)
& ? [Vvar__6__y__19730] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__19703,Vvar__6__y__19730)
& Vvar__3___24Anonymous__19710 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__19703,Vvar__3__b__19727,Vvar__6__y__19730)
& Vvar__2___24Anonymous__19709 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__19703,Vvar__2__a__19726,Vvar__5__x__19729) ) ) ) )
| ? [Vvar__2__a__19737] :
( t(Vvar__2__a__19737,Vvar__0__A__19703)
& ? [Vvar__3__x__19738] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__19703,Vvar__3__x__19738)
& ? [Vvar__4__y__19739] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__19703,Vvar__4__y__19739)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__19703,Vvar__1__leA__19704,Vvar__3__x__19738,Vvar__4__y__19739)
& Vvar__3___24Anonymous__19710 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__19703,Vvar__2__a__19737,Vvar__4__y__19739)
& Vvar__2___24Anonymous__19709 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__19703,Vvar__2__a__19737,Vvar__3__x__19738) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__111,Vvar__1__R__112,Vvar__2__x__113,Vvar__3___24Anonymous__114] :
( cType___24t(Vvar__0__A__111)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__111,Vvar__1__R__112)
=> ( t(Vvar__2__x__113,Vvar__0__A__111)
=> ( t(Vvar__3___24Anonymous__114,Vvar__0__A__111)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__111,Vvar__1__R__112,Vvar__2__x__113,Vvar__3___24Anonymous__114)
=> ( ? [Vvar__3__y__119] :
( t(Vvar__3__y__119,Vvar__0__A__111)
& p(happ(happ(Vvar__1__R__112,Vvar__2__x__113),Vvar__3__y__119))
& Vvar__3___24Anonymous__114 = Vvar__3__y__119 )
| Vvar__3___24Anonymous__114 = Vvar__2__x__113 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__2591,Vvar__1__R__2592,Vvar__2__a__2597,Vvar__3___24Anonymous__2598] :
( cType___24t(Vvar__0__A__2591)
=> ( c_24__type__2628___24t(Vvar__0__A__2591,Vvar__1__R__2592,Vvar__2__a__2597,Vvar__3___24Anonymous__2598,Vvar__1__R__2592)
=> ( t(Vvar__2__a__2597,Vvar__0__A__2591)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2591,Vvar__3___24Anonymous__2598)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__2591,Vvar__1__R__2592,Vvar__2__a__2597,Vvar__3___24Anonymous__2598)
=> ( Vvar__3___24Anonymous__2598 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2591)
| ? [Vvar__3__b__2614] :
( t(Vvar__3__b__2614,Vvar__0__A__2591)
& ? [Vvar__4__l__2615] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2591,Vvar__4__l__2615)
& p(happ(happ(Vvar__1__R__2592,Vvar__2__a__2597),Vvar__3__b__2614))
& Vvar__3___24Anonymous__2598 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2591,Vvar__3__b__2614,Vvar__4__l__2615) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__34670,Vvar__1__R__34671,Vvar__2___24Anonymous__34676] :
( cType___24t(Vvar__0__A__34670)
=> ( c_24__type__34711___24t(Vvar__0__A__34670,Vvar__1__R__34671,Vvar__2___24Anonymous__34676,Vvar__1__R__34671)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34670,Vvar__2___24Anonymous__34676)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__34670,Vvar__1__R__34671,Vvar__2___24Anonymous__34676)
=> ( Vvar__2___24Anonymous__34676 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__34670)
| ? [Vvar__2__a__34690] :
( t(Vvar__2__a__34690,Vvar__0__A__34670)
& Vvar__2___24Anonymous__34676 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34670,Vvar__2__a__34690,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__34670)) )
| ? [Vvar__2__a__34697] :
( t(Vvar__2__a__34697,Vvar__0__A__34670)
& ? [Vvar__3__b__34698] :
( t(Vvar__3__b__34698,Vvar__0__A__34670)
& ? [Vvar__4__l__34699] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34670,Vvar__4__l__34699)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__34670,Vvar__1__R__34671,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34670,Vvar__3__b__34698,Vvar__4__l__34699))
& p(happ(happ(Vvar__1__R__34671,Vvar__2__a__34697),Vvar__3__b__34698))
& Vvar__2___24Anonymous__34676 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34670,Vvar__2__a__34697,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34670,Vvar__3__b__34698,Vvar__4__l__34699)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__2630,Vvar__1__R__2631,Vvar__2___24Anonymous__2636] :
( cType___24t(Vvar__0__A__2630)
=> ( c_24__type__2663___24t(Vvar__0__A__2630,Vvar__1__R__2631,Vvar__2___24Anonymous__2636,Vvar__1__R__2631)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2630,Vvar__2___24Anonymous__2636)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__2630,Vvar__1__R__2631,Vvar__2___24Anonymous__2636)
=> ( Vvar__2___24Anonymous__2636 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2630)
| ? [Vvar__2__a__2650] :
( t(Vvar__2__a__2650,Vvar__0__A__2630)
& ? [Vvar__3__l__2651] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2630,Vvar__3__l__2651)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__2630,Vvar__1__R__2631,Vvar__3__l__2651)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__2630,Vvar__1__R__2631,Vvar__2__a__2650,Vvar__3__l__2651)
& Vvar__2___24Anonymous__2636 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2630,Vvar__2__a__2650,Vvar__3__l__2651) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__4334,Vvar__1__R__4335,Vvar__2___24Anonymous__4340] :
( cType___24t(Vvar__0__A__4334)
=> ( c_24__type__4367___24t(Vvar__0__A__4334,Vvar__1__R__4335,Vvar__2___24Anonymous__4340,Vvar__1__R__4335)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4334,Vvar__2___24Anonymous__4340)
=> ( p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__4334,Vvar__1__R__4335,Vvar__2___24Anonymous__4340))
=> ( Vvar__2___24Anonymous__4340 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4334)
| ? [Vvar__2__a__4354] :
( t(Vvar__2__a__4354,Vvar__0__A__4334)
& ? [Vvar__3__l__4355] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4334,Vvar__3__l__4355)
& p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__4334,Vvar__1__R__4335,Vvar__3__l__4355))
& p(cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__4334,happ(Vvar__1__R__4335,Vvar__2__a__4354),Vvar__3__l__4355))
& Vvar__2___24Anonymous__4340 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4334,Vvar__2__a__4354,Vvar__3__l__4355) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX4744] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX4744)
=> ? [Vvar__0___24Anonymous__4745] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__4745)
& ? [Vvar__1___24Anonymous__4746] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__4746)
& ? [Vvar__2___24Anonymous__4747] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__4747)
& ? [Vvar__3___24Anonymous__4748] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__4748)
& ? [Vvar__4___24Anonymous__4749] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__4749)
& ? [Vvar__5___24Anonymous__4750] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__4750)
& ? [Vvar__6___24Anonymous__4751] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__4751)
& ? [Vvar__7___24Anonymous__4752] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__4752)
& VX4744 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4745,Vvar__1___24Anonymous__4746,Vvar__2___24Anonymous__4747,Vvar__3___24Anonymous__4748,Vvar__4___24Anonymous__4749,Vvar__5___24Anonymous__4750,Vvar__6___24Anonymous__4751,Vvar__7___24Anonymous__4752) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX35366] :
( cCoq_2eStrings_2eString_2estring___24t(VX35366)
=> ( VX35366 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__35367] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__35367)
& ? [Vvar__1___24Anonymous__35368] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__35368)
& VX35366 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__35367,Vvar__1___24Anonymous__35368) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__120167,Vvar__1__lt__120168,Vvar__2__eq__120173,Vvar__3__x__120178,Vvar__4__y__120179,VX120180] :
( cType___24t(Vvar__0__X__120167)
=> ( c_24__type__120240___24t(Vvar__0__X__120167,Vvar__1__lt__120168,Vvar__2__eq__120173,Vvar__3__x__120178,Vvar__4__y__120179,Vvar__1__lt__120168)
=> ( c_24__type__120259___24t(Vvar__0__X__120167,Vvar__1__lt__120168,Vvar__2__eq__120173,Vvar__3__x__120178,Vvar__4__y__120179,Vvar__2__eq__120173)
=> ( t(Vvar__3__x__120178,Vvar__0__X__120167)
=> ( t(Vvar__4__y__120179,Vvar__0__X__120167)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__120167,Vvar__1__lt__120168,Vvar__2__eq__120173,Vvar__3__x__120178,Vvar__4__y__120179,VX120180)
=> ( ( p(happ(happ(Vvar__1__lt__120168,Vvar__3__x__120178),Vvar__4__y__120179))
& VX120180 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__120167,Vvar__1__lt__120168,Vvar__2__eq__120173,Vvar__3__x__120178,Vvar__4__y__120179) )
| ( p(happ(happ(Vvar__2__eq__120173,Vvar__3__x__120178),Vvar__4__y__120179))
& VX120180 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__120167,Vvar__1__lt__120168,Vvar__2__eq__120173,Vvar__3__x__120178,Vvar__4__y__120179) )
| ( p(happ(happ(Vvar__1__lt__120168,Vvar__4__y__120179),Vvar__3__x__120178))
& VX120180 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__120167,Vvar__1__lt__120168,Vvar__2__eq__120173,Vvar__3__x__120178,Vvar__4__y__120179) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX38448] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX38448)
=> ( VX38448 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX38448 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX38448 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__47670,VX47671] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__47670)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__47670,VX47671)
=> ( ? [Vvar__0__n__47672] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__47672)
& Vvar__0___24Anonymous__47670 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__47672)
& VX47671 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__47672) )
| ? [Vvar__0__n__47673] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__47673)
& ? [Vvar__1___24Anonymous__47674] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__47673,Vvar__1___24Anonymous__47674)
& Vvar__0___24Anonymous__47670 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__47673)
& VX47671 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__47673,Vvar__1___24Anonymous__47674) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__36589,Vvar__1___24Anonymous__36590,VX36591] :
( cType___24t(Vvar__0__A__36589)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__36590)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__36589,Vvar__1___24Anonymous__36590,VX36591)
=> ( ( Vvar__1___24Anonymous__36590 = cCoq_2eInit_2eDatatypes_2eO
& VX36591 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__36589) )
| ? [Vvar__1__h__36594] :
( t(Vvar__1__h__36594,Vvar__0__A__36589)
& ? [Vvar__2__n__36595] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__36595)
& ? [Vvar__3___24Anonymous__36596] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__36589,Vvar__2__n__36595,Vvar__3___24Anonymous__36596)
& Vvar__1___24Anonymous__36590 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__36595)
& VX36591 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__36589,Vvar__1__h__36594,Vvar__2__n__36595,Vvar__3___24Anonymous__36596) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__122371,Vvar__1__b__122372,Vvar__2__d__122373] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__122371)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__122372)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__122373)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__122371,Vvar__1__b__122372,Vvar__2__d__122373)
=> ? [Vvar__3__u__122378] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__122378)
& ? [Vvar__4__v__122379] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__122379)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__122378,Vvar__0__a__122371),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__122379,Vvar__1__b__122372)) = Vvar__2__d__122373
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__122346,Vvar__1__b__122347,VX122348] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__122346)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__122347)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__122346,Vvar__1__b__122347,VX122348)
=> ? [Vvar__2__u__122351] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__122351)
& ? [Vvar__3__v__122352] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__122352)
& ? [Vvar__4__d__122353] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__122353)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__122351,Vvar__0__a__122346),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__122352,Vvar__1__b__122347)) = Vvar__4__d__122353
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__122346,Vvar__1__b__122347,Vvar__4__d__122353)
& VX122348 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__122346,Vvar__1__b__122347,Vvar__2__u__122351,Vvar__3__v__122352,Vvar__4__d__122353) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__45211,Vvar__1__b__45212,Vvar__2__g__45213] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__45211)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__45212)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__45213)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__45211,Vvar__1__b__45212,Vvar__2__g__45213)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__45213,Vvar__0__a__45211)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__45213,Vvar__1__b__45212)
& ! [Vvar__var__var__var__var__5__x__45221__45224__45227__45230__45233] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__45221__45224__45227__45230__45233)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__45221__45224__45227__45230__45233,Vvar__0__a__45211)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__45221__45224__45227__45230__45233,Vvar__1__b__45212)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__45221__45224__45227__45230__45233,Vvar__2__g__45213) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__122394,Vvar__1__p__122395,VX122396] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__122394)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__122395)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__122394,Vvar__1__p__122395,VX122396)
=> ? [Vvar__2__q__122399] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__122399)
& ? [Vvar__3__r__122400] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__122400)
& Vvar__0__x__122394 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__122399,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__122395)),Vvar__3__r__122400)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__122400))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__122400,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__122395)))
& VX122396 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__122394,Vvar__1__p__122395,Vvar__2__q__122399,Vvar__3__r__122400) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX5383] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX5383)
=> ( VX5383 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__5384] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5384)
& ? [Vvar__1___24Anonymous__5385] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__5385)
& VX5383 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__5384,Vvar__1___24Anonymous__5385) ) )
| ? [Vvar__0___24Anonymous__5386] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5386)
& ? [Vvar__1___24Anonymous__5387] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__5387)
& VX5383 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__5386,Vvar__1___24Anonymous__5387) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__5125,VX5126] :
( cType___24t(Vvar__0__C__5125)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5125,VX5126)
=> ( ? [Vvar__1___24Anonymous__5128] :
( t(Vvar__1___24Anonymous__5128,Vvar__0__C__5125)
& VX5126 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__5125,Vvar__1___24Anonymous__5128) )
| ? [Vvar__1___24Anonymous__5130] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5130)
& VX5126 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__5125,Vvar__1___24Anonymous__5130) )
| ? [Vvar__1___24Anonymous__5132] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5125,Vvar__1___24Anonymous__5132)
& ? [Vvar__2___24Anonymous__5133] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5125,Vvar__2___24Anonymous__5133)
& VX5126 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__5125,Vvar__1___24Anonymous__5132,Vvar__2___24Anonymous__5133) ) )
| ? [Vvar__1___24Anonymous__5135] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5125,Vvar__1___24Anonymous__5135)
& ? [Vvar__2___24Anonymous__5136] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5125,Vvar__2___24Anonymous__5136)
& VX5126 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__5125,Vvar__1___24Anonymous__5135,Vvar__2___24Anonymous__5136) ) )
| ? [Vvar__1___24Anonymous__5138] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5125,Vvar__1___24Anonymous__5138)
& ? [Vvar__2___24Anonymous__5139] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5125,Vvar__2___24Anonymous__5139)
& VX5126 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__5125,Vvar__1___24Anonymous__5138,Vvar__2___24Anonymous__5139) ) )
| ? [Vvar__1___24Anonymous__5141] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5125,Vvar__1___24Anonymous__5141)
& VX5126 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__5125,Vvar__1___24Anonymous__5141) )
| ? [Vvar__1___24Anonymous__5143] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5125,Vvar__1___24Anonymous__5143)
& ? [Vvar__2___24Anonymous__5144] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__5144)
& VX5126 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__5125,Vvar__1___24Anonymous__5143,Vvar__2___24Anonymous__5144) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__2238,VX2239] :
( cType___24t(Vvar__0__C__2238)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__2238,VX2239)
=> ( ? [Vvar__1___24Anonymous__2241] :
( t(Vvar__1___24Anonymous__2241,Vvar__0__C__2238)
& VX2239 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__2238,Vvar__1___24Anonymous__2241) )
| ? [Vvar__1___24Anonymous__2243] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2243)
& ? [Vvar__2___24Anonymous__2244] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__2238,Vvar__2___24Anonymous__2244)
& VX2239 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__2238,Vvar__1___24Anonymous__2243,Vvar__2___24Anonymous__2244) ) )
| ? [Vvar__1___24Anonymous__2246] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__2238,Vvar__1___24Anonymous__2246)
& ? [Vvar__2___24Anonymous__2247] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2247)
& ? [Vvar__3___24Anonymous__2248] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__2238,Vvar__3___24Anonymous__2248)
& VX2239 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__2238,Vvar__1___24Anonymous__2246,Vvar__2___24Anonymous__2247,Vvar__3___24Anonymous__2248) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__18166,Vvar__1__rO__18167,Vvar__2__rI__18168,Vvar__3__rplus__18169,Vvar__4__rtimes__18174,Vvar__5__rminus__18179,Vvar__6__ropp__18184,Vvar__7__req__18187,Vvar__8__rle__18192,Vvar__9__rlt__18197] :
( cType___24t(Vvar__0__R__18166)
=> ( t(Vvar__1__rO__18167,Vvar__0__R__18166)
=> ( t(Vvar__2__rI__18168,Vvar__0__R__18166)
=> ( c_24__type__18598___24t(Vvar__0__R__18166,Vvar__1__rO__18167,Vvar__2__rI__18168,Vvar__3__rplus__18169,Vvar__4__rtimes__18174,Vvar__5__rminus__18179,Vvar__6__ropp__18184,Vvar__7__req__18187,Vvar__8__rle__18192,Vvar__9__rlt__18197,Vvar__3__rplus__18169)
=> ( c_24__type__18699___24t(Vvar__0__R__18166,Vvar__1__rO__18167,Vvar__2__rI__18168,Vvar__3__rplus__18169,Vvar__4__rtimes__18174,Vvar__5__rminus__18179,Vvar__6__ropp__18184,Vvar__7__req__18187,Vvar__8__rle__18192,Vvar__9__rlt__18197,Vvar__4__rtimes__18174)
=> ( c_24__type__18800___24t(Vvar__0__R__18166,Vvar__1__rO__18167,Vvar__2__rI__18168,Vvar__3__rplus__18169,Vvar__4__rtimes__18174,Vvar__5__rminus__18179,Vvar__6__ropp__18184,Vvar__7__req__18187,Vvar__8__rle__18192,Vvar__9__rlt__18197,Vvar__5__rminus__18179)
=> ( c_24__type__18890___24t(Vvar__0__R__18166,Vvar__1__rO__18167,Vvar__2__rI__18168,Vvar__3__rplus__18169,Vvar__4__rtimes__18174,Vvar__5__rminus__18179,Vvar__6__ropp__18184,Vvar__7__req__18187,Vvar__8__rle__18192,Vvar__9__rlt__18197,Vvar__6__ropp__18184)
=> ( c_24__type__18991___24t(Vvar__0__R__18166,Vvar__1__rO__18167,Vvar__2__rI__18168,Vvar__3__rplus__18169,Vvar__4__rtimes__18174,Vvar__5__rminus__18179,Vvar__6__ropp__18184,Vvar__7__req__18187,Vvar__8__rle__18192,Vvar__9__rlt__18197,Vvar__7__req__18187)
=> ( c_24__type__19092___24t(Vvar__0__R__18166,Vvar__1__rO__18167,Vvar__2__rI__18168,Vvar__3__rplus__18169,Vvar__4__rtimes__18174,Vvar__5__rminus__18179,Vvar__6__ropp__18184,Vvar__7__req__18187,Vvar__8__rle__18192,Vvar__9__rlt__18197,Vvar__8__rle__18192)
=> ( c_24__type__19193___24t(Vvar__0__R__18166,Vvar__1__rO__18167,Vvar__2__rI__18168,Vvar__3__rplus__18169,Vvar__4__rtimes__18174,Vvar__5__rminus__18179,Vvar__6__ropp__18184,Vvar__7__req__18187,Vvar__8__rle__18192,Vvar__9__rlt__18197,Vvar__9__rlt__18197)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__18166,Vvar__1__rO__18167,Vvar__2__rI__18168,Vvar__3__rplus__18169,Vvar__4__rtimes__18174,Vvar__5__rminus__18179,Vvar__6__ropp__18184,Vvar__7__req__18187,Vvar__8__rle__18192,Vvar__9__rlt__18197)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__18166,Vvar__7__req__18187)
& ! [Vvar__var__var__var__var__11__x1__18241__18247__18352__18358__18364] :
( t(Vvar__var__var__var__var__11__x1__18241__18247__18352__18358__18364,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__12__x2__18242__18248__18353__18359__18365] :
( t(Vvar__var__var__var__var__12__x2__18242__18248__18353__18359__18365,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__7__req__18187,Vvar__var__var__var__var__11__x1__18241__18247__18352__18358__18364),Vvar__var__var__var__var__12__x2__18242__18248__18353__18359__18365))
=> ! [Vvar__var__var__var__var__14__y1__18243__18249__18354__18360__18366] :
( t(Vvar__var__var__var__var__14__y1__18243__18249__18354__18360__18366,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__15__y2__18244__18250__18355__18361__18367] :
( t(Vvar__var__var__var__var__15__y2__18244__18250__18355__18361__18367,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__7__req__18187,Vvar__var__var__var__var__14__y1__18243__18249__18354__18360__18366),Vvar__var__var__var__var__15__y2__18244__18250__18355__18361__18367))
=> p(happ(happ(Vvar__7__req__18187,happ(happ(Vvar__3__rplus__18169,Vvar__var__var__var__var__11__x1__18241__18247__18352__18358__18364),Vvar__var__var__var__var__14__y1__18243__18249__18354__18360__18366)),happ(happ(Vvar__3__rplus__18169,Vvar__var__var__var__var__12__x2__18242__18248__18353__18359__18365),Vvar__var__var__var__var__15__y2__18244__18250__18355__18361__18367))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__18254__18260__18370__18376__18382] :
( t(Vvar__var__var__var__var__12__x1__18254__18260__18370__18376__18382,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__13__x2__18255__18261__18371__18377__18383] :
( t(Vvar__var__var__var__var__13__x2__18255__18261__18371__18377__18383,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__7__req__18187,Vvar__var__var__var__var__12__x1__18254__18260__18370__18376__18382),Vvar__var__var__var__var__13__x2__18255__18261__18371__18377__18383))
=> ! [Vvar__var__var__var__var__15__y1__18256__18262__18372__18378__18384] :
( t(Vvar__var__var__var__var__15__y1__18256__18262__18372__18378__18384,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__16__y2__18257__18263__18373__18379__18385] :
( t(Vvar__var__var__var__var__16__y2__18257__18263__18373__18379__18385,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__7__req__18187,Vvar__var__var__var__var__15__y1__18256__18262__18372__18378__18384),Vvar__var__var__var__var__16__y2__18257__18263__18373__18379__18385))
=> p(happ(happ(Vvar__7__req__18187,happ(happ(Vvar__4__rtimes__18174,Vvar__var__var__var__var__12__x1__18254__18260__18370__18376__18382),Vvar__var__var__var__var__15__y1__18256__18262__18372__18378__18384)),happ(happ(Vvar__4__rtimes__18174,Vvar__var__var__var__var__13__x2__18255__18261__18371__18377__18383),Vvar__var__var__var__var__16__y2__18257__18263__18373__18379__18385))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__18267__18270__18388__18391__18394] :
( t(Vvar__var__var__var__var__13__x1__18267__18270__18388__18391__18394,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__14__x2__18268__18271__18389__18392__18395] :
( t(Vvar__var__var__var__var__14__x2__18268__18271__18389__18392__18395,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__7__req__18187,Vvar__var__var__var__var__13__x1__18267__18270__18388__18391__18394),Vvar__var__var__var__var__14__x2__18268__18271__18389__18392__18395))
=> p(happ(happ(Vvar__7__req__18187,happ(Vvar__6__ropp__18184,Vvar__var__var__var__var__13__x1__18267__18270__18388__18391__18394)),happ(Vvar__6__ropp__18184,Vvar__var__var__var__var__14__x2__18268__18271__18389__18392__18395))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__18274__18280__18397__18403__18409] :
( t(Vvar__var__var__var__var__14__x1__18274__18280__18397__18403__18409,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__15__x2__18275__18281__18398__18404__18410] :
( t(Vvar__var__var__var__var__15__x2__18275__18281__18398__18404__18410,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__7__req__18187,Vvar__var__var__var__var__14__x1__18274__18280__18397__18403__18409),Vvar__var__var__var__var__15__x2__18275__18281__18398__18404__18410))
=> ! [Vvar__var__var__var__var__17__y1__18276__18282__18399__18405__18411] :
( t(Vvar__var__var__var__var__17__y1__18276__18282__18399__18405__18411,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__18__y2__18277__18283__18400__18406__18412] :
( t(Vvar__var__var__var__var__18__y2__18277__18283__18400__18406__18412,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__7__req__18187,Vvar__var__var__var__var__17__y1__18276__18282__18399__18405__18411),Vvar__var__var__var__var__18__y2__18277__18283__18400__18406__18412))
=> ( p(happ(happ(Vvar__8__rle__18192,Vvar__var__var__var__var__14__x1__18274__18280__18397__18403__18409),Vvar__var__var__var__var__17__y1__18276__18282__18399__18405__18411))
<=> p(happ(happ(Vvar__8__rle__18192,Vvar__var__var__var__var__15__x2__18275__18281__18398__18404__18410),Vvar__var__var__var__var__18__y2__18277__18283__18400__18406__18412)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__18287__18293__18415__18421__18427] :
( t(Vvar__var__var__var__var__15__x1__18287__18293__18415__18421__18427,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__16__x2__18288__18294__18416__18422__18428] :
( t(Vvar__var__var__var__var__16__x2__18288__18294__18416__18422__18428,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__7__req__18187,Vvar__var__var__var__var__15__x1__18287__18293__18415__18421__18427),Vvar__var__var__var__var__16__x2__18288__18294__18416__18422__18428))
=> ! [Vvar__var__var__var__var__18__y1__18289__18295__18417__18423__18429] :
( t(Vvar__var__var__var__var__18__y1__18289__18295__18417__18423__18429,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__19__y2__18290__18296__18418__18424__18430] :
( t(Vvar__var__var__var__var__19__y2__18290__18296__18418__18424__18430,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__7__req__18187,Vvar__var__var__var__var__18__y1__18289__18295__18417__18423__18429),Vvar__var__var__var__var__19__y2__18290__18296__18418__18424__18430))
=> ( p(happ(happ(Vvar__9__rlt__18197,Vvar__var__var__var__var__15__x1__18287__18293__18415__18421__18427),Vvar__var__var__var__var__18__y1__18289__18295__18417__18423__18429))
<=> p(happ(happ(Vvar__9__rlt__18197,Vvar__var__var__var__var__16__x2__18288__18294__18416__18422__18428),Vvar__var__var__var__var__19__y2__18290__18296__18418__18424__18430)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__18166,Vvar__1__rO__18167,Vvar__2__rI__18168,Vvar__3__rplus__18169,Vvar__4__rtimes__18174,Vvar__5__rminus__18179,Vvar__6__ropp__18184,Vvar__7__req__18187)
& ! [Vvar__var__var__var__17__n__18301__18302__18433__18434] :
( t(Vvar__var__var__var__17__n__18301__18302__18433__18434,Vvar__0__R__18166)
=> p(happ(happ(Vvar__8__rle__18192,Vvar__var__var__var__17__n__18301__18302__18433__18434),Vvar__var__var__var__17__n__18301__18302__18433__18434)) )
& ! [Vvar__var__var__var__var__18__n__18304__18308__18435__18439__18443] :
( t(Vvar__var__var__var__var__18__n__18304__18308__18435__18439__18443,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__19__m__18305__18309__18436__18440__18444] :
( t(Vvar__var__var__var__var__19__m__18305__18309__18436__18440__18444,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__8__rle__18192,Vvar__var__var__var__var__18__n__18304__18308__18435__18439__18443),Vvar__var__var__var__var__19__m__18305__18309__18436__18440__18444))
=> ( p(happ(happ(Vvar__8__rle__18192,Vvar__var__var__var__var__19__m__18305__18309__18436__18440__18444),Vvar__var__var__var__var__18__n__18304__18308__18435__18439__18443))
=> p(happ(happ(Vvar__7__req__18187,Vvar__var__var__var__var__18__n__18304__18308__18435__18439__18443),Vvar__var__var__var__var__19__m__18305__18309__18436__18440__18444)) ) ) ) )
& ! [Vvar__var__var__var__19__n__18313__18318__18447__18452] :
( t(Vvar__var__var__var__19__n__18313__18318__18447__18452,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__20__m__18314__18319__18448__18453] :
( t(Vvar__var__var__var__20__m__18314__18319__18448__18453,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__21__p__18315__18320__18449__18454] :
( t(Vvar__var__var__var__21__p__18315__18320__18449__18454,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__8__rle__18192,Vvar__var__var__var__19__n__18313__18318__18447__18452),Vvar__var__var__var__20__m__18314__18319__18448__18453))
=> ( p(happ(happ(Vvar__8__rle__18192,Vvar__var__var__var__20__m__18314__18319__18448__18453),Vvar__var__var__var__21__p__18315__18320__18449__18454))
=> p(happ(happ(Vvar__8__rle__18192,Vvar__var__var__var__19__n__18313__18318__18447__18452),Vvar__var__var__var__21__p__18315__18320__18449__18454)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__18324__18326__18457__18459__18461__18463] :
( t(Vvar__var__var__var__var__var__20__n__18324__18326__18457__18459__18461__18463,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__var__21__m__18325__18327__18458__18460__18462__18464] :
( t(Vvar__var__var__var__var__var__21__m__18325__18327__18458__18460__18462__18464,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__9__rlt__18197,Vvar__var__var__var__var__var__20__n__18324__18326__18457__18459__18461__18463),Vvar__var__var__var__var__var__21__m__18325__18327__18458__18460__18462__18464))
<=> ( p(happ(happ(Vvar__8__rle__18192,Vvar__var__var__var__var__var__20__n__18324__18326__18457__18459__18461__18463),Vvar__var__var__var__var__var__21__m__18325__18327__18458__18460__18462__18464))
& ~ p(happ(happ(Vvar__7__req__18187,Vvar__var__var__var__var__var__20__n__18324__18326__18457__18459__18461__18463),Vvar__var__var__var__var__var__21__m__18325__18327__18458__18460__18462__18464)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__18329__18331__18465__18467__18469] :
( t(Vvar__var__var__var__var__21__n__18329__18331__18465__18467__18469,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__22__m__18330__18332__18466__18468__18470] :
( t(Vvar__var__var__var__var__22__m__18330__18332__18466__18468__18470,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__9__rlt__18197,Vvar__var__var__var__var__21__n__18329__18331__18465__18467__18469),Vvar__var__var__var__var__22__m__18330__18332__18466__18468__18470))
| p(happ(happ(Vvar__7__req__18187,Vvar__var__var__var__var__21__n__18329__18331__18465__18467__18469),Vvar__var__var__var__var__22__m__18330__18332__18466__18468__18470))
| p(happ(happ(Vvar__9__rlt__18197,Vvar__var__var__var__var__22__m__18330__18332__18466__18468__18470),Vvar__var__var__var__var__21__n__18329__18331__18465__18467__18469)) ) ) )
& ! [Vvar__var__var__var__var__22__n__18334__18338__18471__18475__18479] :
( t(Vvar__var__var__var__var__22__n__18334__18338__18471__18475__18479,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__23__m__18335__18339__18472__18476__18480] :
( t(Vvar__var__var__var__var__23__m__18335__18339__18472__18476__18480,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__24__p__18336__18340__18473__18477__18481] :
( t(Vvar__var__var__var__var__24__p__18336__18340__18473__18477__18481,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__8__rle__18192,Vvar__var__var__var__var__22__n__18334__18338__18471__18475__18479),Vvar__var__var__var__var__23__m__18335__18339__18472__18476__18480))
=> p(happ(happ(Vvar__8__rle__18192,happ(happ(Vvar__3__rplus__18169,Vvar__var__var__var__var__24__p__18336__18340__18473__18477__18481),Vvar__var__var__var__var__22__n__18334__18338__18471__18475__18479)),happ(happ(Vvar__3__rplus__18169,Vvar__var__var__var__var__24__p__18336__18340__18473__18477__18481),Vvar__var__var__var__var__23__m__18335__18339__18472__18476__18480))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__18343__18347__18483__18487__18491__18495] :
( t(Vvar__var__var__var__var__var__23__n__18343__18347__18483__18487__18491__18495,Vvar__0__R__18166)
=> ! [Vvar__var__var__var__var__var__24__m__18344__18348__18484__18488__18492__18496] :
( t(Vvar__var__var__var__var__var__24__m__18344__18348__18484__18488__18492__18496,Vvar__0__R__18166)
=> ( p(happ(happ(Vvar__9__rlt__18197,Vvar__1__rO__18167),Vvar__var__var__var__var__var__23__n__18343__18347__18483__18487__18491__18495))
=> ( p(happ(happ(Vvar__9__rlt__18197,Vvar__1__rO__18167),Vvar__var__var__var__var__var__24__m__18344__18348__18484__18488__18492__18496))
=> p(happ(happ(Vvar__9__rlt__18197,Vvar__1__rO__18167),happ(happ(Vvar__4__rtimes__18174,Vvar__var__var__var__var__var__23__n__18343__18347__18483__18487__18491__18495),Vvar__var__var__var__var__var__24__m__18344__18348__18484__18488__18492__18496))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__18187,Vvar__1__rO__18167),Vvar__2__rI__18168))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX19488] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX19488)
=> ( VX19488 = cCoq_2emicromega_2eRMicromega_2eC0
| VX19488 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__19489] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__19489)
& VX19488 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__19489) )
| ? [Vvar__0__r__19490] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__19490)
& VX19488 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__19490) )
| ? [Vvar__0__r1__19491] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__19491)
& ? [Vvar__1__r2__19492] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__19492)
& VX19488 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__19491,Vvar__1__r2__19492) ) )
| ? [Vvar__0__r1__19493] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__19493)
& ? [Vvar__1__r2__19494] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__19494)
& VX19488 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__19493,Vvar__1__r2__19494) ) )
| ? [Vvar__0__r1__19495] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__19495)
& ? [Vvar__1__r2__19496] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__19496)
& VX19488 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__19495,Vvar__1__r2__19496) ) )
| ? [Vvar__0__r1__19497] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__19497)
& ? [Vvar__1__z__19498] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__19498)
& VX19488 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__19497,Vvar__1__z__19498) ) )
| ? [Vvar__0__r__19499] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__19499)
& VX19488 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__19499) )
| ? [Vvar__0__r__19500] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__19500)
& VX19488 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__19500) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__20657,VX20658] :
( cType___24t(Vvar__0__T__20657)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__20657,VX20658)
=> ? [Vvar__1__Flhs__20660] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__20657,Vvar__1__Flhs__20660)
& ? [Vvar__2__Fop__20661] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__20661)
& ? [Vvar__3__Frhs__20662] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__20657,Vvar__3__Frhs__20662)
& VX20658 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__20657,Vvar__1__Flhs__20660,Vvar__2__Fop__20661,Vvar__3__Frhs__20662) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX2455] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX2455)
=> ( VX2455 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX2455 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX2455 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX2455 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX43921] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX43921)
=> ( VX43921 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX43921 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX43921 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX43921 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX43921 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX43921 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__3293,VX3294] :
( cType___24t(Vvar__0__C__3293)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__3293,VX3294)
=> ( ? [Vvar__1___24Anonymous__3296] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__3296)
& VX3294 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__3293,Vvar__1___24Anonymous__3296) )
| ? [Vvar__1___24Anonymous__3298] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__3293,Vvar__1___24Anonymous__3298)
& VX3294 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__3293,Vvar__1___24Anonymous__3298) )
| ? [Vvar__1___24Anonymous__3300] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__3293,Vvar__1___24Anonymous__3300)
& ? [Vvar__2___24Anonymous__3301] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__3293,Vvar__2___24Anonymous__3301)
& VX3294 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__3293,Vvar__1___24Anonymous__3300,Vvar__2___24Anonymous__3301) ) )
| ? [Vvar__1___24Anonymous__3303] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__3293,Vvar__1___24Anonymous__3303)
& ? [Vvar__2___24Anonymous__3304] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__3293,Vvar__2___24Anonymous__3304)
& VX3294 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__3293,Vvar__1___24Anonymous__3303,Vvar__2___24Anonymous__3304) ) )
| ? [Vvar__1___24Anonymous__3306] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__3293,Vvar__1___24Anonymous__3306)
& ? [Vvar__2___24Anonymous__3307] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__3293,Vvar__2___24Anonymous__3307)
& VX3294 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__3293,Vvar__1___24Anonymous__3306,Vvar__2___24Anonymous__3307) ) )
| ? [Vvar__1___24Anonymous__3309] :
( t(Vvar__1___24Anonymous__3309,Vvar__0__C__3293)
& VX3294 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__3293,Vvar__1___24Anonymous__3309) )
| VX3294 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__3293) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536] :
( cType___24t(Vvar__0__R__38467)
=> ( t(Vvar__1__rO__38468,Vvar__0__R__38467)
=> ( t(Vvar__2__rI__38469,Vvar__0__R__38467)
=> ( c_24__type__39000___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__3__rplus__38470)
=> ( c_24__type__39346___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__4__rtimes__38475)
=> ( c_24__type__39692___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__5__rminus__38480)
=> ( c_24__type__40015___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__6__ropp__38485)
=> ( c_24__type__40361___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__7__req__38488)
=> ( c_24__type__40707___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__8__rle__38493)
=> ( cType___24t(Vvar__9__C__38498)
=> ( t(Vvar__10__cO__38499,Vvar__9__C__38498)
=> ( t(Vvar__11__cI__38500,Vvar__9__C__38498)
=> ( c_24__type__41053___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__12__cplus__38501)
=> ( c_24__type__41399___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__13__ctimes__38506)
=> ( c_24__type__41745___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__14__cminus__38511)
=> ( c_24__type__42068___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__15__copp__38516)
=> ( c_24__type__42414___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__16__ceqb__38519)
=> ( c_24__type__42760___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__17__cleb__38524)
=> ( c_24__type__43083___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__18__phi__38529)
=> ( cType___24t(Vvar__19__E__38532)
=> ( c_24__type__43406___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__20__pow__phi__38533)
=> ( c_24__type__43752___24t(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536,Vvar__21__rpow__38536)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__8__rle__38493,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__17__cleb__38524,Vvar__18__phi__38529,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__38467,Vvar__1__rO__38468,Vvar__2__rI__38469,Vvar__3__rplus__38470,Vvar__4__rtimes__38475,Vvar__5__rminus__38480,Vvar__6__ropp__38485,Vvar__7__req__38488,Vvar__9__C__38498,Vvar__10__cO__38499,Vvar__11__cI__38500,Vvar__12__cplus__38501,Vvar__13__ctimes__38506,Vvar__14__cminus__38511,Vvar__15__copp__38516,Vvar__16__ceqb__38519,Vvar__18__phi__38529)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__38467,Vvar__2__rI__38469,Vvar__4__rtimes__38475,Vvar__7__req__38488,Vvar__19__E__38532,Vvar__20__pow__phi__38533,Vvar__21__rpow__38536)
& ! [Vvar__var__var__var__var__var__24__x__38619__38622__38632__38635__38638__38641] :
( t(Vvar__var__var__var__var__var__24__x__38619__38622__38632__38635__38638__38641,Vvar__9__C__38498)
=> ! [Vvar__var__var__var__var__var__25__y__38620__38623__38633__38636__38639__38642] :
( t(Vvar__var__var__var__var__var__25__y__38620__38623__38633__38636__38639__38642,Vvar__9__C__38498)
=> ( happ(happ(Vvar__16__ceqb__38519,Vvar__var__var__var__var__var__24__x__38619__38622__38632__38635__38638__38641),Vvar__var__var__var__var__var__25__y__38620__38623__38633__38636__38639__38642) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__38488,happ(Vvar__18__phi__38529,Vvar__var__var__var__var__var__24__x__38619__38622__38632__38635__38638__38641)),happ(Vvar__18__phi__38529,Vvar__var__var__var__var__var__25__y__38620__38623__38633__38636__38639__38642))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__38626__38629__38644__38647__38650__38653] :
( t(Vvar__var__var__var__var__var__25__x__38626__38629__38644__38647__38650__38653,Vvar__9__C__38498)
=> ! [Vvar__var__var__var__var__var__26__y__38627__38630__38645__38648__38651__38654] :
( t(Vvar__var__var__var__var__var__26__y__38627__38630__38645__38648__38651__38654,Vvar__9__C__38498)
=> ( happ(happ(Vvar__17__cleb__38524,Vvar__var__var__var__var__var__25__x__38626__38629__38644__38647__38650__38653),Vvar__var__var__var__var__var__26__y__38627__38630__38645__38648__38651__38654) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__38493,happ(Vvar__18__phi__38529,Vvar__var__var__var__var__var__25__x__38626__38629__38644__38647__38650__38653)),happ(Vvar__18__phi__38529,Vvar__var__var__var__var__var__26__y__38627__38630__38645__38648__38651__38654))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,VX674] :
( cType___24t(Vvar__0__TA__670)
=> ( cType___24t(Vvar__1__TX__671)
=> ( cType___24t(Vvar__2__AA__672)
=> ( cType___24t(Vvar__3__AF__673)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,VX674)
=> ( VX674 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673)
| VX674 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673)
| ? [Vvar__4___24Anonymous__687] :
( t(Vvar__4___24Anonymous__687,Vvar__1__TX__671)
& VX674 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__4___24Anonymous__687) )
| ? [Vvar__4___24Anonymous__692] :
( t(Vvar__4___24Anonymous__692,Vvar__0__TA__670)
& ? [Vvar__5___24Anonymous__693] :
( t(Vvar__5___24Anonymous__693,Vvar__2__AA__672)
& VX674 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__4___24Anonymous__692,Vvar__5___24Anonymous__693) ) )
| ? [Vvar__4___24Anonymous__698] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__4___24Anonymous__698)
& ? [Vvar__5___24Anonymous__699] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__5___24Anonymous__699)
& VX674 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__4___24Anonymous__698,Vvar__5___24Anonymous__699) ) )
| ? [Vvar__4___24Anonymous__704] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__4___24Anonymous__704)
& ? [Vvar__5___24Anonymous__705] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__5___24Anonymous__705)
& VX674 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__4___24Anonymous__704,Vvar__5___24Anonymous__705) ) )
| ? [Vvar__4___24Anonymous__710] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__4___24Anonymous__710)
& VX674 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__4___24Anonymous__710) )
| ? [Vvar__4___24Anonymous__715] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__4___24Anonymous__715)
& ? [Vvar__5___24Anonymous__716] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__673,Vvar__5___24Anonymous__716)
& ? [Vvar__6___24Anonymous__717] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__6___24Anonymous__717)
& VX674 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__670,Vvar__1__TX__671,Vvar__2__AA__672,Vvar__3__AF__673,Vvar__4___24Anonymous__715,Vvar__5___24Anonymous__716,Vvar__6___24Anonymous__717) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__116316] :
( cProp___24t(Vvar__0___24Anonymous__116316)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__116316)
=> ( ? [Vvar__0__S__116318] :
( cType___24t(Vvar__0__S__116318)
& ? [Vvar__1__x__116319] :
( t(Vvar__1__x__116319,Vvar__0__S__116318)
& ? [Vvar__2__y__116320] :
( t(Vvar__2__y__116320,Vvar__0__S__116318)
& Vvar__0___24Anonymous__116316 = c_24__prop__116340___24a4(Vvar__0___24Anonymous__116316,Vvar__0__S__116318,Vvar__1__x__116319,Vvar__2__y__116320) ) ) )
| ? [Vvar__0__x__116321] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__116321)
& ? [Vvar__1__y__116322] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__116322)
& Vvar__0___24Anonymous__116316 = c_24__prop__116341___24a3(Vvar__0___24Anonymous__116316,Vvar__0__x__116321,Vvar__1__y__116322) ) )
| ? [Vvar__0__x__116323] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__116323)
& ? [Vvar__1__s__116324] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__116324)
& Vvar__0___24Anonymous__116316 = c_24__prop__116342___24a3(Vvar__0___24Anonymous__116316,Vvar__0__x__116323,Vvar__1__s__116324) ) )
| Vvar__0___24Anonymous__116316 = c_24True
| Vvar__0___24Anonymous__116316 = c_24False
| ? [Vvar__0__P__116325] :
( cProp___24t(Vvar__0__P__116325)
& ? [Vvar__1__Q__116326] :
( cProp___24t(Vvar__1__Q__116326)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__116325)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__116326)
& Vvar__0___24Anonymous__116316 = c_24__prop__116343___24a3(Vvar__0___24Anonymous__116316,Vvar__0__P__116325,Vvar__1__Q__116326) ) )
| ? [Vvar__0__P__116329] :
( cProp___24t(Vvar__0__P__116329)
& ? [Vvar__1__Q__116330] :
( cProp___24t(Vvar__1__Q__116330)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__116329)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__116330)
& Vvar__0___24Anonymous__116316 = c_24__prop__116344___24a3(Vvar__0___24Anonymous__116316,Vvar__0__P__116329,Vvar__1__Q__116330) ) )
| ? [Vvar__0__P__116333] :
( cProp___24t(Vvar__0__P__116333)
& ? [Vvar__1__Q__116334] :
( cProp___24t(Vvar__1__Q__116334)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__116333)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__116334)
& Vvar__0___24Anonymous__116316 = c_24__prop__116345___24a3(Vvar__0___24Anonymous__116316,Vvar__0__P__116333,Vvar__1__Q__116334) ) )
| ? [Vvar__0__P__116338] :
( cProp___24t(Vvar__0__P__116338)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__116338)
& Vvar__0___24Anonymous__116316 = c_24__prop__116346___24a2(Vvar__0___24Anonymous__116316,Vvar__0__P__116338) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX36746] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX36746)
=> ( VX36746 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__36747] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__36747)
& ? [Vvar__1___24Anonymous__36748] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__36748)
& VX36746 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__36747,Vvar__1___24Anonymous__36748) ) )
| ? [Vvar__0___24Anonymous__36749] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__36749)
& ? [Vvar__1___24Anonymous__36750] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__36750)
& VX36746 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__36749,Vvar__1___24Anonymous__36750) ) )
| ? [Vvar__0___24Anonymous__36751] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__36751)
& ? [Vvar__1___24Anonymous__36752] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__36752)
& ? [Vvar__2___24Anonymous__36753] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__36753)
& VX36746 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__36751,Vvar__1___24Anonymous__36752,Vvar__2___24Anonymous__36753) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__10573,VX10574] :
( cType___24t(Vvar__0__C__10573)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__10573,VX10574)
=> ( VX10574 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__10573)
| VX10574 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__10573)
| ? [Vvar__1___24Anonymous__10578] :
( t(Vvar__1___24Anonymous__10578,Vvar__0__C__10573)
& VX10574 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__10573,Vvar__1___24Anonymous__10578) )
| ? [Vvar__1___24Anonymous__10580] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10580)
& VX10574 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__10573,Vvar__1___24Anonymous__10580) )
| ? [Vvar__1___24Anonymous__10582] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__10573,Vvar__1___24Anonymous__10582)
& ? [Vvar__2___24Anonymous__10583] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__10573,Vvar__2___24Anonymous__10583)
& VX10574 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__10573,Vvar__1___24Anonymous__10582,Vvar__2___24Anonymous__10583) ) )
| ? [Vvar__1___24Anonymous__10585] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__10573,Vvar__1___24Anonymous__10585)
& ? [Vvar__2___24Anonymous__10586] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__10573,Vvar__2___24Anonymous__10586)
& VX10574 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__10573,Vvar__1___24Anonymous__10585,Vvar__2___24Anonymous__10586) ) )
| ? [Vvar__1___24Anonymous__10588] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__10573,Vvar__1___24Anonymous__10588)
& ? [Vvar__2___24Anonymous__10589] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__10573,Vvar__2___24Anonymous__10589)
& VX10574 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__10573,Vvar__1___24Anonymous__10588,Vvar__2___24Anonymous__10589) ) )
| ? [Vvar__1___24Anonymous__10591] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__10573,Vvar__1___24Anonymous__10591)
& VX10574 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__10573,Vvar__1___24Anonymous__10591) )
| ? [Vvar__1___24Anonymous__10593] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__10573,Vvar__1___24Anonymous__10593)
& VX10574 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__10573,Vvar__1___24Anonymous__10593) )
| ? [Vvar__1___24Anonymous__10595] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__10573,Vvar__1___24Anonymous__10595)
& ? [Vvar__2___24Anonymous__10596] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__10573,Vvar__2___24Anonymous__10596)
& VX10574 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__10573,Vvar__1___24Anonymous__10595,Vvar__2___24Anonymous__10596) ) )
| ? [Vvar__1___24Anonymous__10598] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__10573,Vvar__1___24Anonymous__10598)
& ? [Vvar__2___24Anonymous__10599] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__10599)
& VX10574 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__10573,Vvar__1___24Anonymous__10598,Vvar__2___24Anonymous__10599) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__6877,Vvar__1__rO__6878,Vvar__2__rI__6879,Vvar__3__radd__6880,Vvar__4__rmul__6885,Vvar__5__rsub__6890,Vvar__6__ropp__6895,Vvar__7__rdiv__6898,Vvar__8__rinv__6903,Vvar__9__req__6906] :
( cType___24t(Vvar__0__R__6877)
=> ( t(Vvar__1__rO__6878,Vvar__0__R__6877)
=> ( t(Vvar__2__rI__6879,Vvar__0__R__6877)
=> ( c_24__type__7071___24t(Vvar__0__R__6877,Vvar__1__rO__6878,Vvar__2__rI__6879,Vvar__3__radd__6880,Vvar__4__rmul__6885,Vvar__5__rsub__6890,Vvar__6__ropp__6895,Vvar__7__rdiv__6898,Vvar__8__rinv__6903,Vvar__9__req__6906,Vvar__3__radd__6880)
=> ( c_24__type__7164___24t(Vvar__0__R__6877,Vvar__1__rO__6878,Vvar__2__rI__6879,Vvar__3__radd__6880,Vvar__4__rmul__6885,Vvar__5__rsub__6890,Vvar__6__ropp__6895,Vvar__7__rdiv__6898,Vvar__8__rinv__6903,Vvar__9__req__6906,Vvar__4__rmul__6885)
=> ( c_24__type__7257___24t(Vvar__0__R__6877,Vvar__1__rO__6878,Vvar__2__rI__6879,Vvar__3__radd__6880,Vvar__4__rmul__6885,Vvar__5__rsub__6890,Vvar__6__ropp__6895,Vvar__7__rdiv__6898,Vvar__8__rinv__6903,Vvar__9__req__6906,Vvar__5__rsub__6890)
=> ( c_24__type__7339___24t(Vvar__0__R__6877,Vvar__1__rO__6878,Vvar__2__rI__6879,Vvar__3__radd__6880,Vvar__4__rmul__6885,Vvar__5__rsub__6890,Vvar__6__ropp__6895,Vvar__7__rdiv__6898,Vvar__8__rinv__6903,Vvar__9__req__6906,Vvar__6__ropp__6895)
=> ( c_24__type__7432___24t(Vvar__0__R__6877,Vvar__1__rO__6878,Vvar__2__rI__6879,Vvar__3__radd__6880,Vvar__4__rmul__6885,Vvar__5__rsub__6890,Vvar__6__ropp__6895,Vvar__7__rdiv__6898,Vvar__8__rinv__6903,Vvar__9__req__6906,Vvar__7__rdiv__6898)
=> ( c_24__type__7514___24t(Vvar__0__R__6877,Vvar__1__rO__6878,Vvar__2__rI__6879,Vvar__3__radd__6880,Vvar__4__rmul__6885,Vvar__5__rsub__6890,Vvar__6__ropp__6895,Vvar__7__rdiv__6898,Vvar__8__rinv__6903,Vvar__9__req__6906,Vvar__8__rinv__6903)
=> ( c_24__type__7607___24t(Vvar__0__R__6877,Vvar__1__rO__6878,Vvar__2__rI__6879,Vvar__3__radd__6880,Vvar__4__rmul__6885,Vvar__5__rsub__6890,Vvar__6__ropp__6895,Vvar__7__rdiv__6898,Vvar__8__rinv__6903,Vvar__9__req__6906,Vvar__9__req__6906)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__6877,Vvar__1__rO__6878,Vvar__2__rI__6879,Vvar__3__radd__6880,Vvar__4__rmul__6885,Vvar__5__rsub__6890,Vvar__6__ropp__6895,Vvar__7__rdiv__6898,Vvar__8__rinv__6903,Vvar__9__req__6906)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__6877,Vvar__1__rO__6878,Vvar__2__rI__6879,Vvar__3__radd__6880,Vvar__4__rmul__6885,Vvar__5__rsub__6890,Vvar__6__ropp__6895,Vvar__9__req__6906)
& ~ p(happ(happ(Vvar__9__req__6906,Vvar__2__rI__6879),Vvar__1__rO__6878))
& ! [Vvar__var__var__var__var__var__var__12__p__6949__6951__6958__6960__6962__6964__6966] :
( t(Vvar__var__var__var__var__var__var__12__p__6949__6951__6958__6960__6962__6964__6966,Vvar__0__R__6877)
=> ! [Vvar__var__var__var__var__var__var__13__q__6950__6952__6959__6961__6963__6965__6967] :
( t(Vvar__var__var__var__var__var__var__13__q__6950__6952__6959__6961__6963__6965__6967,Vvar__0__R__6877)
=> p(happ(happ(Vvar__9__req__6906,happ(happ(Vvar__7__rdiv__6898,Vvar__var__var__var__var__var__var__12__p__6949__6951__6958__6960__6962__6964__6966),Vvar__var__var__var__var__var__var__13__q__6950__6952__6959__6961__6963__6965__6967)),happ(happ(Vvar__4__rmul__6885,Vvar__var__var__var__var__var__var__12__p__6949__6951__6958__6960__6962__6964__6966),happ(Vvar__8__rinv__6903,Vvar__var__var__var__var__var__var__13__q__6950__6952__6959__6961__6963__6965__6967)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__6954__6956__6968__6970__6972__6974__6976__6978] :
( t(Vvar__var__var__var__var__var__var__var__13__p__6954__6956__6968__6970__6972__6974__6976__6978,Vvar__0__R__6877)
=> ( ~ p(happ(happ(Vvar__9__req__6906,Vvar__var__var__var__var__var__var__var__13__p__6954__6956__6968__6970__6972__6974__6976__6978),Vvar__1__rO__6878))
=> p(happ(happ(Vvar__9__req__6906,happ(happ(Vvar__4__rmul__6885,happ(Vvar__8__rinv__6903,Vvar__var__var__var__var__var__var__var__13__p__6954__6956__6968__6970__6972__6974__6976__6978)),Vvar__var__var__var__var__var__var__var__13__p__6954__6956__6968__6970__6972__6974__6976__6978)),Vvar__2__rI__6879)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__11185,VX11186] :
( cType___24t(Vvar__0__C__11185)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__11185,VX11186)
=> ? [Vvar__1__num__11188] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__11185,Vvar__1__num__11188)
& ? [Vvar__2__denum__11189] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__11185,Vvar__2__denum__11189)
& ? [Vvar__3__condition__11190] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__11185),Vvar__3__condition__11190)
& VX11186 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__11185,Vvar__1__num__11188,Vvar__2__denum__11189,Vvar__3__condition__11190) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__11288,VX11289] :
( cType___24t(Vvar__0__C__11288)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__11288,VX11289)
=> ? [Vvar__1__rsplit__left__11291] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__11288,Vvar__1__rsplit__left__11291)
& ? [Vvar__2__rsplit__common__11292] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__11288,Vvar__2__rsplit__common__11292)
& ? [Vvar__3__rsplit__right__11293] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__11288,Vvar__3__rsplit__right__11293)
& VX11289 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__11288,Vvar__1__rsplit__left__11291,Vvar__2__rsplit__common__11292,Vvar__3__rsplit__right__11293) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX21714] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX21714)
=> ( VX21714 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__21715] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21715)
& ? [Vvar__1___24Anonymous__21716] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__21716)
& VX21714 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__21715,Vvar__1___24Anonymous__21716) ) )
| ? [Vvar__0___24Anonymous__21717] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21717)
& ? [Vvar__1___24Anonymous__21718] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__21718)
& VX21714 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__21717,Vvar__1___24Anonymous__21718) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__3463,VX3464] :
( cType___24t(Vvar__0__C__3463)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3463,VX3464)
=> ( VX3464 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__3463)
| VX3464 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__3463)
| ? [Vvar__1___24Anonymous__3468] :
( t(Vvar__1___24Anonymous__3468,Vvar__0__C__3463)
& VX3464 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__3463,Vvar__1___24Anonymous__3468) )
| ? [Vvar__1___24Anonymous__3470] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3470)
& VX3464 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__3463,Vvar__1___24Anonymous__3470) )
| ? [Vvar__1___24Anonymous__3472] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3463,Vvar__1___24Anonymous__3472)
& ? [Vvar__2___24Anonymous__3473] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3463,Vvar__2___24Anonymous__3473)
& VX3464 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__3463,Vvar__1___24Anonymous__3472,Vvar__2___24Anonymous__3473) ) )
| ? [Vvar__1___24Anonymous__3475] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3463,Vvar__1___24Anonymous__3475)
& ? [Vvar__2___24Anonymous__3476] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3463,Vvar__2___24Anonymous__3476)
& VX3464 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__3463,Vvar__1___24Anonymous__3475,Vvar__2___24Anonymous__3476) ) )
| ? [Vvar__1___24Anonymous__3478] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3463,Vvar__1___24Anonymous__3478)
& ? [Vvar__2___24Anonymous__3479] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3463,Vvar__2___24Anonymous__3479)
& VX3464 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__3463,Vvar__1___24Anonymous__3478,Vvar__2___24Anonymous__3479) ) )
| ? [Vvar__1___24Anonymous__3481] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3463,Vvar__1___24Anonymous__3481)
& VX3464 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__3463,Vvar__1___24Anonymous__3481) )
| ? [Vvar__1___24Anonymous__3483] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3463,Vvar__1___24Anonymous__3483)
& ? [Vvar__2___24Anonymous__3484] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__3484)
& VX3464 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__3463,Vvar__1___24Anonymous__3483,Vvar__2___24Anonymous__3484) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__20759,VX20760] :
( cType___24t(Vvar__0__C__20759)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__20759,VX20760)
=> ( ? [Vvar__1___24Anonymous__20762] :
( t(Vvar__1___24Anonymous__20762,Vvar__0__C__20759)
& VX20760 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__20759,Vvar__1___24Anonymous__20762) )
| ? [Vvar__1___24Anonymous__20764] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20764)
& ? [Vvar__2___24Anonymous__20765] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__20759,Vvar__2___24Anonymous__20765)
& VX20760 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__20759,Vvar__1___24Anonymous__20764,Vvar__2___24Anonymous__20765) ) )
| ? [Vvar__1___24Anonymous__20767] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__20759,Vvar__1___24Anonymous__20767)
& ? [Vvar__2___24Anonymous__20768] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20768)
& ? [Vvar__3___24Anonymous__20769] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__20759,Vvar__3___24Anonymous__20769)
& VX20760 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__20759,Vvar__1___24Anonymous__20767,Vvar__2___24Anonymous__20768,Vvar__3___24Anonymous__20769) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__28847,Vvar__1__rO__28848,Vvar__2__rI__28849,Vvar__3__radd__28850,Vvar__4__rmul__28855,Vvar__5__rsub__28860,Vvar__6__ropp__28865,Vvar__7__req__28868] :
( cType___24t(Vvar__0__R__28847)
=> ( t(Vvar__1__rO__28848,Vvar__0__R__28847)
=> ( t(Vvar__2__rI__28849,Vvar__0__R__28847)
=> ( c_24__type__29096___24t(Vvar__0__R__28847,Vvar__1__rO__28848,Vvar__2__rI__28849,Vvar__3__radd__28850,Vvar__4__rmul__28855,Vvar__5__rsub__28860,Vvar__6__ropp__28865,Vvar__7__req__28868,Vvar__3__radd__28850)
=> ( c_24__type__29159___24t(Vvar__0__R__28847,Vvar__1__rO__28848,Vvar__2__rI__28849,Vvar__3__radd__28850,Vvar__4__rmul__28855,Vvar__5__rsub__28860,Vvar__6__ropp__28865,Vvar__7__req__28868,Vvar__4__rmul__28855)
=> ( c_24__type__29222___24t(Vvar__0__R__28847,Vvar__1__rO__28848,Vvar__2__rI__28849,Vvar__3__radd__28850,Vvar__4__rmul__28855,Vvar__5__rsub__28860,Vvar__6__ropp__28865,Vvar__7__req__28868,Vvar__5__rsub__28860)
=> ( c_24__type__29276___24t(Vvar__0__R__28847,Vvar__1__rO__28848,Vvar__2__rI__28849,Vvar__3__radd__28850,Vvar__4__rmul__28855,Vvar__5__rsub__28860,Vvar__6__ropp__28865,Vvar__7__req__28868,Vvar__6__ropp__28865)
=> ( c_24__type__29339___24t(Vvar__0__R__28847,Vvar__1__rO__28848,Vvar__2__rI__28849,Vvar__3__radd__28850,Vvar__4__rmul__28855,Vvar__5__rsub__28860,Vvar__6__ropp__28865,Vvar__7__req__28868,Vvar__7__req__28868)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__28847,Vvar__1__rO__28848,Vvar__2__rI__28849,Vvar__3__radd__28850,Vvar__4__rmul__28855,Vvar__5__rsub__28860,Vvar__6__ropp__28865,Vvar__7__req__28868)
=> ( ! [Vvar__var__var__var__var__var__8__x__28901__28902__28955__28956__28957__28958] :
( t(Vvar__var__var__var__var__var__8__x__28901__28902__28955__28956__28957__28958,Vvar__0__R__28847)
=> p(happ(happ(Vvar__7__req__28868,happ(happ(Vvar__3__radd__28850,Vvar__1__rO__28848),Vvar__var__var__var__var__var__8__x__28901__28902__28955__28956__28957__28958)),Vvar__var__var__var__var__var__8__x__28901__28902__28955__28956__28957__28958)) )
& ! [Vvar__var__var__var__var__9__x__28904__28906__28959__28961__28963] :
( t(Vvar__var__var__var__var__9__x__28904__28906__28959__28961__28963,Vvar__0__R__28847)
=> ! [Vvar__var__var__var__var__10__y__28905__28907__28960__28962__28964] :
( t(Vvar__var__var__var__var__10__y__28905__28907__28960__28962__28964,Vvar__0__R__28847)
=> p(happ(happ(Vvar__7__req__28868,happ(happ(Vvar__3__radd__28850,Vvar__var__var__var__var__9__x__28904__28906__28959__28961__28963),Vvar__var__var__var__var__10__y__28905__28907__28960__28962__28964)),happ(happ(Vvar__3__radd__28850,Vvar__var__var__var__var__10__y__28905__28907__28960__28962__28964),Vvar__var__var__var__var__9__x__28904__28906__28959__28961__28963))) ) )
& ! [Vvar__var__var__var__var__10__x__28909__28912__28965__28968__28971] :
( t(Vvar__var__var__var__var__10__x__28909__28912__28965__28968__28971,Vvar__0__R__28847)
=> ! [Vvar__var__var__var__var__11__y__28910__28913__28966__28969__28972] :
( t(Vvar__var__var__var__var__11__y__28910__28913__28966__28969__28972,Vvar__0__R__28847)
=> ! [Vvar__var__var__var__var__12__z__28911__28914__28967__28970__28973] :
( t(Vvar__var__var__var__var__12__z__28911__28914__28967__28970__28973,Vvar__0__R__28847)
=> p(happ(happ(Vvar__7__req__28868,happ(happ(Vvar__3__radd__28850,Vvar__var__var__var__var__10__x__28909__28912__28965__28968__28971),happ(happ(Vvar__3__radd__28850,Vvar__var__var__var__var__11__y__28910__28913__28966__28969__28972),Vvar__var__var__var__var__12__z__28911__28914__28967__28970__28973))),happ(happ(Vvar__3__radd__28850,happ(happ(Vvar__3__radd__28850,Vvar__var__var__var__var__10__x__28909__28912__28965__28968__28971),Vvar__var__var__var__var__11__y__28910__28913__28966__28969__28972)),Vvar__var__var__var__var__12__z__28911__28914__28967__28970__28973))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__28916__28917__28974__28975__28976__28977] :
( t(Vvar__var__var__var__var__var__11__x__28916__28917__28974__28975__28976__28977,Vvar__0__R__28847)
=> p(happ(happ(Vvar__7__req__28868,happ(happ(Vvar__4__rmul__28855,Vvar__2__rI__28849),Vvar__var__var__var__var__var__11__x__28916__28917__28974__28975__28976__28977)),Vvar__var__var__var__var__var__11__x__28916__28917__28974__28975__28976__28977)) )
& ! [Vvar__var__var__var__var__var__12__x__28919__28920__28978__28979__28980__28981] :
( t(Vvar__var__var__var__var__var__12__x__28919__28920__28978__28979__28980__28981,Vvar__0__R__28847)
=> p(happ(happ(Vvar__7__req__28868,happ(happ(Vvar__4__rmul__28855,Vvar__1__rO__28848),Vvar__var__var__var__var__var__12__x__28919__28920__28978__28979__28980__28981)),Vvar__1__rO__28848)) )
& ! [Vvar__var__var__var__var__13__x__28922__28924__28982__28984__28986] :
( t(Vvar__var__var__var__var__13__x__28922__28924__28982__28984__28986,Vvar__0__R__28847)
=> ! [Vvar__var__var__var__var__14__y__28923__28925__28983__28985__28987] :
( t(Vvar__var__var__var__var__14__y__28923__28925__28983__28985__28987,Vvar__0__R__28847)
=> p(happ(happ(Vvar__7__req__28868,happ(happ(Vvar__4__rmul__28855,Vvar__var__var__var__var__13__x__28922__28924__28982__28984__28986),Vvar__var__var__var__var__14__y__28923__28925__28983__28985__28987)),happ(happ(Vvar__4__rmul__28855,Vvar__var__var__var__var__14__y__28923__28925__28983__28985__28987),Vvar__var__var__var__var__13__x__28922__28924__28982__28984__28986))) ) )
& ! [Vvar__var__var__var__var__14__x__28927__28930__28988__28991__28994] :
( t(Vvar__var__var__var__var__14__x__28927__28930__28988__28991__28994,Vvar__0__R__28847)
=> ! [Vvar__var__var__var__var__15__y__28928__28931__28989__28992__28995] :
( t(Vvar__var__var__var__var__15__y__28928__28931__28989__28992__28995,Vvar__0__R__28847)
=> ! [Vvar__var__var__var__var__16__z__28929__28932__28990__28993__28996] :
( t(Vvar__var__var__var__var__16__z__28929__28932__28990__28993__28996,Vvar__0__R__28847)
=> p(happ(happ(Vvar__7__req__28868,happ(happ(Vvar__4__rmul__28855,Vvar__var__var__var__var__14__x__28927__28930__28988__28991__28994),happ(happ(Vvar__4__rmul__28855,Vvar__var__var__var__var__15__y__28928__28931__28989__28992__28995),Vvar__var__var__var__var__16__z__28929__28932__28990__28993__28996))),happ(happ(Vvar__4__rmul__28855,happ(happ(Vvar__4__rmul__28855,Vvar__var__var__var__var__14__x__28927__28930__28988__28991__28994),Vvar__var__var__var__var__15__y__28928__28931__28989__28992__28995)),Vvar__var__var__var__var__16__z__28929__28932__28990__28993__28996))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__28934__28937__28997__29000__29003__29006] :
( t(Vvar__var__var__var__var__var__15__x__28934__28937__28997__29000__29003__29006,Vvar__0__R__28847)
=> ! [Vvar__var__var__var__var__var__16__y__28935__28938__28998__29001__29004__29007] :
( t(Vvar__var__var__var__var__var__16__y__28935__28938__28998__29001__29004__29007,Vvar__0__R__28847)
=> ! [Vvar__var__var__var__var__var__17__z__28936__28939__28999__29002__29005__29008] :
( t(Vvar__var__var__var__var__var__17__z__28936__28939__28999__29002__29005__29008,Vvar__0__R__28847)
=> p(happ(happ(Vvar__7__req__28868,happ(happ(Vvar__4__rmul__28855,happ(happ(Vvar__3__radd__28850,Vvar__var__var__var__var__var__15__x__28934__28937__28997__29000__29003__29006),Vvar__var__var__var__var__var__16__y__28935__28938__28998__29001__29004__29007)),Vvar__var__var__var__var__var__17__z__28936__28939__28999__29002__29005__29008)),happ(happ(Vvar__3__radd__28850,happ(happ(Vvar__4__rmul__28855,Vvar__var__var__var__var__var__15__x__28934__28937__28997__29000__29003__29006),Vvar__var__var__var__var__var__17__z__28936__28939__28999__29002__29005__29008)),happ(happ(Vvar__4__rmul__28855,Vvar__var__var__var__var__var__16__y__28935__28938__28998__29001__29004__29007),Vvar__var__var__var__var__var__17__z__28936__28939__28999__29002__29005__29008)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__28941__28943__29009__29011__29013__29015] :
( t(Vvar__var__var__var__var__var__16__x__28941__28943__29009__29011__29013__29015,Vvar__0__R__28847)
=> ! [Vvar__var__var__var__var__var__17__y__28942__28944__29010__29012__29014__29016] :
( t(Vvar__var__var__var__var__var__17__y__28942__28944__29010__29012__29014__29016,Vvar__0__R__28847)
=> p(happ(happ(Vvar__7__req__28868,happ(Vvar__6__ropp__28865,happ(happ(Vvar__4__rmul__28855,Vvar__var__var__var__var__var__16__x__28941__28943__29009__29011__29013__29015),Vvar__var__var__var__var__var__17__y__28942__28944__29010__29012__29014__29016))),happ(happ(Vvar__4__rmul__28855,happ(Vvar__6__ropp__28865,Vvar__var__var__var__var__var__16__x__28941__28943__29009__29011__29013__29015)),Vvar__var__var__var__var__var__17__y__28942__28944__29010__29012__29014__29016))) ) )
& ! [Vvar__var__var__var__var__var__17__x__28946__28948__29017__29019__29021__29023] :
( t(Vvar__var__var__var__var__var__17__x__28946__28948__29017__29019__29021__29023,Vvar__0__R__28847)
=> ! [Vvar__var__var__var__var__var__18__y__28947__28949__29018__29020__29022__29024] :
( t(Vvar__var__var__var__var__var__18__y__28947__28949__29018__29020__29022__29024,Vvar__0__R__28847)
=> p(happ(happ(Vvar__7__req__28868,happ(Vvar__6__ropp__28865,happ(happ(Vvar__3__radd__28850,Vvar__var__var__var__var__var__17__x__28946__28948__29017__29019__29021__29023),Vvar__var__var__var__var__var__18__y__28947__28949__29018__29020__29022__29024))),happ(happ(Vvar__3__radd__28850,happ(Vvar__6__ropp__28865,Vvar__var__var__var__var__var__17__x__28946__28948__29017__29019__29021__29023)),happ(Vvar__6__ropp__28865,Vvar__var__var__var__var__var__18__y__28947__28949__29018__29020__29022__29024)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__28951__28953__29025__29027__29029__29031__29033] :
( t(Vvar__var__var__var__var__var__var__18__x__28951__28953__29025__29027__29029__29031__29033,Vvar__0__R__28847)
=> ! [Vvar__var__var__var__var__var__var__19__y__28952__28954__29026__29028__29030__29032__29034] :
( t(Vvar__var__var__var__var__var__var__19__y__28952__28954__29026__29028__29030__29032__29034,Vvar__0__R__28847)
=> p(happ(happ(Vvar__7__req__28868,happ(happ(Vvar__5__rsub__28860,Vvar__var__var__var__var__var__var__18__x__28951__28953__29025__29027__29029__29031__29033),Vvar__var__var__var__var__var__var__19__y__28952__28954__29026__29028__29030__29032__29034)),happ(happ(Vvar__3__radd__28850,Vvar__var__var__var__var__var__var__18__x__28951__28953__29025__29027__29029__29031__29033),happ(Vvar__6__ropp__28865,Vvar__var__var__var__var__var__var__19__y__28952__28954__29026__29028__29030__29032__29034)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__32827,Vvar__1__req__32828,Vvar__2__C__32833,Vvar__3__cadd__32834,Vvar__4__cmul__32839,Vvar__5__phi__32844,Vvar__6__cdiv__32847] :
( cType___24t(Vvar__0__R__32827)
=> ( c_24__type__32967___24t(Vvar__0__R__32827,Vvar__1__req__32828,Vvar__2__C__32833,Vvar__3__cadd__32834,Vvar__4__cmul__32839,Vvar__5__phi__32844,Vvar__6__cdiv__32847,Vvar__1__req__32828)
=> ( cType___24t(Vvar__2__C__32833)
=> ( c_24__type__33017___24t(Vvar__0__R__32827,Vvar__1__req__32828,Vvar__2__C__32833,Vvar__3__cadd__32834,Vvar__4__cmul__32839,Vvar__5__phi__32844,Vvar__6__cdiv__32847,Vvar__3__cadd__32834)
=> ( c_24__type__33067___24t(Vvar__0__R__32827,Vvar__1__req__32828,Vvar__2__C__32833,Vvar__3__cadd__32834,Vvar__4__cmul__32839,Vvar__5__phi__32844,Vvar__6__cdiv__32847,Vvar__4__cmul__32839)
=> ( c_24__type__33109___24t(Vvar__0__R__32827,Vvar__1__req__32828,Vvar__2__C__32833,Vvar__3__cadd__32834,Vvar__4__cmul__32839,Vvar__5__phi__32844,Vvar__6__cdiv__32847,Vvar__5__phi__32844)
=> ( c_24__type__33159___24t(Vvar__0__R__32827,Vvar__1__req__32828,Vvar__2__C__32833,Vvar__3__cadd__32834,Vvar__4__cmul__32839,Vvar__5__phi__32844,Vvar__6__cdiv__32847,Vvar__6__cdiv__32847)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__32827,Vvar__1__req__32828,Vvar__2__C__32833,Vvar__3__cadd__32834,Vvar__4__cmul__32839,Vvar__5__phi__32844,Vvar__6__cdiv__32847)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__32879__32884__32889__32894__32899__32904__32909__32914] :
( t(Vvar__var__var__var__var__var__var__var__7__a__32879__32884__32889__32894__32899__32904__32909__32914,Vvar__2__C__32833)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__32880__32885__32890__32895__32900__32905__32910__32915] :
( t(Vvar__var__var__var__var__var__var__var__8__b__32880__32885__32890__32895__32900__32905__32910__32915,Vvar__2__C__32833)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2433222___24a9(Vvar__0__R__32827,Vvar__1__req__32828,Vvar__2__C__32833,Vvar__3__cadd__32834,Vvar__4__cmul__32839,Vvar__5__phi__32844,Vvar__6__cdiv__32847,Vvar__var__var__var__var__var__var__var__7__a__32879__32884__32889__32894__32899__32904__32909__32914,Vvar__var__var__var__var__var__var__var__8__b__32880__32885__32890__32895__32900__32905__32910__32915) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__33262,Vvar__1__rI__33263,Vvar__2__rmul__33264,Vvar__3__req__33269,Vvar__4__Cpow__33274,Vvar__5__Cp__phi__33275,Vvar__6__rpow__33278] :
( cType___24t(Vvar__0__R__33262)
=> ( t(Vvar__1__rI__33263,Vvar__0__R__33262)
=> ( c_24__type__33364___24t(Vvar__0__R__33262,Vvar__1__rI__33263,Vvar__2__rmul__33264,Vvar__3__req__33269,Vvar__4__Cpow__33274,Vvar__5__Cp__phi__33275,Vvar__6__rpow__33278,Vvar__2__rmul__33264)
=> ( c_24__type__33408___24t(Vvar__0__R__33262,Vvar__1__rI__33263,Vvar__2__rmul__33264,Vvar__3__req__33269,Vvar__4__Cpow__33274,Vvar__5__Cp__phi__33275,Vvar__6__rpow__33278,Vvar__3__req__33269)
=> ( cType___24t(Vvar__4__Cpow__33274)
=> ( c_24__type__33444___24t(Vvar__0__R__33262,Vvar__1__rI__33263,Vvar__2__rmul__33264,Vvar__3__req__33269,Vvar__4__Cpow__33274,Vvar__5__Cp__phi__33275,Vvar__6__rpow__33278,Vvar__5__Cp__phi__33275)
=> ( c_24__type__33488___24t(Vvar__0__R__33262,Vvar__1__rI__33263,Vvar__2__rmul__33264,Vvar__3__req__33269,Vvar__4__Cpow__33274,Vvar__5__Cp__phi__33275,Vvar__6__rpow__33278,Vvar__6__rpow__33278)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__33262,Vvar__1__rI__33263,Vvar__2__rmul__33264,Vvar__3__req__33269,Vvar__4__Cpow__33274,Vvar__5__Cp__phi__33275,Vvar__6__rpow__33278)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__33306__33308__33310__33312__33314__33316__33318__33320] :
( t(Vvar__var__var__var__var__var__var__var__7__r__33306__33308__33310__33312__33314__33316__33318__33320,Vvar__0__R__33262)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__33307__33309__33311__33313__33315__33317__33319__33321] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__33307__33309__33311__33313__33315__33317__33319__33321)
=> p(happ(happ(Vvar__3__req__33269,happ(happ(Vvar__6__rpow__33278,Vvar__var__var__var__var__var__var__var__7__r__33306__33308__33310__33312__33314__33316__33318__33320),happ(Vvar__5__Cp__phi__33275,Vvar__var__var__var__var__var__var__var__8__n__33307__33309__33311__33313__33315__33317__33319__33321))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__33262,Vvar__1__rI__33263,Vvar__2__rmul__33264,Vvar__var__var__var__var__var__var__var__7__r__33306__33308__33310__33312__33314__33316__33318__33320,Vvar__var__var__var__var__var__var__var__8__n__33307__33309__33311__33313__33315__33317__33319__33321))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__29712,Vvar__1__radd__29713,Vvar__2__rmul__29718,Vvar__3__ropp__29723,Vvar__4__req__29726] :
( cType___24t(Vvar__0__R__29712)
=> ( c_24__type__29817___24t(Vvar__0__R__29712,Vvar__1__radd__29713,Vvar__2__rmul__29718,Vvar__3__ropp__29723,Vvar__4__req__29726,Vvar__1__radd__29713)
=> ( c_24__type__29847___24t(Vvar__0__R__29712,Vvar__1__radd__29713,Vvar__2__rmul__29718,Vvar__3__ropp__29723,Vvar__4__req__29726,Vvar__2__rmul__29718)
=> ( c_24__type__29871___24t(Vvar__0__R__29712,Vvar__1__radd__29713,Vvar__2__rmul__29718,Vvar__3__ropp__29723,Vvar__4__req__29726,Vvar__3__ropp__29723)
=> ( c_24__type__29901___24t(Vvar__0__R__29712,Vvar__1__radd__29713,Vvar__2__rmul__29718,Vvar__3__ropp__29723,Vvar__4__req__29726,Vvar__4__req__29726)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__29712,Vvar__1__radd__29713,Vvar__2__rmul__29718,Vvar__3__ropp__29723,Vvar__4__req__29726)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__29931___24a5(Vvar__0__R__29712,Vvar__1__radd__29713,Vvar__2__rmul__29718,Vvar__3__ropp__29723,Vvar__4__req__29726),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29712,c_24__type__29955___24a5(Vvar__0__R__29712,Vvar__1__radd__29713,Vvar__2__rmul__29718,Vvar__3__ropp__29723,Vvar__4__req__29726),Vvar__4__req__29726,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29712,Vvar__0__R__29712,Vvar__4__req__29726,Vvar__4__req__29726)),Vvar__1__radd__29713)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__29988___24a5(Vvar__0__R__29712,Vvar__1__radd__29713,Vvar__2__rmul__29718,Vvar__3__ropp__29723,Vvar__4__req__29726),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29712,c_24__type__30012___24a5(Vvar__0__R__29712,Vvar__1__radd__29713,Vvar__2__rmul__29718,Vvar__3__ropp__29723,Vvar__4__req__29726),Vvar__4__req__29726,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29712,Vvar__0__R__29712,Vvar__4__req__29726,Vvar__4__req__29726)),Vvar__2__rmul__29718)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30039___24a5(Vvar__0__R__29712,Vvar__1__radd__29713,Vvar__2__rmul__29718,Vvar__3__ropp__29723,Vvar__4__req__29726),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29712,Vvar__0__R__29712,Vvar__4__req__29726,Vvar__4__req__29726),Vvar__3__ropp__29723)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX121884] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX121884)
=> ( VX121884 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__121885] :
( cType___24t(Vvar__0__R__121885)
& ? [Vvar__1__req__121886] :
( c_24__type__646___24t(Vvar__0__R__121885,Vvar__1__req__121886)
& ? [Vvar__2__reqb__121891] :
( c_24__type__5381___24t(Vvar__0__R__121885,Vvar__2__reqb__121891)
& ! [Vvar__var__3__x__121897__121900] :
( t(Vvar__var__3__x__121897__121900,Vvar__0__R__121885)
=> ! [Vvar__var__4__y__121898__121901] :
( t(Vvar__var__4__y__121898__121901,Vvar__0__R__121885)
=> ( happ(happ(Vvar__2__reqb__121891,Vvar__var__3__x__121897__121900),Vvar__var__4__y__121898__121901) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__121886,Vvar__var__3__x__121897__121900),Vvar__var__4__y__121898__121901)) ) ) )
& VX121884 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__121885,Vvar__1__req__121886,Vvar__2__reqb__121891) ) ) )
| ? [Vvar__0__R__121903] :
( cType___24t(Vvar__0__R__121903)
& ? [Vvar__1__rO__121904] :
( t(Vvar__1__rO__121904,Vvar__0__R__121903)
& ? [Vvar__2__rI__121905] :
( t(Vvar__2__rI__121905,Vvar__0__R__121903)
& ? [Vvar__3__radd__121906] :
( c_24__type__2952___24t(Vvar__0__R__121903,Vvar__3__radd__121906)
& ? [Vvar__4__rmul__121911] :
( c_24__type__2952___24t(Vvar__0__R__121903,Vvar__4__rmul__121911)
& ? [Vvar__5__rsub__121916] :
( c_24__type__2952___24t(Vvar__0__R__121903,Vvar__5__rsub__121916)
& ? [Vvar__6__ropp__121921] :
( c_24__type__2961___24t(Vvar__0__R__121903,Vvar__6__ropp__121921)
& ? [Vvar__7__req__121924] :
( c_24__type__646___24t(Vvar__0__R__121903,Vvar__7__req__121924)
& ? [Vvar__8__C__121929] :
( cType___24t(Vvar__8__C__121929)
& ? [Vvar__9__cO__121930] :
( t(Vvar__9__cO__121930,Vvar__8__C__121929)
& ? [Vvar__10__cI__121931] :
( t(Vvar__10__cI__121931,Vvar__8__C__121929)
& ? [Vvar__11__cadd__121932] :
( c_24__type__7748___24t(Vvar__0__R__121903,Vvar__8__C__121929,Vvar__11__cadd__121932)
& ? [Vvar__12__cmul__121937] :
( c_24__type__7748___24t(Vvar__0__R__121903,Vvar__8__C__121929,Vvar__12__cmul__121937)
& ? [Vvar__13__csub__121942] :
( c_24__type__7748___24t(Vvar__0__R__121903,Vvar__8__C__121929,Vvar__13__csub__121942)
& ? [Vvar__14__copp__121947] :
( c_24__type__4143___24t(Vvar__0__R__121903,Vvar__8__C__121929,Vvar__14__copp__121947)
& ? [Vvar__15__ceqb__121950] :
( c_24__type__7767___24t(Vvar__0__R__121903,Vvar__8__C__121929,Vvar__15__ceqb__121950)
& ? [Vvar__16__phi__121955] :
( c_24__type__2968___24t(Vvar__0__R__121903,Vvar__8__C__121929,Vvar__16__phi__121955)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__121903,Vvar__1__rO__121904,Vvar__2__rI__121905,Vvar__3__radd__121906,Vvar__4__rmul__121911,Vvar__5__rsub__121916,Vvar__6__ropp__121921,Vvar__7__req__121924,Vvar__8__C__121929,Vvar__9__cO__121930,Vvar__10__cI__121931,Vvar__11__cadd__121932,Vvar__12__cmul__121937,Vvar__13__csub__121942,Vvar__14__copp__121947,Vvar__15__ceqb__121950,Vvar__16__phi__121955)
& VX121884 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__121903,Vvar__1__rO__121904,Vvar__2__rI__121905,Vvar__3__radd__121906,Vvar__4__rmul__121911,Vvar__5__rsub__121916,Vvar__6__ropp__121921,Vvar__7__req__121924,Vvar__8__C__121929,Vvar__9__cO__121930,Vvar__10__cI__121931,Vvar__11__cadd__121932,Vvar__12__cmul__121937,Vvar__13__csub__121942,Vvar__14__copp__121947,Vvar__15__ceqb__121950,Vvar__16__phi__121955) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148] :
( cType___24t(Vvar__0__R__30096)
=> ( t(Vvar__1__rO__30097,Vvar__0__R__30096)
=> ( t(Vvar__2__rI__30098,Vvar__0__R__30096)
=> ( c_24__type__30492___24t(Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148,Vvar__3__radd__30099)
=> ( c_24__type__30705___24t(Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148,Vvar__4__rmul__30104)
=> ( c_24__type__30918___24t(Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148,Vvar__5__rsub__30109)
=> ( c_24__type__31113___24t(Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148,Vvar__6__ropp__30114)
=> ( c_24__type__31326___24t(Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148,Vvar__7__req__30117)
=> ( cType___24t(Vvar__8__C__30122)
=> ( t(Vvar__9__cO__30123,Vvar__8__C__30122)
=> ( t(Vvar__10__cI__30124,Vvar__8__C__30122)
=> ( c_24__type__31539___24t(Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148,Vvar__11__cadd__30125)
=> ( c_24__type__31752___24t(Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148,Vvar__12__cmul__30130)
=> ( c_24__type__31965___24t(Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148,Vvar__13__csub__30135)
=> ( c_24__type__32160___24t(Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148,Vvar__14__copp__30140)
=> ( c_24__type__32373___24t(Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148,Vvar__15__ceqb__30143)
=> ( c_24__type__32568___24t(Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148,Vvar__16__phi__30148)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__30096,Vvar__1__rO__30097,Vvar__2__rI__30098,Vvar__3__radd__30099,Vvar__4__rmul__30104,Vvar__5__rsub__30109,Vvar__6__ropp__30114,Vvar__7__req__30117,Vvar__8__C__30122,Vvar__9__cO__30123,Vvar__10__cI__30124,Vvar__11__cadd__30125,Vvar__12__cmul__30130,Vvar__13__csub__30135,Vvar__14__copp__30140,Vvar__15__ceqb__30143,Vvar__16__phi__30148)
=> ( p(happ(happ(Vvar__7__req__30117,happ(Vvar__16__phi__30148,Vvar__9__cO__30123)),Vvar__1__rO__30097))
& p(happ(happ(Vvar__7__req__30117,happ(Vvar__16__phi__30148,Vvar__10__cI__30124)),Vvar__2__rI__30098))
& ! [Vvar__var__var__var__var__var__var__19__x__30210__30212__30234__30236__30238__30240__30242] :
( t(Vvar__var__var__var__var__var__var__19__x__30210__30212__30234__30236__30238__30240__30242,Vvar__8__C__30122)
=> ! [Vvar__var__var__var__var__var__var__20__y__30211__30213__30235__30237__30239__30241__30243] :
( t(Vvar__var__var__var__var__var__var__20__y__30211__30213__30235__30237__30239__30241__30243,Vvar__8__C__30122)
=> p(happ(happ(Vvar__7__req__30117,happ(Vvar__16__phi__30148,happ(happ(Vvar__11__cadd__30125,Vvar__var__var__var__var__var__var__19__x__30210__30212__30234__30236__30238__30240__30242),Vvar__var__var__var__var__var__var__20__y__30211__30213__30235__30237__30239__30241__30243))),happ(happ(Vvar__3__radd__30099,happ(Vvar__16__phi__30148,Vvar__var__var__var__var__var__var__19__x__30210__30212__30234__30236__30238__30240__30242)),happ(Vvar__16__phi__30148,Vvar__var__var__var__var__var__var__20__y__30211__30213__30235__30237__30239__30241__30243)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__30215__30217__30244__30246__30248__30250__30252] :
( t(Vvar__var__var__var__var__var__var__20__x__30215__30217__30244__30246__30248__30250__30252,Vvar__8__C__30122)
=> ! [Vvar__var__var__var__var__var__var__21__y__30216__30218__30245__30247__30249__30251__30253] :
( t(Vvar__var__var__var__var__var__var__21__y__30216__30218__30245__30247__30249__30251__30253,Vvar__8__C__30122)
=> p(happ(happ(Vvar__7__req__30117,happ(Vvar__16__phi__30148,happ(happ(Vvar__13__csub__30135,Vvar__var__var__var__var__var__var__20__x__30215__30217__30244__30246__30248__30250__30252),Vvar__var__var__var__var__var__var__21__y__30216__30218__30245__30247__30249__30251__30253))),happ(happ(Vvar__5__rsub__30109,happ(Vvar__16__phi__30148,Vvar__var__var__var__var__var__var__20__x__30215__30217__30244__30246__30248__30250__30252)),happ(Vvar__16__phi__30148,Vvar__var__var__var__var__var__var__21__y__30216__30218__30245__30247__30249__30251__30253)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__30220__30222__30254__30256__30258__30260__30262] :
( t(Vvar__var__var__var__var__var__var__21__x__30220__30222__30254__30256__30258__30260__30262,Vvar__8__C__30122)
=> ! [Vvar__var__var__var__var__var__var__22__y__30221__30223__30255__30257__30259__30261__30263] :
( t(Vvar__var__var__var__var__var__var__22__y__30221__30223__30255__30257__30259__30261__30263,Vvar__8__C__30122)
=> p(happ(happ(Vvar__7__req__30117,happ(Vvar__16__phi__30148,happ(happ(Vvar__12__cmul__30130,Vvar__var__var__var__var__var__var__21__x__30220__30222__30254__30256__30258__30260__30262),Vvar__var__var__var__var__var__var__22__y__30221__30223__30255__30257__30259__30261__30263))),happ(happ(Vvar__4__rmul__30104,happ(Vvar__16__phi__30148,Vvar__var__var__var__var__var__var__21__x__30220__30222__30254__30256__30258__30260__30262)),happ(Vvar__16__phi__30148,Vvar__var__var__var__var__var__var__22__y__30221__30223__30255__30257__30259__30261__30263)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__30225__30226__30264__30265__30266__30267__30268] :
( t(Vvar__var__var__var__var__var__var__22__x__30225__30226__30264__30265__30266__30267__30268,Vvar__8__C__30122)
=> p(happ(happ(Vvar__7__req__30117,happ(Vvar__16__phi__30148,happ(Vvar__14__copp__30140,Vvar__var__var__var__var__var__var__22__x__30225__30226__30264__30265__30266__30267__30268))),happ(Vvar__6__ropp__30114,happ(Vvar__16__phi__30148,Vvar__var__var__var__var__var__var__22__x__30225__30226__30264__30265__30266__30267__30268)))) )
& ! [Vvar__var__var__var__var__var__23__x__30228__30231__30269__30272__30275__30278] :
( t(Vvar__var__var__var__var__var__23__x__30228__30231__30269__30272__30275__30278,Vvar__8__C__30122)
=> ! [Vvar__var__var__var__var__var__24__y__30229__30232__30270__30273__30276__30279] :
( t(Vvar__var__var__var__var__var__24__y__30229__30232__30270__30273__30276__30279,Vvar__8__C__30122)
=> ( happ(happ(Vvar__15__ceqb__30143,Vvar__var__var__var__var__var__23__x__30228__30231__30269__30272__30275__30278),Vvar__var__var__var__var__var__24__y__30229__30232__30270__30273__30276__30279) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__30117,happ(Vvar__16__phi__30148,Vvar__var__var__var__var__var__23__x__30228__30231__30269__30272__30275__30278)),happ(Vvar__16__phi__30148,Vvar__var__var__var__var__var__24__y__30229__30232__30270__30273__30276__30279))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__120886,Vvar__1__rO__120887,Vvar__2__rI__120888,Vvar__3__radd__120889,Vvar__4__rmul__120894,Vvar__5__req__120899,Vvar__6__C__120904,Vvar__7__cO__120905,Vvar__8__cI__120906,Vvar__9__cadd__120907,Vvar__10__cmul__120912,Vvar__11__ceqb__120917,Vvar__12__phi__120922] :
( cType___24t(Vvar__0__R__120886)
=> ( t(Vvar__1__rO__120887,Vvar__0__R__120886)
=> ( t(Vvar__2__rI__120888,Vvar__0__R__120886)
=> ( c_24__type__121139___24t(Vvar__0__R__120886,Vvar__1__rO__120887,Vvar__2__rI__120888,Vvar__3__radd__120889,Vvar__4__rmul__120894,Vvar__5__req__120899,Vvar__6__C__120904,Vvar__7__cO__120905,Vvar__8__cI__120906,Vvar__9__cadd__120907,Vvar__10__cmul__120912,Vvar__11__ceqb__120917,Vvar__12__phi__120922,Vvar__3__radd__120889)
=> ( c_24__type__121264___24t(Vvar__0__R__120886,Vvar__1__rO__120887,Vvar__2__rI__120888,Vvar__3__radd__120889,Vvar__4__rmul__120894,Vvar__5__req__120899,Vvar__6__C__120904,Vvar__7__cO__120905,Vvar__8__cI__120906,Vvar__9__cadd__120907,Vvar__10__cmul__120912,Vvar__11__ceqb__120917,Vvar__12__phi__120922,Vvar__4__rmul__120894)
=> ( c_24__type__121389___24t(Vvar__0__R__120886,Vvar__1__rO__120887,Vvar__2__rI__120888,Vvar__3__radd__120889,Vvar__4__rmul__120894,Vvar__5__req__120899,Vvar__6__C__120904,Vvar__7__cO__120905,Vvar__8__cI__120906,Vvar__9__cadd__120907,Vvar__10__cmul__120912,Vvar__11__ceqb__120917,Vvar__12__phi__120922,Vvar__5__req__120899)
=> ( cType___24t(Vvar__6__C__120904)
=> ( t(Vvar__7__cO__120905,Vvar__6__C__120904)
=> ( t(Vvar__8__cI__120906,Vvar__6__C__120904)
=> ( c_24__type__121514___24t(Vvar__0__R__120886,Vvar__1__rO__120887,Vvar__2__rI__120888,Vvar__3__radd__120889,Vvar__4__rmul__120894,Vvar__5__req__120899,Vvar__6__C__120904,Vvar__7__cO__120905,Vvar__8__cI__120906,Vvar__9__cadd__120907,Vvar__10__cmul__120912,Vvar__11__ceqb__120917,Vvar__12__phi__120922,Vvar__9__cadd__120907)
=> ( c_24__type__121639___24t(Vvar__0__R__120886,Vvar__1__rO__120887,Vvar__2__rI__120888,Vvar__3__radd__120889,Vvar__4__rmul__120894,Vvar__5__req__120899,Vvar__6__C__120904,Vvar__7__cO__120905,Vvar__8__cI__120906,Vvar__9__cadd__120907,Vvar__10__cmul__120912,Vvar__11__ceqb__120917,Vvar__12__phi__120922,Vvar__10__cmul__120912)
=> ( c_24__type__121764___24t(Vvar__0__R__120886,Vvar__1__rO__120887,Vvar__2__rI__120888,Vvar__3__radd__120889,Vvar__4__rmul__120894,Vvar__5__req__120899,Vvar__6__C__120904,Vvar__7__cO__120905,Vvar__8__cI__120906,Vvar__9__cadd__120907,Vvar__10__cmul__120912,Vvar__11__ceqb__120917,Vvar__12__phi__120922,Vvar__11__ceqb__120917)
=> ( c_24__type__121875___24t(Vvar__0__R__120886,Vvar__1__rO__120887,Vvar__2__rI__120888,Vvar__3__radd__120889,Vvar__4__rmul__120894,Vvar__5__req__120899,Vvar__6__C__120904,Vvar__7__cO__120905,Vvar__8__cI__120906,Vvar__9__cadd__120907,Vvar__10__cmul__120912,Vvar__11__ceqb__120917,Vvar__12__phi__120922,Vvar__12__phi__120922)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__120886,Vvar__1__rO__120887,Vvar__2__rI__120888,Vvar__3__radd__120889,Vvar__4__rmul__120894,Vvar__5__req__120899,Vvar__6__C__120904,Vvar__7__cO__120905,Vvar__8__cI__120906,Vvar__9__cadd__120907,Vvar__10__cmul__120912,Vvar__11__ceqb__120917,Vvar__12__phi__120922)
=> ( p(happ(happ(Vvar__5__req__120899,happ(Vvar__12__phi__120922,Vvar__7__cO__120905)),Vvar__1__rO__120887))
& p(happ(happ(Vvar__5__req__120899,happ(Vvar__12__phi__120922,Vvar__8__cI__120906)),Vvar__2__rI__120888))
& ! [Vvar__var__var__var__var__var__var__15__x__120968__120970__120984__120986__120988__120990__120992] :
( t(Vvar__var__var__var__var__var__var__15__x__120968__120970__120984__120986__120988__120990__120992,Vvar__6__C__120904)
=> ! [Vvar__var__var__var__var__var__var__16__y__120969__120971__120985__120987__120989__120991__120993] :
( t(Vvar__var__var__var__var__var__var__16__y__120969__120971__120985__120987__120989__120991__120993,Vvar__6__C__120904)
=> p(happ(happ(Vvar__5__req__120899,happ(Vvar__12__phi__120922,happ(happ(Vvar__9__cadd__120907,Vvar__var__var__var__var__var__var__15__x__120968__120970__120984__120986__120988__120990__120992),Vvar__var__var__var__var__var__var__16__y__120969__120971__120985__120987__120989__120991__120993))),happ(happ(Vvar__3__radd__120889,happ(Vvar__12__phi__120922,Vvar__var__var__var__var__var__var__15__x__120968__120970__120984__120986__120988__120990__120992)),happ(Vvar__12__phi__120922,Vvar__var__var__var__var__var__var__16__y__120969__120971__120985__120987__120989__120991__120993)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__120973__120975__120994__120996__120998__121000__121002] :
( t(Vvar__var__var__var__var__var__var__16__x__120973__120975__120994__120996__120998__121000__121002,Vvar__6__C__120904)
=> ! [Vvar__var__var__var__var__var__var__17__y__120974__120976__120995__120997__120999__121001__121003] :
( t(Vvar__var__var__var__var__var__var__17__y__120974__120976__120995__120997__120999__121001__121003,Vvar__6__C__120904)
=> p(happ(happ(Vvar__5__req__120899,happ(Vvar__12__phi__120922,happ(happ(Vvar__10__cmul__120912,Vvar__var__var__var__var__var__var__16__x__120973__120975__120994__120996__120998__121000__121002),Vvar__var__var__var__var__var__var__17__y__120974__120976__120995__120997__120999__121001__121003))),happ(happ(Vvar__4__rmul__120894,happ(Vvar__12__phi__120922,Vvar__var__var__var__var__var__var__16__x__120973__120975__120994__120996__120998__121000__121002)),happ(Vvar__12__phi__120922,Vvar__var__var__var__var__var__var__17__y__120974__120976__120995__120997__120999__121001__121003)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__120978__120981__121004__121007__121010__121013] :
( t(Vvar__var__var__var__var__var__17__x__120978__120981__121004__121007__121010__121013,Vvar__6__C__120904)
=> ! [Vvar__var__var__var__var__var__18__y__120979__120982__121005__121008__121011__121014] :
( t(Vvar__var__var__var__var__var__18__y__120979__120982__121005__121008__121011__121014,Vvar__6__C__120904)
=> ( happ(happ(Vvar__11__ceqb__120917,Vvar__var__var__var__var__var__17__x__120978__120981__121004__121007__121010__121013),Vvar__var__var__var__var__var__18__y__120979__120982__121005__121008__121011__121014) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__120899,happ(Vvar__12__phi__120922,Vvar__var__var__var__var__var__17__x__120978__120981__121004__121007__121010__121013)),happ(Vvar__12__phi__120922,Vvar__var__var__var__var__var__18__y__120979__120982__121005__121008__121011__121014))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__32728,Vvar__1__copp__32729,Vvar__2__ceqb__32732,Vvar__3__get__sign__32737] :
( cType___24t(Vvar__0__C__32728)
=> ( c_24__type__32784___24t(Vvar__0__C__32728,Vvar__1__copp__32729,Vvar__2__ceqb__32732,Vvar__3__get__sign__32737,Vvar__1__copp__32729)
=> ( c_24__type__32803___24t(Vvar__0__C__32728,Vvar__1__copp__32729,Vvar__2__ceqb__32732,Vvar__3__get__sign__32737,Vvar__2__ceqb__32732)
=> ( c_24__type__32817___24t(Vvar__0__C__32728,Vvar__1__copp__32729,Vvar__2__ceqb__32732,Vvar__3__get__sign__32737,Vvar__3__get__sign__32737)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__32728,Vvar__1__copp__32729,Vvar__2__ceqb__32732,Vvar__3__get__sign__32737)
=> ( ! [Vvar__var__var__var__var__var__4__c__32754__32757__32760__32763__32766__32769] :
( t(Vvar__var__var__var__var__var__4__c__32754__32757__32760__32763__32766__32769,Vvar__0__C__32728)
=> ! [Vvar__var__var__var__var__var__5__c_27__32755__32758__32761__32764__32767__32770] :
( t(Vvar__var__var__var__var__var__5__c_27__32755__32758__32761__32764__32767__32770,Vvar__0__C__32728)
=> ( happ(Vvar__3__get__sign__32737,Vvar__var__var__var__var__var__4__c__32754__32757__32760__32763__32766__32769) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__32728,Vvar__var__var__var__var__var__5__c_27__32755__32758__32761__32764__32767__32770)
=> happ(happ(Vvar__2__ceqb__32732,Vvar__var__var__var__var__var__4__c__32754__32757__32760__32763__32766__32769),happ(Vvar__1__copp__32729,Vvar__var__var__var__var__var__5__c_27__32755__32758__32761__32764__32767__32770)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__29467,Vvar__1__radd__29468,Vvar__2__rmul__29473,Vvar__3__req__29478] :
( cType___24t(Vvar__0__R__29467)
=> ( c_24__type__29553___24t(Vvar__0__R__29467,Vvar__1__radd__29468,Vvar__2__rmul__29473,Vvar__3__req__29478,Vvar__1__radd__29468)
=> ( c_24__type__29576___24t(Vvar__0__R__29467,Vvar__1__radd__29468,Vvar__2__rmul__29473,Vvar__3__req__29478,Vvar__2__rmul__29473)
=> ( c_24__type__29599___24t(Vvar__0__R__29467,Vvar__1__radd__29468,Vvar__2__rmul__29473,Vvar__3__req__29478,Vvar__3__req__29478)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__29467,Vvar__1__radd__29468,Vvar__2__rmul__29473,Vvar__3__req__29478)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__29622___24a4(Vvar__0__R__29467,Vvar__1__radd__29468,Vvar__2__rmul__29473,Vvar__3__req__29478),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29467,c_24__type__29640___24a4(Vvar__0__R__29467,Vvar__1__radd__29468,Vvar__2__rmul__29473,Vvar__3__req__29478),Vvar__3__req__29478,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29467,Vvar__0__R__29467,Vvar__3__req__29478,Vvar__3__req__29478)),Vvar__1__radd__29468)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__29666___24a4(Vvar__0__R__29467,Vvar__1__radd__29468,Vvar__2__rmul__29473,Vvar__3__req__29478),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29467,c_24__type__29684___24a4(Vvar__0__R__29467,Vvar__1__radd__29468,Vvar__2__rmul__29473,Vvar__3__req__29478),Vvar__3__req__29478,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29467,Vvar__0__R__29467,Vvar__3__req__29478,Vvar__3__req__29478)),Vvar__2__rmul__29473)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_ExtLib.Core.RelDec.RelDec',axiom,
! [Vvar__0__T__120474,Vvar__1__equ__120475,VX120480] :
( cType___24t(Vvar__0__T__120474)
=> ( c_24__type__120501___24t(Vvar__0__T__120474,Vvar__1__equ__120475,Vvar__1__equ__120475)
=> ( cExtLib_2eCore_2eRelDec_2eRelDec___24t(Vvar__0__T__120474,Vvar__1__equ__120475,VX120480)
=> ? [Vvar__2__rel__dec__120487] :
( c_24__type__120510___24t(Vvar__0__T__120474,Vvar__1__equ__120475,Vvar__2__rel__dec__120487)
& VX120480 = cExtLib_2eCore_2eRelDec_2eBuild__RelDec___24a3(Vvar__0__T__120474,Vvar__1__equ__120475,Vvar__2__rel__dec__120487) ) ) ) ) ).
fof('$_inversion_ExtLib.Data.Member.member',axiom,
! [Vvar__0__T__17506,Vvar__1__a__17507,Vvar__2___24Anonymous__17508,VX17509] :
( cType___24t(Vvar__0__T__17506)
=> ( t(Vvar__1__a__17507,Vvar__0__T__17506)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__17506,Vvar__2___24Anonymous__17508)
=> ( cExtLib_2eData_2eMember_2emember___24t(Vvar__0__T__17506,Vvar__1__a__17507,Vvar__2___24Anonymous__17508,VX17509)
=> ( ? [Vvar__2__ls__17512] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__17506,Vvar__2__ls__17512)
& Vvar__2___24Anonymous__17508 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__17506,Vvar__1__a__17507,Vvar__2__ls__17512)
& VX17509 = cExtLib_2eData_2eMember_2eMZ___24a3(Vvar__0__T__17506,Vvar__1__a__17507,Vvar__2__ls__17512) )
| ? [Vvar__2__l__17515] :
( t(Vvar__2__l__17515,Vvar__0__T__17506)
& ? [Vvar__3__ls__17516] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__17506,Vvar__3__ls__17516)
& ? [Vvar__4___24Anonymous__17517] :
( cExtLib_2eData_2eMember_2emember___24t(Vvar__0__T__17506,Vvar__1__a__17507,Vvar__3__ls__17516,Vvar__4___24Anonymous__17517)
& Vvar__2___24Anonymous__17508 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__17506,Vvar__2__l__17515,Vvar__3__ls__17516)
& VX17509 = cExtLib_2eData_2eMember_2eMN___24a5(Vvar__0__T__17506,Vvar__1__a__17507,Vvar__2__l__17515,Vvar__3__ls__17516,Vvar__4___24Anonymous__17517) ) ) ) ) ) ) ) ) ).
fof('$_inversion_ExtLib.Tactics.Injection.Injective',axiom,
! [Vvar__0__P__15441,VX15442] :
( cProp___24t(Vvar__0__P__15441)
=> ( cExtLib_2eTactics_2eInjection_2eInjective___24t(Vvar__0__P__15441,VX15442)
=> ? [Vvar__1__result__15444] :
( cProp___24t(Vvar__1__result__15444)
& ( p(Vvar__0__P__15441)
=> p(Vvar__1__result__15444) )
& VX15442 = cExtLib_2eTactics_2eInjection_2eBuild__Injective___24a2(Vvar__0__P__15441,Vvar__1__result__15444) ) ) ) ).
fof('$_inversion_HList.hlist.equiv_hlist',axiom,
! [Vvar__0__eqv__126720,Vvar__1__ls__126722,Vvar__2___24Anonymous__126723,Vvar__3___24Anonymous__126724] :
( c_24__type__126742___24t(Vvar__0__eqv__126720,Vvar__1__ls__126722,Vvar__2___24Anonymous__126723,Vvar__3___24Anonymous__126724,Vvar__0__eqv__126720)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vvar__1__ls__126722)
=> ( cHList_2ehlist_2ehlist___24t(Vvar__1__ls__126722,Vvar__2___24Anonymous__126723)
=> ( cHList_2ehlist_2ehlist___24t(Vvar__1__ls__126722,Vvar__3___24Anonymous__126724)
=> ( p(cHList_2ehlist_2eequiv__hlist___24a4(Vvar__0__eqv__126720,Vvar__1__ls__126722,Vvar__2___24Anonymous__126723,Vvar__3___24Anonymous__126724))
=> ( ( Vvar__3___24Anonymous__126724 = cHList_2ehlist_2eHnil
& Vvar__2___24Anonymous__126723 = cHList_2ehlist_2eHnil
& Vvar__1__ls__126722 = cCoq_2eInit_2eDatatypes_2enil___24a1(ciT) )
| ? [Vvar__1__l__126730] :
( ciT___24t(Vvar__1__l__126730)
& ? [Vvar__2__ls__126731] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vvar__2__ls__126731)
& ? [Vvar__3__x__126732] :
( cF___24t(Vvar__1__l__126730,Vvar__3__x__126732)
& ? [Vvar__4__y__126733] :
( cF___24t(Vvar__1__l__126730,Vvar__4__y__126733)
& ? [Vvar__5__h1__126734] :
( cHList_2ehlist_2ehlist___24t(Vvar__2__ls__126731,Vvar__5__h1__126734)
& ? [Vvar__6__h2__126735] :
( cHList_2ehlist_2ehlist___24t(Vvar__2__ls__126731,Vvar__6__h2__126735)
& p(happ(happ(happ(Vvar__0__eqv__126720,Vvar__1__l__126730),Vvar__3__x__126732),Vvar__4__y__126733))
& p(cHList_2ehlist_2eequiv__hlist___24a4(Vvar__0__eqv__126720,Vvar__2__ls__126731,Vvar__5__h1__126734,Vvar__6__h2__126735))
& Vvar__3___24Anonymous__126724 = cHList_2ehlist_2eHcons___24a4(Vvar__1__l__126730,Vvar__2__ls__126731,Vvar__4__y__126733,Vvar__6__h2__126735)
& Vvar__2___24Anonymous__126723 = cHList_2ehlist_2eHcons___24a4(Vvar__1__l__126730,Vvar__2__ls__126731,Vvar__3__x__126732,Vvar__5__h1__126734)
& Vvar__1__ls__126722 = cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,Vvar__1__l__126730,Vvar__2__ls__126731) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_HList.hlist.hlist',axiom,
! [Vvar__0___24Anonymous__46660,VX46661] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vvar__0___24Anonymous__46660)
=> ( cHList_2ehlist_2ehlist___24t(Vvar__0___24Anonymous__46660,VX46661)
=> ( ( Vvar__0___24Anonymous__46660 = cCoq_2eInit_2eDatatypes_2enil___24a1(ciT)
& VX46661 = cHList_2ehlist_2eHnil )
| ? [Vvar__0__l__46662] :
( ciT___24t(Vvar__0__l__46662)
& ? [Vvar__1__ls__46663] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vvar__1__ls__46663)
& ? [Vvar__2___24Anonymous__46664] :
( cF___24t(Vvar__0__l__46662,Vvar__2___24Anonymous__46664)
& ? [Vvar__3___24Anonymous__46665] :
( cHList_2ehlist_2ehlist___24t(Vvar__1__ls__46663,Vvar__3___24Anonymous__46665)
& Vvar__0___24Anonymous__46660 = cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,Vvar__0__l__46662,Vvar__1__ls__46663)
& VX46661 = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46662,Vvar__1__ls__46663,Vvar__2___24Anonymous__46664,Vvar__3___24Anonymous__46665) ) ) ) ) ) ) ) ).
fof('$_lam_126658',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__126658___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eLogic_2eproj2___24a3(c_24__prop__126659___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6),c_24__prop__126660___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6),cHList_2ehlist_2eequiv__hlist__app___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)) ).
fof('$_lam_15512',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__15512___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),c_24__lam__15516___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_15516',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__15516___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ).
fof('$_lam_16626',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__16626___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_16646',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__16646___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__4,happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_lam_16675',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__16675___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__4),Vv__CANONICAL__3) ).
fof('$_lam_17884',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__17884___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(c_24False) ) ).
fof('$_lam_17912',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__17912___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( ( Vv__CANONICAL__2 = Vv__CANONICAL__1
& Vv__CANONICAL__4 = c_24__generic__case__17922 )
| ? [Vv__CANONICAL__5] :
( cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__5)
& Vv__CANONICAL__4 = cExtLib_2eData_2eMember_2eMN___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5) ) ) ) ).
fof('$_lam_2042',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__2042___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esig___24a2(Vv__CANONICAL__0,c_24__lam__2046___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_2046',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__2046___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('$_lam_24987',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11] : c_24__lam__24987___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11) = c_24__let__11__subst__l__24915___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__11)) ).
fof('$_lam_34898',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__34898___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__type__34907___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_34917',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__34917___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ).
fof('$_lam_34982',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__34982___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eLogic_2eand__rect___24a5(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5),cCoq_2eLists_2eList_2eForall___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)),c_24__lam__35023___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6),cCoq_2eSorting_2eSorted_2eStronglySorted__inv___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_35023',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__35023___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6) ).
fof('$_lam_38194',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__38194___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_38202',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__38202___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_46511',axiom,
! [Vv__CANONICAL__0] : c_24__lam__46511___24a1(Vv__CANONICAL__0) = cHList_2ehlist_2eHnil ).
fof('$_lam_46514',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__46514___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cHList_2ehlist_2eHcons___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cHList_2ehlist_2ehlist__hd___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),cHList_2ehlist_2ehlist__tl___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_47639',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__47639___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_47646',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__47646___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cHList_2ehlist_2eHcons___24a4(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eapp___24a3(ciT,Vv__CANONICAL__3,Vv__CANONICAL__1),Vv__CANONICAL__4,cHList_2ehlist_2ehlist__app___24a4(Vv__CANONICAL__3,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__6)) ).
fof('$_lam_48310',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__48310___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = c_24__generic__case__48326___24a1(cHList_2ehlist_2ehlist__rev_27___24a4(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__5,cHList_2ehlist_2eHcons___24a4(Vv__CANONICAL__2,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__6))) ).
fof('$_prop_116340',axiom,
! [Vvar__0___24Anonymous__116316,Vvar__0__S__116318,Vvar__1__x__116319,Vvar__2__y__116320] :
( p(c_24__prop__116340___24a4(Vvar__0___24Anonymous__116316,Vvar__0__S__116318,Vvar__1__x__116319,Vvar__2__y__116320))
<=> Vvar__1__x__116319 = Vvar__2__y__116320 ) ).
fof('$_prop_116341',axiom,
! [Vvar__0___24Anonymous__116316,Vvar__0__x__116321,Vvar__1__y__116322] :
( p(c_24__prop__116341___24a3(Vvar__0___24Anonymous__116316,Vvar__0__x__116321,Vvar__1__y__116322))
<=> Vvar__0__x__116321 = Vvar__1__y__116322 ) ).
fof('$_prop_116342',axiom,
! [Vvar__0___24Anonymous__116316,Vvar__0__x__116323,Vvar__1__s__116324] :
( p(c_24__prop__116342___24a3(Vvar__0___24Anonymous__116316,Vvar__0__x__116323,Vvar__1__s__116324))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__116323,Vvar__1__s__116324) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_116343',axiom,
! [Vvar__0___24Anonymous__116316,Vvar__0__P__116325,Vvar__1__Q__116326] :
( p(c_24__prop__116343___24a3(Vvar__0___24Anonymous__116316,Vvar__0__P__116325,Vvar__1__Q__116326))
<=> ( p(Vvar__0__P__116325)
& p(Vvar__1__Q__116326) ) ) ).
fof('$_prop_116344',axiom,
! [Vvar__0___24Anonymous__116316,Vvar__0__P__116329,Vvar__1__Q__116330] :
( p(c_24__prop__116344___24a3(Vvar__0___24Anonymous__116316,Vvar__0__P__116329,Vvar__1__Q__116330))
<=> ( p(Vvar__0__P__116329)
| p(Vvar__1__Q__116330) ) ) ).
fof('$_prop_116345',axiom,
! [Vvar__0___24Anonymous__116316,Vvar__0__P__116333,Vvar__1__Q__116334] :
( p(c_24__prop__116345___24a3(Vvar__0___24Anonymous__116316,Vvar__0__P__116333,Vvar__1__Q__116334))
<=> ( p(Vvar__0__P__116333)
=> p(Vvar__1__Q__116334) ) ) ).
fof('$_prop_116346',axiom,
! [Vvar__0___24Anonymous__116316,Vvar__0__P__116338] :
( p(c_24__prop__116346___24a2(Vvar__0___24Anonymous__116316,Vvar__0__P__116338))
<=> ~ p(Vvar__0__P__116338) ) ).
fof('$_prop_122450',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__122450___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_126634',axiom,
! [V0__eqv,V1__a,V2__b,V3__c,V4__c_27,V5__d,V6__d_27] :
( p(c_24__prop__126634___24a7(V0__eqv,V1__a,V2__b,V3__c,V4__c_27,V5__d,V6__d_27))
<=> ( p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,V1__a,V3__c,V4__c_27))
& p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,V2__b,V5__d,V6__d_27)) ) ) ).
fof('$_prop_126659',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( p(c_24__prop__126659___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6))
<=> ( ( p(cHList_2ehlist_2eequiv__hlist___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))
& p(cHList_2ehlist_2eequiv__hlist___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__5,Vv__CANONICAL__6)) )
=> p(cHList_2ehlist_2eequiv__hlist___24a4(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(ciT,Vv__CANONICAL__1,Vv__CANONICAL__2),cHList_2ehlist_2ehlist__app___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5),cHList_2ehlist_2ehlist__app___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__6))) ) ) ).
fof('$_prop_126660',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( p(c_24__prop__126660___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6))
<=> ( p(cHList_2ehlist_2eequiv__hlist___24a4(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(ciT,Vv__CANONICAL__1,Vv__CANONICAL__2),cHList_2ehlist_2ehlist__app___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5),cHList_2ehlist_2ehlist__app___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__6)))
=> ( p(cHList_2ehlist_2eequiv__hlist___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))
& p(cHList_2ehlist_2eequiv__hlist___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__5,Vv__CANONICAL__6)) ) ) ) ).
fof('$_prop_126684',axiom,
! [V0__eqv,V1__ls,V2__i,V3__a,V4__b,V5__c,V6__d] :
( p(c_24__prop__126684___24a7(V0__eqv,V1__ls,V2__i,V3__a,V4__b,V5__c,V6__d))
<=> ( p(happ(happ(happ(V0__eqv,V2__i),V3__a),V4__b))
& p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,V1__ls,V5__c,V6__d)) ) ) ).
fof('$_prop_15517',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__15517___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0) ) ).
fof('$_prop_15623',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__15623___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__2 ) ).
fof('$_prop_15624',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__15624___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__2 ) ).
fof('$_prop_15659',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__15659___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> cCoq_2eLists_2eList_2enth___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ).
fof('$_prop_15696',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__15676] :
( p(c_24__prop__15696___24a3(V0__A,V3__x,Vvar__1___24Anonymous__15676))
<=> V3__x = Vvar__1___24Anonymous__15676 ) ).
fof('$_prop_15697',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__15676] :
( p(c_24__prop__15697___24a3(V0__A,V3__x,Vvar__1___24Anonymous__15676))
<=> V3__x != Vvar__1___24Anonymous__15676 ) ).
fof('$_prop_15698',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__15676] :
( p(c_24__prop__15698___24a3(V0__A,V3__x,Vvar__1___24Anonymous__15676))
<=> V3__x = Vvar__1___24Anonymous__15676 ) ).
fof('$_prop_15699',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__15676] :
( p(c_24__prop__15699___24a3(V0__A,V3__x,Vvar__1___24Anonymous__15676))
<=> V3__x != Vvar__1___24Anonymous__15676 ) ).
fof('$_prop_15768',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__15768___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_15769',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__15769___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_15770',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__15770___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_15771',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__15771___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_16607',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__16607___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__2 = Vv__CANONICAL__3 ) ).
fof('$_prop_16608',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__16608___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__2 != Vv__CANONICAL__3 ) ).
fof('$_prop_16616',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__16616___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__2 = Vv__CANONICAL__3 ) ).
fof('$_prop_16617',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__16617___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__2 != Vv__CANONICAL__3 ) ).
fof('$_prop_16914',axiom,
! [V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895] :
( p(c_24__prop__16914___24a3(V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895)) ) ).
fof('$_prop_16926',axiom,
! [V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895] :
( p(c_24__prop__16926___24a3(V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__16894,Vvar__2___24Anonymous__16895)) ) ).
fof('$_prop_34458',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__34458___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_34459',axiom,
! [V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__34414] :
( p(c_24__prop__34459___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__34414))
<=> ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__34414)) ) ).
fof('$_prop_34460',axiom,
! [V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__34414] :
( p(c_24__prop__34460___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__34414))
<=> ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__34414)) ) ).
fof('$_prop_34493',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__34493___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_37864',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__37864___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_37889',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__37889___24a2(V0__A,V1__B))
<=> ( p(V0__A)
| p(V1__B) ) ) ).
fof('$_prop_37890',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__37890___24a2(V0__A,V1__B))
<=> ( p(V0__A)
& p(V1__B) ) ) ).
fof('$_prop_45254',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__45254___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_46976',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__46976___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_46989',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__46989___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_type_109',axiom,
! [Vvar__110] :
( c_24__type__109___24t(Vvar__110)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__110,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11157',axiom,
! [Vvar__11158] :
( c_24__type__11157___24t(Vvar__11158)
<=> ! [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__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__2968___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__2973___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__2982___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__11158,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_11205',axiom,
! [Vvar__11206] :
( c_24__type__11205___24t(Vvar__11206)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__11206,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_11216',axiom,
! [Vvar__11217] :
( c_24__type__11216___24t(Vvar__11217)
<=> ! [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__11217,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11236',axiom,
! [Vvar__11237] :
( c_24__type__11236___24t(Vvar__11237)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__11237,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11239',axiom,
! [Vvar__11240] :
( c_24__type__11239___24t(Vvar__11240)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__11240,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11311',axiom,
! [Vvar__11312] :
( c_24__type__11311___24t(Vvar__11312)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__11312,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11368',axiom,
! [Vvar__11369] :
( c_24__type__11368___24t(Vvar__11369)
<=> ! [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__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__5381___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__11369,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_113947',axiom,
! [Vvar__113948] :
( c_24__type__113947___24t(Vvar__113948)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cProp___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__113948,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_114118',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__114119] :
( c_24__type__114118___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__114119)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__114119,Vv__CANONICAL__6)) ) ) ).
fof('$_type_114199',axiom,
! [Vvar__114200] :
( c_24__type__114199___24t(Vvar__114200)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__114203___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__114200,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_114203',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__114204] :
( c_24__type__114203___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__114204)
<=> ( Vv__CANONICAL__1 = Vv__CANONICAL__1
=> cProp___24t(Vvar__114204) ) ) ).
fof('$_type_116455',axiom,
! [Vvar__116456] :
( c_24__type__116455___24t(Vvar__116456)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__116456,Vv__CANONICAL__0)) ) ) ).
fof('$_type_116538',axiom,
! [Vvar__116539] :
( c_24__type__116538___24t(Vvar__116539)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2961___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__116539,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_118289',axiom,
! [Vvar__118290] :
( c_24__type__118289___24t(Vvar__118290)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__118290,Vv__CANONICAL__0)) ) ) ).
fof('$_type_118488',axiom,
! [Vvar__118489] :
( c_24__type__118488___24t(Vvar__118489)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__118489,Vv__CANONICAL__0)) ) ) ).
fof('$_type_118673',axiom,
! [Vvar__118674] :
( c_24__type__118673___24t(Vvar__118674)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2218___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cProp___24t(happ(happ(happ(happ(Vvar__118674,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_120240',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__120241] :
( c_24__type__120240___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__120241)
<=> ! [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__120241,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_120259',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__120260] :
( c_24__type__120259___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__120260)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__120260,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_120279',axiom,
! [Vvar__120280] :
( c_24__type__120279___24t(Vvar__120280)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__646___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__646___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__120280,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_120501',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__120502] :
( c_24__type__120501___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__120502)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__120502,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_120510',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__120511] :
( c_24__type__120510___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__120511)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__120511,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_120588',axiom,
! [Vvar__120589] :
( c_24__type__120588___24t(Vvar__120589)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__120589,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_121139',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__121140] :
( c_24__type__121139___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__121140)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__121140,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_121264',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__121265] :
( c_24__type__121264___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__121265)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__121265,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_121389',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__121390] :
( c_24__type__121389___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__121390)
<=> ! [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__121390,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_121514',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__121515] :
( c_24__type__121514___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__121515)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__121515,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_121639',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__121640] :
( c_24__type__121639___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__121640)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__121640,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_1217',axiom,
! [Vv__CANONICAL__0,Vvar__1218] :
( c_24__type__1217___24t(Vv__CANONICAL__0,Vvar__1218)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__1218,Vv__CANONICAL__1)) ) ) ).
fof('$_type_121764',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__121765] :
( c_24__type__121764___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__121765)
<=> ! [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__121765,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_121875',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__121876] :
( c_24__type__121875___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__121876)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__121876,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_122416',axiom,
! [Vvar__122417] :
( c_24__type__122416___24t(Vvar__122417)
<=> ! [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__122417,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_122667',axiom,
! [Vvar__122668] :
( c_24__type__122667___24t(Vvar__122668)
<=> ! [Vv__CANONICAL__0] :
( ciT___24t(Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cF___24a1(Vv__CANONICAL__0),happ(Vvar__122668,Vv__CANONICAL__0)) ) ) ).
fof('$_type_122692',axiom,
! [Vvar__122693] :
( c_24__type__122692___24t(Vvar__122693)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__122693,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12420',axiom,
! [Vvar__12421] :
( c_24__type__12420___24t(Vvar__12421)
<=> ! [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__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__2952___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__7767___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__2968___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__12444___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__16)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__12421,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__16),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_12444',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12445] :
( c_24__type__12444___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12445)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__12445,Vv__CANONICAL__2)) ) ) ).
fof('$_type_126485',axiom,
! [Vvar__126486] :
( c_24__type__126485___24t(Vvar__126486)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__126486,Vv__CANONICAL__0)) ) ) ).
fof('$_type_126682',axiom,
! [Vvar__126683] :
( c_24__type__126682___24t(Vvar__126683)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__122667___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__2,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__2,Vv__CANONICAL__6)
=> cExtLib_2eTactics_2eInjection_2eInjective___24t(cHList_2ehlist_2eequiv__hlist___24a4(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(ciT,Vv__CANONICAL__1,Vv__CANONICAL__2),cHList_2ehlist_2ehlist__app___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5),cHList_2ehlist_2ehlist__app___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__6)),happ(happ(happ(happ(happ(happ(happ(Vvar__126683,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_126706',axiom,
! [Vvar__126707] :
( c_24__type__126706___24t(Vvar__126707)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__122667___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( ciT___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cF___24t(Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cF___24t(Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__1,Vv__CANONICAL__6)
=> cExtLib_2eTactics_2eInjection_2eInjective___24t(cHList_2ehlist_2eequiv__hlist___24a4(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,Vv__CANONICAL__2,Vv__CANONICAL__1),cHList_2ehlist_2eHcons___24a4(Vv__CANONICAL__2,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__5),cHList_2ehlist_2eHcons___24a4(Vv__CANONICAL__2,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__6)),happ(happ(happ(happ(happ(happ(happ(Vvar__126707,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_126742',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__126743] :
( c_24__type__126742___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__126743)
<=> ! [Vv__CANONICAL__4] :
( ciT___24t(Vv__CANONICAL__4)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cF___24a1(Vv__CANONICAL__4),happ(Vvar__126743,Vv__CANONICAL__4)) ) ) ).
fof('$_type_12789',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12790] :
( c_24__type__12789___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12790)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__12790,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_13125',axiom,
! [Vvar__13126] :
( c_24__type__13125___24t(Vvar__13126)
<=> ! [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__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__2952___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__7767___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__2968___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cType___24t(Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__2973___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__2982___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( c_24__type__13160___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__13126,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_13160',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13161] :
( c_24__type__13160___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13161)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__13161,Vv__CANONICAL__3)) ) ) ).
fof('$_type_13677',axiom,
! [Vvar__13678] :
( c_24__type__13677___24t(Vvar__13678)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13682___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__13678,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_13682',axiom,
! [Vv__CANONICAL__0,Vvar__13683] :
( c_24__type__13682___24t(Vv__CANONICAL__0,Vvar__13683)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__13683,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_13751',axiom,
! [Vvar__13752] :
( c_24__type__13751___24t(Vvar__13752)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5381___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_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__13752,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_13781',axiom,
! [Vv__CANONICAL__0,Vvar__13782] :
( c_24__type__13781___24t(Vv__CANONICAL__0,Vvar__13782)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__13782,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_13903',axiom,
! [Vvar__13904] :
( c_24__type__13903___24t(Vvar__13904)
<=> ! [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__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__5381___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__13781___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__13904,Vv__CANONICAL__0),Vv__CANONICAL__1),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_14698',axiom,
! [Vvar__14699] :
( c_24__type__14698___24t(Vvar__14699)
<=> ! [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__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__646___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__7748___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__7748___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__7748___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__4143___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__7767___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( c_24__type__2968___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__16)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16)
=> ( ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__19] :
( t(Vv__CANONICAL__19,Vv__CANONICAL__8)
=> ( p(happ(happ(Vv__CANONICAL__7,happ(Vv__CANONICAL__16,Vv__CANONICAL__18)),happ(Vv__CANONICAL__16,Vv__CANONICAL__19)))
=> happ(happ(Vv__CANONICAL__15,Vv__CANONICAL__18),Vv__CANONICAL__19) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
=> ! [Vv__CANONICAL__19] :
( t(Vv__CANONICAL__19,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__20] :
( t(Vv__CANONICAL__20,Vv__CANONICAL__8)
=> cCoq_2eBool_2eBool_2ereflect___24t(happ(happ(Vv__CANONICAL__7,happ(Vv__CANONICAL__16,Vv__CANONICAL__19)),happ(Vv__CANONICAL__16,Vv__CANONICAL__20)),happ(happ(Vv__CANONICAL__15,Vv__CANONICAL__19),Vv__CANONICAL__20),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__14699,Vv__CANONICAL__0),Vv__CANONICAL__1),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__19),Vv__CANONICAL__20)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_15282',axiom,
! [Vvar__15283] :
( c_24__type__15282___24t(Vvar__15283)
<=> ! [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__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2961___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__15283,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('$_type_15293',axiom,
! [Vvar__15294] :
( c_24__type__15293___24t(Vvar__15294)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__15294,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15309',axiom,
! [Vvar__15310] :
( c_24__type__15309___24t(Vvar__15310)
<=> ! [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__15310,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15311',axiom,
! [Vvar__15312] :
( c_24__type__15311___24t(Vvar__15312)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__15312,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15345',axiom,
! [Vvar__15346] :
( c_24__type__15345___24t(Vvar__15346)
<=> ! [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__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___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__15346,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_15387',axiom,
! [Vvar__15388] :
( c_24__type__15387___24t(Vvar__15388)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__5381___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__15388,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_15433',axiom,
! [Vv__CANONICAL__0,Vvar__15434] :
( c_24__type__15433___24t(Vv__CANONICAL__0,Vvar__15434)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__15434,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_15450',axiom,
! [Vvar__15451] :
( c_24__type__15450___24t(Vvar__15451)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__15451,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15463',axiom,
! [Vvar__15464] :
( c_24__type__15463___24t(Vvar__15464)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( ( p(Vv__CANONICAL__0)
=> p(Vv__CANONICAL__1) )
=> cExtLib_2eTactics_2eInjection_2eInjective___24t(Vv__CANONICAL__0,happ(happ(Vvar__15464,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_15477',axiom,
! [Vvar__15478] :
( c_24__type__15477___24t(Vvar__15478)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cExtLib_2eTactics_2eInjection_2eInjective___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__15478,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15488',axiom,
! [Vvar__15489] :
( c_24__type__15488___24t(Vvar__15489)
<=> ! [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__15489,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_15497',axiom,
! [Vvar__15498] :
( c_24__type__15497___24t(Vvar__15498)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__15498,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15505',axiom,
! [Vvar__15506] :
( c_24__type__15505___24t(Vvar__15506)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esigT___24a2(Vv__CANONICAL__0,c_24__lam__15512___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),c_24__prop__15517___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__15506,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15621',axiom,
! [Vv__CANONICAL__0,Vvar__15622] :
( c_24__type__15621___24t(Vv__CANONICAL__0,Vvar__15622)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__15623___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__15624___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(Vvar__15622,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_15649',axiom,
! [Vvar__15650] :
( c_24__type__15649___24t(Vvar__15650)
<=> ! [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__15650,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_15657',axiom,
! [Vvar__15658] :
( c_24__type__15657___24t(Vvar__15658)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eLists_2eList_2eIn___24a3(Vv__CANONICAL__0,cCoq_2eLists_2eList_2enth___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__2),c_24__prop__15659___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(happ(happ(Vvar__15658,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_15670',axiom,
! [Vvar__15671] :
( c_24__type__15670___24t(Vvar__15671)
<=> ! [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__15671,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_15709',axiom,
! [Vvar__15710] :
( c_24__type__15709___24t(Vvar__15710)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__15621___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__15710,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_15781',axiom,
! [Vvar__15782] :
( c_24__type__15781___24t(Vvar__15782)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__15621___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__15782,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_159676',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__159677] :
( c_24__type__159676___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__159677)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( Vv__CANONICAL__1 = Vv__CANONICAL__2
=> cProp___24t(happ(Vvar__159677,Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_159686',axiom,
! [Vvar__159687] :
( c_24__type__159686___24t(Vvar__159687)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2218___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__1))
=> cProp___24t(happ(happ(happ(happ(Vvar__159687,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_159798',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__159799] :
( c_24__type__159798___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__159799)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__159799,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_16605',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16606] :
( c_24__type__16605___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16606)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__16607___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__16608___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__16606,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_16614',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16615] :
( c_24__type__16614___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16615)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__16616___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__16617___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__16615,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_16632',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__16633] :
( c_24__type__16632___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__16633)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__16633,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_16735',axiom,
! [Vvar__16736] :
( c_24__type__16735___24t(Vvar__16736)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1217___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__16736,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_16770',axiom,
! [Vvar__16771] :
( c_24__type__16770___24t(Vvar__16771)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1217___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(happ(happ(Vvar__16771,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_16820',axiom,
! [Vvar__16821] :
( c_24__type__16820___24t(Vvar__16821)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),happ(happ(happ(Vvar__16821,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_16933',axiom,
! [Vvar__16934] :
( c_24__type__16933___24t(Vvar__16934)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__15621___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__16934,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_16977',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__16978] :
( c_24__type__16977___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__16978)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__16978,Vv__CANONICAL__3)) ) ) ).
fof('$_type_17166',axiom,
! [Vvar__17167] :
( c_24__type__17166___24t(Vvar__17167)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2177___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1954___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__17185___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)
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5))
=> t(happ(happ(happ(happ(happ(happ(Vvar__17167,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('$_type_17185',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17186] :
( c_24__type__17185___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17186)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(Vvar__17186,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ) ).
fof('$_type_17419',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__17420] :
( c_24__type__17419___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__17420)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(Vvar__17420,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_17451',axiom,
! [Vvar__17452] :
( c_24__type__17451___24t(Vvar__17452)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__646___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__17452,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17485',axiom,
! [Vvar__17486] :
( c_24__type__17485___24t(Vvar__17486)
<=> ! [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__17486,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17521',axiom,
! [Vvar__17522] :
( c_24__type__17521___24t(Vvar__17522)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__17522,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17550',axiom,
! [Vvar__17551] :
( c_24__type__17550___24t(Vvar__17551)
<=> ! [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)
=> cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__17551,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17562',axiom,
! [Vvar__17563] :
( c_24__type__17562___24t(Vvar__17563)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(happ(happ(happ(Vvar__17563,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_17592',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17593] :
( c_24__type__17592___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17593)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> cType___24t(happ(happ(Vvar__17593,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_17645',axiom,
! [Vvar__17646] :
( c_24__type__17645___24t(Vvar__17646)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__17652___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__17661___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__17685___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__17646,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_17652',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__17653] :
( c_24__type__17652___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__17653)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cType___24t(happ(happ(Vvar__17653,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_17661',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17662] :
( c_24__type__17661___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17662)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> t(happ(Vvar__17662,Vv__CANONICAL__3),happ(happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)),cExtLib_2eData_2eMember_2eMZ___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ).
fof('$_type_17685',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17686] :
( c_24__type__17685___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17686)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__4),Vv__CANONICAL__5))
=> t(happ(happ(happ(happ(Vvar__17686,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),happ(happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)),cExtLib_2eData_2eMember_2eMN___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5))) ) ) ) ) ) ).
fof('$_type_17692',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__17693] :
( c_24__type__17692___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__17693)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(Vvar__17693,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_17771',axiom,
! [Vvar__17772] :
( c_24__type__17771___24t(Vvar__17772)
<=> ! [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] :
( cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__17772,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_18076',axiom,
! [Vvar__18077] :
( c_24__type__18076___24t(Vvar__18077)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cExtLib_2eData_2eMember_2emember___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__4)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cExtLib_2eData_2eMember_2emember___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1),happ(happ(happ(happ(happ(Vvar__18077,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_18130',axiom,
! [Vvar__18131] :
( c_24__type__18130___24t(Vvar__18131)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__18131,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18598',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18599] :
( c_24__type__18598___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18599)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18599,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18699',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__18700] :
( c_24__type__18699___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__18700)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18700,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18800',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18801] :
( c_24__type__18800___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18801)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18801,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18890',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__18891] :
( c_24__type__18890___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__18891)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__18891,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_18991',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18992] :
( c_24__type__18991___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18992)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__18992,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_1905',axiom,
! [Vvar__1906] :
( c_24__type__1905___24t(Vvar__1906)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__1906,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1907',axiom,
! [Vvar__1908] :
( c_24__type__1907___24t(Vvar__1908)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1908,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19092',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__19093] :
( c_24__type__19092___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__19093)
<=> ! [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__19093,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_1912',axiom,
! [Vvar__1913] :
( c_24__type__1912___24t(Vvar__1913)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__1913,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1914',axiom,
! [Vvar__1915] :
( c_24__type__1914___24t(Vvar__1915)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__1915,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19193',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19194] :
( c_24__type__19193___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19194)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__19194,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_1926',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1927] :
( c_24__type__1926___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1927)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__1927,Vv__CANONICAL__2)) ) ) ).
fof('$_type_19434',axiom,
! [Vvar__19435] :
( c_24__type__19434___24t(Vvar__19435)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__19435,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19437',axiom,
! [Vvar__19438] :
( c_24__type__19437___24t(Vvar__19438)
<=> ! [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__19438,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19443',axiom,
! [Vvar__19444] :
( c_24__type__19443___24t(Vvar__19444)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__19444,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1951',axiom,
! [Vvar__1952] :
( c_24__type__1951___24t(Vvar__1952)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1954___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__1966___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__1952,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_1954',axiom,
! [Vv__CANONICAL__0,Vvar__1955] :
( c_24__type__1954___24t(Vv__CANONICAL__0,Vvar__1955)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__1955,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1966',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1967] :
( c_24__type__1966___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1967)
<=> ! [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__1967,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('$_type_19666',axiom,
! [Vvar__19667] :
( c_24__type__19666___24t(Vvar__19667)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__19667,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19669',axiom,
! [Vvar__19670] :
( c_24__type__19669___24t(Vvar__19670)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__19670,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19675',axiom,
! [Vvar__19676] :
( c_24__type__19675___24t(Vvar__19676)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__19676,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19693',axiom,
! [Vvar__19694] :
( c_24__type__19693___24t(Vvar__19694)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2177___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__19694,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_19752',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__19753] :
( c_24__type__19752___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__19753)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__19753,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_1976',axiom,
! [Vvar__1977] :
( c_24__type__1976___24t(Vvar__1977)
<=> ! [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__1977,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19798',axiom,
! [Vvar__19799] :
( c_24__type__19798___24t(Vvar__19799)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__646___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__19799,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2',axiom,
! [Vvar__3] :
( c_24__type__2___24t(Vvar__3)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__3,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2001',axiom,
! [Vvar__2002] :
( c_24__type__2001___24t(Vvar__2002)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__2002,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_2023',axiom,
! [Vvar__2024] :
( c_24__type__2023___24t(Vvar__2024)
<=> ! [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__2024,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2035',axiom,
! [Vvar__2036] :
( c_24__type__2035___24t(Vvar__2036)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( Vv__CANONICAL__1 != cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esigT___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),c_24__lam__2042___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__2036,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_20451',axiom,
! [Vvar__20452] :
( c_24__type__20451___24t(Vvar__20452)
<=> ! [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__20452,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2055',axiom,
! [Vvar__2056] :
( c_24__type__2055___24t(Vvar__2056)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__2056,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2071',axiom,
! [Vvar__2072] :
( c_24__type__2071___24t(Vvar__2072)
<=> ! [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__2072,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_20807',axiom,
! [Vvar__20808] :
( c_24__type__20807___24t(Vvar__20808)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__20808,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20812',axiom,
! [Vvar__20813] :
( c_24__type__20812___24t(Vvar__20813)
<=> ! [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__20813,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_20820',axiom,
! [Vvar__20821] :
( c_24__type__20820___24t(Vvar__20821)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__20821,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_20962',axiom,
! [Vvar__20963] :
( c_24__type__20962___24t(Vvar__20963)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5381___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__20963,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2118',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2119] :
( c_24__type__2118___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2119)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2119,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_2125',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2126] :
( c_24__type__2125___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2126)
<=> ! [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__2126,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_2143',axiom,
! [Vvar__2144] :
( c_24__type__2143___24t(Vvar__2144)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__2144,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2153',axiom,
! [Vvar__2154] :
( c_24__type__2153___24t(Vvar__2154)
<=> ! [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__2154,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2170',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2171] :
( c_24__type__2170___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2171)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2171,Vv__CANONICAL__2)) ) ) ).
fof('$_type_21736',axiom,
! [Vvar__21737] :
( c_24__type__21736___24t(Vvar__21737)
<=> ! [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__21737,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2174',axiom,
! [Vvar__2175] :
( c_24__type__2174___24t(Vvar__2175)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2177___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2175,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2177',axiom,
! [Vv__CANONICAL__0,Vvar__2178] :
( c_24__type__2177___24t(Vv__CANONICAL__0,Vvar__2178)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2178,Vv__CANONICAL__1)) ) ) ).
fof('$_type_2194',axiom,
! [Vvar__2195] :
( c_24__type__2194___24t(Vvar__2195)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2177___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__2195,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_220',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__221] :
( c_24__type__220___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__221)
<=> ! [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__221,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_2211',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2212] :
( c_24__type__2211___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2212)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__2212,Vv__CANONICAL__2)) ) ) ).
fof('$_type_2215',axiom,
! [Vvar__2216] :
( c_24__type__2215___24t(Vvar__2216)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2218___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2216,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2218',axiom,
! [Vv__CANONICAL__0,Vvar__2219] :
( c_24__type__2218___24t(Vv__CANONICAL__0,Vvar__2219)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__2219,Vv__CANONICAL__1)) ) ) ).
fof('$_type_2235',axiom,
! [Vvar__2236] :
( c_24__type__2235___24t(Vvar__2236)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2218___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__2236,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2286',axiom,
! [Vvar__2287] :
( c_24__type__2286___24t(Vvar__2287)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__2287,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23083',axiom,
! [Vvar__23084] :
( c_24__type__23083___24t(Vvar__23084)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2968___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__23084,Vv__CANONICAL__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('$_type_2310',axiom,
! [Vvar__2311] :
( c_24__type__2310___24t(Vvar__2311)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__2311,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_23156',axiom,
! [Vvar__23157] :
( c_24__type__23156___24t(Vvar__23157)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__646___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2968___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__23157,Vv__CANONICAL__0),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('$_type_23220',axiom,
! [Vvar__23221] :
( c_24__type__23220___24t(Vvar__23221)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__23221,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_2357',axiom,
! [Vvar__2358] :
( c_24__type__2357___24t(Vvar__2358)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2361___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__2358,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2361',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2362] :
( c_24__type__2361___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2362)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__2362,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_23647',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23648] :
( c_24__type__23647___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23648)
<=> ! [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__23648,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_2379',axiom,
! [Vvar__2380] :
( c_24__type__2379___24t(Vvar__2380)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1217___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2380,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2401',axiom,
! [Vvar__2402] :
( c_24__type__2401___24t(Vvar__2402)
<=> ! [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__2402,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_24174',axiom,
! [Vvar__24175] :
( c_24__type__24174___24t(Vvar__24175)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__24175,Vv__CANONICAL__0)) ) ) ).
fof('$_type_24177',axiom,
! [Vvar__24178] :
( c_24__type__24177___24t(Vvar__24178)
<=> ! [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__24178,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24180',axiom,
! [Vvar__24181] :
( c_24__type__24180___24t(Vvar__24181)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__24181,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24185',axiom,
! [Vvar__24186] :
( c_24__type__24185___24t(Vvar__24186)
<=> ! [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__24186,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_24194',axiom,
! [Vvar__24195] :
( c_24__type__24194___24t(Vvar__24195)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__24195,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24199',axiom,
! [Vvar__24200] :
( c_24__type__24199___24t(Vvar__24200)
<=> ! [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__24200,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2434',axiom,
! [Vv__CANONICAL__0,Vvar__2435] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vvar__2435)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__2435,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_2445',axiom,
! [Vvar__2446] :
( c_24__type__2445___24t(Vvar__2446)
<=> ! [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__2446,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2511',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__2512] :
( c_24__type__2511___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__2512)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__2512,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_25119',axiom,
! [Vvar__25120] :
( c_24__type__25119___24t(Vvar__25120)
<=> ! [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__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__5381___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__13781___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__25120,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_2522',axiom,
! [Vvar__2523] :
( c_24__type__2522___24t(Vvar__2523)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__646___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__2523,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2533',axiom,
! [Vv__CANONICAL__0,Vvar__2534] :
( c_24__type__2533___24t(Vv__CANONICAL__0,Vvar__2534)
<=> ! [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__2534,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_25373',axiom,
! [Vvar__25374] :
( c_24__type__25373___24t(Vvar__25374)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__646___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__2968___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__2973___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__2982___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8)),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__25374,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_2554',axiom,
! [Vv__CANONICAL__0,Vvar__2555] :
( c_24__type__2554___24t(Vv__CANONICAL__0,Vvar__2555)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__2555,Vv__CANONICAL__1)) ) ) ).
fof('$_type_25658',axiom,
! [Vvar__25659] :
( c_24__type__25658___24t(Vvar__25659)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__5381___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__13781___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__25659,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_2628',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__2629] :
( c_24__type__2628___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__2629)
<=> ! [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__2629,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_26565',axiom,
! [Vvar__26566] :
( c_24__type__26565___24t(Vvar__26566)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),happ(happ(happ(happ(Vvar__26566,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2663',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2664] :
( c_24__type__2663___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2664)
<=> ! [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__2664,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_2671',axiom,
! [Vvar__2672] :
( c_24__type__2671___24t(Vvar__2672)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2672,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2684',axiom,
! [Vvar__2685] :
( c_24__type__2684___24t(Vvar__2685)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__2685,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2686',axiom,
! [Vvar__2687] :
( c_24__type__2686___24t(Vvar__2687)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2687,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2699',axiom,
! [Vvar__2700] :
( c_24__type__2699___24t(Vvar__2700)
<=> ! [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__2700,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27980',axiom,
! [Vvar__27981] :
( c_24__type__27980___24t(Vvar__27981)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__27981,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_28',axiom,
! [Vvar__29] :
( c_24__type__28___24t(Vvar__29)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__29,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28367',axiom,
! [Vvar__28368] :
( c_24__type__28367___24t(Vvar__28368)
<=> ! [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__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___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__7767___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__2968___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__2973___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__2982___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__13160___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__28368,Vv__CANONICAL__0),Vv__CANONICAL__1),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_28821',axiom,
! [Vvar__28822] :
( c_24__type__28821___24t(Vvar__28822)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2952___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__28822,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_28842',axiom,
! [Vvar__28843] :
( c_24__type__28842___24t(Vvar__28843)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__28843,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_29096',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__29097] :
( c_24__type__29096___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__29097)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29097,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29159',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29160] :
( c_24__type__29159___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29160)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29160,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29222',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__29223] :
( c_24__type__29222___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__29223)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29223,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29276',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29277] :
( c_24__type__29276___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29277)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__29277,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_29339',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__29340] :
( c_24__type__29339___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__29340)
<=> ! [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__29340,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_2947',axiom,
! [Vvar__2948] :
( c_24__type__2947___24t(Vvar__2948)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__646___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__2968___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__2973___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__2982___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__2948,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_2952',axiom,
! [Vv__CANONICAL__0,Vvar__2953] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vvar__2953)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2953,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29553',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29554] :
( c_24__type__29553___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29554)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29554,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29576',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29577] :
( c_24__type__29576___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29577)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29577,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29599',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29600] :
( c_24__type__29599___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29600)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__29600,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_2961',axiom,
! [Vv__CANONICAL__0,Vvar__2962] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vvar__2962)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__2962,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_29622',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29623] :
( c_24__type__29622___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29623)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29623,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29640',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29641] :
( c_24__type__29640___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29641)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__29641,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_29666',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29667] :
( c_24__type__29666___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29667)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29667,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2968',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2969] :
( c_24__type__2968___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2969)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__2969,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_29684',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29685] :
( c_24__type__29684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29685)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__29685,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_2973',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2974] :
( c_24__type__2973___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2974)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__2974,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_29817',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29818] :
( c_24__type__29817___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29818)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29818,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2982',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2983] :
( c_24__type__2982___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2983)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__2983,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29847',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29848] :
( c_24__type__29847___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29848)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29848,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29871',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29872] :
( c_24__type__29871___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29872)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__29872,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_29901',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29902] :
( c_24__type__29901___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29902)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__29902,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_29931',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29932] :
( c_24__type__29931___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29932)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29932,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29955',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29956] :
( c_24__type__29955___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29956)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__29956,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_29988',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29989] :
( c_24__type__29988___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__29989)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29989,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30012',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30013] :
( c_24__type__30012___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30013)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__30013,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_30039',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30040] :
( c_24__type__30039___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30040)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__30040,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_30492',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__30493] :
( c_24__type__30492___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__30493)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30493,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3064',axiom,
! [Vvar__3065] :
( c_24__type__3064___24t(Vvar__3065)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3068___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__3065,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3068',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3069] :
( c_24__type__3068___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3069)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(Vvar__3069,Vv__CANONICAL__2)) ) ) ).
fof('$_type_30705',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__30706] :
( c_24__type__30705___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__30706)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30706,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30918',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__30919] :
( c_24__type__30918___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__30919)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30919,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3103',axiom,
! [Vvar__3104] :
( c_24__type__3103___24t(Vvar__3104)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3110___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__3104,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_3110',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3111] :
( c_24__type__3110___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3111)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__3111,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31113',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__31114] :
( c_24__type__31113___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__31114)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__31114,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_31326',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__31327] :
( c_24__type__31326___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__31327)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31327,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_3139',axiom,
! [Vvar__3140] :
( c_24__type__3139___24t(Vvar__3140)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3146___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__3140,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_3146',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3147] :
( c_24__type__3146___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3147)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3147,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3153',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3154] :
( c_24__type__3153___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3154)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__3154,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_31539',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__31540] :
( c_24__type__31539___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__31540)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__31540,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_3166',axiom,
! [Vvar__3167] :
( c_24__type__3166___24t(Vvar__3167)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1217___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__3167,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31752',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__31753] :
( c_24__type__31752___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__31753)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__31753,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_3185',axiom,
! [Vvar__3186] :
( c_24__type__3185___24t(Vvar__3186)
<=> ! [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__3186,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31965',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__31966] :
( c_24__type__31965___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__31966)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__31966,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_32160',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__32161] :
( c_24__type__32160___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__32161)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__32161,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_3218',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3219] :
( c_24__type__3218___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3219)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3219,Vv__CANONICAL__3)) ) ) ).
fof('$_type_32373',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__32374] :
( c_24__type__32373___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__32374)
<=> ! [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__32374,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_32568',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__32569] :
( c_24__type__32568___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__32569)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__32569,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_3259',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3260] :
( c_24__type__3259___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3260)
<=> ! [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__3260,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_3262',axiom,
! [Vv__CANONICAL__0,Vvar__3263] :
( c_24__type__3262___24t(Vv__CANONICAL__0,Vvar__3263)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__3263,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_32784',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32785] :
( c_24__type__32784___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32785)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__32785,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_32803',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32804] :
( c_24__type__32803___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32804)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__32804,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_32817',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32818] :
( c_24__type__32817___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32818)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__32818,Vv__CANONICAL__4)) ) ) ).
fof('$_type_3288',axiom,
! [Vvar__3289] :
( c_24__type__3288___24t(Vvar__3289)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2177___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__3289,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_32967',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32968] :
( c_24__type__32967___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32968)
<=> ! [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__32968,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_33017',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33018] :
( c_24__type__33017___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33018)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__33018,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_33067',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33068] :
( c_24__type__33067___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33068)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__33068,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_33109',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33110] :
( c_24__type__33109___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33110)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__33110,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_33159',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33160] :
( c_24__type__33159___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33160)
<=> ! [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__33160,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_33241',axiom,
! [Vvar__33242] :
( c_24__type__33241___24t(Vvar__33242)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__33242,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_33364',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33365] :
( c_24__type__33364___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33365)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__33365,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_33408',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33409] :
( c_24__type__33408___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33409)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__33409,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_33444',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33445] :
( c_24__type__33444___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33445)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__33445,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_33488',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33489] :
( c_24__type__33488___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__33489)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__33489,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_33500',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33501] :
( c_24__type__33500___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33501)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__33501,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_33536',axiom,
! [Vvar__33537] :
( c_24__type__33536___24t(Vvar__33537)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__33537,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_33708',axiom,
! [Vvar__33709] :
( c_24__type__33708___24t(Vvar__33709)
<=> ! [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__33709,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33790',axiom,
! [Vv__CANONICAL__0,Vvar__33791] :
( c_24__type__33790___24t(Vv__CANONICAL__0,Vvar__33791)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__33791,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_33834',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33835] :
( c_24__type__33834___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33835)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__33835,Vv__CANONICAL__2)) ) ) ).
fof('$_type_34438',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34439] :
( c_24__type__34438___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34439)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34439,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_34447',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34448] :
( c_24__type__34447___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34448)
<=> ! [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__34448,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_34456',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34457] :
( c_24__type__34456___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34457)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__34458___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__34457,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_34479',axiom,
! [Vvar__34480] :
( c_24__type__34479___24t(Vvar__34480)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__646___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__34491___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(Vvar__34480,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_34491',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34492] :
( c_24__type__34491___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34492)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__34493___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__34492,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_34711',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34712] :
( c_24__type__34711___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34712)
<=> ! [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__34712,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_34826',axiom,
! [Vvar__34827] :
( c_24__type__34826___24t(Vvar__34827)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__646___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1954___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__4] :
( c_24__type__34861___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__34827,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ) ).
fof('$_type_34861',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34862] :
( c_24__type__34861___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34862)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,happ(Vv__CANONICAL__2,Vv__CANONICAL__4))
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> t(happ(happ(happ(Vvar__34862,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__6),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ) ) ) ).
fof('$_type_34907',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34908] :
( c_24__type__34907___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34908)
<=> ( p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(Vvar__34908,happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ).
fof('$_type_35080',axiom,
! [Vvar__35081] :
( c_24__type__35080___24t(Vvar__35081)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__646___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1954___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__35115___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)
=> ( p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5))
=> t(happ(happ(happ(happ(happ(happ(Vvar__35081,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('$_type_35115',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35116] :
( c_24__type__35115___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35116)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4))
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,happ(Vv__CANONICAL__2,Vv__CANONICAL__4))
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
=> t(happ(happ(happ(Vvar__35116,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__6),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ) ) ) ).
fof('$_type_35187',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35188] :
( c_24__type__35187___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35188)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35188,Vv__CANONICAL__2)) ) ) ).
fof('$_type_35193',axiom,
! [Vvar__35194] :
( c_24__type__35193___24t(Vvar__35194)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2177___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__35194,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_35210',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35211] :
( c_24__type__35210___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35211)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__35211,Vv__CANONICAL__2)) ) ) ).
fof('$_type_35216',axiom,
! [Vvar__35217] :
( c_24__type__35216___24t(Vvar__35217)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2218___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__35217,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_35233',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35234] :
( c_24__type__35233___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35234)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__35234,Vv__CANONICAL__2)) ) ) ).
fof('$_type_35239',axiom,
! [Vvar__35240] :
( c_24__type__35239___24t(Vvar__35240)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2218___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__35240,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__1,cCoq_2eInit_2eSpecif_2eprojT1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_type_35252',axiom,
! [Vvar__35253] :
( c_24__type__35252___24t(Vvar__35253)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__35253,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35275',axiom,
! [Vvar__35276] :
( c_24__type__35275___24t(Vvar__35276)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__35276,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_35280',axiom,
! [Vvar__35281] :
( c_24__type__35280___24t(Vvar__35281)
<=> ! [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__35281,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_35306',axiom,
! [Vvar__35307] :
( c_24__type__35306___24t(Vvar__35307)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__35310___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__35317___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__35324___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__35307,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_35310',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35311] :
( c_24__type__35310___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35311)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__35311,Vv__CANONICAL__2)) ) ) ).
fof('$_type_35317',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35318] :
( c_24__type__35317___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35318)
<=> ( p(Vv__CANONICAL__0)
=> t(Vvar__35318,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_35324',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35325] :
( c_24__type__35324___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35325)
<=> ( p(Vv__CANONICAL__1)
=> t(Vvar__35325,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_35336',axiom,
! [Vvar__35337] :
( c_24__type__35336___24t(Vvar__35337)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__35337,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35359',axiom,
! [Vvar__35360] :
( c_24__type__35359___24t(Vvar__35360)
<=> ! [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__35360,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35364',axiom,
! [Vvar__35365] :
( c_24__type__35364___24t(Vvar__35365)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__35365,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_35376',axiom,
! [Vvar__35377] :
( c_24__type__35376___24t(Vvar__35377)
<=> ! [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__35377,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35414',axiom,
! [Vvar__35415] :
( c_24__type__35414___24t(Vvar__35415)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,Vv__CANONICAL__0)
=> cCoq_2eStrings_2eString_2estring___24t(happ(Vvar__35415,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35420',axiom,
! [Vvar__35421] :
( c_24__type__35420___24t(Vvar__35421)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,happ(Vvar__35421,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35433',axiom,
! [Vvar__35434] :
( c_24__type__35433___24t(Vvar__35434)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__35434,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35588',axiom,
! [Vvar__35589] :
( c_24__type__35588___24t(Vvar__35589)
<=> ! [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__2177___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__33834___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__35589,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_36141',axiom,
! [Vvar__36142] :
( c_24__type__36141___24t(Vvar__36142)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2125___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__36142,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_36170',axiom,
! [Vvar__36171] :
( c_24__type__36170___24t(Vvar__36171)
<=> ! [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__2125___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_2eclause___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__36171,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_36199',axiom,
! [Vvar__36200] :
( c_24__type__36199___24t(Vvar__36200)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2125___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__36200,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_36319',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36320] :
( c_24__type__36319___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36320)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__36320,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_36343',axiom,
! [Vvar__36344] :
( c_24__type__36343___24t(Vvar__36344)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__36319___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(happ(happ(Vvar__36344,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_36598',axiom,
! [Vvar__36599] :
( c_24__type__36598___24t(Vvar__36599)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__36599,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36615',axiom,
! [Vvar__36616] :
( c_24__type__36615___24t(Vvar__36616)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__36616,Vv__CANONICAL__0)) ) ) ).
fof('$_type_36623',axiom,
! [Vvar__36624] :
( c_24__type__36623___24t(Vvar__36624)
<=> ! [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__36624,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_36633',axiom,
! [Vvar__36634] :
( c_24__type__36633___24t(Vvar__36634)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__36634,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36706',axiom,
! [Vvar__36707] :
( c_24__type__36706___24t(Vvar__36707)
<=> ! [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__36707,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_36729',axiom,
! [Vvar__36730] :
( c_24__type__36729___24t(Vvar__36730)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__36730,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37027',axiom,
! [Vvar__37028] :
( c_24__type__37027___24t(Vvar__37028)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__37028,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37032',axiom,
! [Vvar__37033] :
( c_24__type__37032___24t(Vvar__37033)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__37033,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37581',axiom,
! [Vvar__37582] :
( c_24__type__37581___24t(Vvar__37582)
<=> ! [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__37582,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37593',axiom,
! [Vvar__37594] :
( c_24__type__37593___24t(Vvar__37594)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(happ(Vvar__37594,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37596',axiom,
! [Vvar__37597] :
( c_24__type__37596___24t(Vvar__37597)
<=> ! [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__37597,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37617',axiom,
! [Vvar__37618] :
( c_24__type__37617___24t(Vvar__37618)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__37618,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37624',axiom,
! [Vvar__37625] :
( c_24__type__37624___24t(Vvar__37625)
<=> ! [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__37625,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37627',axiom,
! [Vvar__37628] :
( c_24__type__37627___24t(Vvar__37628)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__37628,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37660',axiom,
! [Vvar__37661] :
( c_24__type__37660___24t(Vvar__37661)
<=> ! [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__37661,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37700',axiom,
! [Vvar__37701] :
( c_24__type__37700___24t(Vvar__37701)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(happ(happ(Vvar__37701,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37702',axiom,
! [Vvar__37703] :
( c_24__type__37702___24t(Vvar__37703)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(happ(Vvar__37703,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37717',axiom,
! [Vvar__37718] :
( c_24__type__37717___24t(Vvar__37718)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,happ(happ(happ(Vvar__37718,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37722',axiom,
! [Vvar__37723] :
( c_24__type__37722___24t(Vvar__37723)
<=> ! [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__37723,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37724',axiom,
! [Vvar__37725] :
( c_24__type__37724___24t(Vvar__37725)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__37725,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37742',axiom,
! [Vvar__37743] :
( c_24__type__37742___24t(Vvar__37743)
<=> ! [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_2eZ___24t(happ(happ(Vvar__37743,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37757',axiom,
! [Vvar__37758] :
( c_24__type__37757___24t(Vvar__37758)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__37758,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37761',axiom,
! [Vvar__37762] :
( c_24__type__37761___24t(Vvar__37762)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__37762,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37782',axiom,
! [Vvar__37783] :
( c_24__type__37782___24t(Vvar__37783)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__37783,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37785',axiom,
! [Vvar__37786] :
( c_24__type__37785___24t(Vvar__37786)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__37786,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37852',axiom,
! [Vvar__37853] :
( c_24__type__37852___24t(Vvar__37853)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(happ(Vvar__37853,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37914',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__37915] :
( c_24__type__37914___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__37915)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__37915,Vv__CANONICAL__6)) ) ) ).
fof('$_type_38089',axiom,
! [Vvar__38090] :
( c_24__type__38089___24t(Vvar__38090)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(Vvar__38090,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38092',axiom,
! [Vvar__38093] :
( c_24__type__38092___24t(Vvar__38093)
<=> ! [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__38093,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38095',axiom,
! [Vvar__38096] :
( c_24__type__38095___24t(Vvar__38096)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__38096,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38100',axiom,
! [Vvar__38101] :
( c_24__type__38100___24t(Vvar__38101)
<=> ! [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__38101,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38109',axiom,
! [Vvar__38110] :
( c_24__type__38109___24t(Vvar__38110)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__38110,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38118',axiom,
! [Vvar__38119] :
( c_24__type__38118___24t(Vvar__38119)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__38119,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38174',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38175] :
( c_24__type__38174___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38175)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__38175,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_38179',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38180] :
( c_24__type__38179___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38180)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__38180,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_38186',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38187] :
( c_24__type__38186___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38187)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__38187,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_38205',axiom,
! [Vvar__38206] :
( c_24__type__38205___24t(Vvar__38206)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__38206,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38243',axiom,
! [Vvar__38244] :
( c_24__type__38243___24t(Vvar__38244)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__38244,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_38366',axiom,
! [Vvar__38367] :
( c_24__type__38366___24t(Vvar__38367)
<=> ! [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__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___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__38367,Vv__CANONICAL__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('$_type_38450',axiom,
! [Vvar__38451] :
( c_24__type__38450___24t(Vvar__38451)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__38451,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38465',axiom,
! [Vvar__38466] :
( c_24__type__38465___24t(Vvar__38466)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__38466,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3876',axiom,
! [Vvar__3877] :
( c_24__type__3876___24t(Vvar__3877)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__2968___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__2973___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__2982___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__3877,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_39000',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__39001] :
( c_24__type__39000___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__39001)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__39001,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_39346',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39347] :
( c_24__type__39346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39347)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__39347,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3945',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3946] :
( c_24__type__3945___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3946)
<=> ! [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__3946,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_39692',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39693] :
( c_24__type__39692___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39693)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__39693,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3988',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__3989] :
( c_24__type__3988___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__3989)
<=> ! [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__3989,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_40015',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40016] :
( c_24__type__40015___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40016)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__40016,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_40361',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__40362] :
( c_24__type__40361___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__40362)
<=> ! [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__40362,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_4063',axiom,
! [Vvar__4064] :
( c_24__type__4063___24t(Vvar__4064)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__646___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3153___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__4064,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_40707',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__40708] :
( c_24__type__40707___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__40708)
<=> ! [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__40708,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_4104',axiom,
! [Vvar__4105] :
( c_24__type__4104___24t(Vvar__4105)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__646___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__4114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__3153___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__4105,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_41053',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__41054] :
( c_24__type__41053___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__41054)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__41054,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_4114',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4115] :
( c_24__type__4114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4115)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__4115,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_4129',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4130] :
( c_24__type__4129___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4130)
<=> ! [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__4130,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_41399',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__41400] :
( c_24__type__41399___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__41400)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__41400,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_4143',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4144] :
( c_24__type__4143___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4144)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__4144,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_41745',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__41746] :
( c_24__type__41745___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__41746)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__41746,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_42068',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__42069] :
( c_24__type__42068___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__42069)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__42069,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_42414',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__42415] :
( c_24__type__42414___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__42415)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__42415,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_42760',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__42761] :
( c_24__type__42760___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__42761)
<=> ! [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__42761,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_43083',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__43084] :
( c_24__type__43083___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__43084)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__43084,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_43406',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__43407] :
( c_24__type__43406___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__43407)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__43407,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_4367',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__4368] :
( c_24__type__4367___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__4368)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__4368,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_43752',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__43753] :
( c_24__type__43752___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__43753)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__43753,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_44',axiom,
! [Vvar__45] :
( c_24__type__44___24t(Vvar__45)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__45,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_44204',axiom,
! [Vvar__44205] :
( c_24__type__44204___24t(Vvar__44205)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2952___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__44205,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_4436',axiom,
! [Vvar__4437] :
( c_24__type__4436___24t(Vvar__4437)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__4437,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_45001',axiom,
! [Vvar__45002] :
( c_24__type__45001___24t(Vvar__45002)
<=> ! [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__45002,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45156',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45157] :
( c_24__type__45156___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45157)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__45157,Vv__CANONICAL__3)) ) ) ).
fof('$_type_45164',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45165] :
( c_24__type__45164___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45165)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__45165,Vv__CANONICAL__3)) ) ) ).
fof('$_type_45172',axiom,
! [Vvar__45173] :
( c_24__type__45172___24t(Vvar__45173)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2218___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2218___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__45173,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_45240',axiom,
! [Vvar__45241] :
( c_24__type__45240___24t(Vvar__45241)
<=> ! [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__45241,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45243',axiom,
! [Vvar__45244] :
( c_24__type__45243___24t(Vvar__45244)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__45244,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45258',axiom,
! [Vvar__45259] :
( c_24__type__45258___24t(Vvar__45259)
<=> ! [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__45259,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_45279',axiom,
! [Vvar__45280] :
( c_24__type__45279___24t(Vvar__45280)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__45280,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45285',axiom,
! [Vvar__45286] :
( c_24__type__45285___24t(Vvar__45286)
<=> ! [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__45286,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45330',axiom,
! [Vvar__45331] :
( c_24__type__45330___24t(Vvar__45331)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__45331,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45384',axiom,
! [Vvar__45385] :
( c_24__type__45384___24t(Vvar__45385)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(happ(happ(Vvar__45385,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45389',axiom,
! [Vvar__45390] :
( c_24__type__45389___24t(Vvar__45390)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(happ(happ(Vvar__45390,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46391',axiom,
! [Vvar__46392] :
( c_24__type__46391___24t(Vvar__46392)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( Vv__CANONICAL__1 = Vv__CANONICAL__2
=> cProp___24t(happ(happ(happ(Vvar__46392,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_46401',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__46402] :
( c_24__type__46401___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__46402)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__46402,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_46406',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__46407] :
( c_24__type__46406___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__46407)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__46407,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_46415',axiom,
! [Vvar__46416] :
( c_24__type__46415___24t(Vvar__46416)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__46417___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__46417___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__46416,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46417',axiom,
! [Vvar__46418] :
( c_24__type__46417___24t(Vvar__46418)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__46418,Vv__CANONICAL__0)) ) ) ).
fof('$_type_46443',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__46444] :
( c_24__type__46443___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__46444)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__46444,Vv__CANONICAL__3)) ) ) ).
fof('$_type_46451',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__46452] :
( c_24__type__46451___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__46452)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__46452,Vv__CANONICAL__3)) ) ) ).
fof('$_type_46459',axiom,
! [Vvar__46460] :
( c_24__type__46459___24t(Vvar__46460)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2177___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2177___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__46460,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_46478',axiom,
! [Vvar__46479] :
( c_24__type__46478___24t(Vvar__46479)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__46480___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__46480___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__46479,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46480',axiom,
! [Vvar__46481] :
( c_24__type__46480___24t(Vvar__46481)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__46481,Vv__CANONICAL__0)) ) ) ).
fof('$_type_46488',axiom,
! [Vvar__46489] :
( c_24__type__46488___24t(Vvar__46489)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__46490___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__46490___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__46489,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46490',axiom,
! [Vvar__46491] :
( c_24__type__46490___24t(Vvar__46491)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__46491,Vv__CANONICAL__0)) ) ) ).
fof('$_type_46515',axiom,
! [Vvar__46516] :
( c_24__type__46515___24t(Vvar__46516)
<=> ! [Vv__CANONICAL__0] :
( ciT___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__46516,Vv__CANONICAL__0)) ) ) ).
fof('$_type_46531',axiom,
! [Vvar__46532] :
( c_24__type__46531___24t(Vvar__46532)
<=> ! [Vv__CANONICAL__0] :
( ciT___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cHList_2ehlist_2ehlist___24t(cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2)
=> cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__1,happ(happ(happ(Vvar__46532,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_46547',axiom,
! [Vvar__46548] :
( c_24__type__46547___24t(Vvar__46548)
<=> ! [Vv__CANONICAL__0] :
( ciT___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cHList_2ehlist_2ehlist___24t(cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2)
=> cF___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__46548,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_46580',axiom,
! [Vvar__46581] :
( c_24__type__46580___24t(Vvar__46581)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__46583___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2enil___24a1(ciT)),cHList_2ehlist_2eHnil))
=> ! [Vv__CANONICAL__2] :
( c_24__type__46600___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__3,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__46581,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_46583',axiom,
! [Vvar__46584] :
( c_24__type__46583___24t(Vvar__46584)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__46584,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46600',axiom,
! [Vv__CANONICAL__0,Vvar__46601] :
( c_24__type__46600___24t(Vv__CANONICAL__0,Vvar__46601)
<=> ! [Vv__CANONICAL__1] :
( ciT___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cF___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__4))
=> t(happ(happ(happ(happ(happ(Vvar__46601,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,Vv__CANONICAL__1,Vv__CANONICAL__2)),cHList_2ehlist_2eHcons___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ) ) ) ).
fof('$_type_46603',axiom,
! [Vvar__46604] :
( c_24__type__46603___24t(Vvar__46604)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__46604,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46627',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__46628] :
( c_24__type__46627___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__46628)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cType___24t(happ(happ(Vvar__46628,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_46666',axiom,
! [Vvar__46667] :
( c_24__type__46666___24t(Vvar__46667)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__46667,Vv__CANONICAL__0)) ) ) ).
fof('$_type_46686',axiom,
! [Vvar__46687] :
( c_24__type__46686___24t(Vvar__46687)
<=> ! [Vv__CANONICAL__0] :
( ciT___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cF___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cHList_2ehlist_2ehlist___24t(cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__46687,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_46974',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__46975] :
( c_24__type__46974___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__46975)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__46976___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__46975,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_46987',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__46988] :
( c_24__type__46987___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__46988)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__46989___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__46988,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_47653',axiom,
! [Vvar__47654] :
( c_24__type__47653___24t(Vvar__47654)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cHList_2ehlist_2ehlist___24t(cCoq_2eInit_2eDatatypes_2eapp___24a3(ciT,Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__47654,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_47675',axiom,
! [Vvar__47676] :
( c_24__type__47675___24t(Vvar__47676)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__47676,Vv__CANONICAL__0)) ) ) ).
fof('$_type_48237',axiom,
! [Vvar__48238] :
( c_24__type__48237___24t(Vvar__48238)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cHList_2ehlist_2ehlist___24t(cCoq_2eLists_2eList_2erev___24a2(ciT,Vv__CANONICAL__0),happ(happ(Vvar__48238,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_48333',axiom,
! [Vvar__48334] :
( c_24__type__48333___24t(Vvar__48334)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cHList_2ehlist_2ehlist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cHList_2ehlist_2ehlist___24t(cCoq_2eInit_2eDatatypes_2eapp___24a3(ciT,cCoq_2eLists_2eList_2erev___24a2(ciT,Vv__CANONICAL__0),Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__48334,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4998',axiom,
! [Vvar__4999] :
( c_24__type__4998___24t(Vvar__4999)
<=> ! [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__4999,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5009',axiom,
! [Vvar__5010] :
( c_24__type__5009___24t(Vvar__5010)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__5010,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_5011',axiom,
! [Vvar__5012] :
( c_24__type__5011___24t(Vvar__5012)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__5012,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5024',axiom,
! [Vvar__5025] :
( c_24__type__5024___24t(Vvar__5025)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__5025,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5034',axiom,
! [Vvar__5035] :
( c_24__type__5034___24t(Vvar__5035)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__5035,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5063',axiom,
! [Vvar__5064] :
( c_24__type__5063___24t(Vvar__5064)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__5064,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5068',axiom,
! [Vvar__5069] :
( c_24__type__5068___24t(Vvar__5069)
<=> ! [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__5069,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5080',axiom,
! [Vvar__5081] :
( c_24__type__5080___24t(Vvar__5081)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__5081,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_5092',axiom,
! [Vvar__5093] :
( c_24__type__5092___24t(Vvar__5093)
<=> ! [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__5093,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_5123',axiom,
! [Vv__CANONICAL__0,Vvar__5124] :
( c_24__type__5123___24t(Vv__CANONICAL__0,Vvar__5124)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__5124,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_5381',axiom,
! [Vv__CANONICAL__0,Vvar__5382] :
( c_24__type__5381___24t(Vv__CANONICAL__0,Vvar__5382)
<=> ! [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__5382,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_64',axiom,
! [Vvar__65] :
( c_24__type__64___24t(Vvar__65)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__65,Vv__CANONICAL__0)) ) ) ).
fof('$_type_646',axiom,
! [Vv__CANONICAL__0,Vvar__647] :
( c_24__type__646___24t(Vv__CANONICAL__0,Vvar__647)
<=> ! [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__647,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_6868',axiom,
! [Vvar__6869] :
( c_24__type__6868___24t(Vvar__6869)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__6875___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__2),cCoq_2eInit_2eLogic_2eeq__refl___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)))
=> ( Vv__CANONICAL__1 = Vv__CANONICAL__2
=> t(happ(happ(happ(happ(happ(Vvar__6869,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__3,Vv__CANONICAL__1)) ) ) ) ) ) ) ) ).
fof('$_type_6875',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6876] :
( c_24__type__6875___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6876)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( Vv__CANONICAL__2 = Vv__CANONICAL__1
=> cType___24t(happ(Vvar__6876,Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_69',axiom,
! [Vvar__70] :
( c_24__type__69___24t(Vvar__70)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__70,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7071',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__7072] :
( c_24__type__7071___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__7072)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7072,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7164',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7165] :
( c_24__type__7164___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7165)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7165,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_72',axiom,
! [Vv__CANONICAL__0,Vvar__73] :
( c_24__type__72___24t(Vv__CANONICAL__0,Vvar__73)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__73,Vv__CANONICAL__1)) ) ) ).
fof('$_type_724',axiom,
! [Vvar__725] :
( c_24__type__724___24t(Vvar__725)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__725,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_7257',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__7258] :
( c_24__type__7257___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__7258)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7258,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7339',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7340] :
( c_24__type__7339___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7340)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__7340,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_7432',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__7433] :
( c_24__type__7432___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__7433)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7433,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7514',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7515] :
( c_24__type__7514___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7515)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__7515,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_7607',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__7608] :
( c_24__type__7607___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__7608)
<=> ! [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__7608,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_7748',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7749] :
( c_24__type__7748___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7749)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__7749,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_7767',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7768] :
( c_24__type__7767___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7768)
<=> ! [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__7768,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_7969',axiom,
! [Vvar__7970] :
( c_24__type__7969___24t(Vvar__7970)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2952___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__646___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__2968___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__2973___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__2982___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__7970,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_8672',axiom,
! [Vvar__8673] :
( c_24__type__8672___24t(Vvar__8673)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5381___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_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__8673,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_87',axiom,
! [Vvar__88] :
( c_24__type__87___24t(Vvar__88)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__88,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9',axiom,
! [Vvar__10] :
( c_24__type__9___24t(Vvar__10)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__10,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9700',axiom,
! [Vvar__9701] :
( c_24__type__9700___24t(Vvar__9701)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2961___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__9701,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_99',axiom,
! [Vvar__100] :
( c_24__type__99___24t(Vvar__100)
<=> ! [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__100,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
c_24__type__2153___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__46415___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__118289___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__5034___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
c_24__type__37724___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__37722___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__45258___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.add',axiom,
c_24__type__37700___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd) ).
fof('$_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.mem',axiom,
c_24__type__45279___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev',axiom,
c_24__type__37702___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
c_24__type__45285___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('$_typeof_Coq.FSets.FSetPositive.PositiveSet.xelements',axiom,
c_24__type__37717___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__113947___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_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__1914___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__1905___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__1912___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__2699___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__87___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_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__69___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__5080___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__5063___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__5068___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__1976___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__9___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.list_rec',axiom,
c_24__type__1951___24t(cCoq_2eInit_2eDatatypes_2elist__rec) ).
fof('$_typeof_Coq.Init.Datatypes.list_rect',axiom,
c_24__type__1951___24t(cCoq_2eInit_2eDatatypes_2elist__rect) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__2___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__64___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__9___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__2699___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__44___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__28___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__5092___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__28___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.xorb',axiom,
c_24__type__2699___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__2143___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__2143___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__2143___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__2143___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__2143___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__1905___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__2143___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__2153___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__2153___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__2153___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__2194___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__2235___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__35359___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__35364___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__35275___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__35193___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.projT1',axiom,
c_24__type__35216___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).
fof('$_typeof_Coq.Init.Specif.projT2',axiom,
c_24__type__35239___24t(cCoq_2eInit_2eSpecif_2eprojT2) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__35280___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__2174___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__46459___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__2215___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__45172___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__35252___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
c_24__type__35306___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__35336___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Lists.List.ForallPairs',axiom,
c_24__type__17451___24t(cCoq_2eLists_2eList_2eForallPairs) ).
fof('$_typeof_Coq.Lists.List.Forall_rect',axiom,
c_24__type__17166___24t(cCoq_2eLists_2eList_2eForall__rect) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__99___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.combine',axiom,
c_24__type__2401___24t(cCoq_2eLists_2eList_2ecombine) ).
fof('$_typeof_Coq.Lists.List.concat',axiom,
c_24__type__2055___24t(cCoq_2eLists_2eList_2econcat) ).
fof('$_typeof_Coq.Lists.List.count_occ',axiom,
c_24__type__15781___24t(cCoq_2eLists_2eList_2ecount__occ) ).
fof('$_typeof_Coq.Lists.List.destruct_list',axiom,
c_24__type__15505___24t(cCoq_2eLists_2eList_2edestruct__list) ).
fof('$_typeof_Coq.Lists.List.exists_last',axiom,
c_24__type__2035___24t(cCoq_2eLists_2eList_2eexists__last) ).
fof('$_typeof_Coq.Lists.List.existsb',axiom,
c_24__type__3166___24t(cCoq_2eLists_2eList_2eexistsb) ).
fof('$_typeof_Coq.Lists.List.filter',axiom,
c_24__type__2379___24t(cCoq_2eLists_2eList_2efilter) ).
fof('$_typeof_Coq.Lists.List.find',axiom,
c_24__type__16735___24t(cCoq_2eLists_2eList_2efind) ).
fof('$_typeof_Coq.Lists.List.firstn',axiom,
c_24__type__2071___24t(cCoq_2eLists_2eList_2efirstn) ).
fof('$_typeof_Coq.Lists.List.flat_map',axiom,
c_24__type__3064___24t(cCoq_2eLists_2eList_2eflat__map) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__3103___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__3139___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.forallb',axiom,
c_24__type__3166___24t(cCoq_2eLists_2eList_2eforallb) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__15488___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.hd_error',axiom,
c_24__type__15497___24t(cCoq_2eLists_2eList_2ehd__error) ).
fof('$_typeof_Coq.Lists.List.incl',axiom,
c_24__type__3185___24t(cCoq_2eLists_2eList_2eincl) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__2310___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.lel',axiom,
c_24__type__3185___24t(cCoq_2eLists_2eList_2elel) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__2357___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nodup',axiom,
c_24__type__16933___24t(cCoq_2eLists_2eList_2enodup) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__2001___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.nth_default',axiom,
c_24__type__15670___24t(cCoq_2eLists_2eList_2enth__default) ).
fof('$_typeof_Coq.Lists.List.nth_error',axiom,
c_24__type__2023___24t(cCoq_2eLists_2eList_2enth__error) ).
fof('$_typeof_Coq.Lists.List.nth_in_or_default',axiom,
c_24__type__15657___24t(cCoq_2eLists_2eList_2enth__in__or__default) ).
fof('$_typeof_Coq.Lists.List.nth_ok',axiom,
c_24__type__15649___24t(cCoq_2eLists_2eList_2enth__ok) ).
fof('$_typeof_Coq.Lists.List.partition',axiom,
c_24__type__16770___24t(cCoq_2eLists_2eList_2epartition) ).
fof('$_typeof_Coq.Lists.List.remove',axiom,
c_24__type__15709___24t(cCoq_2eLists_2eList_2eremove) ).
fof('$_typeof_Coq.Lists.List.removelast',axiom,
c_24__type__109___24t(cCoq_2eLists_2eList_2eremovelast) ).
fof('$_typeof_Coq.Lists.List.repeat',axiom,
c_24__type__17485___24t(cCoq_2eLists_2eList_2erepeat) ).
fof('$_typeof_Coq.Lists.List.rev',axiom,
c_24__type__109___24t(cCoq_2eLists_2eList_2erev) ).
fof('$_typeof_Coq.Lists.List.rev\'',axiom,
c_24__type__109___24t(cCoq_2eLists_2eList_2erev_27) ).
fof('$_typeof_Coq.Lists.List.rev_append',axiom,
c_24__type__87___24t(cCoq_2eLists_2eList_2erev__append) ).
fof('$_typeof_Coq.Lists.List.seq',axiom,
c_24__type__2445___24t(cCoq_2eLists_2eList_2eseq) ).
fof('$_typeof_Coq.Lists.List.skipn',axiom,
c_24__type__2071___24t(cCoq_2eLists_2eList_2eskipn) ).
fof('$_typeof_Coq.Lists.List.split',axiom,
c_24__type__16820___24t(cCoq_2eLists_2eList_2esplit) ).
fof('$_typeof_Coq.Lists.List.tl',axiom,
c_24__type__109___24t(cCoq_2eLists_2eList_2etl) ).
fof('$_typeof_Coq.Lists.SetoidList.equivlistA',axiom,
c_24__type__2522___24t(cCoq_2eLists_2eSetoidList_2eequivlistA) ).
fof('$_typeof_Coq.Lists.SetoidList.inclA',axiom,
c_24__type__2522___24t(cCoq_2eLists_2eSetoidList_2einclA) ).
fof('$_typeof_Coq.Lists.SetoidList.removeA',axiom,
c_24__type__34479___24t(cCoq_2eLists_2eSetoidList_2eremoveA) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__4063___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__4063___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__4104___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__4104___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__118488___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
c_24__type__118673___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq_on',axiom,
c_24__type__159686___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
c_24__type__114199___24t(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
c_24__type__46391___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.internal_eq_rew_r_dep',axiom,
c_24__type__6868___24t(cCoq_2eLogic_2eEqdepFacts_2einternal__eq__rew__r__dep) ).
fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
c_24__type__45243___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__46478___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__45243___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__45243___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__15309___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__37624___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__37617___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__15309___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__15311___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__37617___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__37627___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__5011___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__5024___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__5024___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__2684___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__2684___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__45240___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('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
c_24__type__116455___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__37660___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__116538___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
c_24__type__2684___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__37660___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__2684___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qdiv',axiom,
c_24__type__19443___24t(cCoq_2eQArith_2eQArith__base_2eQdiv) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq',axiom,
c_24__type__19437___24t(cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__19434___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qminus',axiom,
c_24__type__19443___24t(cCoq_2eQArith_2eQArith__base_2eQminus) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmult',axiom,
c_24__type__19443___24t(cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__19675___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__19666___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__38450___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__38450___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__19669___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__38450___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__38450___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__19666___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__19666___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__19669___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__19666___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__120588___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__33708___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__9___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__45001___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Transitive',axiom,
c_24__type__38465___24t(cCoq_2eSets_2eRelations__1_2eTransitive) ).
fof('$_typeof_Coq.Sorting.Sorted.Sorted_rect',axiom,
c_24__type__34826___24t(cCoq_2eSorting_2eSorted_2eSorted__rect) ).
fof('$_typeof_Coq.Sorting.Sorted.StronglySorted_rec',axiom,
c_24__type__35080___24t(cCoq_2eSorting_2eSorted_2eStronglySorted__rec) ).
fof('$_typeof_Coq.Sorting.Sorted.StronglySorted_rect',axiom,
c_24__type__35080___24t(cCoq_2eSorting_2eSorted_2eStronglySorted__rect) ).
fof('$_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__35376___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.list_ascii_of_string',axiom,
c_24__type__35420___24t(cCoq_2eStrings_2eString_2elist__ascii__of__string) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Strings.String.string_of_list_ascii',axiom,
c_24__type__35414___24t(cCoq_2eStrings_2eString_2estring__of__list__ascii) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__120279___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
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.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__45240___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__47675___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__36623___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__36615___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.of_list',axiom,
c_24__type__36633___24t(cCoq_2eVectors_2eVectorDef_2eof__list) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__36598___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.to_list',axiom,
c_24__type__36706___24t(cCoq_2eVectors_2eVectorDef_2eto__list) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__4998___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__46488___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__4998___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__4998___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__4998___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__4998___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__4998___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__37761___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__37757___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__45330___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__37757___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gtb',axiom,
c_24__type__37581___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egtb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__37581___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__37757___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__37757___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__37757___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__37757___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__37785___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__37782___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__37761___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pos_sub',axiom,
c_24__type__37742___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__37757___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__37852___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__37757___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__37761___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__37581___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength',axiom,
c_24__type__37596___24t(cCoq_2eZArith_2eZcomplements_2eZlength) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength_aux',axiom,
c_24__type__37593___24t(cCoq_2eZArith_2eZcomplements_2eZlength__aux) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__120588___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__122416___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__9___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__9___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__2286___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__9___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__3288___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__19693___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__9___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__9___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_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__9___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__9___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__9___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.ge_bool',axiom,
c_24__type__20451___24t(cCoq_2emicromega_2eRingMicromega_2ege__bool) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__724___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__28___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.Tauto.cnf',axiom,
c_24__type__28___24t(cCoq_2emicromega_2eTauto_2ecnf) ).
fof('$_typeof_Coq.micromega.Tauto.cnf_checker',axiom,
c_24__type__36343___24t(cCoq_2emicromega_2eTauto_2ecnf__checker) ).
fof('$_typeof_Coq.micromega.Tauto.collect_annot',axiom,
c_24__type__4436___24t(cCoq_2emicromega_2eTauto_2ecollect__annot) ).
fof('$_typeof_Coq.micromega.Tauto.cons_id',axiom,
c_24__type__35433___24t(cCoq_2emicromega_2eTauto_2econs__id) ).
fof('$_typeof_Coq.micromega.Tauto.eval_clause',axiom,
c_24__type__36170___24t(cCoq_2emicromega_2eTauto_2eeval__clause) ).
fof('$_typeof_Coq.micromega.Tauto.eval_cnf',axiom,
c_24__type__36199___24t(cCoq_2emicromega_2eTauto_2eeval__cnf) ).
fof('$_typeof_Coq.micromega.Tauto.eval_f',axiom,
c_24__type__35588___24t(cCoq_2emicromega_2eTauto_2eeval__f) ).
fof('$_typeof_Coq.micromega.Tauto.eval_tt',axiom,
c_24__type__36141___24t(cCoq_2emicromega_2eTauto_2eeval__tt) ).
fof('$_typeof_Coq.micromega.ZMicromega.DoneProof',axiom,
cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(cCoq_2emicromega_2eZMicromega_2eDoneProof) ).
fof('$_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.Zunsat',axiom,
c_24__type__36729___24t(cCoq_2emicromega_2eZMicromega_2eZunsat) ).
fof('$_typeof_Coq.micromega.ZMicromega.is_pol_Z0',axiom,
c_24__type__37027___24t(cCoq_2emicromega_2eZMicromega_2eis__pol__Z0) ).
fof('$_typeof_Coq.micromega.ZMicromega.make_conj',axiom,
c_24__type__3288___24t(cCoq_2emicromega_2eZMicromega_2emake__conj) ).
fof('$_typeof_Coq.micromega.ZMicromega.make_impl',axiom,
c_24__type__19693___24t(cCoq_2emicromega_2eZMicromega_2emake__impl) ).
fof('$_typeof_Coq.micromega.ZMicromega.valid_cut_sign',axiom,
c_24__type__37032___24t(cCoq_2emicromega_2eZMicromega_2evalid__cut__sign) ).
fof('$_typeof_Coq.setoid_ring.BinList.jump',axiom,
c_24__type__2671___24t(cCoq_2esetoid__ring_2eBinList_2ejump) ).
fof('$_typeof_Coq.setoid_ring.BinList.nth',axiom,
c_24__type__5009___24t(cCoq_2esetoid__ring_2eBinList_2enth) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEI',axiom,
c_24__type__38089___24t(cCoq_2esetoid__ring_2eField__theory_2eFEI) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEO',axiom,
c_24__type__38089___24t(cCoq_2esetoid__ring_2eField__theory_2eFEO) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__38095___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__38100___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__38092___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEdiv',axiom,
c_24__type__38100___24t(cCoq_2esetoid__ring_2eField__theory_2eFEdiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__11157___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__38109___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__38100___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEopp',axiom,
c_24__type__38109___24t(cCoq_2esetoid__ring_2eField__theory_2eFEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEpow',axiom,
c_24__type__38118___24t(cCoq_2esetoid__ring_2eField__theory_2eFEpow) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEsub',axiom,
c_24__type__38100___24t(cCoq_2esetoid__ring_2eField__theory_2eFEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__9___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__13677___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons',axiom,
c_24__type__13751___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons00',axiom,
c_24__type__13903___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons00) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons2',axiom,
c_24__type__13903___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons2) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
c_24__type__7969___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEopp',axiom,
c_24__type__9700___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__2947___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PExpr_eq',axiom,
c_24__type__8672___24t(cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.absurd_PCond',axiom,
c_24__type__11239___24t(cCoq_2esetoid__ring_2eField__theory_2eabsurd__PCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.ceqb_spec\'',axiom,
c_24__type__14698___24t(cCoq_2esetoid__ring_2eField__theory_2eceqb__spec_27) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__11236___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__11216___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.display_linear',axiom,
c_24__type__12420___24t(cCoq_2esetoid__ring_2eField__theory_2edisplay__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.display_pow_linear',axiom,
c_24__type__13125___24t(cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__9___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__11205___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__11216___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__9___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_common',axiom,
c_24__type__11311___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__common) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
c_24__type__11311___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__left) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
c_24__type__11311___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__right) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.split',axiom,
c_24__type__11368___24t(cCoq_2esetoid__ring_2eField__theory_2esplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__15311___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nsub',axiom,
c_24__type__15309___24t(cCoq_2esetoid__ring_2eInitialRing_2eNsub) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nwadd',axiom,
c_24__type__45389___24t(cCoq_2esetoid__ring_2eInitialRing_2eNwadd) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nwcons',axiom,
c_24__type__45384___24t(cCoq_2esetoid__ring_2eInitialRing_2eNwcons) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__15345___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiNword',axiom,
c_24__type__38366___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__38243___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__15282___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.get_signZ',axiom,
c_24__type__15293___24t(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.triv_div',axiom,
c_24__type__15387___24t(cCoq_2esetoid__ring_2eInitialRing_2etriv__div) ).
fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
c_24__type__2699___24t(cCoq_2esetoid__ring_2eRing_2ebool__eq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mphi',axiom,
c_24__type__23220___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.P0',axiom,
c_24__type__20807___24t(cCoq_2esetoid__ring_2eRing__polynom_2eP0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.P1',axiom,
c_24__type__20807___24t(cCoq_2esetoid__ring_2eRing__polynom_2eP1) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__24174___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__24174___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__24180___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__24185___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__24177___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__3876___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__24185___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__24194___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__24199___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__24185___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__9___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__20820___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__20807___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__20962___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pequiv',axiom,
c_24__type__23156___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePequiv) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__20812___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__9___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi',axiom,
c_24__type__23083___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__28367___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.add_pow_list',axiom,
c_24__type__26565___24t(cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
c_24__type__25373___24t(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkPinj',axiom,
c_24__type__20812___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkPinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkZmon',axiom,
c_24__type__21736___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkZmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
c_24__type__25658___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__44204___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__25119___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.r_list_pow',axiom,
c_24__type__27980___24t(cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.vmon',axiom,
c_24__type__21736___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
c_24__type__21736___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__33241___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__33241___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__33536___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
c_24__type__1912___24t(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__15311___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__28842___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__28821___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).
fof('$_typeof_ExtLib.Core.RelDec.RelDec',axiom,
c_24__type__19798___24t(cExtLib_2eCore_2eRelDec_2eRelDec) ).
fof('$_typeof_ExtLib.Data.Member.MN',axiom,
c_24__type__17562___24t(cExtLib_2eData_2eMember_2eMN) ).
fof('$_typeof_ExtLib.Data.Member.MZ',axiom,
c_24__type__17550___24t(cExtLib_2eData_2eMember_2eMZ) ).
fof('$_typeof_ExtLib.Data.Member.get_next',axiom,
c_24__type__18076___24t(cExtLib_2eData_2eMember_2eget__next) ).
fof('$_typeof_ExtLib.Data.Member.member',axiom,
c_24__type__17521___24t(cExtLib_2eData_2eMember_2emember) ).
fof('$_typeof_ExtLib.Data.Member.member_rec',axiom,
c_24__type__17645___24t(cExtLib_2eData_2eMember_2emember__rec) ).
fof('$_typeof_ExtLib.Data.Member.member_rect',axiom,
c_24__type__17645___24t(cExtLib_2eData_2eMember_2emember__rect) ).
fof('$_typeof_ExtLib.Data.Member.to_nat',axiom,
c_24__type__17771___24t(cExtLib_2eData_2eMember_2eto__nat) ).
fof('$_typeof_ExtLib.Structures.Functor.ID',axiom,
c_24__type__38205___24t(cExtLib_2eStructures_2eFunctor_2eID) ).
fof('$_typeof_ExtLib.Tactics.Injection.Build_Injective',axiom,
c_24__type__15463___24t(cExtLib_2eTactics_2eInjection_2eBuild__Injective) ).
fof('$_typeof_ExtLib.Tactics.Injection.Injective',axiom,
c_24__type__15450___24t(cExtLib_2eTactics_2eInjection_2eInjective) ).
fof('$_typeof_ExtLib.Tactics.Injection.result',axiom,
c_24__type__15477___24t(cExtLib_2eTactics_2eInjection_2eresult) ).
fof('$_typeof_F',axiom,
c_24__type__46515___24t(cF) ).
fof('$_typeof_HList.hlist.Hcons',axiom,
c_24__type__46686___24t(cHList_2ehlist_2eHcons) ).
fof('$_typeof_HList.hlist.Hnil',axiom,
cHList_2ehlist_2ehlist___24t(cCoq_2eInit_2eDatatypes_2enil___24a1(ciT),cHList_2ehlist_2eHnil) ).
fof('$_typeof_HList.hlist.Injection_equiv_hlist_app',axiom,
c_24__type__126682___24t(cHList_2ehlist_2eInjection__equiv__hlist__app) ).
fof('$_typeof_HList.hlist.Injection_equiv_hlist_cons',axiom,
c_24__type__126706___24t(cHList_2ehlist_2eInjection__equiv__hlist__cons) ).
fof('$_typeof_HList.hlist.hlist',axiom,
c_24__type__46666___24t(cHList_2ehlist_2ehlist) ).
fof('$_typeof_HList.hlist.hlist_app',axiom,
c_24__type__47653___24t(cHList_2ehlist_2ehlist__app) ).
fof('$_typeof_HList.hlist.hlist_hd',axiom,
c_24__type__46547___24t(cHList_2ehlist_2ehlist__hd) ).
fof('$_typeof_HList.hlist.hlist_rec',axiom,
c_24__type__46580___24t(cHList_2ehlist_2ehlist__rec) ).
fof('$_typeof_HList.hlist.hlist_rect',axiom,
c_24__type__46580___24t(cHList_2ehlist_2ehlist__rect) ).
fof('$_typeof_HList.hlist.hlist_rev',axiom,
c_24__type__48237___24t(cHList_2ehlist_2ehlist__rev) ).
fof('$_typeof_HList.hlist.hlist_rev\'',axiom,
c_24__type__48333___24t(cHList_2ehlist_2ehlist__rev_27) ).
fof('$_typeof_HList.hlist.hlist_tl',axiom,
c_24__type__46531___24t(cHList_2ehlist_2ehlist__tl) ).
fof('$_typeof_iT',axiom,
cType___24t(ciT) ).
fof('Coq.Arith.Gt.gt_S_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Gt.gt_Sn_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.Gt.gt_irrefl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V0__n) ) ).
fof('Coq.Arith.Gt.gt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Gt.gt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
=> ~ 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)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Le.le_n_0_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO)
=> cCoq_2eInit_2eDatatypes_2eO = V0__n ) ) ).
fof('Coq.Arith.Le.le_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Lt.lt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Lt.lt_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.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.PeanoNat.Nat.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_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.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO)
<=> V0__n = cCoq_2eInit_2eDatatypes_2eO ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_sym',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.PeanoNat.Nat.nlt_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.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
<=> 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)
=> ( 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__2143,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__1905,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.PeanoNat.Nat.succ_inj',axiom,
! [V0__n1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n2)
=> ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n2)
=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.Arith.Plus.le_plus_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Plus.le_plus_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Bool.Bool.absurd_eq_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( p(c_24False)
=> V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.Bool.Bool.eq_true_iff_eq',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue )
=> V0__b1 = V1__b2 ) ) ) ).
fof('Coq.Bool.Bool.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.Bool.Bool.orb_prop',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__a = cCoq_2eInit_2eDatatypes_2etrue
| V1__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.Bool.Bool.orb_true_intro',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
| V1__b2 = cCoq_2eInit_2eDatatypes_2etrue )
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.Bool.Bool.trans_eq_bool',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.tree_ind',axiom,
! [V0__P] :
( c_24__type__126485___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf))
=> ( ! [V2__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V2__t)
=> ( p(happ(V0__P,V2__t))
=> ! [V4__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V4__b)
=> ! [V5__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V5__t)
=> ( p(happ(V0__P,V5__t))
=> p(happ(V0__P,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V2__t,V4__b,V5__t))) ) ) ) ) )
=> ! [V3__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V3__t)
=> p(happ(V0__P,V3__t)) ) ) ) ) ).
fof('Coq.Init.Datatypes.andb_prop',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__a = cCoq_2eInit_2eDatatypes_2etrue
& V1__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__72___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__72___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__1907___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.eq_add_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Init.Peano.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__3262___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Init.Peano.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.Init.Peano.le_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Init.Peano.plus_n_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Init.Peano.plus_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ).
fof('Coq.Lists.List.Add_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l2))) ) ) ) ) ).
fof('Coq.Lists.List.Add_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V3__l,V4__l_27)
=> cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V4__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l)) ) ) ) ).
fof('Coq.Lists.List.Add_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V3__l_27))
<=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l))) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__P] :
( c_24__type__2434___24t(V0__A,V2__P)
=> ( ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> p(happ(happ(V2__P,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l))) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l_27)
=> ( p(happ(happ(V2__P,V5__l),V6__l_27))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l_27))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l)
=> p(happ(happ(V2__P,V5__l),V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V2__l))
=> ? [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
& cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V4__l_27,V2__l) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l_27) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__P] :
( c_24__type__2434___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_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',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l))
<=> ( p(happ(V1__P,V2__x))
| cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V3__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(happ(V1__P,V2__x))
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V3__l)
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_dec_subproof',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ~ cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.Exists_dec_subproof0',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( ~ cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V3__l_27)
=> ( ~ p(happ(V1__P,V2__a))
=> ~ cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_exists',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V2__l)
<=> ? [V3__x] :
( t(V3__x,V0__A)
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
& p(happ(V1__P,V3__x)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_impl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__2177___24t(V0__A,V2__Q)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
=> p(happ(V2__Q,V3__x)) ) )
=> ! [V4__xs] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__xs)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V4__xs)
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V2__Q,V4__xs) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__72___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__2177___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V3__x))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V5__l)
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l))) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.FOP_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,happ(V1__R,V2__a),V3__l))
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V3__l)
=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall2_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__2125___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__2125___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__2125___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__2125___24t(V0__A,V1__B,V2__R)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V6__l_27)
=> ( p(happ(happ(V2__R,V3__x),V4__y))
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V5__l,V6__l_27)
=> cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V5__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,V4__y,V6__l_27)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall2_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__2125___24t(V0__A,V1__B,V2__R)
=> ! [V3__P] :
( c_24__type__17419___24t(V0__A,V1__B,V3__P)
=> ( p(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V1__B)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ! [V8__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V8__l_27)
=> ( p(happ(happ(V2__R,V5__x),V6__y))
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V7__l,V8__l_27)
=> ( p(happ(happ(V3__P,V7__l),V8__l_27))
=> p(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x,V7__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,V6__y,V8__l_27))) ) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V7__l)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V6__l,V7__l)
=> p(happ(happ(V3__P,V6__l),V7__l)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall2_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__2125___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.Forall2_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__2125___24t(V0__A,V1__B,V2__R)
=> ! [V3__P] :
( c_24__type__17419___24t(V0__A,V1__B,V3__P)
=> ( p(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V1__B)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ! [V8__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V8__l_27)
=> ( p(happ(happ(V2__R,V5__x),V6__y))
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V7__l,V8__l_27)
=> ( p(happ(happ(V3__P,V7__l),V8__l_27))
=> p(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x,V7__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,V6__y,V8__l_27))) ) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V7__l)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V6__l,V7__l)
=> p(happ(happ(V3__P,V6__l),V7__l)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.ForallOrdPairs_ForallPairs',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ( ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) )
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V1__R,V4__y),V3__x)) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V4__l)
=> cCoq_2eLists_2eList_2eForallPairs___24a3(V0__A,V1__R,V4__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.ForallOrdPairs_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V2__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V2__l))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__y,V2__l))
=> ( V4__x = V5__y
| p(happ(happ(V1__R,V4__x),V5__y))
| p(happ(happ(V1__R,V5__y),V4__x)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.ForallOrdPairs_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,happ(V1__R,V4__a),V5__l))
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V5__l)
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V5__l))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.ForallOrdPairs_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,happ(V1__R,V4__a),V5__l))
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V5__l)
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V5__l))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.ForallPairs_ForallOrdPairs',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForallPairs___24a3(V0__A,V1__R,V2__l)
=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V2__l) ) ) ) ) ).
fof('Coq.Lists.List.Forall_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___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))
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l))
=> p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l))) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_dec_subproof',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( ~ p(happ(V1__P,V2__a))
=> ~ p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l_27))) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_dec_subproof0',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( ~ p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l_27))
=> ~ p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l_27))) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_forall',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l))
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
=> p(happ(V1__P,V3__x)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_impl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__2177___24t(V0__A,V2__Q)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(happ(V1__P,V3__a))
=> p(happ(V2__Q,V3__a)) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V4__l))
=> p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V2__Q,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(happ(V1__P,V4__x))
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V5__l))
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V5__l))
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)))
=> p(happ(V1__P,V2__a)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_inv_tail',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__x0] :
( t(V2__x0,V0__A)
=> ! [V3__xs] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__xs)
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x0,V3__xs)))
=> p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__xs)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ).
fof('Coq.Lists.List.Forall_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2177___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(happ(V1__P,V4__x))
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V5__l))
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V5__l))
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.In_nth',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)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V1__l))
=> ? [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
& cCoq_2eInit_2ePeano_2elt___24a2(V5__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V5__n,V1__l,V3__d) = V2__x ) ) ) ) ) ) ).
fof('Coq.Lists.List.In_nth_error',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V1__l))
=> ? [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V4__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V2__x) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_Add',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l_27)
<=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l)
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V2__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V2__l))
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_cons_iff',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_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l))
<=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V2__l))
& cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_incl_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__72___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V4__l))
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_map_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l))
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ).
fof('Coq.Lists.List.NoDup_nodup',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__decA] :
( c_24__type__15621___24t(V0__A,V1__decA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,V2__l)) ) ) ) ).
fof('Coq.Lists.List.NoDup_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__d] :
( t(V2__d,V0__A)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l)
<=> ! [V3__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__i)
=> ! [V4__j] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__j)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V3__i,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V4__j,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))
=> ( cCoq_2eLists_2eList_2enth___24a4(V0__A,V3__i,V1__l,V2__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__j,V1__l,V2__d)
=> V3__i = V4__j ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_nth_error',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l)
<=> ! [V2__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
=> ! [V3__j] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__j)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__i,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))
=> ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V2__i) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V3__j)
=> V2__i = V3__j ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_remove',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))
& ~ p(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.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)))
=> ~ p(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.NoDup_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__72___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V4__l))
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.app_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_eq_unit',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_2eapp___24a3(V0__A,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))
=> ( ( V1__x = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& V2__y = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) )
| ( V1__x = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))
& V2__y = 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)
=> ( 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.app_removelast_last',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__d] :
( t(V2__d,V0__A)
=> ( V1__l != cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
=> V1__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,cCoq_2eLists_2eList_2elast___24a3(V0__A,V1__l,V2__d),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ) ) ).
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.count_occ_cons_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eq__dec] :
( c_24__type__15621___24t(V0__A,V1__eq__dec)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( V3__x = V4__y
=> cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V2__l),V4__y) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V2__l,V4__y)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.count_occ_cons_neq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eq__dec] :
( c_24__type__15621___24t(V0__A,V1__eq__dec)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( V3__x != V4__y
=> cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V2__l),V4__y) = cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V2__l,V4__y) ) ) ) ) ) ) ).
fof('Coq.Lists.List.count_occ_inv_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eq__dec] :
( c_24__type__15621___24t(V0__A,V1__eq__dec)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V2__l,V3__x) = cCoq_2eInit_2eDatatypes_2eO )
<=> V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ) ).
fof('Coq.Lists.List.count_occ_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__decA] :
( c_24__type__16605___24t(V0__A,V1__B,V3__decA)
=> ! [V4__decB] :
( c_24__type__16614___24t(V0__A,V1__B,V4__decB)
=> ( ! [V5__x1] :
( t(V5__x1,V0__A)
=> ! [V6__x2] :
( t(V6__x2,V0__A)
=> ( happ(V2__f,V5__x1) = happ(V2__f,V6__x2)
=> V5__x1 = V6__x2 ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V3__decA,V7__l,V6__x) = cCoq_2eLists_2eList_2ecount__occ___24a4(V1__B,V4__decB,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V7__l),happ(V2__f,V6__x)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.count_occ_not_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eq__dec] :
( c_24__type__15621___24t(V0__A,V1__eq__dec)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
<=> cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V2__l,V3__x) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ) ).
fof('Coq.Lists.List.existsb_exists',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1217___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2etrue
<=> ? [V3__x] :
( t(V3__x,V0__A)
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
& happ(V1__f,V3__x) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ).
fof('Coq.Lists.List.existsb_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1217___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__d] :
( t(V4__d,V0__A)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V3__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l))
=> ( cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2efalse
=> happ(V1__f,cCoq_2eLists_2eList_2enth___24a4(V0__A,V3__n,V2__l,V4__d)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
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__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__2361___24t(V0__A,V1__B,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V4__l)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V6__a,V4__l))
=> happ(V2__f,V6__a) = happ(V3__g,V6__a) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.filter_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1217___24t(V0__A,V1__f)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l)))
<=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V3__l))
& happ(V1__f,V2__x) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('Coq.Lists.List.find_none',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1217___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V2__l))
=> happ(V1__f,V4__x) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('Coq.Lists.List.find_some',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1217___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__x)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
& happ(V1__f,V3__x) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('Coq.Lists.List.firstn_O',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_2eO,V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__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)
=> ( 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_cons',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_2eLists_2eList_2efirstn___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V3__l)) ) ) ) ) ).
fof('Coq.Lists.List.firstn_firstn',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
=> ! [V3__j] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__j)
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__i,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V3__j,V1__l)) = cCoq_2eLists_2eList_2efirstn___24a3(V0__A,cCoq_2eInit_2eNat_2emin___24a2(V2__i,V3__j),V1__l) ) ) ) ) ).
fof('Coq.Lists.List.firstn_le_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l)),V1__n) ) ) ) ).
fof('Coq.Lists.List.firstn_length_le',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)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V2__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V1__l)) = V2__n ) ) ) ) ).
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__3110___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_left_rev_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__3153___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__i] :
( t(V4__i,V1__B)
=> cCoq_2eLists_2eList_2efold__right___24a5(V1__B,V0__A,V2__f,V4__i,cCoq_2eLists_2eList_2erev___24a2(V0__A,V3__l)) = cCoq_2eLists_2eList_2efold__left___24a5(V1__B,V0__A,c_24__lam__16675___24a3(V0__A,V1__B,V2__f),V3__l,V4__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__3153___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ! [V5__i] :
( t(V5__i,V1__B)
=> cCoq_2eLists_2eList_2efold__right___24a5(V1__B,V0__A,V2__f,V5__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27)) = cCoq_2eLists_2eList_2efold__right___24a5(V1__B,V0__A,V2__f,cCoq_2eLists_2eList_2efold__right___24a5(V1__B,V0__A,V2__f,V5__i,V4__l_27),V3__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.fold_symmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__2952___24t(V0__A,V1__f)
=> ( ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> happ(happ(V1__f,V2__x),happ(happ(V1__f,V3__y),V4__z)) = happ(happ(V1__f,happ(happ(V1__f,V2__x),V3__y)),V4__z) ) ) )
=> ! [V3__a0] :
( t(V3__a0,V0__A)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> happ(happ(V1__f,V3__a0),V4__y) = happ(happ(V1__f,V4__y),V3__a0) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V0__A,V1__f,V5__l,V3__a0) = cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V0__A,V1__f,V3__a0,V5__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.forallb_forall',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1217___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2etrue
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
=> happ(V1__f,V3__x) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('Coq.Lists.List.hd_error_cons',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_2ehd__error___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V1__l)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V2__x) ) ) ) ).
fof('Coq.Lists.List.hd_error_some_nil',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_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V2__a)
=> V1__l != cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ) ).
fof('Coq.Lists.List.hd_error_tl_repr',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)
=> ! [V3__r] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__r)
=> ( ( cCoq_2eLists_2eList_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V2__a)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = V3__r )
<=> V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__r) ) ) ) ) ) ).
fof('Coq.Lists.List.in_app_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)))
<=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_app_or',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m)))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,V3__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l))) ) ) ) ) ) ).
fof('Coq.Lists.List.in_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l))) ) ) ) ).
fof('Coq.Lists.List.in_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l)))
=> ( V1__a = V2__b
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,happ(V2__f,V4__x),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l))) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_map_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V4__y,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)))
<=> ? [V5__x] :
( t(V5__x,V0__A)
& happ(V2__f,V5__x) = V4__y
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V3__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ).
fof('Coq.Lists.List.in_or_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m)) )
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m))) ) ) ) ) ) ).
fof('Coq.Lists.List.in_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V1__l))
<=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l))) ) ) ) ) ).
fof('Coq.Lists.List.in_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V2__l))
=> ? [V4__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
& ? [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
& V2__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V5__l2)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_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)
=> ! [V3__u] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__u)
=> ! [V4__v] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__v)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V2__l))
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l),V4__v)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V3__u,V4__v)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__u) ) ) ) ) ) ) ) ) ).
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.incl_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V3__m))
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__m)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l),V3__m) ) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V1__l) ) ) ).
fof('Coq.Lists.List.incl_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__m)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__m)) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_tran',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__m,V3__n)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n) ) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__b] :
( t(V1__b,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V2__l,V3__m)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__b,V3__m)) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_cons_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V3__l,V4__m)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__b,V4__m)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l_27)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l_27,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))
=> cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) = V1__l_27 ) ) ) ).
fof('Coq.Lists.List.lel_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V1__l) ) ) ).
fof('Coq.Lists.List.lel_tail',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__b,V4__m))
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,V3__l,V4__m) ) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V2__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V2__m,V3__n)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V3__n) ) ) ) ) ) ) ).
fof('Coq.Lists.List.length_zero_iff_nil',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,V1__l) = cCoq_2eInit_2eDatatypes_2eO
<=> V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ).
fof('Coq.Lists.List.map_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___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_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l)) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,happ(V2__f,V3__x),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.map_eq_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
=> V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ) ) ).
fof('Coq.Lists.List.map_ext',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__2361___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__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__2361___24t(V0__A,V1__B,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__a,V4__l))
=> happ(V2__f,V5__a) = happ(V3__g,V5__a) ) )
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V4__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.map_ext_in_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__2361___24t(V0__A,V1__B,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V4__l)
<=> ! [V5__a] :
( t(V5__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__a,V4__l))
=> happ(V2__f,V5__a) = happ(V3__g,V5__a) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.map_id',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V0__A,c_24__lam__16626___24a1(V0__A),V1__l) = V1__l ) ) ).
fof('Coq.Lists.List.map_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l) ) ) ) ) ).
fof('Coq.Lists.List.map_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__2361___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__16632___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__16646___24a5(V0__A,V1__B,V2__C,V3__f,V4__g),V5__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.map_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__d] :
( t(V4__d,V0__A)
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> cCoq_2eLists_2eList_2enth___24a4(V1__B,V5__n,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l),happ(V2__f,V4__d)) = happ(V2__f,cCoq_2eLists_2eList_2enth___24a4(V0__A,V5__n,V3__l,V4__d)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nil_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) != cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l) ) ) ) ).
fof('Coq.Lists.List.nodup_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__decA] :
( c_24__type__15621___24t(V0__A,V1__decA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,V2__l)))
<=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.nodup_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__decA] :
( c_24__type__15621___24t(V0__A,V1__decA)
=> ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__k)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__a] :
( t(V4__a,V0__A)
=> ( cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,V2__k) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V3__l)
=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__a,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.not_in_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)))
<=> ( V1__x != V2__a
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,cCoq_2eLists_2eList_2enth___24a4(V0__A,V1__n,V2__l,V3__d),V2__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_S_cons',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)
=> ! [V4__a] :
( t(V4__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,cCoq_2eLists_2eList_2enth___24a4(V0__A,V1__n,V2__l,V3__d),V2__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,cCoq_2eLists_2eList_2enth___24a4(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V2__l),V3__d),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V2__l))) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_default_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V3__d,V2__l,V1__n) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V1__n,V2__l,V3__d) ) ) ) ) ).
fof('Coq.Lists.List.nth_error_In',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__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V2__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__x)
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V1__l)) ) ) ) ) ) ).
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_indep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ! [V4__d_27] :
( t(V4__d_27,V0__A)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V4__d_27) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_overflow',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V2__n)
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V3__d) = V3__d ) ) ) ) ) ).
fof('Coq.Lists.List.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)
=> ( 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.partition_cons1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1217___24t(V0__A,V1__f)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
=> ! [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
=> ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V4__l1,V5__l2)
=> ( happ(V1__f,V2__a) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V4__l1),V5__l2) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.partition_cons2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1217___24t(V0__A,V1__f)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
=> ! [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
=> ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V4__l1,V5__l2)
=> ( happ(V1__f,V2__a) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V4__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V5__l2)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.remove_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eq__dec] :
( c_24__type__15621___24t(V0__A,V1__eq__dec)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,V2__l))) ) ) ) ) ).
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_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__72___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__72___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.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_cons',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_2eLists_2eList_2eskipn___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) = cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,V3__l) ) ) ) ) ).
fof('Coq.Lists.List.skipn_none',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_2elength___24a2(V0__A,V1__l),V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ).
fof('Coq.Lists.SetoidList.InA_InfA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__ltA] :
( c_24__type__646___24t(V0__A,V3__ltA)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ( ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V6__y,V4__l)
=> p(happ(happ(V3__ltA,V5__x),V6__y)) ) )
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V3__ltA,V5__x,V4__l) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_alt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V3__l)
<=> ? [V4__y] :
( t(V4__y,V0__A)
& p(happ(happ(V1__eqA,V2__x),V4__y))
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__y,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_altdef',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V3__l)
<=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,happ(V1__eqA,V2__x),V3__l) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___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__646___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__646___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__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2533___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__72___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__646___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__646___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__646___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V4__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_double_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_eqA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__eqA,V4__x),V5__y))
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V5__y,V3__l) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__72___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_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))
<=> p(c_24False) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_permute_heads',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__z,V5__l)))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__z,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V5__l))) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__p] :
( t(V2__p,V0__A)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__p,cCoq_2eLists_2eList_2erev___24a2(V0__A,V3__m))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__p,V3__m) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__72___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__646___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__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l))
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.In_InfA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__ltA] :
( c_24__type__646___24t(V0__A,V1__ltA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__y,V2__l))
=> p(happ(happ(V1__ltA,V3__x),V4__y)) ) )
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V3__x,V2__l) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InfA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__ltA] :
( c_24__type__646___24t(V0__A,V1__ltA)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ! [V4__a] :
( t(V4__a,V0__A)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V4__a,V2__l1)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V4__a,V3__l2)
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V4__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InfA_ltA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__ltA] :
( c_24__type__646___24t(V0__A,V1__ltA)
=> ( cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(V0__A,V1__ltA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__ltA,V4__x),V5__y))
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V5__y,V3__l)
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V4__x,V3__l) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___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_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V5__l)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,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_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V3__l)
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eLists_2eList_2erev___24a2(V0__A,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V5__l)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,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_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___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.NoDupA_swap',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___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)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x,V4__l_27)))
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27))) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqarefl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___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__646___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_altdef',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
<=> cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V0__A,V1__eqA,V2__l,V3__l_27) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___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__646___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__646___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__646___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__646___24t(V0__A,V1__eqA)
=> ! [V2__P] :
( c_24__type__2434___24t(V0__A,V2__P)
=> ( p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__x_27] :
( t(V5__x_27,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27)
=> ( p(happ(happ(V1__eqA,V4__x),V5__x_27))
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V6__l,V7__l_27)
=> ( p(happ(happ(V2__P,V6__l),V7__l_27))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x_27,V7__l_27))) ) ) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V5__l,V6__l)
=> p(happ(happ(V2__P,V5__l),V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l_27) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l1_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V2__l1,V3__l1_27)
=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l1),cCoq_2eLists_2eList_2erev___24a2(V0__A,V3__l1_27)) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__P] :
( c_24__type__2434___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.equivlistA_NoDupA_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___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__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
=> ! [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ( p(happ(happ(V1__eqA,V6__x),V7__y))
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__x,V3__l))
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V7__y,V5__l2)))
=> ( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__x,V3__l),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V7__y,V5__l2)))
=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V3__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,V5__l2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_app_idem',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___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_cons_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ~ cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_cons_proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33790___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__2554___24a1(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_2econs___24a1(V0__A)) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_double_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_nil_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V3__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))
=> V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_permute_heads',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V4__l))) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlist_equiv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___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.filter_InA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__f] :
( c_24__type__1217___24t(V0__A,V2__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1217___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cCoq_2eInit_2eDatatypes_2ebool,V1__eqA,c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V2__f)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V5__x,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V2__f,V4__l))
<=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V5__x,V4__l)
& happ(V2__f,V5__x) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_add',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__4129___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__3153___24t(V0__A,V3__B,V6__f)
=> ! [V7__i] :
( t(V7__i,V3__B)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V3__B,V4__eqB,V6__f)
=> ! [V10__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V10__s_27)
=> ! [V11__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V11__s)
=> ! [V12__x] :
( t(V12__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V11__s)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V10__s_27)
=> ( ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V12__x,V11__s)
=> ( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V10__s_27,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V12__x,V11__s))
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,V10__s_27)),happ(happ(V6__f,V12__x),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,V11__s)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_add2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__4129___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__3153___24t(V0__A,V3__B,V6__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ( cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V0__A,V3__B,V4__eqB,V6__f)
=> ! [V9__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V9__s_27)
=> ! [V10__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V10__s)
=> ! [V11__i] :
( t(V11__i,V3__B)
=> ! [V12__j] :
( t(V12__j,V3__B)
=> ! [V13__x] :
( t(V13__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V10__s)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V9__s_27)
=> ( p(happ(happ(V4__eqB,V11__i),V12__j))
=> ( ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V13__x,V10__s)
=> ( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V9__s_27,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V13__x,V10__s))
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V11__i,V9__s_27)),happ(happ(V6__f,V13__x),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V12__j,V10__s)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_add_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__4129___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__3153___24t(V0__A,V3__B,V6__f)
=> ! [V7__i] :
( t(V7__i,V3__B)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ! [V9__R] :
( c_24__type__4114___24t(V0__A,V3__B,V9__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V9__R)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4114___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__33834___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cProp,V1__eqA,c_3c_3d_3e)),V9__R)
=> ( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V3__B,V4__eqB,V9__R,V6__f)
=> ! [V13__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V13__s_27)
=> ! [V14__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V14__s)
=> ! [V15__x] :
( t(V15__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V14__s)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V13__s_27)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V9__R,V13__s_27)
=> ( ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V15__x,V14__s)
=> ( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V13__s_27,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V15__x,V14__s))
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,V13__s_27)),happ(happ(V6__f,V15__x),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,V14__s)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_add_restr2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__4129___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__3153___24t(V0__A,V3__B,V6__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ! [V8__R] :
( c_24__type__4114___24t(V0__A,V3__B,V8__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V8__R)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4114___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__33834___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cProp,V1__eqA,c_3c_3d_3e)),V8__R)
=> ( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V3__B,V4__eqB,V8__R,V6__f)
=> ! [V12__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V12__s_27)
=> ! [V13__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V13__s)
=> ! [V14__i] :
( t(V14__i,V3__B)
=> ! [V15__j] :
( t(V15__j,V3__B)
=> ! [V16__x] :
( t(V16__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V13__s)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V12__s_27)
=> ( p(happ(happ(V4__eqB,V14__i),V15__j))
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V8__R,V12__s_27)
=> ( ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V16__x,V13__s)
=> ( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V12__s_27,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V16__x,V13__s))
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V14__i,V12__s_27)),happ(happ(V6__f,V16__x),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V15__j,V13__s)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_commutes',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__4129___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__3153___24t(V0__A,V3__B,V6__f)
=> ! [V7__i] :
( t(V7__i,V3__B)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V3__B,V4__eqB,V6__f)
=> ! [V10__s1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V10__s1)
=> ! [V11__s2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V11__s2)
=> ! [V12__x] :
( t(V12__x,V0__A)
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V10__s1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V12__x,V11__s2)))),happ(happ(V6__f,V12__x),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V10__s1,V11__s2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_commutes2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__4129___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__3153___24t(V0__A,V3__B,V6__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ( cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V0__A,V3__B,V4__eqB,V6__f)
=> ! [V9__s1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V9__s1)
=> ! [V10__s2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V10__s2)
=> ! [V11__i] :
( t(V11__i,V3__B)
=> ! [V12__x] :
( t(V12__x,V0__A)
=> ! [V13__x_27] :
( t(V13__x_27,V0__A)
=> ( p(happ(happ(V1__eqA,V12__x),V13__x_27))
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V11__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V9__s1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V12__x,V10__s2)))),happ(happ(V6__f,V13__x_27),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V11__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V9__s1,V10__s2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_commutes_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__4129___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__3153___24t(V0__A,V3__B,V6__f)
=> ! [V7__i] :
( t(V7__i,V3__B)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ! [V9__R] :
( c_24__type__4114___24t(V0__A,V3__B,V9__R)
=> ( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V3__B,V4__eqB,V9__R,V6__f)
=> ! [V11__s1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V11__s1)
=> ! [V12__s2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V12__s2)
=> ! [V13__x] :
( t(V13__x,V0__A)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V9__R,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V11__s1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V13__x,V12__s2)))
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V11__s1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V13__x,V12__s2)))),happ(happ(V6__f,V13__x),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V11__s1,V12__s2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_commutes_restr2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__4129___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__3153___24t(V0__A,V3__B,V6__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ! [V8__R] :
( c_24__type__4114___24t(V0__A,V3__B,V8__R)
=> ( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V3__B,V4__eqB,V8__R,V6__f)
=> ! [V10__s1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V10__s1)
=> ! [V11__s2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V11__s2)
=> ! [V12__x] :
( t(V12__x,V0__A)
=> ! [V13__i] :
( t(V13__i,V3__B)
=> ! [V14__j] :
( t(V14__j,V3__B)
=> ( p(happ(happ(V4__eqB,V13__i),V14__j))
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V8__R,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V10__s1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V12__x,V11__s2)))
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V13__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V10__s1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V12__x,V11__s2)))),happ(happ(V6__f,V12__x),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V14__j,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V10__s1,V11__s2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_eqlistA2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__eqB] :
( c_24__type__4129___24t(V0__A,V2__B,V3__eqB)
=> ! [V4__f] :
( c_24__type__3153___24t(V0__A,V2__B,V4__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V2__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V2__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V2__B,V2__B,V3__eqB,V3__eqB)),V4__f)
=> ! [V6__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__s)
=> ! [V7__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__s_27)
=> ! [V8__i] :
( t(V8__i,V2__B)
=> ! [V9__j] :
( t(V9__j,V2__B)
=> ( p(happ(happ(V3__eqB,V8__i),V9__j))
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V6__s,V7__s_27)
=> p(happ(happ(V3__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V2__B,V0__A,V4__f,V8__i,V6__s)),cCoq_2eLists_2eList_2efold__right___24a5(V2__B,V0__A,V4__f,V9__j,V7__s_27))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_equivlistA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__4129___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__3153___24t(V0__A,V3__B,V6__f)
=> ! [V7__i] :
( t(V7__i,V3__B)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V3__B,V4__eqB,V6__f)
=> ! [V10__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V10__s)
=> ! [V11__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V11__s_27)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V10__s)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V11__s_27)
=> ( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V10__s,V11__s_27)
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,V10__s)),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,V11__s_27))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_equivlistA2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__4129___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__3153___24t(V0__A,V3__B,V6__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ( cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V0__A,V3__B,V4__eqB,V6__f)
=> ! [V9__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V9__s)
=> ! [V10__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V10__s_27)
=> ! [V11__i] :
( t(V11__i,V3__B)
=> ! [V12__j] :
( t(V12__j,V3__B)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V9__s)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V10__s_27)
=> ( p(happ(happ(V4__eqB,V11__i),V12__j))
=> ( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V9__s,V10__s_27)
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V11__i,V9__s)),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V12__j,V10__s_27))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_equivlistA_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__4129___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__3153___24t(V0__A,V3__B,V6__f)
=> ! [V7__i] :
( t(V7__i,V3__B)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ! [V9__R] :
( c_24__type__4114___24t(V0__A,V3__B,V9__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V9__R)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4114___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__33834___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cProp,V1__eqA,c_3c_3d_3e)),V9__R)
=> ( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V3__B,V4__eqB,V9__R,V6__f)
=> ! [V13__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V13__s)
=> ! [V14__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V14__s_27)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V13__s)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V14__s_27)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V9__R,V13__s)
=> ( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V13__s,V14__s_27)
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,V13__s)),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,V14__s_27))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_equivlistA_restr2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__4129___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__3153___24t(V0__A,V3__B,V6__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3153___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4143___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ! [V8__R] :
( c_24__type__4114___24t(V0__A,V3__B,V8__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V8__R)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4114___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__33834___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cProp,V1__eqA,c_3c_3d_3e)),V8__R)
=> ( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V3__B,V4__eqB,V8__R,V6__f)
=> ! [V12__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V12__s)
=> ! [V13__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V13__s_27)
=> ! [V14__i] :
( t(V14__i,V3__B)
=> ! [V15__j] :
( t(V15__j,V3__B)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V12__s)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V13__s_27)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V8__R,V12__s)
=> ( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V12__s,V13__s_27)
=> ( p(happ(happ(V4__eqB,V14__i),V15__j))
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V14__i,V12__s)),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V15__j,V13__s_27))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.incl_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eSetoidList_2einclA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),V2__l) ) ) ) ).
fof('Coq.Lists.SetoidList.removeA_InA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__eqA__dec] :
( c_24__type__46974___24t(V0__A,V1__eqA,V3__eqA__dec)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V6__y,cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V3__eqA__dec,V5__x,V4__l))
<=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V6__y,V4__l)
& ~ p(happ(happ(V1__eqA,V5__x),V6__y)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.removeA_equivlistA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__646___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__eqA__dec] :
( c_24__type__46987___24t(V0__A,V1__eqA,V3__eqA__dec)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l_27)
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ( ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V6__x,V4__l)
=> ( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__x,V4__l),V5__l_27)
=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V4__l,cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V3__eqA__dec,V6__x,V5__l_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__37890___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.dec_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__37889___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
& p(V1__B) )
=> ( ~ p(V0__A)
| ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ~ ( p(V0__A)
| p(V1__B) )
=> ( ~ p(V0__A)
& ~ p(V1__B) ) ) ) ) ).
fof('Coq.Logic.Eqdep.Eq_rect_eq.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__2218___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.Streicher_K',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__P] :
( c_24__type__114203___24t(V0__U,V1__x,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x)))
=> ( V1__x = V1__x
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.UIP',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.eq_dep_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__2218___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> ! [V4__y] :
( t(V4__y,happ(V1__P,V2__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
=> V3__x = V4__y ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__2218___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.EqdepFacts.eq_indd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__P] :
( c_24__type__159676___24t(V0__A,V1__x,V2__P)
=> ( p(happ(happ(V2__P,V1__x),cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( V1__x = V4__y
=> p(happ(V2__P,V4__y)) ) ) ) ) ) ) ).
fof('Coq.Logic.EqdepFacts.internal_eq_sym_internal',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
=> V2__y = V1__x ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) ) )
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V2__x = V3__y
=> ( V2__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity_on',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ( ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) )
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V1__x = V3__y
=> ( V1__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.equal_f',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__2361___24t(V0__A,V1__B,V3__g)
=> ( V2__f = V3__g
=> ! [V5__x] :
( t(V5__x,V0__A)
=> happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.equal_f_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__2218___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__46401___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__46406___24t(V0__A,V1__B,V3__g)
=> ( V2__f = V3__g
=> ! [V5__x] :
( t(V5__x,V0__A)
=> happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.eta_expansion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__38202___24a3(V0__A,V1__B,V2__f) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.eta_expansion_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__2218___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__38186___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__38194___24a3(V0__A,V1__B,V2__f) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.functional_extensionality',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__2361___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) )
=> V2__f = V3__g ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.functional_extensionality_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__2218___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__38174___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__38179___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) )
=> V2__f = V3__g ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.PI.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.Eq_rect_eq.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__2218___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.Streicher_K',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__P] :
( c_24__type__114203___24t(V0__U,V1__x,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x)))
=> ( V1__x = V1__x
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.UIP',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.eq_dep_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__2218___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> ! [V4__y] :
( t(V4__y,happ(V1__P,V2__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
=> V3__x = V4__y ) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__2218___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.eq_indd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__P] :
( c_24__type__159676___24t(V0__A,V1__x,V2__P)
=> ( p(happ(happ(V2__P,V1__x),cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( V1__x = V4__y
=> p(happ(V2__P,V4__y)) ) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
fof('Coq.NArith.BinNat.N.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ).
fof('Coq.NArith.BinNat.N.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.neq_sym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__2686___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.PArith.BinPos.Pos.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.add_succ_l',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(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V0__p),V1__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V1__q)) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_spec',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(c_24__prop__45254___24a2(V0__x,V1__y),cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y),cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__y,V0__x),cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.PArith.BinPos.Pos.iter_swap_gen',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__159798___24t(V0__A,V1__B,V3__g)
=> ! [V4__h] :
( c_24__type__4143___24t(V0__A,V1__B,V4__h)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> happ(V2__f,happ(V3__g,V5__a)) = happ(V4__h,happ(V2__f,V5__a)) )
=> ! [V6__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> happ(V2__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V3__g,V7__a,V6__p)) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__B,V4__h,happ(V2__f,V7__a),V6__p) ) ) ) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.peano_ind',axiom,
! [V0__P] :
( c_24__type__2686___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.PArith.BinPos.Pos.sub_add',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__q,V0__p))
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__p,V1__q),V1__q) = V0__p ) ) ) ).
fof('Coq.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.Relations.Relation_Operators.Desc_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__646___24t(V0__A,V1__leA)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__leA,V5__x,V6__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))))
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))))) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V0__A,V1__leA,V6__l)
=> p(happ(V2__P,V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.Desc_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__646___24t(V0__A,V1__leA)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__leA,V5__x,V6__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))))
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))))) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V0__A,V1__leA,V6__l)
=> p(happ(V2__P,V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.Lt_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__646___24t(V0__A,V1__leA)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(happ(happ(V1__leA,V2__a),V3__b))
=> ! [V5__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__x)
=> ! [V6__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__y)
=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V5__x),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__b,V6__y)) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.Lt_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__646___24t(V0__A,V1__leA)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__x)
=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__x)) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.Lt_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__646___24t(V0__A,V1__leA)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__x)
=> ! [V4__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,V3__x,V4__y)
=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__x),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V4__y)) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.Ltl_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__646___24t(V0__A,V1__leA)
=> ! [V2__P] :
( c_24__type__2434___24t(V0__A,V2__P)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__x)
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__x))) ) )
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(happ(V1__leA,V4__a),V5__b))
=> ! [V7__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__x)
=> ! [V8__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V8__y)
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V7__x)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__b,V8__y))) ) ) ) ) )
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__x)
=> ! [V7__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,V6__x,V7__y)
=> ( p(happ(happ(V2__P,V6__x),V7__y))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__a,V6__x)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__a,V7__y))) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,V6__l,V7__l)
=> p(happ(happ(V2__P,V6__l),V7__l)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.Ltl_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__646___24t(V0__A,V1__leA)
=> ! [V2__P] :
( c_24__type__2434___24t(V0__A,V2__P)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__x)
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__x))) ) )
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(happ(V1__leA,V4__a),V5__b))
=> ! [V7__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__x)
=> ! [V8__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V8__y)
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V7__x)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__b,V8__y))) ) ) ) ) )
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__x)
=> ! [V7__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,V6__x,V7__y)
=> ( p(happ(happ(V2__P,V6__x),V7__y))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__a,V6__x)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__a,V7__y))) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,V6__l,V7__l)
=> p(happ(happ(V2__P,V6__l),V7__l)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.d_conc',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__646___24t(V0__A,V1__leA)
=> ! [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_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__leA,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))))
=> cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))) ) ) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Build_Setoid_Theory',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__A,V1__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V1__Aeq,V3__x),V3__x)) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> p(happ(happ(V1__Aeq,V4__y),V3__x)) ) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ! [V5__z] :
( t(V5__z,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> ( p(happ(happ(V1__Aeq,V4__y),V5__z))
=> p(happ(happ(V1__Aeq,V3__x),V5__z)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.HdRel_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___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_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__P] :
( c_24__type__72___24t(V0__A,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V5__b] :
( t(V5__b,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( p(happ(happ(V1__R,V2__a),V5__b))
=> p(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__b,V6__l))) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V2__a,V6__l)
=> p(happ(V3__P,V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.HdRel_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V2__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__b,V4__l))
=> p(happ(happ(V1__R,V2__a),V3__b)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.HdRel_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___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.HdRel_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__P] :
( c_24__type__72___24t(V0__A,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V5__b] :
( t(V5__b,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( p(happ(happ(V1__R,V2__a),V5__b))
=> p(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__b,V6__l))) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V2__a,V6__l)
=> p(happ(V3__P,V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.LSorted_cons1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ) ).
fof('Coq.Sorting.Sorted.LSorted_consn',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__b,V4__l))
=> ( p(happ(happ(V1__R,V2__a),V3__b))
=> cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__b,V4__l))) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.LocallySorted_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))) )
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__b,V7__l))
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__b,V7__l)))
=> ( p(happ(happ(V1__R,V5__a),V6__b))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__b,V7__l)))) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V0__A,V1__R,V6__l)
=> p(happ(V2__P,V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.LocallySorted_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))) )
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__b,V7__l))
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__b,V7__l)))
=> ( p(happ(happ(V1__R,V5__a),V6__b))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__b,V7__l)))) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V0__A,V1__R,V6__l)
=> p(happ(V2__P,V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.SSorted_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V3__l))
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,happ(V1__R,V2__a),V3__l))
=> p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l))) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_StronglySorted',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__A,V1__R)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V3__l)
=> p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V3__l)) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V3__l)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V2__a,V3__l)
=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_extends',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__A,V1__R)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__l))
=> p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,happ(V1__R,V3__a),V4__l)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V5__l)
=> ( p(happ(V2__P,V5__l))
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V4__a,V5__l)
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V5__l))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___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,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__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) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V5__l)
=> ( p(happ(V2__P,V5__l))
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V4__a,V5__l)
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V5__l))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.StronglySorted_Sorted',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V2__l))
=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V2__l) ) ) ) ) ).
fof('Coq.Sorting.Sorted.StronglySorted_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V5__l))
=> ( p(happ(V2__P,V5__l))
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,happ(V1__R,V4__a),V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V5__l))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V5__l))
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.StronglySorted_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__646___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__72___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V5__l))
=> ( p(happ(V2__P,V5__l))
=> ( p(cCoq_2eLists_2eList_2eForall___24a3(V0__A,happ(V1__R,V4__a),V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V5__l))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V5__l))
=> p(happ(V2__P,V5__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.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_sym',axiom,
! [V0__x] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.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_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.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__37864___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
fof('Coq.ZArith.BinInt.Z.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_sym_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
<=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| 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_eq_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| 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.max_spec',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_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.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.neq_sym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_inj',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.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_2437861___24a2(V0__p,V1__q) ) ) ).
fof('Coq.ZArith.Zbool.Zeq_bool_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.Zcomplements.Zlength_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_2eZArith_2eZcomplements_2eZlength___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZcomplements_2eZlength___24a2(V0__A,V2__l)) ) ) ) ).
fof('Coq.ZArith.Zcomplements.Zlength_correct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eZArith_2eZcomplements_2eZlength___24a2(V0__A,V1__l) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)) ) ) ).
fof('Coq.ZArith.Zcomplements.Zlength_nil_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( cCoq_2eZArith_2eZcomplements_2eZlength___24a2(V0__A,V1__l) = cCoq_2eNumbers_2eBinNums_2eZ0
=> V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ).
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_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_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.Nat2Z.is_nonneg',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n))) ) ).
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.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.SORrt',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__2952___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2952___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2952___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__646___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__646___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.ropp_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__2952___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2952___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2952___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__646___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__646___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2961___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req),V6__ropp) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.rplus_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__2952___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2952___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2952___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__646___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__646___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V3__rplus) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.rtimes_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__2952___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2952___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2952___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__646___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__646___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V4__rtimes) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.sor_setoid_Reflexive',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__2952___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2952___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2952___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__646___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__646___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.sor_setoid_Symmetric',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__2952___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2952___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2952___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__646___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__646___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_conj_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__2177___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__2177___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__2177___24t(V0__A,V1__eval)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__g] :
( cProp___24t(V3__g)
=> ( ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V2__l)
=> p(V3__g) )
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V0__A,V1__eval,V2__l,V3__g) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_conj_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__2177___24t(V0__A,V1__eval)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V2__l)
=> ! [V4__p] :
( t(V4__p,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__p,V2__l))
=> p(happ(V1__eval,V4__p)) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_impl_true',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__2177___24t(V0__A,V1__eval)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V0__A,V1__eval,V2__l,c_24True) ) ) ) ).
fof('Coq.micromega.Refl.not_make_conj_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__t] :
( t(V1__t,V0__A)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__a)
=> ! [V3__eval] :
( c_24__type__2177___24t(V0__A,V3__eval)
=> ( ( p(happ(V3__eval,V1__t))
| ~ p(happ(V3__eval,V1__t)) )
=> ( ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__t,V2__a))
=> ( ~ p(happ(V3__eval,V1__t))
| ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,V2__a) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.micomega_sor_setoid_Reflexive',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__2952___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2952___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2952___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__646___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__646___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.micomega_sor_setoid_Symmetric',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__2952___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2952___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2952___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__646___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__646___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.micomega_sor_setoid_Transitive',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__2952___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2952___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2952___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__646___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__646___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.ropp_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__2952___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2952___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2952___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__646___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__646___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2961___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req),V6__ropp) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.rplus_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__2952___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2952___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2952___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__646___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__646___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V3__rplus) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.rtimes_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__2952___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2952___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2952___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__646___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__646___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V4__rtimes) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Tauto.map_simpl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2361___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694___24a4(V0__A,V1__B,V2__f,V3__l) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.E_ST',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive)) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.add_iff',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ! [V2__y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__y)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__x,V0__s))
<=> ( V1__x = V2__y
| cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,V0__s) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.dec_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__122450___24a2(V0__x,V1__y)) ) ) ).
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.OMEGA6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA8',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__18130___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x))) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_plus_distr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__18130___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__18130___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__18130___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__18130___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__18130___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__18130___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor5',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__18130___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.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.BinList.jump_add',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [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__A,V3__l)
=> cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__i,V2__j),V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V1__i,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__j,V3__l)) ) ) ) ) ).
fof('Coq.setoid_ring.BinList.jump_pred_double',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__i] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__i)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__i),cCoq_2eLists_2eList_2etl___24a2(V0__A,V2__l)) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V1__i,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V1__i,V2__l)) ) ) ) ).
fof('Coq.setoid_ring.BinList.jump_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__j] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__j)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2etl___24a2(V0__A,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V1__j,V2__l)) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V1__j,cCoq_2eLists_2eList_2etl___24a2(V0__A,V2__l)) ) ) ) ).
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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___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.NPEequiv_eq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__phi] :
( c_24__type__2968___24t(V0__R,V9__C,V10__phi)
=> ! [V11__Cpow] :
( cType___24t(V11__Cpow)
=> ! [V12__Cp__phi] :
( c_24__type__2973___24t(V0__R,V9__C,V11__Cpow,V12__Cp__phi)
=> ! [V13__rpow] :
( c_24__type__2982___24t(V0__R,V9__C,V11__Cpow,V13__rpow)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V9__C),cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a13(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__2973___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__2982___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.PCond_cons',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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__2973___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__2982___24t(V0__R,V8__C,V10__Cpow,V12__rpow)
=> ! [V13__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V13__l)
=> ! [V14__a] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,V14__a)
=> ! [V15__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__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,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V14__a,V15__l1))
<=> ( ~ 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,V13__l,V14__a)),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,V13__l,V15__l1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.PCond_cons_inv_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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__2973___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__2982___24t(V0__R,V8__C,V10__Cpow,V12__rpow)
=> ! [V13__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V13__l)
=> ! [V14__a] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,V14__a)
=> ! [V15__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__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,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V14__a,V15__l1))
=> ~ 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,V13__l,V14__a)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.PCond_cons_inv_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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__2973___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__2982___24t(V0__R,V8__C,V10__Cpow,V12__rpow)
=> ! [V13__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V13__l)
=> ! [V14__a] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,V14__a)
=> ! [V15__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__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,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V14__a,V15__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__l1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.absurd_PCond_bottom',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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__7748___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__7748___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__7748___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__4143___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__7767___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__Cpow] :
( cType___24t(V18__Cpow)
=> ! [V19__Cp__phi] :
( c_24__type__2973___24t(V0__R,V8__C,V18__Cpow,V19__Cp__phi)
=> ! [V20__rpow] :
( c_24__type__2982___24t(V0__R,V8__C,V18__Cpow,V20__rpow)
=> ! [V21__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V21__l)
=> ~ 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,V16__phi,V18__Cpow,V19__Cp__phi,V20__rpow,V21__l,cCoq_2esetoid__ring_2eField__theory_2eabsurd__PCond___24a2(V8__C,V9__cO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ceqb_spec',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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__7748___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__7748___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__7748___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__4143___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__7767___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__c] :
( t(V18__c,V8__C)
=> ! [V19__c_27] :
( t(V19__c_27,V8__C)
=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(happ(happ(V7__req,happ(V16__phi,V18__c)),happ(V16__phi,V19__c_27)),c_24True,happ(happ(V15__ceqb,V18__c),V19__c_27)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.field_is_integral_domain',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__r1] :
( t(V13__r1,V0__R)
=> ! [V14__r2] :
( t(V14__r2,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__r1),V1__rO))
=> ( ~ p(happ(happ(V9__req,V14__r2),V1__rO))
=> ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V13__r1),V14__r2)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.radd_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2961___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__646___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__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__r] :
( t(V13__r,V0__R)
=> p(happ(happ(V9__req,V13__r),happ(happ(V7__rdiv,V13__r),V2__rI))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv8',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> ( p(happ(happ(V9__req,V13__a),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V13__a),V14__b)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___24a1(V0__R),V9__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V9__req,V9__req)),V7__rdiv) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv_r_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___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.rinv_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rinv] :
( c_24__type__2961___24t(V0__R,V1__rinv)
=> ! [V2__req] :
( c_24__type__646___24t(V0__R,V2__req)
=> ( ! [V3__p] :
( t(V3__p,V0__R)
=> ! [V4__q] :
( t(V4__q,V0__R)
=> ( p(happ(happ(V2__req,V3__p),V4__q))
=> p(happ(happ(V2__req,happ(V1__rinv,V3__p)),happ(V1__rinv,V4__q))) ) ) )
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2961___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V2__req,V2__req),V1__rinv) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rinv_nz',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__a),V1__rO))
=> ~ p(happ(happ(V9__req,happ(V8__rinv,V13__a)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2961___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__646___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__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q1] :
( t(V14__q1,V0__R)
=> ! [V15__q2] :
( t(V15__q2,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__p),V1__rO))
=> ( p(happ(happ(V9__req,happ(happ(V4__rmul,V13__p),V14__q1)),happ(happ(V4__rmul,V13__p),V15__q2)))
=> p(happ(happ(V9__req,V14__q1),V15__q2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ropp_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2961___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__646___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__2961___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ropp_neq_0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__2952___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2961___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__646___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__r] :
( t(V13__r,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(V6__ropp,V2__rI)),V1__rO))
=> ( ~ p(happ(happ(V9__req,V13__r),V1__rO))
=> ~ p(happ(happ(V9__req,happ(V6__ropp,V13__r)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.Neqb_ok',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
=> V0__x = V1__y ) ) ) ).
fof('Coq.setoid_ring.InitialRing.R_setoid5_Reflexive',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__646___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__R,V1__req) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.Ztriv_div_th',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__646___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> ! [V3__zphi] :
( c_24__type__15433___24t(V0__R,V3__zphi)
=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V0__R,V1__req,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V3__zphi,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.gen_phiNword_cons',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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___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__w] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,V11__w)
=> ! [V12__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V12__n)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,V12__n,V11__w))),happ(happ(V5__rsub,cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V12__n)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V11__w)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.get_signZ_th',axiom,
cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
fof('Coq.setoid_ring.InitialRing.radd_ext5_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2961___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__646___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__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___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.bool_eq_ok',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue
=> V0__b1 = V1__b2 ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.Pphi0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__7748___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__7748___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__7748___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__4143___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__7767___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V18__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V8__C,V16__phi,V18__l,cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V8__C,V9__cO))),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.Pphi1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__7748___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__7748___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__7748___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__4143___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__7767___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V18__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V8__C,V16__phi,V18__l,cCoq_2esetoid__ring_2eRing__polynom_2eP1___24a2(V8__C,V10__cI))),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.ceqb_spec',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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__7748___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__7748___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__7748___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__4143___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__7767___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__c] :
( t(V18__c,V8__C)
=> ! [V19__c_27] :
( t(V19__c_27,V8__C)
=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(happ(happ(V7__req,happ(V16__phi,V18__c)),happ(V16__phi,V19__c_27)),c_24True,happ(happ(V15__ceqb,V18__c),V19__c_27)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2961___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__646___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__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___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__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2961___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__646___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__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.ropp_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2961___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__646___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__2961___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),happ(happ(V3__radd,V10__y),V11__z))),happ(happ(V3__radd,happ(happ(V3__radd,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_assoc1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ! [V12__z] :
( t(V12__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z)),happ(happ(V3__radd,happ(happ(V3__radd,V11__y),V12__z)),V10__x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_assoc2',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),happ(happ(V4__rmul,V10__y),V11__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_assoc1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ! [V12__z] :
( t(V12__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V4__rmul,V10__x),V11__y)),V12__z)),happ(happ(V4__rmul,happ(happ(V4__rmul,V11__y),V12__z)),V10__x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_assoc2',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_add',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V3__radd,V9__x),V10__y))),happ(happ(V3__radd,happ(V6__ropp,V9__x)),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARth_SRth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V7__req) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2961___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__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ! [V9__reqb] :
( c_24__type__5381___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__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2961___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__646___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__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___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__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2961___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__646___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__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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.SReqe_Reqe',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__646___24t(V0__R,V3__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V0__R,V1__radd,V2__rmul,V3__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V0__R),V3__req) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.SRth_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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__req] :
( c_24__type__646___24t(V0__R,V5__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V5__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(V0__R,V3__radd),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V0__R),V5__req) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.get_sign_None_th',axiom,
! [V0__C] :
( cType___24t(V0__C)
=> ! [V1__copp] :
( c_24__type__2961___24t(V0__C,V1__copp)
=> ! [V2__ceqb] :
( c_24__type__5381___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__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2961___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__646___24t(V0__R,V4__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___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__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___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__2961___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.mk_seqe',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__2952___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__646___24t(V0__R,V3__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___24a1(V0__R),V3__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V3__req,V3__req)),V1__radd)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2952___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2961___24a1(V0__R),V3__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V3__req,V3__req)),V2__rmul)
=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V0__R,V1__radd,V2__rmul,V3__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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__7748___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__7748___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__7748___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__4143___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__7767___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2968___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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__7748___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__7748___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__7748___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__4143___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__7767___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_add',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__7748___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__7748___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__7748___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__4143___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__7767___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V11__cadd,V18__x),V19__y))),happ(happ(V3__radd,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_eq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__7748___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__7748___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__7748___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__4143___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__7767___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> ( happ(happ(V15__ceqb,V18__x),V19__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V7__req,happ(V16__phi,V18__x)),happ(V16__phi,V19__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_mul',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__7748___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__7748___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__7748___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__4143___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__7767___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V12__cmul,V18__x),V19__y))),happ(happ(V4__rmul,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_opp',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__7748___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__7748___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__7748___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__4143___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__7767___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(V14__copp,V18__x))),happ(V6__ropp,happ(V16__phi,V18__x)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_sub',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__2952___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2952___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2952___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2961___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__646___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__7748___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__7748___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__7748___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__4143___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__7767___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2968___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V13__csub,V18__x),V19__y))),happ(happ(V5__rsub,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.rpow_pow_N',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__2952___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__646___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__33500___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__3110___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('ExtLib.Data.Member.member_In',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__ls)
=> ! [V2__t] :
( t(V2__t,V0__T)
=> ! [V3___24Anonymous] :
( cExtLib_2eData_2eMember_2emember___24t(V0__T,V2__t,V1__ls,V3___24Anonymous)
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V2__t,V1__ls)) ) ) ) ) ).
fof('ExtLib.Data.Member.member_case',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__x] :
( t(V1__x,V0__T)
=> ! [V2__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__ls)
=> ! [V3__m] :
( cExtLib_2eData_2eMember_2emember___24t(V0__T,V1__x,V2__ls,V3__m)
=> c_24__case__Coq_2eInit_2eDatatypes_2elist_2417865___24a4(V0__T,V1__x,V2__ls,V3__m) ) ) ) ) ).
fof('ExtLib.Data.Member.member_eta',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__x] :
( t(V1__x,V0__T)
=> ! [V2__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__ls)
=> ! [V3__m] :
( cExtLib_2eData_2eMember_2emember___24t(V0__T,V1__x,V2__ls,V3__m)
=> V3__m = c_24__case__ExtLib_2eData_2eMember_2emember_2417801___24a4(V0__T,V1__x,V2__ls,V3__m) ) ) ) ) ).
fof('ExtLib.Data.Member.member_ind',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__a] :
( t(V1__a,V0__T)
=> ! [V2__P] :
( c_24__type__17692___24t(V0__T,V1__a,V2__P)
=> ( ! [V3__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V3__ls)
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V1__a,V3__ls)),cExtLib_2eData_2eMember_2eMZ___24a3(V0__T,V1__a,V3__ls))) )
=> ( ! [V4__l] :
( t(V4__l,V0__T)
=> ! [V5__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V5__ls)
=> ! [V6__m] :
( cExtLib_2eData_2eMember_2emember___24t(V0__T,V1__a,V5__ls,V6__m)
=> ( p(happ(happ(V2__P,V5__ls),V6__m))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V4__l,V5__ls)),cExtLib_2eData_2eMember_2eMN___24a5(V0__T,V1__a,V4__l,V5__ls,V6__m))) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V5__l)
=> ! [V6__m] :
( cExtLib_2eData_2eMember_2emember___24t(V0__T,V1__a,V5__l,V6__m)
=> p(happ(happ(V2__P,V5__l),V6__m)) ) ) ) ) ) ) ) ).
fof('ExtLib.Tactics.EqDep.UIP_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dec] :
( cCoq_2eClasses_2eEquivDec_2eEqDec___24t(V0__A,c_3d___24a1(V0__A),cCoq_2eClasses_2eRelationClasses_2eeq__equivalence___24a1(V0__A),V1__dec)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( V2__x = V2__x
=> c_24Proof = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V2__x) ) ) ) ) ).
fof('HList.app_ass_trans',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__a)
=> ! [V2__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__b)
=> ! [V3__c] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V3__c)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__T,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__T,V1__a,V2__b),V3__c) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__T,V1__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__T,V2__b,V3__c)) ) ) ) ) ).
fof('HList.app_nil_r_trans',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__a)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__T,V1__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T)) = V1__a ) ) ).
fof('HList.hlist.Reflexive_equiv_hlist',axiom,
! [V0__eqv] :
( c_24__type__122667___24t(V0__eqv)
=> ( ! [V1__t] :
( ciT___24t(V1__t)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(cF___24a1(V1__t),happ(V0__eqv,V1__t)) )
=> ! [V2__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V2__ls)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(cHList_2ehlist_2ehlist___24a1(V2__ls),cHList_2ehlist_2eequiv__hlist___24a2(V0__eqv,V2__ls)) ) ) ) ).
fof('HList.hlist.Symmetric_equiv_hlist',axiom,
! [V0__eqv] :
( c_24__type__122667___24t(V0__eqv)
=> ( ! [V1__t] :
( ciT___24t(V1__t)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(cF___24a1(V1__t),happ(V0__eqv,V1__t)) )
=> ! [V2__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V2__ls)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(cHList_2ehlist_2ehlist___24a1(V2__ls),cHList_2ehlist_2eequiv__hlist___24a2(V0__eqv,V2__ls)) ) ) ) ).
fof('HList.hlist.Transitive_equiv_hlist',axiom,
! [V0__eqv] :
( c_24__type__122667___24t(V0__eqv)
=> ( ! [V1__t] :
( ciT___24t(V1__t)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(cF___24a1(V1__t),happ(V0__eqv,V1__t)) )
=> ! [V2__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V2__ls)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(cHList_2ehlist_2ehlist___24a1(V2__ls),cHList_2ehlist_2eequiv__hlist___24a2(V0__eqv,V2__ls)) ) ) ) ).
fof('HList.hlist.equiv_hlist_Hcons',axiom,
! [V0__eqv] :
( c_24__type__122667___24t(V0__eqv)
=> ! [V1__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V1__ls)
=> ! [V2__i] :
( ciT___24t(V2__i)
=> ! [V3__a] :
( cF___24t(V2__i,V3__a)
=> ! [V4__b] :
( cF___24t(V2__i,V4__b)
=> ! [V5__c] :
( cHList_2ehlist_2ehlist___24t(V1__ls,V5__c)
=> ! [V6__d] :
( cHList_2ehlist_2ehlist___24t(V1__ls,V6__d)
=> ( p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,V2__i,V1__ls),cHList_2ehlist_2eHcons___24a4(V2__i,V1__ls,V3__a,V5__c),cHList_2ehlist_2eHcons___24a4(V2__i,V1__ls,V4__b,V6__d)))
=> ( p(happ(happ(happ(V0__eqv,V2__i),V3__a),V4__b))
& p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,V1__ls,V5__c,V6__d)) ) ) ) ) ) ) ) ) ) ).
fof('HList.hlist.equiv_hlist_app',axiom,
! [V0__eqv] :
( c_24__type__122667___24t(V0__eqv)
=> ! [V1__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V1__a)
=> ! [V2__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V2__b)
=> ! [V3__c] :
( cHList_2ehlist_2ehlist___24t(V1__a,V3__c)
=> ! [V4__c_27] :
( cHList_2ehlist_2ehlist___24t(V1__a,V4__c_27)
=> ! [V5__d] :
( cHList_2ehlist_2ehlist___24t(V2__b,V5__d)
=> ! [V6__d_27] :
( cHList_2ehlist_2ehlist___24t(V2__b,V6__d_27)
=> ( ( p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,V1__a,V3__c,V4__c_27))
& p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,V2__b,V5__d,V6__d_27)) )
<=> p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,cCoq_2eInit_2eDatatypes_2eapp___24a3(ciT,V1__a,V2__b),cHList_2ehlist_2ehlist__app___24a4(V1__a,V2__b,V3__c,V5__d),cHList_2ehlist_2ehlist__app___24a4(V1__a,V2__b,V4__c_27,V6__d_27))) ) ) ) ) ) ) ) ) ).
fof('HList.hlist.equiv_hlist_ind',axiom,
! [V0__eqv] :
( c_24__type__122667___24t(V0__eqv)
=> ! [V1__P] :
( c_24__type__122692___24t(V1__P)
=> ( p(happ(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(ciT)),cHList_2ehlist_2eHnil),cHList_2ehlist_2eHnil))
=> ( ! [V3__l] :
( ciT___24t(V3__l)
=> ! [V4__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V4__ls)
=> ! [V5__x] :
( cF___24t(V3__l,V5__x)
=> ! [V6__y] :
( cF___24t(V3__l,V6__y)
=> ! [V7__h1] :
( cHList_2ehlist_2ehlist___24t(V4__ls,V7__h1)
=> ! [V8__h2] :
( cHList_2ehlist_2ehlist___24t(V4__ls,V8__h2)
=> ( p(happ(happ(happ(V0__eqv,V3__l),V5__x),V6__y))
=> ( p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,V4__ls,V7__h1,V8__h2))
=> ( p(happ(happ(happ(V1__P,V4__ls),V7__h1),V8__h2))
=> p(happ(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,V3__l,V4__ls)),cHList_2ehlist_2eHcons___24a4(V3__l,V4__ls,V5__x,V7__h1)),cHList_2ehlist_2eHcons___24a4(V3__l,V4__ls,V6__y,V8__h2))) ) ) ) ) ) ) ) ) )
=> ! [V4__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V4__ls)
=> ! [V5__h] :
( cHList_2ehlist_2ehlist___24t(V4__ls,V5__h)
=> ! [V6__h] :
( cHList_2ehlist_2ehlist___24t(V4__ls,V6__h)
=> ( p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,V4__ls,V5__h,V6__h))
=> p(happ(happ(happ(V1__P,V4__ls),V5__h),V6__h)) ) ) ) ) ) ) ) ) ).
fof('HList.hlist.hlist_app_nil_r',axiom,
! [V0__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V0__ls)
=> ! [V1__h] :
( cHList_2ehlist_2ehlist___24t(V0__ls,V1__h)
=> cHList_2ehlist_2ehlist__app___24a4(V0__ls,cCoq_2eInit_2eDatatypes_2enil___24a1(ciT),V1__h,cHList_2ehlist_2eHnil) = c_24__generic__case__47111 ) ) ).
fof('HList.hlist.hlist_cons_eta',axiom,
! [V0__a] :
( ciT___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V1__b)
=> ! [V2__h] :
( cHList_2ehlist_2ehlist___24t(cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,V0__a,V1__b),V2__h)
=> V2__h = cHList_2ehlist_2eHcons___24a4(V0__a,V1__b,cHList_2ehlist_2ehlist__hd___24a3(V0__a,V1__b,V2__h),cHList_2ehlist_2ehlist__tl___24a3(V0__a,V1__b,V2__h)) ) ) ) ).
fof('HList.hlist.hlist_eqv_cons',axiom,
! [V0__eqv] :
( c_24__type__122667___24t(V0__eqv)
=> ! [V1__l] :
( ciT___24t(V1__l)
=> ! [V2__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V2__ls)
=> ! [V3__x] :
( cF___24t(V1__l,V3__x)
=> ! [V4__y] :
( cF___24t(V1__l,V4__y)
=> ! [V5__h1] :
( cHList_2ehlist_2ehlist___24t(V2__ls,V5__h1)
=> ! [V6__h2] :
( cHList_2ehlist_2ehlist___24t(V2__ls,V6__h2)
=> ( p(happ(happ(happ(V0__eqv,V1__l),V3__x),V4__y))
=> ( p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,V2__ls,V5__h1,V6__h2))
=> p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,V1__l,V2__ls),cHList_2ehlist_2eHcons___24a4(V1__l,V2__ls,V3__x,V5__h1),cHList_2ehlist_2eHcons___24a4(V1__l,V2__ls,V4__y,V6__h2))) ) ) ) ) ) ) ) ) ) ).
fof('HList.hlist.hlist_eqv_nil',axiom,
! [V0__eqv] :
( c_24__type__122667___24t(V0__eqv)
=> p(cHList_2ehlist_2eequiv__hlist___24a4(V0__eqv,cCoq_2eInit_2eDatatypes_2enil___24a1(ciT),cHList_2ehlist_2eHnil,cHList_2ehlist_2eHnil)) ) ).
fof('HList.hlist.hlist_eta',axiom,
! [V0__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V0__ls)
=> ! [V1__h] :
( cHList_2ehlist_2ehlist___24t(V0__ls,V1__h)
=> V1__h = c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a2(V0__ls,V1__h) ) ) ).
fof('HList.hlist.hlist_ind',axiom,
! [V0__P] :
( c_24__type__46603___24t(V0__P)
=> ( p(happ(happ(V0__P,cCoq_2eInit_2eDatatypes_2enil___24a1(ciT)),cHList_2ehlist_2eHnil))
=> ( ! [V2__l] :
( ciT___24t(V2__l)
=> ! [V3__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V3__ls)
=> ! [V4__f] :
( cF___24t(V2__l,V4__f)
=> ! [V5__h] :
( cHList_2ehlist_2ehlist___24t(V3__ls,V5__h)
=> ( p(happ(happ(V0__P,V3__ls),V5__h))
=> p(happ(happ(V0__P,cCoq_2eInit_2eDatatypes_2econs___24a3(ciT,V2__l,V3__ls)),cHList_2ehlist_2eHcons___24a4(V2__l,V3__ls,V4__f,V5__h))) ) ) ) ) )
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V3__l)
=> ! [V4__h] :
( cHList_2ehlist_2ehlist___24t(V3__l,V4__h)
=> p(happ(happ(V0__P,V3__l),V4__h)) ) ) ) ) ) ).
fof('HList.hlist.hlist_nil_eta',axiom,
! [V0__h] :
( cHList_2ehlist_2ehlist___24t(cCoq_2eInit_2eDatatypes_2enil___24a1(ciT),V0__h)
=> V0__h = cHList_2ehlist_2eHnil ) ).
fof('HList.hlist.hlist_rev_nil',axiom,
cHList_2ehlist_2ehlist__rev___24a2(cCoq_2eInit_2eDatatypes_2enil___24a1(ciT),cHList_2ehlist_2eHnil) = cHList_2ehlist_2eHnil ).
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('$adef_Coq.Lists.List.seq_$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('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
fof('$adef_$_prop_34460_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__34460,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__34460___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_15659_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__15659,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__15659___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_prop_126684_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__prop__126684,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__prop__126684___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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.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.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.ZArith.BinIntDef.Z.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.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_$_prop_16608_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16608,V_24X1),V_24X2),V_24X3) = c_24__prop__16608___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rfunctions.ZintPos_$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('$adef_$_prop_116341_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__116341,V_24X1),V_24X2),V_24X3) = c_24__prop__116341___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_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_HList.hlist.Injection_equiv_hlist_cons_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cHList_2ehlist_2eInjection__equiv__hlist__cons,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cHList_2ehlist_2eInjection__equiv__hlist__cons___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Tauto.eval_tt_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__tt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eeval__tt___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_HList.hlist.hlist_$a1',axiom,
! [V_24X1] : happ(cHList_2ehlist_2ehlist,V_24X1) = cHList_2ehlist_2ehlist___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.partition_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2epartition,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2epartition___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_$_lam_17912_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__17912,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__17912___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Logic.JMeq.JMeq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLogic_2eJMeq_2eJMeq,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLogic_2eJMeq_2eJMeq___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('$adef_$_case_Coq.Numbers.BinNums.Z$120576_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24120576,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24120576___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_prop_15769_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__15769,V_24X1),V_24X2),V_24X3) = c_24__prop__15769___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_15517_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__15517,V_24X1),V_24X2) = c_24__prop__15517___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Specif.projT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.collect_annot_$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('$adef_$_lam_47639_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__47639,V_24X1),V_24X2),V_24X3) = c_24__lam__47639___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_126634_$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__prop__126634,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__prop__126634___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('$adef_Coq.ZArith.BinIntDef.Z.leb_$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_var_7_n_15725_15729_15738_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__var__7__n__15725__15729__15738,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__var__7__n__15725__15729__15738___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$505_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_24505,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24505___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.ZArith.BinIntDef.Z.mul_$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('$adef_$_prop_15697_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__15697,V_24X1),V_24X2),V_24X3) = c_24__prop__15697___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Classes.RelationClasses.StrictOrder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eStrictOrder,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.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.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_$_prop_45254_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__45254,V_24X1),V_24X2) = c_24__prop__45254___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.check_inconsistent_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_prop_126660_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__prop__126660,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__prop__126660___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Init.Nat.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_$_prop_15771_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__15771,V_24X1),V_24X2),V_24X3) = c_24__prop__15771___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_generic_case_48326_$a1',axiom,
! [V_24X1] : happ(c_24__generic__case__48326,V_24X1) = c_24__generic__case__48326___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.forallb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eforallb,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eforallb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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.setoid_ring.Field_theory.Fcons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFcons___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.skipn_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eskipn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eskipn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_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_Coq.Init.Logic.and_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eand__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eand__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_15698_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__15698,V_24X1),V_24X2),V_24X3) = c_24__prop__15698___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_$_lam_38194_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__38194,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__38194___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_lam_24987_$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__24987,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__24987___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_case_Coq.setoid_ring.Ring_polynom.Pol$12766_$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_2412766,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),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_2412766___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('$adef_ExtLib.Data.Member.member_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cExtLib_2eData_2eMember_2emember,V_24X1),V_24X2),V_24X3) = cExtLib_2eData_2eMember_2emember___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.micromega.Tauto.eval_cnf_$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('$adef_Coq.setoid_ring.Ring_polynom.interp_PElist_$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('$adef_HList.hlist.hlist_rev\'_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cHList_2ehlist_2ehlist__rev_27,V_24X1),V_24X2),V_24X3),V_24X4) = cHList_2ehlist_2ehlist__rev_27___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_let_18_mkmult_pow_28089_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__28089,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__28089___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_$_lam_46514_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__46514,V_24X1),V_24X2) = c_24__lam__46514___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.display_pow_linear_$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('$adef_$_lam_17912_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__17912,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__17912___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_lam_16675_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__16675,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__16675___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkZmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkZmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2edivide,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.SetoidList.transpose2_$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('$adef_Coq.Vectors.VectorDef.of_list_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2eof__list,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2eof__list___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Vectors.VectorDef.to_list_$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('$adef_Coq.Logic.EqdepFacts.Streicher_K_on__$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_116344_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__116344,V_24X1),V_24X2),V_24X3) = c_24__prop__116344___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_dep_eq_on_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring.bool_eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing_2ebool__eq,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V_24X1,V_24X2) ).
fof('$adef_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_$_prop_46989_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__46989,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__46989___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_HList.hlist.hlist_tl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHList_2ehlist_2ehlist__tl,V_24X1),V_24X2),V_24X3) = cHList_2ehlist_2ehlist__tl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.cons_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1) = cCoq_2eInit_2eDatatypes_2econs___24a1(V_24X1) ).
fof('$adef_$_lam_15512_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__15512,V_24X1),V_24X2),V_24X3) = c_24__lam__15512___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__left,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.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_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.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.cnf_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.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_Coq.setoid_ring.Ring_polynom.P0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eP0,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_prop_34493_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__34493,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__34493___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$120559_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24120559,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24120559___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_HList.hlist.hlist_rect_$a1',axiom,
! [V_24X1] : happ(cHList_2ehlist_2ehlist__rect,V_24X1) = cHList_2ehlist_2ehlist__rect___24a1(V_24X1) ).
fof('$adef_$_let_16_mkpow_28087_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__28087,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__28087___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_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.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_HList.hlist.hlist_app_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cHList_2ehlist_2ehlist__app,V_24X1),V_24X2),V_24X3),V_24X4) = cHList_2ehlist_2ehlist__app___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_lam_2042_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2042,V_24X1),V_24X2),V_24X3) = c_24__lam__2042___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_$_let_11_subst_l_24915_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__11__subst__l__24915,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__11__subst__l__24915___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Lists.List.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_HList.hlist.hlist_rev\'_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHList_2ehlist_2ehlist__rev_27,V_24X1),V_24X2),V_24X3) = cHList_2ehlist_2ehlist__rev_27___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.P1_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eP1,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2eP1___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Even.odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
<=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).
fof('$adef_$_lam_24987_$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__24987,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__24987___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('$adef_Coq.Lists.List.ForallOrdPairs_$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('$adef_$_lam_17884_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__17884,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__17884___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Lists.List.split_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2esplit,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2esplit___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.setoid_ring.Field_theory.display_linear_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2edisplay__linear,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eField__theory_2edisplay__linear___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).
fof('$adef_Coq.ZArith.Zcomplements.Zlength_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZcomplements_2eZlength,V_24X1),V_24X2) = cCoq_2eZArith_2eZcomplements_2eZlength___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_34982_$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__lam__34982,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__34982___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_HList.hlist.hlist_rec_$a1',axiom,
! [V_24X1] : happ(cHList_2ehlist_2ehlist__rec,V_24X1) = cHList_2ehlist_2ehlist__rec___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_48310_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__48310,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__48310___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Init.Logic.eq_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eeq__refl,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_ExtLib.Data.Member.member_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cExtLib_2eData_2eMember_2emember__rec,V_24X1),V_24X2),V_24X3) = cExtLib_2eData_2eMember_2emember__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.ForallPairs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallPairs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForallPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Classes.RelationClasses.eq_equivalence_$a1',axiom,
! [V_24X1] : happ(cCoq_2eClasses_2eRelationClasses_2eeq__equivalence,V_24X1) = cCoq_2eClasses_2eRelationClasses_2eeq__equivalence___24a1(V_24X1) ).
fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3) = cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_48310_$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__lam__48310,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__48310___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Add_$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('$adef_$_lam_35023_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__35023,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__35023___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_$_lam_34898_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__34898,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__34898___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_case_Coq.Init.Datatypes.list$35694_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_HList.hlist.hlist_app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHList_2ehlist_2ehlist__app,V_24X1),V_24X2),V_24X3) = cHList_2ehlist_2ehlist__app___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.ZMicromega.RatProof_$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('$adef_HList.hlist.hlist_rev_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cHList_2ehlist_2ehlist__rev,V_24X1),V_24X2) = cHList_2ehlist_2ehlist__rev___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('$adef_Coq.Sorting.Sorted.StronglySorted_rect_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eSorting_2eSorted_2eStronglySorted__rect___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_$_lam_16646_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__16646,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__16646___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_prop_15696_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__15696,V_24X1),V_24X2),V_24X3) = c_24__prop__15696___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2epow,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$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('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.List.flat_map_$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('$adef_$_prop_116342_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__116342,V_24X1),V_24X2),V_24X3) = c_24__prop__116342___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.Rinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRinv,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V_24X1) ).
fof('$adef_Coq.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_HList.hlist.equiv_hlist_app_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cHList_2ehlist_2eequiv__hlist__app,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cHList_2ehlist_2eequiv__hlist__app___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_ExtLib.Data.Member.get_next_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cExtLib_2eData_2eMember_2eget__next,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cExtLib_2eData_2eMember_2eget__next___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.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_$_let_var_6_p_28809_28811_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__28809__28811,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__28809__28811___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_case_Coq.Init.Datatypes.prod$33222_$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_2433222,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_2433222___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
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('$adef_$_lam_17884_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__17884,V_24X1),V_24X2) = c_24__lam__17884___24a2(V_24X1,V_24X2) ).
fof('$adef_ExtLib.Data.Member.member_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cExtLib_2eData_2eMember_2emember__rect,V_24X1),V_24X2),V_24X3) = cExtLib_2eData_2eMember_2emember__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_17_lnum_11934_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__lnum__11934,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = c_24__let__17__lnum__11934___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$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('$adef_$_prop_37890_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__37890,V_24X1),V_24X2) = c_24__prop__37890___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.absurd_PCond_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eabsurd__PCond,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eabsurd__PCond___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_37864_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__37864,V_24X1),V_24X2) = c_24__prop__37864___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_aux_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.InitialRing.triv_div_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2etriv__div,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_let_var_6_p_28807_28810_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__28807__28810,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__28807__28810___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_Coq.Init.Logic.proj2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eLogic_2eproj2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eLogic_2eproj2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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_Coq.Init.Datatypes.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_fix_36692_v_CANONICAL_2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__fix__36692__v__CANONICAL__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__fix__36692__v__CANONICAL__2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$120581_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24120581,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24120581___24a1(V_24X1) ).
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('$adef_$_lam_16675_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__16675,V_24X1),V_24X2),V_24X3) = c_24__lam__16675___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2edivide,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$418_$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_24418,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24418___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_ExtLib.Tactics.Injection.Injective_$a1',axiom,
! [V_24X1] : happ(cExtLib_2eTactics_2eInjection_2eInjective,V_24X1) = cExtLib_2eTactics_2eInjection_2eInjective___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('$adef_Coq.micromega.ZMicromega.is_pol_Z0_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eis__pol__Z0,V_24X1) = cCoq_2emicromega_2eZMicromega_2eis__pol__Z0___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$46502_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a1(V_24X1) ).
fof('$adef_ExtLib.Core.RelDec.Build_RelDec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cExtLib_2eCore_2eRelDec_2eBuild__RelDec,V_24X1),V_24X2),V_24X3) = cExtLib_2eCore_2eRelDec_2eBuild__RelDec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_17_mkopp_pow_28088_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__28088,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__28088___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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.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.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.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_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_prop_126659_$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__prop__126659,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__prop__126659___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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_15624_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__15624,V_24X1),V_24X2),V_24X3) = c_24__prop__15624___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_16926_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16926,V_24X1),V_24X2),V_24X3) = c_24__prop__16926___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_dev_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_HList.hlist.Injection_equiv_hlist_app_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cHList_2ehlist_2eInjection__equiv__hlist__app,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cHList_2ehlist_2eInjection__equiv__hlist__app___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_HList.hlist.hlist_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cHList_2ehlist_2ehlist__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cHList_2ehlist_2ehlist__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_ExtLib.Data.Member.MN_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cExtLib_2eData_2eMember_2eMN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cExtLib_2eData_2eMember_2eMN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.List.remove_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2eremove,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2eremove___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('$adef_Coq.Lists.List.lel_$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_46514_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__46514,V_24X1),V_24X2),V_24X3) = c_24__lam__46514___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_46511_$a1',axiom,
! [V_24X1] : happ(c_24__lam__46511,V_24X1) = c_24__lam__46511___24a1(V_24X1) ).
fof('$adef_$_prop_15623_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__15623,V_24X1),V_24X2),V_24X3) = c_24__prop__15623___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_2046_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__2046,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__2046___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Operators.Desc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eDesc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.xelements_$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('$adef_ExtLib.Data.Member.MZ_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cExtLib_2eData_2eMember_2eMZ,V_24X1),V_24X2),V_24X3) = cExtLib_2eData_2eMember_2eMZ___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('$adef_$_prop_15699_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__15699,V_24X1),V_24X2),V_24X3) = c_24__prop__15699___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_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.setoid_ring.InitialRing.Nwadd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eInitialRing_2eNwadd,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eInitialRing_2eNwadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$17865_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2417865,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2417865___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_case_Coq.Init.Datatypes.list$46502_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.concat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2econcat,V_24X1),V_24X2) = cCoq_2eLists_2eList_2econcat___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_47646_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__47646,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__47646___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_let_20_lnum_12462_$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__12462,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),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__12462___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('$adef_$_prop_116343_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__116343,V_24X1),V_24X2),V_24X3) = c_24__prop__116343___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_15768_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__15768,V_24X1),V_24X2),V_24X3) = c_24__prop__15768___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_2046_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2046,V_24X1),V_24X2),V_24X3) = c_24__lam__2046___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_HList.hlist.equiv_hlist_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cHList_2ehlist_2eequiv__hlist,V_24X1),V_24X2) = cHList_2ehlist_2eequiv__hlist___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_ExtLib.Data.Member.member_rect_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cExtLib_2eData_2eMember_2emember__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cExtLib_2eData_2eMember_2emember__rect___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.r_list_pow_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2edouble,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(V_24X1) ).
fof('$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.Sets.Relations_1.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons0_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons0,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_lam_34898_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__34898,V_24X1),V_24X2),V_24X3) = c_24__lam__34898___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.InitialRing.Nwcons_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eInitialRing_2eNwcons,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eInitialRing_2eNwcons___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEopp_$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('$adef_$_case_Coq.Init.Specif.sumbool$15756_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eSpecif_2esumbool_2415756,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_2415756___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_case_Coq.setoid_ring.Ring_polynom.Pol$12167_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2412167,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2412167___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('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$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('$adef_$_lam_16626_$a1',axiom,
! [V_24X1] : happ(c_24__lam__16626,V_24X1) = c_24__lam__16626___24a1(V_24X1) ).
fof('$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_HList.hlist.equiv_hlist_Hcons_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cHList_2ehlist_2eequiv__hlist__Hcons,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cHList_2ehlist_2eequiv__hlist__Hcons___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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.micromega.Tauto.cnf_checker_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2ecnf__checker,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2ecnf__checker___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_prop_16617_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16617,V_24X1),V_24X2),V_24X3) = c_24__prop__16617___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.eqlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Specif.exist2_$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('$adef_Coq.Init.Datatypes.xorb_$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('$adef_$_prop_122450_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__122450,V_24X1),V_24X2) = c_24__prop__122450___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_37630_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__37630__1__add__carry,V_24X1),V_24X2) = c_24__fix__37630__1__add__carry___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('$adef_$_lam_47639_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__47639,V_24X1),V_24X2) = c_24__lam__47639___24a2(V_24X1,V_24X2) ).
fof('$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.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_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.NArith.BinNatDef.N.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.in_dec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2ein__dec,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2ein__dec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.list_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rect,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_let_17_mkopp_pow_28088_$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__28088,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__28088___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
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('$adef_ExtLib.Structures.Functor.ID_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cExtLib_2eStructures_2eFunctor_2eID,V_24X1),V_24X2))
<=> cExtLib_2eStructures_2eFunctor_2eID___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double___24a1(V_24X1) ).
fof('$adef_Coq.Sorting.Sorted.StronglySorted_inv_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted__inv,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eSorting_2eSorted_2eStronglySorted__inv___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_prop_16616_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16616,V_24X1),V_24X2),V_24X3) = c_24__prop__16616___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_HList.hlist.hlist_hd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHList_2ehlist_2ehlist__hd,V_24X1),V_24X2),V_24X3) = cHList_2ehlist_2ehlist__hd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_ExtLib.Core.RelDec.RelDec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cExtLib_2eCore_2eRelDec_2eRelDec,V_24X1),V_24X2) = cExtLib_2eCore_2eRelDec_2eRelDec___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_126658_$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__lam__126658,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__126658___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_lam_34982_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__34982,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__34982___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_F_$a1',axiom,
! [V_24X1] : happ(cF,V_24X1) = cF___24a1(V_24X1) ).
fof('$adef_ExtLib.Tactics.Injection.Build_Injective_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cExtLib_2eTactics_2eInjection_2eBuild__Injective,V_24X1),V_24X2) = cExtLib_2eTactics_2eInjection_2eBuild__Injective___24a2(V_24X1,V_24X2) ).
fof('$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.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.Logic.EqdepFacts.UIP_on__$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_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_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.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_$_lam_15516_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__15516,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__15516___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.Sorting.Sorted.Sorted_$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('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_16626_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__16626,V_24X1),V_24X2) = c_24__lam__16626___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_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_$_prop_116345_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__116345,V_24X1),V_24X2),V_24X3) = c_24__prop__116345___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.projT1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT1,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rpow_def.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRpow__def_2epow,V_24X1),V_24X2) = cCoq_2eReals_2eRpow__def_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_HList.hlist.Hcons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cHList_2ehlist_2eHcons,V_24X1),V_24X2),V_24X3),V_24X4) = cHList_2ehlist_2eHcons___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_16_mkpow_28087_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__let__16__mkpow__28087,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__28087___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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_$_lam_2042_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2042,V_24X1),V_24X2) = c_24__lam__2042___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Mphi_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eMphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEequiv_$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] : 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) = cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___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('$adef_Coq.Init.Specif.inleft_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.cons_$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('$adef_ExtLib.Data.Member.to_nat_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cExtLib_2eData_2eMember_2eto__nat,V_24X1),V_24X2),V_24X3),V_24X4) = cExtLib_2eData_2eMember_2eto__nat___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred__double,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred__double___24a1(V_24X1) ).
fof('$adef_$_let_18_mkmult_pow_28089_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__28089,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__28089___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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_$_prop_116346_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__116346,V_24X1),V_24X2) = c_24__prop__116346___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_34458_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__34458,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__34458___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_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_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_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_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.setoid_ring.Ring_polynom.add_pow_list_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.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_Coq.Lists.List.nodup_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2enodup,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2enodup___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_HList.hlist.equiv_hlist_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cHList_2ehlist_2eequiv__hlist,V_24X1),V_24X2),V_24X3),V_24X4) = cHList_2ehlist_2eequiv__hlist___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_ExtLib.Tactics.Injection.result_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cExtLib_2eTactics_2eInjection_2eresult,V_24X1),V_24X2))
<=> cExtLib_2eTactics_2eInjection_2eresult___24a2(V_24X1,V_24X2) ) ).
fof('$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_Coq.Lists.SetoidList.removeA_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eremoveA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons00_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons00,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.setoid_ring.Field_theory.PExpr_eq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_34917_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__34917,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__34917___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('$adef_Coq.Lists.List.hd_error_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2ehd__error,V_24X1),V_24X2) = cCoq_2eLists_2eList_2ehd__error___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mon_of_pol_$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('$adef_$_lam_38194_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38194,V_24X1),V_24X2),V_24X3) = c_24__lam__38194___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_38202_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__38202,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__38202___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_prop_46976_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__46976,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__46976___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_47646_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__47646,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__47646___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_$_case_ExtLib.Data.Member.member$17801_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__ExtLib_2eData_2eMember_2emember_2417801,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__ExtLib_2eData_2eMember_2emember_2417801___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_16914_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16914,V_24X1),V_24X2),V_24X3) = c_24__prop__16914___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_15770_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__15770,V_24X1),V_24X2),V_24X3) = c_24__prop__15770___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_$_prop_34459_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__34459,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__34459___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_fix_550_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__550__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__550__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.micromega.Tauto.eval_clause_$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__clause,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__clause___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
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('$adef_$_case_Coq.Init.Datatypes.list$17865_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2417865,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__case__Coq_2eInit_2eDatatypes_2elist_2417865___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_prop_116340_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__116340,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__116340___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_ExtLib.Tactics.Injection.Build_Injective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cExtLib_2eTactics_2eInjection_2eBuild__Injective,V_24X1),V_24X2),V_24X3) = cExtLib_2eTactics_2eInjection_2eBuild__Injective___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_38202_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38202,V_24X1),V_24X2),V_24X3) = c_24__lam__38202___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_case_Coq.Numbers.BinNums.Z$37861_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2437861,V_24X1),V_24X2))
<=> c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2437861___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_15512_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__15512,V_24X1),V_24X2) = c_24__lam__15512___24a2(V_24X1,V_24X2) ).
fof('$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_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_rect_eq_on_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Specif.left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_15516_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__15516,V_24X1),V_24X2),V_24X3) = c_24__lam__15516___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.NFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eNFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$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('$adef_$_lam_16646_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__16646,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__16646___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_prop_16607_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16607,V_24X1),V_24X2),V_24X3) = c_24__prop__16607___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('$adef_Coq.NArith.BinNat.N.le_$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_37889_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__37889,V_24X1),V_24X2) = c_24__prop__37889___24a2(V_24X1,V_24X2) ).
fof('$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_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$tdef_$_type_36343',axiom,
! [V_24Y] :
( c_24__type__36343___24t(V_24Y)
<=> t(V_24Y,c_24__type__36343) ) ).
fof('$tdef_$_type_46391',axiom,
! [V_24Y] :
( c_24__type__46391___24t(V_24Y)
<=> t(V_24Y,c_24__type__46391) ) ).
fof('$tdef_$_type_35306',axiom,
! [V_24Y] :
( c_24__type__35306___24t(V_24Y)
<=> t(V_24Y,c_24__type__35306) ) ).
fof('$tdef_$_type_11216',axiom,
! [V_24Y] :
( c_24__type__11216___24t(V_24Y)
<=> t(V_24Y,c_24__type__11216) ) ).
fof('$tdef_$_type_23220',axiom,
! [V_24Y] :
( c_24__type__23220___24t(V_24Y)
<=> t(V_24Y,c_24__type__23220) ) ).
fof('$tdef_$_type_1954',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1954___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1954___24a1(V_24X1)) ) ).
fof('$tdef_$_type_41399',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__41399___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__41399___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_42068',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__42068___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__42068___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_19669',axiom,
! [V_24Y] :
( c_24__type__19669___24t(V_24Y)
<=> t(V_24Y,c_24__type__19669) ) ).
fof('$tdef_$_type_7257',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7257___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7257___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_6875',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__6875___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__6875___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_69',axiom,
! [V_24Y] :
( c_24__type__69___24t(V_24Y)
<=> t(V_24Y,c_24__type__69) ) ).
fof('$tdef_$_type_6868',axiom,
! [V_24Y] :
( c_24__type__6868___24t(V_24Y)
<=> t(V_24Y,c_24__type__6868) ) ).
fof('$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_46583',axiom,
! [V_24Y] :
( c_24__type__46583___24t(V_24Y)
<=> t(V_24Y,c_24__type__46583) ) ).
fof('$tdef_$_type_36633',axiom,
! [V_24Y] :
( c_24__type__36633___24t(V_24Y)
<=> t(V_24Y,c_24__type__36633) ) ).
fof('$tdef_$_type_45279',axiom,
! [V_24Y] :
( c_24__type__45279___24t(V_24Y)
<=> t(V_24Y,c_24__type__45279) ) ).
fof('$tdef_$_type_37624',axiom,
! [V_24Y] :
( c_24__type__37624___24t(V_24Y)
<=> t(V_24Y,c_24__type__37624) ) ).
fof('$tdef_$_type_37722',axiom,
! [V_24Y] :
( c_24__type__37722___24t(V_24Y)
<=> t(V_24Y,c_24__type__37722) ) ).
fof('$tdef_$_type_19798',axiom,
! [V_24Y] :
( c_24__type__19798___24t(V_24Y)
<=> t(V_24Y,c_24__type__19798) ) ).
fof('$tdef_$_type_46401',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__46401___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__46401___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_29339',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__29339___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__29339___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_37627',axiom,
! [V_24Y] :
( c_24__type__37627___24t(V_24Y)
<=> t(V_24Y,c_24__type__37627) ) ).
fof('$tdef_$_type_23083',axiom,
! [V_24Y] :
( c_24__type__23083___24t(V_24Y)
<=> t(V_24Y,c_24__type__23083) ) ).
fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_24185',axiom,
! [V_24Y] :
( c_24__type__24185___24t(V_24Y)
<=> t(V_24Y,c_24__type__24185) ) ).
fof('$tdef_$_type_18598',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__18598___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__18598___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_33017',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__33017___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__33017___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_2023',axiom,
! [V_24Y] :
( c_24__type__2023___24t(V_24Y)
<=> t(V_24Y,c_24__type__2023) ) ).
fof('$tdef_$_type_41745',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__41745___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__41745___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_34491',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34491___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34491___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_17652',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__17652___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__17652___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_37742',axiom,
! [V_24Y] :
( c_24__type__37742___24t(V_24Y)
<=> t(V_24Y,c_24__type__37742) ) ).
fof('$tdef_$_type_11368',axiom,
! [V_24Y] :
( c_24__type__11368___24t(V_24Y)
<=> t(V_24Y,c_24__type__11368) ) ).
fof('$tdef_$_type_18699',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__18699___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__18699___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_47675',axiom,
! [V_24Y] :
( c_24__type__47675___24t(V_24Y)
<=> t(V_24Y,c_24__type__47675) ) ).
fof('$tdef_$_type_113947',axiom,
! [V_24Y] :
( c_24__type__113947___24t(V_24Y)
<=> t(V_24Y,c_24__type__113947) ) ).
fof('$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_35233',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35233___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35233___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35364',axiom,
! [V_24Y] :
( c_24__type__35364___24t(V_24Y)
<=> t(V_24Y,c_24__type__35364) ) ).
fof('$tdef_$_type_121389',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__121389___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__121389___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_24174',axiom,
! [V_24Y] :
( c_24__type__24174___24t(V_24Y)
<=> t(V_24Y,c_24__type__24174) ) ).
fof('$tdef_$_type_37852',axiom,
! [V_24Y] :
( c_24__type__37852___24t(V_24Y)
<=> t(V_24Y,c_24__type__37852) ) ).
fof('$tdef_$_type_121875',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__121875___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__121875___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_9',axiom,
! [V_24Y] :
( c_24__type__9___24t(V_24Y)
<=> t(V_24Y,c_24__type__9) ) ).
fof('$tdef_$_type_30039',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__30039___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__30039___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_24194',axiom,
! [V_24Y] :
( c_24__type__24194___24t(V_24Y)
<=> t(V_24Y,c_24__type__24194) ) ).
fof('$tdef_$_type_126706',axiom,
! [V_24Y] :
( c_24__type__126706___24t(V_24Y)
<=> t(V_24Y,c_24__type__126706) ) ).
fof('$tdef_$_type_15311',axiom,
! [V_24Y] :
( c_24__type__15311___24t(V_24Y)
<=> t(V_24Y,c_24__type__15311) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_$_type_1907',axiom,
! [V_24Y] :
( c_24__type__1907___24t(V_24Y)
<=> t(V_24Y,c_24__type__1907) ) ).
fof('$tdef_$_type_14698',axiom,
! [V_24Y] :
( c_24__type__14698___24t(V_24Y)
<=> t(V_24Y,c_24__type__14698) ) ).
fof('$tdef_$_type_33067',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__33067___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__33067___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_36141',axiom,
! [V_24Y] :
( c_24__type__36141___24t(V_24Y)
<=> t(V_24Y,c_24__type__36141) ) ).
fof('$tdef_$_type_2522',axiom,
! [V_24Y] :
( c_24__type__2522___24t(V_24Y)
<=> t(V_24Y,c_24__type__2522) ) ).
fof('$tdef_$_type_109',axiom,
! [V_24Y] :
( c_24__type__109___24t(V_24Y)
<=> t(V_24Y,c_24__type__109) ) ).
fof('$tdef_$_type_29847',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__29847___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__29847___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_45330',axiom,
! [V_24Y] :
( c_24__type__45330___24t(V_24Y)
<=> t(V_24Y,c_24__type__45330) ) ).
fof('$tdef_$_type_35193',axiom,
! [V_24Y] :
( c_24__type__35193___24t(V_24Y)
<=> t(V_24Y,c_24__type__35193) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.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_3139',axiom,
! [V_24Y] :
( c_24__type__3139___24t(V_24Y)
<=> t(V_24Y,c_24__type__3139) ) ).
fof('$tdef_$_type_32803',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__32803___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__32803___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_29817',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__29817___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__29817___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_16632',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__16632___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__16632___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_15670',axiom,
! [V_24Y] :
( c_24__type__15670___24t(V_24Y)
<=> t(V_24Y,c_24__type__15670) ) ).
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_$_type_34456',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34456___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34456___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_17521',axiom,
! [V_24Y] :
( c_24__type__17521___24t(V_24Y)
<=> t(V_24Y,c_24__type__17521) ) ).
fof('$tdef_$_type_5381',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5381___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5381___24a1(V_24X1)) ) ).
fof('$tdef_$_type_19693',axiom,
! [V_24Y] :
( c_24__type__19693___24t(V_24Y)
<=> t(V_24Y,c_24__type__19693) ) ).
fof('$tdef_$_type_18991',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__18991___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__18991___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_2973',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2973___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2973___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_46451',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__46451___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__46451___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_17592',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17592___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17592___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_34438',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34438___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34438___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5034',axiom,
! [V_24Y] :
( c_24__type__5034___24t(V_24Y)
<=> t(V_24Y,c_24__type__5034) ) ).
fof('$tdef_$_type_29222',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__29222___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__29222___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_29931',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__29931___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__29931___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_35317',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__35317___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__35317___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_16614',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__16614___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__16614___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30012',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__30012___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__30012___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
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_$_type_39000',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__39000___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__39000___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_36615',axiom,
! [V_24Y] :
( c_24__type__36615___24t(V_24Y)
<=> t(V_24Y,c_24__type__36615) ) ).
fof('$tdef_$_type_3146',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3146___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3146___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Strings.Ascii.ascii',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).
fof('$tdef_$_type_33408',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__33408___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__33408___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_19443',axiom,
! [V_24Y] :
( c_24__type__19443___24t(V_24Y)
<=> t(V_24Y,c_24__type__19443) ) ).
fof('$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_114199',axiom,
! [V_24Y] :
( c_24__type__114199___24t(V_24Y)
<=> t(V_24Y,c_24__type__114199) ) ).
fof('$tdef_$_type_35420',axiom,
! [V_24Y] :
( c_24__type__35420___24t(V_24Y)
<=> t(V_24Y,c_24__type__35420) ) ).
fof('$tdef_$_type_17185',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__17185___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__17185___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32967',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__32967___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__32967___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_17692',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__17692___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__17692___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12444',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__12444___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__12444___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_159686',axiom,
! [V_24Y] :
( c_24__type__159686___24t(V_24Y)
<=> t(V_24Y,c_24__type__159686) ) ).
fof('$tdef_$_type_45389',axiom,
! [V_24Y] :
( c_24__type__45389___24t(V_24Y)
<=> t(V_24Y,c_24__type__45389) ) ).
fof('$tdef_$_type_19434',axiom,
! [V_24Y] :
( c_24__type__19434___24t(V_24Y)
<=> t(V_24Y,c_24__type__19434) ) ).
fof('$tdef_$_type_46580',axiom,
! [V_24Y] :
( c_24__type__46580___24t(V_24Y)
<=> t(V_24Y,c_24__type__46580) ) ).
fof('$tdef_$_type_46515',axiom,
! [V_24Y] :
( c_24__type__46515___24t(V_24Y)
<=> t(V_24Y,c_24__type__46515) ) ).
fof('$tdef_$_type_37757',axiom,
! [V_24Y] :
( c_24__type__37757___24t(V_24Y)
<=> t(V_24Y,c_24__type__37757) ) ).
fof('$tdef_$_type_17419',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__17419___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__17419___24a2(V_24X1,V_24X2)) ) ).
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_$_type_118488',axiom,
! [V_24Y] :
( c_24__type__118488___24t(V_24Y)
<=> t(V_24Y,c_24__type__118488) ) ).
fof('$tdef_$_type_16735',axiom,
! [V_24Y] :
( c_24__type__16735___24t(V_24Y)
<=> t(V_24Y,c_24__type__16735) ) ).
fof('$tdef_$_type_2379',axiom,
! [V_24Y] :
( c_24__type__2379___24t(V_24Y)
<=> t(V_24Y,c_24__type__2379) ) ).
fof('$tdef_$_type_4998',axiom,
! [V_24Y] :
( c_24__type__4998___24t(V_24Y)
<=> t(V_24Y,c_24__type__4998) ) ).
fof('$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_37700',axiom,
! [V_24Y] :
( c_24__type__37700___24t(V_24Y)
<=> t(V_24Y,c_24__type__37700) ) ).
fof('$tdef_$_type_39692',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__39692___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__39692___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_2947',axiom,
! [V_24Y] :
( c_24__type__2947___24t(V_24Y)
<=> t(V_24Y,c_24__type__2947) ) ).
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_$_type_33241',axiom,
! [V_24Y] :
( c_24__type__33241___24t(V_24Y)
<=> t(V_24Y,c_24__type__33241) ) ).
fof('$tdef_$_type_38092',axiom,
! [V_24Y] :
( c_24__type__38092___24t(V_24Y)
<=> t(V_24Y,c_24__type__38092) ) ).
fof('$tdef_$_type_1976',axiom,
! [V_24Y] :
( c_24__type__1976___24t(V_24Y)
<=> t(V_24Y,c_24__type__1976) ) ).
fof('$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_$_type_5068',axiom,
! [V_24Y] :
( c_24__type__5068___24t(V_24Y)
<=> t(V_24Y,c_24__type__5068) ) ).
fof('$tdef_$_type_2286',axiom,
! [V_24Y] :
( c_24__type__2286___24t(V_24Y)
<=> t(V_24Y,c_24__type__2286) ) ).
fof('$tdef_$_type_15657',axiom,
! [V_24Y] :
( c_24__type__15657___24t(V_24Y)
<=> t(V_24Y,c_24__type__15657) ) ).
fof('$tdef_$_type_46627',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__46627___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__46627___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3103',axiom,
! [V_24Y] :
( c_24__type__3103___24t(V_24Y)
<=> t(V_24Y,c_24__type__3103) ) ).
fof('$tdef_$_type_3064',axiom,
! [V_24Y] :
( c_24__type__3064___24t(V_24Y)
<=> t(V_24Y,c_24__type__3064) ) ).
fof('$tdef_$_type_24199',axiom,
! [V_24Y] :
( c_24__type__24199___24t(V_24Y)
<=> t(V_24Y,c_24__type__24199) ) ).
fof('$tdef_$_type_2554',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2554___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2554___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13682',axiom,
! [V_24X1,V_24Y] :
( c_24__type__13682___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__13682___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2671',axiom,
! [V_24Y] :
( c_24__type__2671___24t(V_24Y)
<=> t(V_24Y,c_24__type__2671) ) ).
fof('$tdef_$_type_18076',axiom,
! [V_24Y] :
( c_24__type__18076___24t(V_24Y)
<=> t(V_24Y,c_24__type__18076) ) ).
fof('$tdef_$_type_3068',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3068___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3068___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_121139',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__121139___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__121139___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_2143',axiom,
! [V_24Y] :
( c_24__type__2143___24t(V_24Y)
<=> t(V_24Y,c_24__type__2143) ) ).
fof('$tdef_$_type_29684',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29684___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29684___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Init.Specif.sigT',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12789',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__12789___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__12789___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_5092',axiom,
! [V_24Y] :
( c_24__type__5092___24t(V_24Y)
<=> t(V_24Y,c_24__type__5092) ) ).
fof('$tdef_$_type_1966',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1966___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1966___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_159798',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__159798___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__159798___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_120501',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__120501___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__120501___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_17562',axiom,
! [V_24Y] :
( c_24__type__17562___24t(V_24Y)
<=> t(V_24Y,c_24__type__17562) ) ).
fof('$tdef_$_type_120510',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__120510___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__120510___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2174',axiom,
! [V_24Y] :
( c_24__type__2174___24t(V_24Y)
<=> t(V_24Y,c_24__type__2174) ) ).
fof('$tdef_$_type_1914',axiom,
! [V_24Y] :
( c_24__type__1914___24t(V_24Y)
<=> t(V_24Y,c_24__type__1914) ) ).
fof('$tdef_$_type_46547',axiom,
! [V_24Y] :
( c_24__type__46547___24t(V_24Y)
<=> t(V_24Y,c_24__type__46547) ) ).
fof('$tdef_$_type_25373',axiom,
! [V_24Y] :
( c_24__type__25373___24t(V_24Y)
<=> t(V_24Y,c_24__type__25373) ) ).
fof('$tdef_$_type_2628',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__2628___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__2628___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_32373',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__32373___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__32373___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_4143',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4143___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4143___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35588',axiom,
! [V_24Y] :
( c_24__type__35588___24t(V_24Y)
<=> t(V_24Y,c_24__type__35588) ) ).
fof('$tdef_$_type_36706',axiom,
! [V_24Y] :
( c_24__type__36706___24t(V_24Y)
<=> t(V_24Y,c_24__type__36706) ) ).
fof('$tdef_$_type_29553',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29553___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29553___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_29276',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__29276___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__29276___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_45285',axiom,
! [V_24Y] :
( c_24__type__45285___24t(V_24Y)
<=> t(V_24Y,c_24__type__45285) ) ).
fof('$tdef_$_type_37761',axiom,
! [V_24Y] :
( c_24__type__37761___24t(V_24Y)
<=> t(V_24Y,c_24__type__37761) ) ).
fof('$tdef_$_type_116538',axiom,
! [V_24Y] :
( c_24__type__116538___24t(V_24Y)
<=> t(V_24Y,c_24__type__116538) ) ).
fof('$tdef_$_type_122692',axiom,
! [V_24Y] :
( c_24__type__122692___24t(V_24Y)
<=> t(V_24Y,c_24__type__122692) ) ).
fof('$tdef_$_type_17645',axiom,
! [V_24Y] :
( c_24__type__17645___24t(V_24Y)
<=> t(V_24Y,c_24__type__17645) ) ).
fof('$tdef_$_type_19437',axiom,
! [V_24Y] :
( c_24__type__19437___24t(V_24Y)
<=> t(V_24Y,c_24__type__19437) ) ).
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_46600',axiom,
! [V_24X1,V_24Y] :
( c_24__type__46600___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__46600___24a1(V_24X1)) ) ).
fof('$tdef_$_type_99',axiom,
! [V_24Y] :
( c_24__type__99___24t(V_24Y)
<=> t(V_24Y,c_24__type__99) ) ).
fof('$tdef_$_type_3153',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3153___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3153___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_48333',axiom,
! [V_24Y] :
( c_24__type__48333___24t(V_24Y)
<=> t(V_24Y,c_24__type__48333) ) ).
fof('$tdef_$_type_45172',axiom,
! [V_24Y] :
( c_24__type__45172___24t(V_24Y)
<=> t(V_24Y,c_24__type__45172) ) ).
fof('$tdef_$_type_16770',axiom,
! [V_24Y] :
( c_24__type__16770___24t(V_24Y)
<=> t(V_24Y,c_24__type__16770) ) ).
fof('$tdef_$_type_3218',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__3218___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__3218___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_15477',axiom,
! [V_24Y] :
( c_24__type__15477___24t(V_24Y)
<=> t(V_24Y,c_24__type__15477) ) ).
fof('$tdef_$_type_1912',axiom,
! [V_24Y] :
( c_24__type__1912___24t(V_24Y)
<=> t(V_24Y,c_24__type__1912) ) ).
fof('$tdef_$_type_37593',axiom,
! [V_24Y] :
( c_24__type__37593___24t(V_24Y)
<=> t(V_24Y,c_24__type__37593) ) ).
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_$_type_1926',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1926___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1926___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23156',axiom,
! [V_24Y] :
( c_24__type__23156___24t(V_24Y)
<=> t(V_24Y,c_24__type__23156) ) ).
fof('$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_5123',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5123___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5123___24a1(V_24X1)) ) ).
fof('$tdef_$_type_30492',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__30492___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__30492___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('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_$_type_33109',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__33109___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__33109___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_40361',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__40361___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__40361___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_$_type_46488',axiom,
! [V_24Y] :
( c_24__type__46488___24t(V_24Y)
<=> t(V_24Y,c_24__type__46488) ) ).
fof('$tdef_$_type_34711',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__34711___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__34711___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_33488',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__33488___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__33488___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$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_724',axiom,
! [V_24Y] :
( c_24__type__724___24t(V_24Y)
<=> t(V_24Y,c_24__type__724) ) ).
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_$_type_7432',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7432___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7432___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_38118',axiom,
! [V_24Y] :
( c_24__type__38118___24t(V_24Y)
<=> t(V_24Y,c_24__type__38118) ) ).
fof('$tdef_$_type_31326',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__31326___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__31326___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.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_4104',axiom,
! [V_24Y] :
( c_24__type__4104___24t(V_24Y)
<=> t(V_24Y,c_24__type__4104) ) ).
fof('$tdef_$_type_36199',axiom,
! [V_24Y] :
( c_24__type__36199___24t(V_24Y)
<=> t(V_24Y,c_24__type__36199) ) ).
fof('$tdef_$_type_27980',axiom,
! [V_24Y] :
( c_24__type__27980___24t(V_24Y)
<=> t(V_24Y,c_24__type__27980) ) ).
fof('$tdef_$_type_11205',axiom,
! [V_24Y] :
( c_24__type__11205___24t(V_24Y)
<=> t(V_24Y,c_24__type__11205) ) ).
fof('$tdef_$_type_17661',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__17661___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__17661___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1951',axiom,
! [V_24Y] :
( c_24__type__1951___24t(V_24Y)
<=> t(V_24Y,c_24__type__1951) ) ).
fof('$tdef_$_type_2511',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__2511___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__2511___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_21736',axiom,
! [V_24Y] :
( c_24__type__21736___24t(V_24Y)
<=> t(V_24Y,c_24__type__21736) ) ).
fof('$tdef_$_type_87',axiom,
! [V_24Y] :
( c_24__type__87___24t(V_24Y)
<=> t(V_24Y,c_24__type__87) ) ).
fof('$tdef_$_type_4436',axiom,
! [V_24Y] :
( c_24__type__4436___24t(V_24Y)
<=> t(V_24Y,c_24__type__4436) ) ).
fof('$tdef_$_type_38366',axiom,
! [V_24Y] :
( c_24__type__38366___24t(V_24Y)
<=> t(V_24Y,c_24__type__38366) ) ).
fof('$tdef_$_type_25658',axiom,
! [V_24Y] :
( c_24__type__25658___24t(V_24Y)
<=> t(V_24Y,c_24__type__25658) ) ).
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_$_type_36598',axiom,
! [V_24Y] :
( c_24__type__36598___24t(V_24Y)
<=> t(V_24Y,c_24__type__36598) ) ).
fof('$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_13781',axiom,
! [V_24X1,V_24Y] :
( c_24__type__13781___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__13781___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15488',axiom,
! [V_24Y] :
( c_24__type__15488___24t(V_24Y)
<=> t(V_24Y,c_24__type__15488) ) ).
fof('$tdef_$_type_7164',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__7164___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__7164___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
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_$_type_38100',axiom,
! [V_24Y] :
( c_24__type__38100___24t(V_24Y)
<=> t(V_24Y,c_24__type__38100) ) ).
fof('$tdef_$_type_120279',axiom,
! [V_24Y] :
( c_24__type__120279___24t(V_24Y)
<=> t(V_24Y,c_24__type__120279) ) ).
fof('$tdef_$_type_28',axiom,
! [V_24Y] :
( c_24__type__28___24t(V_24Y)
<=> t(V_24Y,c_24__type__28) ) ).
fof('$tdef_$_type_37027',axiom,
! [V_24Y] :
( c_24__type__37027___24t(V_24Y)
<=> t(V_24Y,c_24__type__37027) ) ).
fof('$tdef_$_type_44204',axiom,
! [V_24Y] :
( c_24__type__44204___24t(V_24Y)
<=> t(V_24Y,c_24__type__44204) ) ).
fof('$tdef_$_type_2125',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2125___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2125___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_646',axiom,
! [V_24X1,V_24Y] :
( c_24__type__646___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__646___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15621',axiom,
! [V_24X1,V_24Y] :
( c_24__type__15621___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__15621___24a1(V_24X1)) ) ).
fof('$tdef_$_type_19666',axiom,
! [V_24Y] :
( c_24__type__19666___24t(V_24Y)
<=> t(V_24Y,c_24__type__19666) ) ).
fof('$tdef_$_type_2177',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2177___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2177___24a1(V_24X1)) ) ).
fof('$tdef_$_type_126742',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__126742___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__126742___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_7339',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7339___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7339___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$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_2968',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2968___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2968___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_26565',axiom,
! [V_24Y] :
( c_24__type__26565___24t(V_24Y)
<=> t(V_24Y,c_24__type__26565) ) ).
fof('$tdef_$_type_35280',axiom,
! [V_24Y] :
( c_24__type__35280___24t(V_24Y)
<=> t(V_24Y,c_24__type__35280) ) ).
fof('$tdef_$_type_2035',axiom,
! [V_24Y] :
( c_24__type__2035___24t(V_24Y)
<=> t(V_24Y,c_24__type__2035) ) ).
fof('$tdef_ExtLib.Core.RelDec.RelDec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cExtLib_2eCore_2eRelDec_2eRelDec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cExtLib_2eCore_2eRelDec_2eRelDec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_45240',axiom,
! [V_24Y] :
( c_24__type__45240___24t(V_24Y)
<=> t(V_24Y,c_24__type__45240) ) ).
fof('$tdef_$_type_3876',axiom,
! [V_24Y] :
( c_24__type__3876___24t(V_24Y)
<=> t(V_24Y,c_24__type__3876) ) ).
fof('$tdef_$_type_33536',axiom,
! [V_24Y] :
( c_24__type__33536___24t(V_24Y)
<=> t(V_24Y,c_24__type__33536) ) ).
fof('$tdef_$_type_19193',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19193___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19193___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_31965',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__31965___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__31965___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_7071',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7071___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7071___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_35336',axiom,
! [V_24Y] :
( c_24__type__35336___24t(V_24Y)
<=> t(V_24Y,c_24__type__35336) ) ).
fof('$tdef_$_type_15505',axiom,
! [V_24Y] :
( c_24__type__15505___24t(V_24Y)
<=> t(V_24Y,c_24__type__15505) ) ).
fof('$tdef_$_type_38450',axiom,
! [V_24Y] :
( c_24__type__38450___24t(V_24Y)
<=> t(V_24Y,c_24__type__38450) ) ).
fof('$tdef_$_type_2118',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__2118___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__2118___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_46603',axiom,
! [V_24Y] :
( c_24__type__46603___24t(V_24Y)
<=> t(V_24Y,c_24__type__46603) ) ).
fof('$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_$_type_7514',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7514___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7514___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).
fof('$tdef_$_type_20451',axiom,
! [V_24Y] :
( c_24__type__20451___24t(V_24Y)
<=> t(V_24Y,c_24__type__20451) ) ).
fof('$tdef_$_type_7607',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__7607___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__7607___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_iT',axiom,
! [V_24Y] :
( ciT___24t(V_24Y)
<=> t(V_24Y,ciT) ) ).
fof('$tdef_$_type_38205',axiom,
! [V_24Y] :
( c_24__type__38205___24t(V_24Y)
<=> t(V_24Y,c_24__type__38205) ) ).
fof('$tdef_ExtLib.Data.Member.member',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cExtLib_2eData_2eMember_2emember___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cExtLib_2eData_2eMember_2emember___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_46459',axiom,
! [V_24Y] :
( c_24__type__46459___24t(V_24Y)
<=> t(V_24Y,c_24__type__46459) ) ).
fof('$tdef_$_type_7748',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__7748___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__7748___24a2(V_24X1,V_24X2)) ) ).
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_$_type_3110',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3110___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3110___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2361',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2361___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2361___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_29576',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29576___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29576___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_17550',axiom,
! [V_24Y] :
( c_24__type__17550___24t(V_24Y)
<=> t(V_24Y,c_24__type__17550) ) ).
fof('$tdef_$_type_31539',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__31539___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__31539___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_2982',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2982___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2982___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_43083',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__43083___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__43083___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_12420',axiom,
! [V_24Y] :
( c_24__type__12420___24t(V_24Y)
<=> t(V_24Y,c_24__type__12420) ) ).
fof('$tdef_$_type_15293',axiom,
! [V_24Y] :
( c_24__type__15293___24t(V_24Y)
<=> t(V_24Y,c_24__type__15293) ) ).
fof('$tdef_$_type_118289',axiom,
! [V_24Y] :
( c_24__type__118289___24t(V_24Y)
<=> t(V_24Y,c_24__type__118289) ) ).
fof('$tdef_$_type_4367',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__4367___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__4367___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_3988',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__3988___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__3988___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_38243',axiom,
! [V_24Y] :
( c_24__type__38243___24t(V_24Y)
<=> t(V_24Y,c_24__type__38243) ) ).
fof('$tdef_ExtLib.Tactics.Injection.Injective',axiom,
! [V_24X1,V_24Y] :
( cExtLib_2eTactics_2eInjection_2eInjective___24t(V_24X1,V_24Y)
<=> t(V_24Y,cExtLib_2eTactics_2eInjection_2eInjective___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2401',axiom,
! [V_24Y] :
( c_24__type__2401___24t(V_24Y)
<=> t(V_24Y,c_24__type__2401) ) ).
fof('$tdef_$_type_2310',axiom,
! [V_24Y] :
( c_24__type__2310___24t(V_24Y)
<=> t(V_24Y,c_24__type__2310) ) ).
fof('$tdef_Coq.Init.Datatypes.list',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_46417',axiom,
! [V_24Y] :
( c_24__type__46417___24t(V_24Y)
<=> t(V_24Y,c_24__type__46417) ) ).
fof('$tdef_$_type_13677',axiom,
! [V_24Y] :
( c_24__type__13677___24t(V_24Y)
<=> t(V_24Y,c_24__type__13677) ) ).
fof('$tdef_$_type_46443',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__46443___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__46443___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_34826',axiom,
! [V_24Y] :
( c_24__type__34826___24t(V_24Y)
<=> t(V_24Y,c_24__type__34826) ) ).
fof('$tdef_$_type_28367',axiom,
! [V_24Y] :
( c_24__type__28367___24t(V_24Y)
<=> t(V_24Y,c_24__type__28367) ) ).
fof('$tdef_$_type_29159',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__29159___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__29159___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_15282',axiom,
! [V_24Y] :
( c_24__type__15282___24t(V_24Y)
<=> t(V_24Y,c_24__type__15282) ) ).
fof('$tdef_$_type_16933',axiom,
! [V_24Y] :
( c_24__type__16933___24t(V_24Y)
<=> t(V_24Y,c_24__type__16933) ) ).
fof('$tdef_$_type_37032',axiom,
! [V_24Y] :
( c_24__type__37032___24t(V_24Y)
<=> t(V_24Y,c_24__type__37032) ) ).
fof('$tdef_$_type_29955',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__29955___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__29955___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_17485',axiom,
! [V_24Y] :
( c_24__type__17485___24t(V_24Y)
<=> t(V_24Y,c_24__type__17485) ) ).
fof('$tdef_$_type_33444',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__33444___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__33444___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_114118',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__114118___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__114118___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_37717',axiom,
! [V_24Y] :
( c_24__type__37717___24t(V_24Y)
<=> t(V_24Y,c_24__type__37717) ) ).
fof('$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_159676',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__159676___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__159676___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28821',axiom,
! [V_24Y] :
( c_24__type__28821___24t(V_24Y)
<=> t(V_24Y,c_24__type__28821) ) ).
fof('$tdef_$_type_2211',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2211___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2211___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15497',axiom,
! [V_24Y] :
( c_24__type__15497___24t(V_24Y)
<=> t(V_24Y,c_24__type__15497) ) ).
fof('$tdef_$_type_5063',axiom,
! [V_24Y] :
( c_24__type__5063___24t(V_24Y)
<=> t(V_24Y,c_24__type__5063) ) ).
fof('$tdef_$_type_37724',axiom,
! [V_24Y] :
( c_24__type__37724___24t(V_24Y)
<=> t(V_24Y,c_24__type__37724) ) ).
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_$_type_31113',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__31113___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__31113___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_39346',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__39346___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__39346___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_18800',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__18800___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__18800___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_15345',axiom,
! [V_24Y] :
( c_24__type__15345___24t(V_24Y)
<=> t(V_24Y,c_24__type__15345) ) ).
fof('$tdef_$_type_29599',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29599___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29599___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_3945',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__3945___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__3945___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_48237',axiom,
! [V_24Y] :
( c_24__type__48237___24t(V_24Y)
<=> t(V_24Y,c_24__type__48237) ) ).
fof('$tdef_$_type_45243',axiom,
! [V_24Y] :
( c_24__type__45243___24t(V_24Y)
<=> t(V_24Y,c_24__type__45243) ) ).
fof('$tdef_$_type_11239',axiom,
! [V_24Y] :
( c_24__type__11239___24t(V_24Y)
<=> t(V_24Y,c_24__type__11239) ) ).
fof('$tdef_F',axiom,
! [V_24X1,V_24Y] :
( cF___24t(V_24X1,V_24Y)
<=> t(V_24Y,cF___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23647',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__23647___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__23647___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_36729',axiom,
! [V_24Y] :
( c_24__type__36729___24t(V_24Y)
<=> t(V_24Y,c_24__type__36729) ) ).
fof('$tdef_$_type_42760',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__42760___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__42760___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_36319',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36319___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36319___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_2071',axiom,
! [V_24Y] :
( c_24__type__2071___24t(V_24Y)
<=> t(V_24Y,c_24__type__2071) ) ).
fof('$tdef_$_type_17451',axiom,
! [V_24Y] :
( c_24__type__17451___24t(V_24Y)
<=> t(V_24Y,c_24__type__17451) ) ).
fof('$tdef_$_type_8672',axiom,
! [V_24Y] :
( c_24__type__8672___24t(V_24Y)
<=> t(V_24Y,c_24__type__8672) ) ).
fof('$tdef_$_type_36170',axiom,
! [V_24Y] :
( c_24__type__36170___24t(V_24Y)
<=> t(V_24Y,c_24__type__36170) ) ).
fof('$tdef_$_type_7969',axiom,
! [V_24Y] :
( c_24__type__7969___24t(V_24Y)
<=> t(V_24Y,c_24__type__7969) ) ).
fof('$tdef_$_type_46686',axiom,
! [V_24Y] :
( c_24__type__46686___24t(V_24Y)
<=> t(V_24Y,c_24__type__46686) ) ).
fof('$tdef_$_type_38089',axiom,
! [V_24Y] :
( c_24__type__38089___24t(V_24Y)
<=> t(V_24Y,c_24__type__38089) ) ).
fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).
fof('$tdef_$_type_46415',axiom,
! [V_24Y] :
( c_24__type__46415___24t(V_24Y)
<=> t(V_24Y,c_24__type__46415) ) ).
fof('$tdef_$_type_2686',axiom,
! [V_24Y] :
( c_24__type__2686___24t(V_24Y)
<=> t(V_24Y,c_24__type__2686) ) ).
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_$_type_37782',axiom,
! [V_24Y] :
( c_24__type__37782___24t(V_24Y)
<=> t(V_24Y,c_24__type__37782) ) ).
fof('$tdef_$_type_114203',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__114203___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__114203___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_46974',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__46974___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__46974___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_16820',axiom,
! [V_24Y] :
( c_24__type__16820___24t(V_24Y)
<=> t(V_24Y,c_24__type__16820) ) ).
fof('$tdef_$_type_2235',axiom,
! [V_24Y] :
( c_24__type__2235___24t(V_24Y)
<=> t(V_24Y,c_24__type__2235) ) ).
fof('$tdef_$_type_2215',axiom,
! [V_24Y] :
( c_24__type__2215___24t(V_24Y)
<=> t(V_24Y,c_24__type__2215) ) ).
fof('$tdef_$_type_32784',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__32784___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__32784___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_2055',axiom,
! [V_24Y] :
( c_24__type__2055___24t(V_24Y)
<=> t(V_24Y,c_24__type__2055) ) ).
fof('$tdef_$_type_122667',axiom,
! [V_24Y] :
( c_24__type__122667___24t(V_24Y)
<=> t(V_24Y,c_24__type__122667) ) ).
fof('$tdef_$_type_11236',axiom,
! [V_24Y] :
( c_24__type__11236___24t(V_24Y)
<=> t(V_24Y,c_24__type__11236) ) ).
fof('$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_40707',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__40707___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__40707___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_2952',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2952___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2952___24a1(V_24X1)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_$_type_35080',axiom,
! [V_24Y] :
( c_24__type__35080___24t(V_24Y)
<=> t(V_24Y,c_24__type__35080) ) ).
fof('$tdef_$_type_35239',axiom,
! [V_24Y] :
( c_24__type__35239___24t(V_24Y)
<=> t(V_24Y,c_24__type__35239) ) ).
fof('$tdef_$_type_17685',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__17685___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__17685___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_37617',axiom,
! [V_24Y] :
( c_24__type__37617___24t(V_24Y)
<=> t(V_24Y,c_24__type__37617) ) ).
fof('$tdef_$_type_35115',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__35115___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__35115___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_37914',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__37914___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__37914___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_5009',axiom,
! [V_24Y] :
( c_24__type__5009___24t(V_24Y)
<=> t(V_24Y,c_24__type__5009) ) ).
fof('$tdef_$_type_18130',axiom,
! [V_24Y] :
( c_24__type__18130___24t(V_24Y)
<=> t(V_24Y,c_24__type__18130) ) ).
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_$_type_45384',axiom,
! [V_24Y] :
( c_24__type__45384___24t(V_24Y)
<=> t(V_24Y,c_24__type__45384) ) ).
fof('$tdef_$_type_3185',axiom,
! [V_24Y] :
( c_24__type__3185___24t(V_24Y)
<=> t(V_24Y,c_24__type__3185) ) ).
fof('$tdef_$_type_20812',axiom,
! [V_24Y] :
( c_24__type__20812___24t(V_24Y)
<=> t(V_24Y,c_24__type__20812) ) ).
fof('$tdef_$_type_35433',axiom,
! [V_24Y] :
( c_24__type__35433___24t(V_24Y)
<=> t(V_24Y,c_24__type__35433) ) ).
fof('$tdef_$_type_13751',axiom,
! [V_24Y] :
( c_24__type__13751___24t(V_24Y)
<=> t(V_24Y,c_24__type__13751) ) ).
fof('$tdef_$_type_2170',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2170___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2170___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2961',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2961___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2961___24a1(V_24X1)) ) ).
fof('$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_35310',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35310___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35310___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1905',axiom,
! [V_24Y] :
( c_24__type__1905___24t(V_24Y)
<=> t(V_24Y,c_24__type__1905) ) ).
fof('$tdef_$_type_72',axiom,
! [V_24X1,V_24Y] :
( c_24__type__72___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__72___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35216',axiom,
! [V_24Y] :
( c_24__type__35216___24t(V_24Y)
<=> t(V_24Y,c_24__type__35216) ) ).
fof('$tdef_$_type_29988',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__29988___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__29988___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_46478',axiom,
! [V_24Y] :
( c_24__type__46478___24t(V_24Y)
<=> t(V_24Y,c_24__type__46478) ) ).
fof('$tdef_$_type_2684',axiom,
! [V_24Y] :
( c_24__type__2684___24t(V_24Y)
<=> t(V_24Y,c_24__type__2684) ) ).
fof('$tdef_$_type_15709',axiom,
! [V_24Y] :
( c_24__type__15709___24t(V_24Y)
<=> t(V_24Y,c_24__type__15709) ) ).
fof('$tdef_$_type_24177',axiom,
! [V_24Y] :
( c_24__type__24177___24t(V_24Y)
<=> t(V_24Y,c_24__type__24177) ) ).
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_$_type_28842',axiom,
! [V_24Y] :
( c_24__type__28842___24t(V_24Y)
<=> t(V_24Y,c_24__type__28842) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_45001',axiom,
! [V_24Y] :
( c_24__type__45001___24t(V_24Y)
<=> t(V_24Y,c_24__type__45001) ) ).
fof('$tdef_$_type_11311',axiom,
! [V_24Y] :
( c_24__type__11311___24t(V_24Y)
<=> t(V_24Y,c_24__type__11311) ) ).
fof('$tdef_$_type_4063',axiom,
! [V_24Y] :
( c_24__type__4063___24t(V_24Y)
<=> t(V_24Y,c_24__type__4063) ) ).
fof('$tdef_$_type_32817',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__32817___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__32817___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_38095',axiom,
! [V_24Y] :
( c_24__type__38095___24t(V_24Y)
<=> t(V_24Y,c_24__type__38095) ) ).
fof('$tdef_$_type_2194',axiom,
! [V_24Y] :
( c_24__type__2194___24t(V_24Y)
<=> t(V_24Y,c_24__type__2194) ) ).
fof('$tdef_$_type_17771',axiom,
! [V_24Y] :
( c_24__type__17771___24t(V_24Y)
<=> t(V_24Y,c_24__type__17771) ) ).
fof('$tdef_$_type_18890',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__18890___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__18890___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_29666',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29666___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29666___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_37596',axiom,
! [V_24Y] :
( c_24__type__37596___24t(V_24Y)
<=> t(V_24Y,c_24__type__37596) ) ).
fof('$tdef_$_type_13160',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__13160___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__13160___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_29096',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__29096___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__29096___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_20962',axiom,
! [V_24Y] :
( c_24__type__20962___24t(V_24Y)
<=> t(V_24Y,c_24__type__20962) ) ).
fof('$tdef_$_type_15781',axiom,
! [V_24Y] :
( c_24__type__15781___24t(V_24Y)
<=> t(V_24Y,c_24__type__15781) ) ).
fof('$tdef_$_type_13125',axiom,
! [V_24Y] :
( c_24__type__13125___24t(V_24Y)
<=> t(V_24Y,c_24__type__13125) ) ).
fof('$tdef_$_type_2218',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2218___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2218___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2663',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2663___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2663___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_11157',axiom,
! [V_24Y] :
( c_24__type__11157___24t(V_24Y)
<=> t(V_24Y,c_24__type__11157) ) ).
fof('$tdef_$_type_19752',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__19752___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__19752___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_47653',axiom,
! [V_24Y] :
( c_24__type__47653___24t(V_24Y)
<=> t(V_24Y,c_24__type__47653) ) ).
fof('$tdef_$_type_33500',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33500___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33500___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Classes.EquivDec.EqDec',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eClasses_2eEquivDec_2eEqDec___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eClasses_2eEquivDec_2eEqDec___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_64',axiom,
! [V_24Y] :
( c_24__type__64___24t(V_24Y)
<=> t(V_24Y,c_24__type__64) ) ).
fof('$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_$_type_15450',axiom,
! [V_24Y] :
( c_24__type__15450___24t(V_24Y)
<=> t(V_24Y,c_24__type__15450) ) ).
fof('$tdef_$_type_38174',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38174___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38174___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_17166',axiom,
! [V_24Y] :
( c_24__type__17166___24t(V_24Y)
<=> t(V_24Y,c_24__type__17166) ) ).
fof('$tdef_$_type_15649',axiom,
! [V_24Y] :
( c_24__type__15649___24t(V_24Y)
<=> t(V_24Y,c_24__type__15649) ) ).
fof('$tdef_$_type_126682',axiom,
! [V_24Y] :
( c_24__type__126682___24t(V_24Y)
<=> t(V_24Y,c_24__type__126682) ) ).
fof('$tdef_$_type_37660',axiom,
! [V_24Y] :
( c_24__type__37660___24t(V_24Y)
<=> t(V_24Y,c_24__type__37660) ) ).
fof('$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_15433',axiom,
! [V_24X1,V_24Y] :
( c_24__type__15433___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__15433___24a1(V_24X1)) ) ).
fof('$tdef_$_type_120240',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__120240___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__120240___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_45258',axiom,
! [V_24Y] :
( c_24__type__45258___24t(V_24Y)
<=> t(V_24Y,c_24__type__45258) ) ).
fof('$tdef_$_type_44',axiom,
! [V_24Y] :
( c_24__type__44___24t(V_24Y)
<=> t(V_24Y,c_24__type__44) ) ).
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_$_type_46490',axiom,
! [V_24Y] :
( c_24__type__46490___24t(V_24Y)
<=> t(V_24Y,c_24__type__46490) ) ).
fof('$tdef_$_type_2357',axiom,
! [V_24Y] :
( c_24__type__2357___24t(V_24Y)
<=> t(V_24Y,c_24__type__2357) ) ).
fof('$tdef_$_type_7767',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__7767___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__7767___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15387',axiom,
! [V_24Y] :
( c_24__type__15387___24t(V_24Y)
<=> t(V_24Y,c_24__type__15387) ) ).
fof('$tdef_$_type_32160',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__32160___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__32160___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_38186',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38186___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38186___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34861',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__34861___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__34861___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_120259',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__120259___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__120259___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_126485',axiom,
! [V_24Y] :
( c_24__type__126485___24t(V_24Y)
<=> t(V_24Y,c_24__type__126485) ) ).
fof('$tdef_$_type_116455',axiom,
! [V_24Y] :
( c_24__type__116455___24t(V_24Y)
<=> t(V_24Y,c_24__type__116455) ) ).
fof('$tdef_$_type_15463',axiom,
! [V_24Y] :
( c_24__type__15463___24t(V_24Y)
<=> t(V_24Y,c_24__type__15463) ) ).
fof('$tdef_$_type_5080',axiom,
! [V_24Y] :
( c_24__type__5080___24t(V_24Y)
<=> t(V_24Y,c_24__type__5080) ) ).
fof('$tdef_$_type_36623',axiom,
! [V_24Y] :
( c_24__type__36623___24t(V_24Y)
<=> t(V_24Y,c_24__type__36623) ) ).
fof('$tdef_$_type_121764',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__121764___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__121764___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_34447',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34447___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34447___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30705',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__30705___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__30705___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_40015',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__40015___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__40015___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.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_2153',axiom,
! [V_24Y] :
( c_24__type__2153___24t(V_24Y)
<=> t(V_24Y,c_24__type__2153) ) ).
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_$_type_33790',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33790___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33790___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2001',axiom,
! [V_24Y] :
( c_24__type__2001___24t(V_24Y)
<=> t(V_24Y,c_24__type__2001) ) ).
fof('$tdef_$_type_29640',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29640___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29640___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_5024',axiom,
! [V_24Y] :
( c_24__type__5024___24t(V_24Y)
<=> t(V_24Y,c_24__type__5024) ) ).
fof('$tdef_$_type_45164',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__45164___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__45164___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_45156',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__45156___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__45156___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_2699',axiom,
! [V_24Y] :
( c_24__type__2699___24t(V_24Y)
<=> t(V_24Y,c_24__type__2699) ) ).
fof('$tdef_$_type_38109',axiom,
! [V_24Y] :
( c_24__type__38109___24t(V_24Y)
<=> t(V_24Y,c_24__type__38109) ) ).
fof('$tdef_$_type_46406',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__46406___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__46406___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_220',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__220___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__220___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_46531',axiom,
! [V_24Y] :
( c_24__type__46531___24t(V_24Y)
<=> t(V_24Y,c_24__type__46531) ) ).
fof('$tdef_$_type_38179',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38179___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38179___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_37702',axiom,
! [V_24Y] :
( c_24__type__37702___24t(V_24Y)
<=> t(V_24Y,c_24__type__37702) ) ).
fof('$tdef_$_type_34479',axiom,
! [V_24Y] :
( c_24__type__34479___24t(V_24Y)
<=> t(V_24Y,c_24__type__34479) ) ).
fof('$tdef_$_type_118673',axiom,
! [V_24Y] :
( c_24__type__118673___24t(V_24Y)
<=> t(V_24Y,c_24__type__118673) ) ).
fof('$tdef_$_type_33708',axiom,
! [V_24Y] :
( c_24__type__33708___24t(V_24Y)
<=> t(V_24Y,c_24__type__33708) ) ).
fof('$tdef_$_type_46666',axiom,
! [V_24Y] :
( c_24__type__46666___24t(V_24Y)
<=> t(V_24Y,c_24__type__46666) ) ).
fof('$tdef_$_type_37581',axiom,
! [V_24Y] :
( c_24__type__37581___24t(V_24Y)
<=> t(V_24Y,c_24__type__37581) ) ).
fof('$tdef_$_type_30918',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__30918___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__30918___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_HList.hlist.hlist',axiom,
! [V_24X1,V_24Y] :
( cHList_2ehlist_2ehlist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cHList_2ehlist_2ehlist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34907',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34907___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34907___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_9700',axiom,
! [V_24Y] :
( c_24__type__9700___24t(V_24Y)
<=> t(V_24Y,c_24__type__9700) ) ).
fof('$tdef_$_type_4129',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4129___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4129___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_37785',axiom,
! [V_24Y] :
( c_24__type__37785___24t(V_24Y)
<=> t(V_24Y,c_24__type__37785) ) ).
fof('$tdef_$_type_29622',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29622___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29622___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_29871',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__29871___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__29871___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_19092',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__19092___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__19092___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_16977',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__16977___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__16977___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_35359',axiom,
! [V_24Y] :
( c_24__type__35359___24t(V_24Y)
<=> t(V_24Y,c_24__type__35359) ) ).
fof('$tdef_$_type_13903',axiom,
! [V_24Y] :
( c_24__type__13903___24t(V_24Y)
<=> t(V_24Y,c_24__type__13903) ) ).
fof('$tdef_$_type_35376',axiom,
! [V_24Y] :
( c_24__type__35376___24t(V_24Y)
<=> t(V_24Y,c_24__type__35376) ) ).
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_121639',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__121639___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__121639___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_33364',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__33364___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__33364___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_3288',axiom,
! [V_24Y] :
( c_24__type__3288___24t(V_24Y)
<=> t(V_24Y,c_24__type__3288) ) ).
fof('$tdef_$_type_41053',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__41053___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__41053___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_4114',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4114___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4114___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_43752',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__43752___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__43752___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_15309',axiom,
! [V_24Y] :
( c_24__type__15309___24t(V_24Y)
<=> t(V_24Y,c_24__type__15309) ) ).
fof('$tdef_$_type_2445',axiom,
! [V_24Y] :
( c_24__type__2445___24t(V_24Y)
<=> t(V_24Y,c_24__type__2445) ) ).
fof('$tdef_$_type_32568',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__32568___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__32568___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_35414',axiom,
! [V_24Y] :
( c_24__type__35414___24t(V_24Y)
<=> t(V_24Y,c_24__type__35414) ) ).
fof('$tdef_$_type_20807',axiom,
! [V_24Y] :
( c_24__type__20807___24t(V_24Y)
<=> t(V_24Y,c_24__type__20807) ) ).
fof('$tdef_$_type_31752',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__31752___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__31752___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_35187',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35187___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35187___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_120588',axiom,
! [V_24Y] :
( c_24__type__120588___24t(V_24Y)
<=> t(V_24Y,c_24__type__120588) ) ).
fof('$tdef_Coq.Sets.Relations_1.Relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2533',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2533___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2533___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35252',axiom,
! [V_24Y] :
( c_24__type__35252___24t(V_24Y)
<=> t(V_24Y,c_24__type__35252) ) ).
fof('$tdef_$_type_24180',axiom,
! [V_24Y] :
( c_24__type__24180___24t(V_24Y)
<=> t(V_24Y,c_24__type__24180) ) ).
fof('$tdef_$_type_1217',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1217___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1217___24a1(V_24X1)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_121514',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__121514___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__121514___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('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).
fof('$tdef_$_type_5011',axiom,
! [V_24Y] :
( c_24__type__5011___24t(V_24Y)
<=> t(V_24Y,c_24__type__5011) ) ).
fof('$tdef_$_type_35210',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35210___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35210___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.NFormula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_19675',axiom,
! [V_24Y] :
( c_24__type__19675___24t(V_24Y)
<=> t(V_24Y,c_24__type__19675) ) ).
fof('$tdef_$_type_35275',axiom,
! [V_24Y] :
( c_24__type__35275___24t(V_24Y)
<=> t(V_24Y,c_24__type__35275) ) ).
fof('$tdef_$_type_35324',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__35324___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__35324___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_25119',axiom,
! [V_24Y] :
( c_24__type__25119___24t(V_24Y)
<=> t(V_24Y,c_24__type__25119) ) ).
fof('$tdef_$_type_38465',axiom,
! [V_24Y] :
( c_24__type__38465___24t(V_24Y)
<=> t(V_24Y,c_24__type__38465) ) ).
fof('$tdef_$_type_33834',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33834___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33834___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3166',axiom,
! [V_24Y] :
( c_24__type__3166___24t(V_24Y)
<=> t(V_24Y,c_24__type__3166) ) ).
fof('$tdef_$_type_2434',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2434___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2434___24a1(V_24X1)) ) ).
fof('$tdef_$_type_46480',axiom,
! [V_24Y] :
( c_24__type__46480___24t(V_24Y)
<=> t(V_24Y,c_24__type__46480) ) ).
fof('$tdef_$_type_2',axiom,
! [V_24Y] :
( c_24__type__2___24t(V_24Y)
<=> t(V_24Y,c_24__type__2) ) ).
fof('$tdef_$_type_16605',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__16605___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__16605___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_46987',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__46987___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__46987___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_33159',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__33159___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__33159___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_121264',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__121264___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__121264___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.Nword',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2eNword) ) ).
fof('$tdef_$_type_42414',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__42414___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__42414___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_3259',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__3259___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__3259___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_29901',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__29901___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__29901___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3262',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3262___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3262___24a1(V_24X1)) ) ).
fof('$tdef_$_type_43406',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__43406___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__43406___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_122416',axiom,
! [V_24Y] :
( c_24__type__122416___24t(V_24Y)
<=> t(V_24Y,c_24__type__122416) ) ).
fof('$tdef_$_type_20820',axiom,
! [V_24Y] :
( c_24__type__20820___24t(V_24Y)
<=> t(V_24Y,c_24__type__20820) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__l] :
( ciT___24t(V0__l)
=> ! [V1__ls] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,V1__ls)
=> ! [V2__a] :
( cF___24t(V0__l,V2__a)
=> ! [V3__b] :
( cHList_2ehlist_2ehlist___24t(V1__ls,V3__b)
=> ! [V4__c] :
( cF___24t(V0__l,V4__c)
=> ! [V5__d] :
( cHList_2ehlist_2ehlist___24t(V1__ls,V5__d)
=> ( cHList_2ehlist_2eHcons___24a4(V0__l,V1__ls,V2__a,V3__b) = cHList_2ehlist_2eHcons___24a4(V0__l,V1__ls,V4__c,V5__d)
=> ( V2__a = V4__c
& V3__b = V5__d ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------