TPTP Problem File: SEV642+1.p
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%------------------------------------------------------------------------------
% File : SEV642+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - list utils In concat
% 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 : list.utils.In.concat.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 2926 ( 961 unt; 0 def)
% Number of atoms : 14090 (3344 equ)
% Maximal formula atoms : 531 ( 4 avg)
% Number of connectives : 11335 ( 171 ~;1035 |;2342 &)
% (1116 <=>;6671 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 8 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 549 ( 548 usr; 0 prp; 1-23 aty)
% Number of functors : 1728 (1728 usr;1084 con; 0-22 aty)
% Number of variables : 12726 (11677 !;1049 ?)
% SPC : FOF_UNK_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.list$1895',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_241982___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_241895___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__1899] :
( t(Vvar__1___24Anonymous__1899,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__1900] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__1900)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_241982___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__1899,Vvar__2___24Anonymous__1900)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_241895___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__1899,c_24__fix__2027__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__1900,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$1982',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_241982___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__1986] :
( t(Vvar__1___24Anonymous__1986,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__1987] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__1987)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__1986,Vvar__2___24Anonymous__1987)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_241982___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__1986,c_24__fix__2027__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__1987,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$55702',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2455702___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__1) )
| ? [Vvar__1___24Anonymous__55706] :
( t(Vvar__1___24Anonymous__55706,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__55707] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__55707)
& Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__55706,Vvar__2___24Anonymous__55707)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2455702___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vvar__1___24Anonymous__55706),cCoq_2eLists_2eList_2emap___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2___24Anonymous__55707)) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$25086',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__25099___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__25091] :
( t(Vvar__2___24Anonymous__25091,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__25092] :
( t(Vvar__3___24Anonymous__25092,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__25091,Vvar__3___24Anonymous__25092)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2425086___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__25091)),Vvar__3___24Anonymous__25092)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$53424',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__25099___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__53429] :
( t(Vvar__2___24Anonymous__53429,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__53430] :
( t(Vvar__3___24Anonymous__53430,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__53429,Vvar__3___24Anonymous__53430)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2453424___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__53429)),Vvar__3___24Anonymous__53430)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Specif.sumbool$28890',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( c_24__type__28902___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__3 = Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__28906___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__28907___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_2428890___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__let__var__var__7__n__28859__28863__28872___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)) )
| ( Vv__CANONICAL__3 != Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__28908___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__28909___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_2428890___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__let__var__var__7__n__28859__28863__28872___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$54884',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZ0
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2454884___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) )
| ? [Vvar__0___24Anonymous__54885] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54885)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__54885)
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2454884___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__54885) ) )
| ? [Vvar__0___24Anonymous__54886] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54886)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__54886)
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2454884___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__1 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__54886) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.positive$53203',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__1)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__5)
=> ( ? [Vvar__0___24Anonymous__53204] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__53204)
& Vv__CANONICAL__5 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__53204)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2453203___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vv__CANONICAL__5))) )
| ? [Vvar__0___24Anonymous__53205] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__53205)
& Vv__CANONICAL__5 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__53205)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2453203___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vv__CANONICAL__5))) )
| ( Vv__CANONICAL__5 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2453203___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__4 ) ) ) ) ) ).
fof('$_case_Coq.setoid_ring.Ring_polynom.Pol$27568',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__27571] :
( t(Vvar__1___24Anonymous__27571,Vv__CANONICAL__8)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ( c_24__type__15860___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ( t(Vvar__1___24Anonymous__27571,Vv__CANONICAL__8)
=> ( Vv__CANONICAL__16 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vv__CANONICAL__8,Vvar__1___24Anonymous__27571)
& ( ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__27571),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2427568___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__27335___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__27571),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2427568___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__27335___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__27574] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__27574)
& ? [Vvar__2___24Anonymous__27575] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__2___24Anonymous__27575)
& Vv__CANONICAL__16 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vv__CANONICAL__8,Vvar__1___24Anonymous__27574,Vvar__2___24Anonymous__27575)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2427568___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__27335___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__27578] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__1___24Anonymous__27578)
& ? [Vvar__2___24Anonymous__27579] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__27579)
& ? [Vvar__3___24Anonymous__27580] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__3___24Anonymous__27580)
& Vv__CANONICAL__16 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vv__CANONICAL__8,Vvar__1___24Anonymous__27578,Vvar__2___24Anonymous__27579,Vvar__3___24Anonymous__27580)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2427568___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__27335___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$28165',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__28168] :
( t(Vvar__1___24Anonymous__28168,Vv__CANONICAL__8)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ( c_24__type__28188___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__11)
=> ( cType___24t(Vv__CANONICAL__13)
=> ( t(Vvar__1___24Anonymous__28168,Vv__CANONICAL__8)
=> ( Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vv__CANONICAL__8,Vvar__1___24Anonymous__28168)
& ( ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__28168),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2428165___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__27861___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__28168),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2428165___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__27861___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__28171] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__28171)
& ? [Vvar__2___24Anonymous__28172] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__2___24Anonymous__28172)
& Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vv__CANONICAL__8,Vvar__1___24Anonymous__28171,Vvar__2___24Anonymous__28172)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2428165___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__27861___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__28175] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__1___24Anonymous__28175)
& ? [Vvar__2___24Anonymous__28176] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__28176)
& ? [Vvar__3___24Anonymous__28177] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__3___24Anonymous__28177)
& Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vv__CANONICAL__8,Vvar__1___24Anonymous__28175,Vvar__2___24Anonymous__28176,Vvar__3___24Anonymous__28177)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2428165___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__27861___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__19)) ) ) ) ) ) ) ) ) ).
fof('$_def_$_let_11_subst_l_18148',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__18148___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_19023',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__19026] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19026)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19026)
& c_24__let__16__mkpow__19023___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__19027] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19027)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19027)
& c_24__let__16__mkpow__19023___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__19023___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_lnum_27335',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num] : c_24__let__17__lnum__27335___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__get__sign,V14__l,V15__num) ).
fof('$_def_$_let_17_mkopp_pow_19024',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__19024___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__19023___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_19025',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__19025___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__19023___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_20_lnum_27861',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num] : c_24__let__20__lnum__27861___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num) ).
fof('$_def_$_let_var_6_p_35941_35944',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__35940] : c_24__let__var__6__p__35941__35944___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__35940) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__35940) ).
fof('$_def_$_let_var_6_p_35943_35945',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__35942] : c_24__let__var__6__p__35943__35945___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__35942) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__35942) ).
fof('$_def_$_let_var_var_7_n_28859_28863_28872',axiom,
! [V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__28856] : c_24__let__var__var__7__n__28859__28863__28872___24a4(V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__28856) = cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,Vvar__2___24Anonymous__28856,V4__x) ).
fof('$_def_Coq.Arith.Wf_nat.ltof',axiom,
! [V0__A,V1__f,V2__a,V3__b] :
( cCoq_2eArith_2eWf__nat_2eltof___24a4(V0__A,V1__f,V2__a,V3__b)
<=> cCoq_2eInit_2ePeano_2elt___24a2(happ(V1__f,V2__a),happ(V1__f,V3__b)) ) ).
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.elements',axiom,
! [V0__m] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V0__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V0__m,cCoq_2eNumbers_2eBinNums_2exH,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt)) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__26637] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__26637)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__26637) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__26653] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__26653)
& ? [Vvar__1___24Anonymous__26654] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__26654)
& ? [Vvar__2___24Anonymous__26655] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__26655)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__26653,Vvar__1___24Anonymous__26654,Vvar__2___24Anonymous__26655)
& ( ? [Vvar__0___24Anonymous__26668] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26668)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26668)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__26668,Vvar__2___24Anonymous__26655) )
| ? [Vvar__0___24Anonymous__26669] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26669)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26669)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__26669,Vvar__0___24Anonymous__26653) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__26654 ) ) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
! [V1__y,V2__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__y)
=> ( ? [Vvar__0___24Anonymous__55764] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55764)
& V1__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55764)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__55764,cCoq_2eNumbers_2eBinNums_2exI___24a1(V2__x)) )
| ? [Vvar__0___24Anonymous__55765] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55765)
& V1__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55765)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__55765,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__x)) )
| ( V1__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = V2__x ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__26651] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__26651)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__26651) ) ).
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__80] :
( t(Vvar__1___24Anonymous__80,V0__A)
& ? [Vvar__2___24Anonymous__81] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__81)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__80,Vvar__2___24Anonymous__81)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__80,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__81,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__12116] :
( t(Vvar__2___24Anonymous__12116,V0__A)
& ? [Vvar__3___24Anonymous__12117] :
( t(Vvar__3___24Anonymous__12117,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__12116,Vvar__3___24Anonymous__12117)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__12116 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.id',axiom,
! [V0__A,V1__x] : cCoq_2eInit_2eDatatypes_2eid___24a2(V0__A,V1__x) = V1__x ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__70] :
( t(Vvar__1___24Anonymous__70,V0__A)
& ? [Vvar__2___24Anonymous__71] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__71)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__70,Vvar__2___24Anonymous__71)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__71)) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Datatypes.list_rect',axiom,
! [V0__A,V1__P,V2__f,V3__f,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__382___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = V2__f )
| ? [Vvar__1___24Anonymous__376] :
( t(Vvar__1___24Anonymous__376,V0__A)
& ? [Vvar__2___24Anonymous__377] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__377)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__376,Vvar__2___24Anonymous__377)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = happ(happ(happ(V3__f,Vvar__1___24Anonymous__376),Vvar__2___24Anonymous__377),cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,Vvar__2___24Anonymous__377)) ) ) ) ) ) ) ).
fof('$_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__12128] :
( t(Vvar__2___24Anonymous__12128,V0__A)
& ? [Vvar__3___24Anonymous__12129] :
( t(Vvar__3___24Anonymous__12129,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__12128,Vvar__3___24Anonymous__12129)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__12129 ) ) ) ) ) ).
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__136] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__136)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__136)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__136,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__1530] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1530)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1530)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__1533] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1533)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1533)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__1530,Vvar__0___24Anonymous__1533)) ) ) ) ) ) ) ) ).
fof('$_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__17544] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17544)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17544)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__17547] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17547)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17547)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__17544,Vvar__0___24Anonymous__17547)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__1527] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1527)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1527)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__1527,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__17542] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17542)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17542)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__17542 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__141] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__141)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__141)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__144] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__144)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__144)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__141,Vvar__0___24Anonymous__144) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__25591___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__25585] :
( t(Vvar__2__x__25585,V0__A)
& p(happ(V1__P,Vvar__2__x__25585))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__25585)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__25585 ) ) ) ) ).
fof('$_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__171] :
( t(Vvar__1___24Anonymous__171,V0__A)
& ? [Vvar__2___24Anonymous__172] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__172)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__171,Vvar__2___24Anonymous__172)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> ( Vvar__1___24Anonymous__171 = V2__a
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__172)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.combine',axiom,
! [V0__A,V1__B,V3__l,V4__l_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__28989] :
( t(Vvar__1___24Anonymous__28989,V0__A)
& ? [Vvar__2___24Anonymous__28990] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28990)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l_27)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28989,Vvar__2___24Anonymous__28990)
& ( ( V4__l_27 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__29001] :
( t(Vvar__1___24Anonymous__29001,V1__B)
& ? [Vvar__2___24Anonymous__29002] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__29002)
& V4__l_27 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__29001,Vvar__2___24Anonymous__29002)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__1___24Anonymous__28989,Vvar__1___24Anonymous__29001),cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,Vvar__2___24Anonymous__28990,Vvar__2___24Anonymous__29002)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__514] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__1___24Anonymous__514)
& ? [Vvar__2___24Anonymous__515] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__515)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__1___24Anonymous__514,Vvar__2___24Anonymous__515)
& cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__1___24Anonymous__514,cCoq_2eLists_2eList_2econcat___24a2(V0__A,Vvar__2___24Anonymous__515)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.count_occ',axiom,
! [V0__A,V1__eq__dec,V3__l,V4__x] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__28855] :
( t(Vvar__1___24Anonymous__28855,V0__A)
& ? [Vvar__2___24Anonymous__28856] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28856)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28855,Vvar__2___24Anonymous__28856)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_2428890___24a5(V0__A,V1__eq__dec,V4__x,Vvar__1___24Anonymous__28855,Vvar__2___24Anonymous__28856) ) ) ) ) ) ).
fof('$_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__183] :
( t(Vvar__1___24Anonymous__183,V0__A)
& ? [Vvar__2___24Anonymous__184] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__184)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__183,Vvar__2___24Anonymous__184)
& cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(happ(V1__f,Vvar__1___24Anonymous__183),cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__184)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.filter',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__212] :
( t(Vvar__1___24Anonymous__212,V0__A)
& ? [Vvar__2___24Anonymous__213] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__213)
& ( cType___24t(V0__A)
=> ( c_24__type__193___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__212,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__212,Vvar__2___24Anonymous__213)
& ( ( happ(V1__f,Vvar__1___24Anonymous__212) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__212,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__213)) )
| ( happ(V1__f,Vvar__1___24Anonymous__212) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__213) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__28972] :
( t(Vvar__1___24Anonymous__28972,V0__A)
& ? [Vvar__2___24Anonymous__28973] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28973)
& ( cType___24t(V0__A)
=> ( c_24__type__193___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__28972,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28972,Vvar__2___24Anonymous__28973)
& ( ( happ(V1__f,Vvar__1___24Anonymous__28972) = 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__28972) )
| ( happ(V1__f,Vvar__1___24Anonymous__28972) = 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__28973) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.firstn',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__0___24Anonymous__226] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__226)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__226)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__233] :
( t(Vvar__1___24Anonymous__233,V0__A)
& ? [Vvar__2___24Anonymous__234] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__234)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__233,Vvar__2___24Anonymous__234)
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__233,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,Vvar__0___24Anonymous__226,Vvar__2___24Anonymous__234)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__1379] :
( t(Vvar__1___24Anonymous__1379,V0__A)
& ? [Vvar__2___24Anonymous__1380] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1380)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1379,Vvar__2___24Anonymous__1380)
& 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__1379),cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__1380)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_left',axiom,
! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
| ? [Vvar__1___24Anonymous__547] :
( t(Vvar__1___24Anonymous__547,V1__B)
& ? [Vvar__2___24Anonymous__548] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__548)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__547,Vvar__2___24Anonymous__548)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__548,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__547)) ) ) ) ) ) ) ).
fof('$_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__583] :
( t(Vvar__1___24Anonymous__583,V1__B)
& ? [Vvar__2___24Anonymous__584] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__584)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__583,Vvar__2___24Anonymous__584)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__583),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__584)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.forallb',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__1___24Anonymous__200] :
( t(Vvar__1___24Anonymous__200,V0__A)
& ? [Vvar__2___24Anonymous__201] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__201)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__200,Vvar__2___24Anonymous__201)
& cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eandb___24a2(happ(V1__f,Vvar__1___24Anonymous__200),cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__201)) ) ) ) ) ) ).
fof('$_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__28790] :
( t(Vvar__1___24Anonymous__28790,V0__A)
& ? [Vvar__2___24Anonymous__28791] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28791)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28790,Vvar__2___24Anonymous__28791)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__28790 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd_error',axiom,
! [V0__A,V1__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__55137] :
( t(Vvar__1___24Anonymous__55137,V0__A)
& ? [Vvar__2___24Anonymous__55138] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__55138)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__55137,Vvar__2___24Anonymous__55138)
& cCoq_2eLists_2eList_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__55137) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.incl',axiom,
! [V0__A,V1__l,V2__m] :
( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m))
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m)) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__428] :
( t(Vvar__1___24Anonymous__428,V0__A)
& ? [Vvar__2___24Anonymous__429] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__429)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__429)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__428,Vvar__2___24Anonymous__429)
& ( ( Vvar__2___24Anonymous__429 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__428 )
| ? [Vvar__1___24Anonymous__440] :
( t(Vvar__1___24Anonymous__440,V0__A)
& ? [Vvar__2___24Anonymous__441] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__441)
& Vvar__2___24Anonymous__429 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__440,Vvar__2___24Anonymous__441)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__429,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.lel',axiom,
! [V0__A,V1__l,V2__m] :
( cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V2__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__m))) ) ).
fof('$_def_Coq.Lists.List.list_power',axiom,
! [V1__A,V2__B,V3__l,V4__l_27] :
( cType___24t(V1__A)
=> ( cType___24t(V2__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& cCoq_2eLists_2eList_2elist__power___24a4(V1__A,V2__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V1__A,V2__B)),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V1__A,V2__B)),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V1__A,V2__B)))) )
| ? [Vvar__1___24Anonymous__57872] :
( t(Vvar__1___24Anonymous__57872,V1__A)
& ? [Vvar__2___24Anonymous__57873] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__57873)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__57872,Vvar__2___24Anonymous__57873)
& cCoq_2eLists_2eList_2elist__power___24a4(V1__A,V2__B,V3__l,V4__l_27) = cCoq_2eLists_2eList_2eflat__map___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V1__A,V2__B)),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V1__A,V2__B)),c_24__lam__57888___24a4(V1__A,V2__B,V4__l_27,Vvar__1___24Anonymous__57872),cCoq_2eLists_2eList_2elist__power___24a4(V1__A,V2__B,Vvar__2___24Anonymous__57873,V4__l_27)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.list_prod',axiom,
! [V0__A,V1__B,V3__l,V4__l_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__1434] :
( t(Vvar__1___24Anonymous__1434,V0__A)
& ? [Vvar__2___24Anonymous__1435] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1435)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1434,Vvar__2___24Anonymous__1435)
& cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eLists_2eList_2emap___24a4(V1__B,cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),c_24__lam__1442___24a3(V0__A,V1__B,Vvar__1___24Anonymous__1434),V4__l_27),cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,Vvar__2___24Anonymous__1435,V4__l_27)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__524] :
( t(Vvar__1___24Anonymous__524,V0__A)
& ? [Vvar__2___24Anonymous__525] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__525)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__524,Vvar__2___24Anonymous__525)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__524),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__525)) ) ) ) ) ) ) ).
fof('$_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__36944] :
( t(Vvar__1___24Anonymous__36944,V0__A)
& ? [Vvar__2___24Anonymous__36945] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__36945)
& ( cType___24t(V0__A)
=> ( c_24__type__28902___24t(V0__A,V1__decA)
=> ( t(Vvar__1___24Anonymous__36944,V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__36945)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945)
& ( ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945))
& cCoq_2eLists_2eList_2ein__dec___24a4(V0__A,V1__decA,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945),c_24__prop__36964___24a3(V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945))
& cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,V3__l) = cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,Vvar__2___24Anonymous__36945) )
| ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945))
& cCoq_2eLists_2eList_2ein__dec___24a4(V0__A,V1__decA,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945),c_24__prop__36976___24a3(V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945))
& cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__36944,cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,Vvar__2___24Anonymous__36945)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__92] :
( t(Vvar__1___24Anonymous__92,V0__A)
& ? [Vvar__2___24Anonymous__93] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__93)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__92,Vvar__2___24Anonymous__93)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__92 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__95] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__95)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__95)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__102] :
( t(Vvar__1___24Anonymous__102,V0__A)
& ? [Vvar__2___24Anonymous__103] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__103)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__102,Vvar__2___24Anonymous__103)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__95,Vvar__2___24Anonymous__103,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__28841] :
( t(Vvar__1___24Anonymous__28841,V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__28841)
& cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V1__default,V2__l,V3__n) = Vvar__1___24Anonymous__28841 )
| ( 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('$_def_Coq.Lists.List.nth_error',axiom,
! [V0__A,V2__l,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__117] :
( t(Vvar__1___24Anonymous__117,V0__A)
& ? [Vvar__2___24Anonymous__118] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__118)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__117,Vvar__2___24Anonymous__118)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__117) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__120] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120)
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__127] :
( t(Vvar__1___24Anonymous__127,V0__A)
& ? [Vvar__2___24Anonymous__128] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__128)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__127,Vvar__2___24Anonymous__128)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,Vvar__2___24Anonymous__128,Vvar__0___24Anonymous__120) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__28809] :
( t(Vvar__1___24Anonymous__28809,V0__A)
& ? [Vvar__2___24Anonymous__28810] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28810)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28809,Vvar__2___24Anonymous__28810)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__28812] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28812)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28812)
& ( ( 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__28819] :
( t(Vvar__1___24Anonymous__28819,V0__A)
& ? [Vvar__2___24Anonymous__28820] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28820)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28819,Vvar__2___24Anonymous__28820)
& 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__28812,Vvar__2___24Anonymous__28820,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__1400] :
( t(Vvar__1___24Anonymous__1400,V0__A)
& ? [Vvar__2___24Anonymous__1401] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1401)
& ( cType___24t(V0__A)
=> ( c_24__type__193___24t(V0__A,V1__f)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1401)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1400,Vvar__2___24Anonymous__1401)
& ? [Vvar__2___24Anonymous__1415] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1415)
& ? [Vvar__3___24Anonymous__1416] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__3___24Anonymous__1416)
& ( cType___24t(V0__A)
=> ( c_24__type__193___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__1400,V0__A)
=> ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,Vvar__2___24Anonymous__1401) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__1415,Vvar__3___24Anonymous__1416)
& ( ( happ(V1__f,Vvar__1___24Anonymous__1400) = 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__1400,Vvar__2___24Anonymous__1415),Vvar__3___24Anonymous__1416) )
| ( happ(V1__f,Vvar__1___24Anonymous__1400) = 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__1415,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1400,Vvar__3___24Anonymous__1416)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__36892] :
( t(Vvar__1___24Anonymous__36892,V0__A)
& ? [Vvar__2___24Anonymous__36893] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__36893)
& ( cType___24t(V0__A)
=> ( c_24__type__28902___24t(V0__A,V1__eq__dec)
=> ( t(V3__x,V0__A)
=> ( t(Vvar__1___24Anonymous__36892,V0__A)
=> ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__36892,Vvar__2___24Anonymous__36893)
& ( ( V3__x = Vvar__1___24Anonymous__36892
& happ(happ(V1__eq__dec,V3__x),Vvar__1___24Anonymous__36892) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__36912___24a3(V0__A,V3__x,Vvar__1___24Anonymous__36892),c_24__prop__36913___24a3(V0__A,V3__x,Vvar__1___24Anonymous__36892))
& 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__36893) )
| ( V3__x != Vvar__1___24Anonymous__36892
& happ(happ(V1__eq__dec,V3__x),Vvar__1___24Anonymous__36892) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__36914___24a3(V0__A,V3__x,Vvar__1___24Anonymous__36892),c_24__prop__36915___24a3(V0__A,V3__x,Vvar__1___24Anonymous__36892))
& cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__36892,cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,Vvar__2___24Anonymous__36893)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.removelast',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__452] :
( t(Vvar__1___24Anonymous__452,V0__A)
& ? [Vvar__2___24Anonymous__453] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__453)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__453)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__452,Vvar__2___24Anonymous__453)
& ( ( Vvar__2___24Anonymous__453 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__464] :
( t(Vvar__1___24Anonymous__464,V0__A)
& ? [Vvar__2___24Anonymous__465] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__465)
& Vvar__2___24Anonymous__453 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__464,Vvar__2___24Anonymous__465)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__452,cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,Vvar__2___24Anonymous__453)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__29051] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29051)
& V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29051)
& 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__29051)) ) ) ) ) ).
fof('$_def_Coq.Lists.List.rev',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__496] :
( t(Vvar__1___24Anonymous__496,V0__A)
& ? [Vvar__2___24Anonymous__497] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__497)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__496,Vvar__2___24Anonymous__497)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,Vvar__2___24Anonymous__497),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__496,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Lists.List.rev_append',axiom,
! [V0__A,V2__l,V3__l_27] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V2__l,V3__l_27) = V3__l_27 )
| ? [Vvar__1___24Anonymous__504] :
( t(Vvar__1___24Anonymous__504,V0__A)
& ? [Vvar__2___24Anonymous__505] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__505)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__504,Vvar__2___24Anonymous__505)
& cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V2__l,V3__l_27) = cCoq_2eLists_2eList_2erev__append___24a3(V0__A,Vvar__2___24Anonymous__505,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__504,V3__l_27)) ) ) ) ) ) ).
fof('$_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__1457] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1457)
& V2__len = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1457)
& 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__1457)) ) ) ) ).
fof('$_def_Coq.Lists.List.skipn',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = V3__l )
| ? [Vvar__0___24Anonymous__242] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__242)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__242)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__249] :
( t(Vvar__1___24Anonymous__249,V0__A)
& ? [Vvar__2___24Anonymous__250] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__250)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__249,Vvar__2___24Anonymous__250)
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = cCoq_2eLists_2eList_2eskipn___24a3(V0__A,Vvar__0___24Anonymous__242,Vvar__2___24Anonymous__250) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__37016] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,Vvar__1___24Anonymous__37016)
& ? [Vvar__2___24Anonymous__37017] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),Vvar__2___24Anonymous__37017)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,Vvar__1___24Anonymous__37016)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),Vvar__1___24Anonymous__37016,Vvar__2___24Anonymous__37017)
& ? [Vvar__2___24Anonymous__37035] :
( t(Vvar__2___24Anonymous__37035,V0__A)
& ? [Vvar__3___24Anonymous__37036] :
( t(Vvar__3___24Anonymous__37036,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__37017)
=> ( Vvar__1___24Anonymous__37016 = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__37035,Vvar__3___24Anonymous__37036)
& ? [Vvar__2___24Anonymous__37048] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__37048)
& ? [Vvar__3___24Anonymous__37049] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__3___24Anonymous__37049)
& cCoq_2eLists_2eList_2esplit___24a3(V0__A,V1__B,Vvar__2___24Anonymous__37017) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),Vvar__2___24Anonymous__37048,Vvar__3___24Anonymous__37049)
& 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__37035,Vvar__2___24Anonymous__37048),cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__3___24Anonymous__37036,Vvar__3___24Anonymous__37049)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.tl',axiom,
! [V0__A,V1__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__28801] :
( t(Vvar__1___24Anonymous__28801,V0__A)
& ? [Vvar__2___24Anonymous__28802] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__28802)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__28801,Vvar__2___24Anonymous__28802)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__28802 ) ) ) ) ) ).
fof('$_def_Coq.Lists.ListDec.In_dec',axiom,
! [V0__A,V1__dec] : cCoq_2eLists_2eListDec_2eIn__dec___24a2(V0__A,V1__dec) = cCoq_2eLists_2eList_2ein__dec___24a2(V0__A,V1__dec) ).
fof('$_def_Coq.Lists.ListDec.decidable_eq',axiom,
! [V0__A] :
( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
<=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__29057___24a3(V0__A,V1__x,V2__y)) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.equivlistA',axiom,
! [V0__A,V1__eqA,V2__l,V3__l_27] :
( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l)
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l_27) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.inclA',axiom,
! [V0__A,V1__eqA,V2__l,V3__l_27] :
( cCoq_2eLists_2eSetoidList_2einclA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l_27) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.removeA',axiom,
! [V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__55565___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__55541] :
( t(Vvar__1___24Anonymous__55541,V0__A)
& ? [Vvar__2___24Anonymous__55542] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__55542)
& ( cType___24t(V0__A)
=> ( c_24__type__55574___24t(V0__A,V1__eqA,V1__eqA)
=> ( c_24__type__55583___24t(V0__A,V1__eqA,V2__eqA__dec)
=> ( t(V4__x,V0__A)
=> ( t(Vvar__1___24Anonymous__55541,V0__A)
=> ( V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__55541,Vvar__2___24Anonymous__55542)
& ( ( p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__55541))
& happ(happ(V2__eqA__dec,V4__x),Vvar__1___24Anonymous__55541) = cCoq_2eInit_2eSpecif_2eleft___24a2(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__55541),c_24__prop__55586___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__55541))
& 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__55542) )
| ( ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__55541))
& happ(happ(V2__eqA__dec,V4__x),Vvar__1___24Anonymous__55541) = cCoq_2eInit_2eSpecif_2eright___24a2(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__55541),c_24__prop__55587___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__55541))
& 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__55541,cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,Vvar__2___24Anonymous__55542)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V6__z)))) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose2',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> ! [V7__z_27] :
( t(V7__z_27,V1__B)
=> ( p(happ(happ(V2__eqB,V6__z),V7__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V7__z_27)))) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V7__z)))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr2',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ! [V8__z_27] :
( t(V8__z_27,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> ( p(happ(happ(V2__eqB,V7__z),V8__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V8__z_27)))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.Logic.FinFun.Finite',axiom,
! [V0__A] :
( cCoq_2eLogic_2eFinFun_2eFinite___24a1(V0__A)
<=> ? [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
& cCoq_2eLogic_2eFinFun_2eFull___24a2(V0__A,V1__l) ) ) ).
fof('$_def_Coq.Logic.FinFun.Finite\'',axiom,
! [V0__A] :
( cCoq_2eLogic_2eFinFun_2eFinite_27___24a1(V0__A)
<=> ? [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
& cCoq_2eLogic_2eFinFun_2eListing___24a2(V0__A,V1__l) ) ) ).
fof('$_def_Coq.Logic.FinFun.Full',axiom,
! [V0__A,V1__l] :
( cCoq_2eLogic_2eFinFun_2eFull___24a2(V0__A,V1__l)
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V1__l)) ) ) ).
fof('$_def_Coq.Logic.FinFun.Injective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eInjective___24a3(V0__A,V1__B,V2__f)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( happ(V2__f,V3__x) = happ(V2__f,V4__y)
=> V3__x = V4__y ) ) ) ) ).
fof('$_def_Coq.Logic.FinFun.Listing',axiom,
! [V0__A,V1__l] :
( cCoq_2eLogic_2eFinFun_2eListing___24a2(V0__A,V1__l)
<=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
& cCoq_2eLogic_2eFinFun_2eFull___24a2(V0__A,V1__l) ) ) ).
fof('$_def_Coq.Logic.FinFun.Surjective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eSurjective___24a3(V0__A,V1__B,V2__f)
<=> ! [V3__y] :
( t(V3__y,V1__B)
=> ? [V4__x] :
( t(V4__x,V0__A)
& happ(V2__f,V4__x) = V3__y ) ) ) ).
fof('$_def_Coq.Logic.FinFun.bFun',axiom,
! [V0__n,V1__f] :
( cCoq_2eLogic_2eFinFun_2ebFun___24a2(V0__n,V1__f)
<=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__x,V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(happ(V1__f,V2__x),V0__n) ) ) ) ).
fof('$_def_Coq.Logic.FinFun.bInjective',axiom,
! [V0__n,V1__f] :
( cCoq_2eLogic_2eFinFun_2ebInjective___24a2(V0__n,V1__f)
<=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__x,V0__n)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V3__y,V0__n)
=> ( happ(V1__f,V2__x) = happ(V1__f,V3__y)
=> V2__x = V3__y ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.FinFun.bSurjective',axiom,
! [V0__n,V1__f] :
( cCoq_2eLogic_2eFinFun_2ebSurjective___24a2(V0__n,V1__f)
<=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__y)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__y,V0__n)
=> ? [V4__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__x)
& cCoq_2eInit_2ePeano_2elt___24a2(V4__x,V0__n)
& happ(V1__f,V4__x) = V2__y ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__26397] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26397)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26397)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__26400] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26400)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26400)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__26397,Vvar__0___24Anonymous__26400)) ) ) ) ) ) ) ) ).
fof('$_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__26425] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26425)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26425)
& ( ( 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__26428] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26428)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26428)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__26425,V1__b) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__26408] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26408)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26408)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__26409] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26409)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26409)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__26412] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26412)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26412)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__26409,Vvar__0___24Anonymous__26412) ) ) ) ) ) ) ) ).
fof('$_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__26402] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26402)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26402)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__26405] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26405)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26405)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__26402,Vvar__0___24Anonymous__26405)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__26442] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26442)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26442)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__26442) ) ) ) ).
fof('$_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__26517] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26517)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26517)
& ( ? [Vvar__0___24Anonymous__26521] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26521)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26521)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__26516__1__add__carry___24a2(Vvar__0___24Anonymous__26517,Vvar__0___24Anonymous__26521)) )
| ? [Vvar__0___24Anonymous__26522] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26522)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26522)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__26517,Vvar__0___24Anonymous__26522)) )
| ( 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__26517)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__26523] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26523)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26523)
& ( ? [Vvar__0___24Anonymous__26527] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26527)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26527)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__26523,Vvar__0___24Anonymous__26527)) )
| ? [Vvar__0___24Anonymous__26528] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26528)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26528)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__26523,Vvar__0___24Anonymous__26528)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26523) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__26529] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26529)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26529)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__26529)) )
| ? [Vvar__0___24Anonymous__26530] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26530)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26530)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26530) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__36707] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36707)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__36707)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__36707)) )
| ? [Vvar__0___24Anonymous__36708] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36708)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__36708)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__36708)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__36709] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36709)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__36709)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__36709 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__26514] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26514)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26514)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__26514)) )
| ? [Vvar__0___24Anonymous__26515] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26515)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26515)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26515) )
| ( 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.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__17816] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17816)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17816)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__17816) )
| ? [Vvar__0___24Anonymous__17817] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17817)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17817)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__17817)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__25520] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__25520)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__25520)
& 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__25520)) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__259___24a1(V0__A) ).
fof('$_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.Strings.String.append',axiom,
! [V1__s1,V2__s2] :
( cCoq_2eStrings_2eString_2estring___24t(V1__s1)
=> ( ( V1__s1 = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2eappend___24a2(V1__s1,V2__s2) = V2__s2 )
| ? [Vvar__0___24Anonymous__64177] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__64177)
& ? [Vvar__1___24Anonymous__64178] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__64178)
& V1__s1 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__64177,Vvar__1___24Anonymous__64178)
& cCoq_2eStrings_2eString_2eappend___24a2(V1__s1,V2__s2) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__64177,cCoq_2eStrings_2eString_2eappend___24a2(Vvar__1___24Anonymous__64178,V2__s2)) ) ) ) ) ).
fof('$_def_Coq.Strings.String.string_of_list_ascii',axiom,
! [V1__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,V1__s)
=> ( ( V1__s = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eStrings_2eAscii_2eascii)
& cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(V1__s) = cCoq_2eStrings_2eString_2eEmptyString )
| ? [Vvar__1___24Anonymous__58561] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1___24Anonymous__58561)
& ? [Vvar__2___24Anonymous__58562] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,Vvar__2___24Anonymous__58562)
& V1__s = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eStrings_2eAscii_2eascii,Vvar__1___24Anonymous__58561,Vvar__2___24Anonymous__58562)
& cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(V1__s) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1___24Anonymous__58561,cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(Vvar__2___24Anonymous__58562)) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Vectors.VectorDef.of_list',axiom,
! [V1__A,V2__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& cCoq_2eVectors_2eVectorDef_2eof__list___24a2(V1__A,V2__l) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A) )
| ? [Vvar__1___24Anonymous__42755] :
( t(Vvar__1___24Anonymous__42755,V1__A)
& ? [Vvar__2___24Anonymous__42756] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__42756)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__42755,Vvar__2___24Anonymous__42756)
& cCoq_2eVectors_2eVectorDef_2eof__list___24a2(V1__A,V2__l) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1___24Anonymous__42755,cCoq_2eInit_2eDatatypes_2elength___24a2(V1__A,Vvar__2___24Anonymous__42756),cCoq_2eVectors_2eVectorDef_2eof__list___24a2(V1__A,Vvar__2___24Anonymous__42756)) ) ) ) ) ) ).
fof('$_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__36598__v__CANONICAL__2___24a5(V0__A,V1__n,V1__n,V2__v,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_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.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__26854] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26854)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26854)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__26858] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26858)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26858)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__26854,Vvar__0___24Anonymous__26858)) )
| ? [Vvar__0___24Anonymous__26859] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26859)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26859)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__26854,Vvar__0___24Anonymous__26859) ) ) ) ) )
| ? [Vvar__0___24Anonymous__26860] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26860)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26860)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__26864] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26864)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26864)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__26864,Vvar__0___24Anonymous__26860) )
| ? [Vvar__0___24Anonymous__26865] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26865)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26865)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__26860,Vvar__0___24Anonymous__26865)) ) ) ) ) ) ) ) ).
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__41952] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41952)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__41952)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__41953] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41953)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__41953)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__41954] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41954)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__41954)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__41958] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41958)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__41958)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__41954,Vvar__0___24Anonymous__41958) )
| ? [Vvar__0___24Anonymous__41959] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41959)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__41959)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__41960] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41960)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__41960)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__41964] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41964)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__41964)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__41965] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41965)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__41965)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__41960,Vvar__0___24Anonymous__41965)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.gtb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.mul',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__26874] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26874)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26874)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__26878] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26878)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26878)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__26874,Vvar__0___24Anonymous__26878)) )
| ? [Vvar__0___24Anonymous__26879] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26879)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26879)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__26874,Vvar__0___24Anonymous__26879)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__26880] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26880)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26880)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__26884] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26884)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26884)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__26880,Vvar__0___24Anonymous__26884)) )
| ? [Vvar__0___24Anonymous__26885] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26885)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26885)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__26880,Vvar__0___24Anonymous__26885)) ) ) ) ) ) ) ) ).
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__26904] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26904)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26904)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26904) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__26901] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26901)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26901)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__26901)) ) ) ) ).
fof('$_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__26869] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26869)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26869)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26869) )
| ? [Vvar__0___24Anonymous__26870] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26870)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26870)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26870) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pos_sub',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__54861] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54861)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54861)
& ( ? [Vvar__0___24Anonymous__54865] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54865)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54865)
& 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__54861,Vvar__0___24Anonymous__54865)) )
| ? [Vvar__0___24Anonymous__54866] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54866)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54866)
& 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__54861,Vvar__0___24Anonymous__54866)) )
| ( 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__54861)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__54867] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54867)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54867)
& ( ? [Vvar__0___24Anonymous__54871] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54871)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54871)
& 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__54867,Vvar__0___24Anonymous__54871)) )
| ? [Vvar__0___24Anonymous__54872] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54872)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54872)
& 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__54867,Vvar__0___24Anonymous__54872)) )
| ( 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__54867)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__54873] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54873)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54873)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54873)) )
| ? [Vvar__0___24Anonymous__54874] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54874)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54874)
& 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__54874)) )
| ( 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__42732] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42732)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__42732)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__42732) )
| ? [Vvar__0___24Anonymous__42733] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42733)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__42733)
& 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__26907] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26907)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26907)
& ( ( 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__26917] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26917)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26907)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26917)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26917)
& ? [Vvar__2___24Anonymous__26925] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__26925)
& ? [Vvar__3___24Anonymous__26926] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__26926)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__26907,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26917)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__26925,Vvar__3___24Anonymous__26926)
& 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__26925),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__26926)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__26928] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26928)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26907)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26928)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26928)
& ? [Vvar__2___24Anonymous__26936] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__26936)
& ? [Vvar__3___24Anonymous__26937] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__26937)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__26907,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26928)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__26936,Vvar__3___24Anonymous__26937)
& 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__26936)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__26937)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__26939] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26939)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26939)
& ( ( 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__26949] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26949)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26939)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26949)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26949)
& ? [Vvar__2___24Anonymous__26957] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__26957)
& ? [Vvar__3___24Anonymous__26958] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__26958)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__26939,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26949)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__26957,Vvar__3___24Anonymous__26958)
& 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__26957)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__26958))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__26960] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26960)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26939)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26960)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26960)
& ? [Vvar__2___24Anonymous__26968] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__26968)
& ? [Vvar__3___24Anonymous__26969] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__26969)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__26939,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26960)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__26968,Vvar__3___24Anonymous__26969)
& 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__26968),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__26969))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__36684] :
( t(Vvar__1___24Anonymous__36684,V2__A)
& ? [Vvar__2___24Anonymous__36685] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V2__A,Vvar__2___24Anonymous__36685)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__A,Vvar__1___24Anonymous__36684,Vvar__2___24Anonymous__36685)
& 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__36685) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__27058___24a1(V0__D) ).
fof('$_def_Coq.micromega.EnvRing.Pphi',axiom,
! [V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V6__l,V7__P] :
( cType___24t(V0__R)
=> ( cType___24t(V3__C)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V3__C,V7__P)
=> ( ? [Vvar__1___24Anonymous__37299] :
( t(Vvar__1___24Anonymous__37299,V3__C)
& V7__P = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V3__C,Vvar__1___24Anonymous__37299)
& cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V6__l,V7__P) = happ(V4__phi,Vvar__1___24Anonymous__37299) )
| ? [Vvar__1___24Anonymous__37301] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__37301)
& ? [Vvar__2___24Anonymous__37302] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V3__C,Vvar__2___24Anonymous__37302)
& V7__P = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V3__C,Vvar__1___24Anonymous__37301,Vvar__2___24Anonymous__37302)
& cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V6__l,V7__P) = cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,cCoq_2emicromega_2eEnv_2ejump___24a3(V0__R,Vvar__1___24Anonymous__37301,V6__l),Vvar__2___24Anonymous__37302) ) )
| ? [Vvar__1___24Anonymous__37305] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V3__C,Vvar__1___24Anonymous__37305)
& ? [Vvar__2___24Anonymous__37306] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__37306)
& ? [Vvar__3___24Anonymous__37307] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V3__C,Vvar__3___24Anonymous__37307)
& V7__P = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V3__C,Vvar__1___24Anonymous__37305,Vvar__2___24Anonymous__37306,Vvar__3___24Anonymous__37307)
& cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V6__l,V7__P) = happ(happ(V1__radd,happ(happ(V2__rmul,cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V6__l,Vvar__1___24Anonymous__37305)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,cCoq_2emicromega_2eEnv_2ehd___24a2(V0__R,V6__l),Vvar__2___24Anonymous__37306))),cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,cCoq_2emicromega_2eEnv_2etail___24a2(V0__R,V6__l),Vvar__3___24Anonymous__37307)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.QMicromega.QWitness',axiom,
! [Vvar__55356] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(Vvar__55356)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__55356) ) ).
fof('$_def_Coq.micromega.RMicromega.RWitness',axiom,
! [Vvar__55357] :
( cCoq_2emicromega_2eRMicromega_2eRWitness___24t(Vvar__55357)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__55357) ) ).
fof('$_def_Coq.micromega.Refl.make_conj',axiom,
! [V1__A,V2__eval,V3__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__1561] :
( t(Vvar__1___24Anonymous__1561,V1__A)
& ? [Vvar__2___24Anonymous__1562] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__1562)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__1562)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__1561,Vvar__2___24Anonymous__1562)
& ( ( Vvar__2___24Anonymous__1562 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(happ(V2__eval,Vvar__1___24Anonymous__1561)) ) )
| ? [Vvar__1___24Anonymous__1573] :
( t(Vvar__1___24Anonymous__1573,V1__A)
& ? [Vvar__2___24Anonymous__1574] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__1574)
& Vvar__2___24Anonymous__1562 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__1573,Vvar__2___24Anonymous__1574)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__1561))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__1562) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__30299] :
( t(Vvar__1___24Anonymous__30299,V1__A)
& ? [Vvar__2___24Anonymous__30300] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__30300)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__30299,Vvar__2___24Anonymous__30300)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__30299))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__30300,V4__goal) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.NFormula',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C) = cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_def_Coq.micromega.RingMicromega.PolC',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V0__C) ).
fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).
fof('$_def_Coq.micromega.RingMicromega.cltb',axiom,
! [V0__C,V1__ceqb,V2__cleb,V3__x,V4__y] : cCoq_2emicromega_2eRingMicromega_2ecltb___24a5(V0__C,V1__ceqb,V2__cleb,V3__x,V4__y) = cCoq_2eInit_2eDatatypes_2eandb___24a2(happ(happ(V2__cleb,V3__x),V4__y),cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V0__C,V1__ceqb,V3__x,V4__y)) ).
fof('$_def_Coq.micromega.RingMicromega.eval_nformula',axiom,
! [V0__R,V1__rO,V2__rplus,V3__rtimes,V4__req,V5__rle,V6__rlt,V7__C,V8__phi,V9__env,V10__f] :
( cType___24t(V0__R)
=> ( cType___24t(V7__C)
=> ( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V7__C,V10__f)
=> ? [Vvar__2___24Anonymous__37754] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V7__C,Vvar__2___24Anonymous__37754)
& ? [Vvar__3___24Anonymous__37755] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vvar__3___24Anonymous__37755)
& V10__f = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V7__C),cCoq_2emicromega_2eRingMicromega_2eOp1,Vvar__2___24Anonymous__37754,Vvar__3___24Anonymous__37755)
& ( cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a11(V0__R,V1__rO,V2__rplus,V3__rtimes,V4__req,V5__rle,V6__rlt,V7__C,V8__phi,V9__env,V10__f)
<=> cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a7(V0__R,V1__rO,V4__req,V5__rle,V6__rlt,Vvar__3___24Anonymous__37755,cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a7(V0__R,V2__rplus,V3__rtimes,V7__C,V8__phi,V9__env,Vvar__2___24Anonymous__37754)) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op1',axiom,
! [V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V5__o)
=> ( ( V5__o = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__37672___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__37680___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__37688___24a3(V0__R,V1__rO,V4__rlt) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__37696___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.eval_pol',axiom,
! [V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi] : cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a5(V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi) = cCoq_2emicromega_2eEnvRing_2ePphi___24a5(V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi) ).
fof('$_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__55408] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__55408)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__55408)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__55409] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__55409)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__55409)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__55412] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__55412)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__55412)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(Vvar__0___24Anonymous__55409,Vvar__0___24Anonymous__55412) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.map_option',axiom,
! [V0__A,V1__B,V2__f,V3__o] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V3__o)
=> ( ? [Vvar__1___24Anonymous__37927] :
( t(Vvar__1___24Anonymous__37927,V0__A)
& V3__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__37927)
& cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = happ(V2__f,Vvar__1___24Anonymous__37927) )
| ( V3__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.map_option2',axiom,
! [V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cType___24t(V2__C)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V4__o)
=> ( ? [Vvar__1___24Anonymous__37945] :
( t(Vvar__1___24Anonymous__37945,V0__A)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cType___24t(V2__C)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V1__B,V5__o_27)
=> ( V4__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__37945)
& ( ? [Vvar__1___24Anonymous__37950] :
( t(Vvar__1___24Anonymous__37950,V1__B)
& V5__o_27 = cCoq_2eInit_2eDatatypes_2eSome___24a2(V1__B,Vvar__1___24Anonymous__37950)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = happ(happ(V3__f,Vvar__1___24Anonymous__37945),Vvar__1___24Anonymous__37950) )
| ( V5__o_27 = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V2__C) ) ) ) ) ) ) ) )
| ( V4__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V2__C) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.nhyps_of_psatz',axiom,
! [V0__C,V2__prf] :
( cType___24t(V0__C)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,V2__prf)
=> ( ? [Vvar__1___24Anonymous__2295] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__2295)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V0__C,Vvar__1___24Anonymous__2295)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__1___24Anonymous__2295,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat)) )
| ? [Vvar__1___24Anonymous__2297] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V0__C,Vvar__1___24Anonymous__2297)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V0__C,Vvar__1___24Anonymous__2297)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__1___24Anonymous__2299] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V0__C,Vvar__1___24Anonymous__2299)
& ? [Vvar__2___24Anonymous__2300] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__2___24Anonymous__2300)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V0__C,Vvar__1___24Anonymous__2299,Vvar__2___24Anonymous__2300)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__2___24Anonymous__2300) ) )
| ? [Vvar__1___24Anonymous__2303] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__1___24Anonymous__2303)
& ? [Vvar__2___24Anonymous__2304] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__2___24Anonymous__2304)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V0__C,Vvar__1___24Anonymous__2303,Vvar__2___24Anonymous__2304)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__1___24Anonymous__2303),cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__2___24Anonymous__2304)) ) )
| ? [Vvar__1___24Anonymous__2307] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__1___24Anonymous__2307)
& ? [Vvar__2___24Anonymous__2308] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__2___24Anonymous__2308)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V0__C,Vvar__1___24Anonymous__2307,Vvar__2___24Anonymous__2308)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__1___24Anonymous__2307),cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__2___24Anonymous__2308)) ) )
| ? [Vvar__1___24Anonymous__2311] :
( t(Vvar__1___24Anonymous__2311,V0__C)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V0__C,Vvar__1___24Anonymous__2311)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ( V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V0__C)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.psubC',axiom,
! [V0__C,V1__cminus] : cCoq_2emicromega_2eRingMicromega_2epsubC___24a2(V0__C,V1__cminus) = cCoq_2emicromega_2eEnvRing_2ePsubC___24a2(V0__C,V1__cminus) ).
fof('$_def_Coq.micromega.Tauto.BFormula',axiom,
! [V0__A] : cCoq_2emicromega_2eTauto_2eBFormula___24a1(V0__A) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__A,cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_def_Coq.micromega.Tauto.TFormula',axiom,
! [V0__Term,V1__Annot,V2__TX,V3__AF] : cCoq_2emicromega_2eTauto_2eTFormula___24a4(V0__Term,V1__Annot,V2__TX,V3__AF) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__Term,V2__TX,V1__Annot,V3__AF) ).
fof('$_def_Coq.micromega.Tauto.clause',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).
fof('$_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__42634] :
( cCoq_2emicromega_2eTauto_2eclause___24t(V0__Term_27,V1__Annot,Vvar__1___24Anonymous__42634)
& ? [Vvar__2___24Anonymous__42635] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot),Vvar__2___24Anonymous__42635)
& ( 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__42634,Vvar__2___24Anonymous__42635)
& ( ( 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__42648] :
( t(Vvar__1___24Anonymous__42648,V2__Witness)
& ? [Vvar__2___24Anonymous__42649] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V2__Witness,Vvar__2___24Anonymous__42649)
& ( cType___24t(V0__Term_27)
=> ( cType___24t(V1__Annot)
=> ( cType___24t(V2__Witness)
=> ( c_24__type__42660___24t(V0__Term_27,V1__Annot,V2__Witness,V3__checker)
=> ( cCoq_2emicromega_2eTauto_2eclause___24t(V0__Term_27,V1__Annot,Vvar__1___24Anonymous__42634)
=> ( t(Vvar__1___24Anonymous__42648,V2__Witness)
=> ( V6__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__Witness,Vvar__1___24Anonymous__42648,Vvar__2___24Anonymous__42649)
& ( ( happ(happ(V3__checker,Vvar__1___24Anonymous__42634),Vvar__1___24Anonymous__42648) = 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__42635,Vvar__2___24Anonymous__42649) )
| ( happ(happ(V3__checker,Vvar__1___24Anonymous__42634),Vvar__1___24Anonymous__42648) = 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.cnf_tt',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.cons_id',axiom,
! [V0__AF,V1__id,V2__l] :
( cType___24t(V0__AF)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__AF,V1__id)
=> ( ? [Vvar__1___24Anonymous__55678] :
( t(Vvar__1___24Anonymous__55678,V0__AF)
& V1__id = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__AF,Vvar__1___24Anonymous__55678)
& cCoq_2emicromega_2eTauto_2econs__id___24a3(V0__AF,V1__id,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__AF,Vvar__1___24Anonymous__55678,V2__l) )
| ( V1__id = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__AF)
& cCoq_2emicromega_2eTauto_2econs__id___24a3(V0__AF,V1__id,V2__l) = V2__l ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.eval_cnf',axiom,
! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__f] :
( cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__f)
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V1__Term_27,V2__Annot),cCoq_2emicromega_2eTauto_2eeval__clause___24a5(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env),V5__f) ) ).
fof('$_def_Coq.micromega.Tauto.eval_f',axiom,
! [V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f] :
( cType___24t(V0__TA)
=> ( cType___24t(V1__TX)
=> ( cType___24t(V2__AA)
=> ( cType___24t(V3__AF)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,V7__f)
=> ( ( V7__f = cCoq_2emicromega_2eTauto_2eTT___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(c_24True) ) )
| ( V7__f = cCoq_2emicromega_2eTauto_2eFF___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(c_24False) ) )
| ? [Vvar__4___24Anonymous__53526] :
( t(Vvar__4___24Anonymous__53526,V1__TX)
& V7__f = cCoq_2emicromega_2eTauto_2eX___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__53526)
& ( 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__53526)) ) )
| ? [Vvar__4___24Anonymous__53531] :
( t(Vvar__4___24Anonymous__53531,V0__TA)
& ? [Vvar__5___24Anonymous__53532] :
( t(Vvar__5___24Anonymous__53532,V2__AA)
& V7__f = cCoq_2emicromega_2eTauto_2eA___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__53531,Vvar__5___24Anonymous__53532)
& ( 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__53531)) ) ) )
| ? [Vvar__4___24Anonymous__53538] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__53538)
& ? [Vvar__5___24Anonymous__53539] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__53539)
& V7__f = cCoq_2emicromega_2eTauto_2eCj___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__53538,Vvar__5___24Anonymous__53539)
& ( 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__53538)
& cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__53539) ) ) ) )
| ? [Vvar__4___24Anonymous__53545] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__53545)
& ? [Vvar__5___24Anonymous__53546] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__53546)
& V7__f = cCoq_2emicromega_2eTauto_2eD___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__53545,Vvar__5___24Anonymous__53546)
& ( 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__53545)
| cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__53546) ) ) ) )
| ? [Vvar__4___24Anonymous__53552] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__53552)
& V7__f = cCoq_2emicromega_2eTauto_2eN___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__53552)
& ( 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__53552) ) )
| ? [Vvar__4___24Anonymous__53557] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__53557)
& ? [Vvar__5___24Anonymous__53558] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V3__AF,Vvar__5___24Anonymous__53558)
& ? [Vvar__6___24Anonymous__53559] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__53559)
& V7__f = cCoq_2emicromega_2eTauto_2eI___24a7(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__53557,Vvar__5___24Anonymous__53558,Vvar__6___24Anonymous__53559)
& ( 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__53557)
=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__6___24Anonymous__53559) ) ) ) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.eqb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( V0__x = V1__y
& cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__38644___24a2(V0__x,V1__y),c_24__prop__38645___24a2(V0__x,V1__y))
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V0__x != V1__y
& cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__38646___24a2(V0__x,V1__y),c_24__prop__38647___24a2(V0__x,V1__y))
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.Vars.Facts.MP.to_list',axiom,
cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eto__list = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements ).
fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
! [Vvar__41442] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__41442)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__41442) ) ).
fof('$_def_Coq.micromega.ZMicromega.bdepth',axiom,
! [V1__pf] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V1__pf)
=> ( ( V1__pf = cCoq_2emicromega_2eZMicromega_2eDoneProof
& cCoq_2emicromega_2eZMicromega_2ebdepth___24a1(V1__pf) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__41449] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__41449)
& ? [Vvar__1___24Anonymous__41450] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__41450)
& V1__pf = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__41449,Vvar__1___24Anonymous__41450)
& cCoq_2emicromega_2eZMicromega_2ebdepth___24a1(V1__pf) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2emicromega_2eZMicromega_2ebdepth___24a1(Vvar__1___24Anonymous__41450)) ) )
| ? [Vvar__0___24Anonymous__41452] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__41452)
& ? [Vvar__1___24Anonymous__41453] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__41453)
& V1__pf = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__41452,Vvar__1___24Anonymous__41453)
& cCoq_2emicromega_2eZMicromega_2ebdepth___24a1(V1__pf) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2emicromega_2eZMicromega_2ebdepth___24a1(Vvar__1___24Anonymous__41453)) ) )
| ? [Vvar__0___24Anonymous__41455] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__41455)
& ? [Vvar__1___24Anonymous__41456] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__41456)
& ? [Vvar__2___24Anonymous__41457] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__41457)
& V1__pf = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__41455,Vvar__1___24Anonymous__41456,Vvar__2___24Anonymous__41457)
& cCoq_2emicromega_2eZMicromega_2ebdepth___24a1(V1__pf) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eLists_2eList_2efold__right___24a5(cCoq_2eInit_2eDatatypes_2enat,cCoq_2emicromega_2eZMicromega_2eZArithProof,c_24__lam__41468,cCoq_2eInit_2eDatatypes_2eO,Vvar__2___24Anonymous__41457)) ) ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.make_conj',axiom,
cCoq_2emicromega_2eZMicromega_2emake__conj = cCoq_2emicromega_2eRefl_2emake__conj ).
fof('$_def_Coq.micromega.ZMicromega.make_impl',axiom,
cCoq_2emicromega_2eZMicromega_2emake__impl = cCoq_2emicromega_2eRefl_2emake__impl ).
fof('$_def_Coq.micromega.ZMicromega.valid_cut_sign',axiom,
! [V0__op] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V0__op)
=> ( ( V0__op = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V0__op = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__op = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__op = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_def_Coq.omega.PreOmega.Z_of_nat\'',axiom,
cCoq_2eomega_2ePreOmega_2eZ__of__nat_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat ).
fof('$_def_Coq.setoid_ring.BinList.jump',axiom,
! [V0__A,V2__p,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( ? [Vvar__0___24Anonymous__26976] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26976)
& V2__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26976)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__26976,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__26976,cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l))) )
| ? [Vvar__0___24Anonymous__26977] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26977)
& V2__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26977)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__26977,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__26977,V3__l)) )
| ( V2__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l) ) ) ) ) ).
fof('$_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__26984] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26984)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26984)
& 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__26984,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__26984,cCoq_2eLists_2eList_2etl___24a2(V0__A,V4__l))) )
| ? [Vvar__0___24Anonymous__26985] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26985)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26985)
& 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__26985,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__26985,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__15398] :
( t(Vvar__1___24Anonymous__15398,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__15398)
& 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__15398) )
| ? [Vvar__1___24Anonymous__15400] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15400)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__15400)
& 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__15400,V15__l) )
| ? [Vvar__1___24Anonymous__15402] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15402)
& ? [Vvar__2___24Anonymous__15403] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__15403)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__15402,Vvar__2___24Anonymous__15403)
& 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__15402)),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__15403)) ) )
| ? [Vvar__1___24Anonymous__15406] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15406)
& ? [Vvar__2___24Anonymous__15407] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__15407)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__15406,Vvar__2___24Anonymous__15407)
& 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__15406)),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__15407)) ) )
| ? [Vvar__1___24Anonymous__15410] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15410)
& ? [Vvar__2___24Anonymous__15411] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__15411)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__15410,Vvar__2___24Anonymous__15411)
& 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__15410)),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__15411)) ) )
| ? [Vvar__1___24Anonymous__15414] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15414)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__15414)
& 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__15414)) )
| ? [Vvar__1___24Anonymous__15416] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15416)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__15416)
& 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__15416)) )
| ? [Vvar__1___24Anonymous__15418] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15418)
& ? [Vvar__2___24Anonymous__15419] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__15419)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__15418,Vvar__2___24Anonymous__15419)
& 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__15418)),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__15419)) ) )
| ? [Vvar__1___24Anonymous__15422] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15422)
& ? [Vvar__2___24Anonymous__15423] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__15423)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__15422,Vvar__2___24Anonymous__15423)
& 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__15422)),happ(V12__Cp__phi,Vvar__2___24Anonymous__15423)) ) ) ) ) ) ) ) ).
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__28563] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__28563)
& ? [Vvar__2___24Anonymous__28564] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__28564)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__28563,Vvar__2___24Anonymous__28564)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__28563),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__28564,V4__m)) ) ) ) ) ) ).
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__44773] :
( t(Vvar__1___24Anonymous__44773,V0__C)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__44773)
& 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__44775] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__44775)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__44775)
& 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__44777] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__44777)
& ? [Vvar__2___24Anonymous__44778] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__44778)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__44777,Vvar__2___24Anonymous__44778)
& 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__44781] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__44781)
& ? [Vvar__2___24Anonymous__44782] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__44782)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__44781,Vvar__2___24Anonymous__44782)
& 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__44785] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__44785)
& ? [Vvar__2___24Anonymous__44786] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__44786)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__44785,Vvar__2___24Anonymous__44786)
& 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__44785,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__44786,V11__l)) ) )
| ? [Vvar__1___24Anonymous__44789] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__44789)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__44789)
& 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__44791] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__44791)
& ? [Vvar__2___24Anonymous__44792] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__44792)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__44791,Vvar__2___24Anonymous__44792)
& 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__44791,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.NPEadd',axiom,
! [V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e1)
=> ( ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13350] :
( t(Vvar__1___24Anonymous__13350,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13350,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13350)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13350),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13350),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13353] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13353)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13353)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13355] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13355)
& ? [Vvar__2___24Anonymous__13356] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13356)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13355,Vvar__2___24Anonymous__13356)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13359] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13359)
& ? [Vvar__2___24Anonymous__13360] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13360)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13359,Vvar__2___24Anonymous__13360)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13363] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13363)
& ? [Vvar__2___24Anonymous__13364] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13364)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13363,Vvar__2___24Anonymous__13364)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13367] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13367)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13367)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13369] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13369)
& ? [Vvar__2___24Anonymous__13370] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13370)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13369,Vvar__2___24Anonymous__13370)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13377] :
( t(Vvar__1___24Anonymous__13377,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13377,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13377)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13377),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13377),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13380] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13380)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13380)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13382] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13382)
& ? [Vvar__2___24Anonymous__13383] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13383)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13382,Vvar__2___24Anonymous__13383)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13386] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13386)
& ? [Vvar__2___24Anonymous__13387] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13387)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13386,Vvar__2___24Anonymous__13387)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13390] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13390)
& ? [Vvar__2___24Anonymous__13391] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13391)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13390,Vvar__2___24Anonymous__13391)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13394] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13394)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13394)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13396] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13396)
& ? [Vvar__2___24Anonymous__13397] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13397)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13396,Vvar__2___24Anonymous__13397)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13400] :
( t(Vvar__1___24Anonymous__13400,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13400)
& ( ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13400,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13400,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13425] :
( t(Vvar__1___24Anonymous__13425,V0__C)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13425)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,happ(happ(V2__cadd,Vvar__1___24Anonymous__13400),Vvar__1___24Anonymous__13425)) )
| ? [Vvar__1___24Anonymous__13427] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13427)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13400,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13427)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13430] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13430)
& ? [Vvar__2___24Anonymous__13431] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13431)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13400,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13430,Vvar__2___24Anonymous__13431)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13436] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13436)
& ? [Vvar__2___24Anonymous__13437] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13437)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13400,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13436,Vvar__2___24Anonymous__13437)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13442] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13442)
& ? [Vvar__2___24Anonymous__13443] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13443)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13400,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13442,Vvar__2___24Anonymous__13443)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13448] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13448)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13400,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13448)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13451] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13451)
& ? [Vvar__2___24Anonymous__13452] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13452)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13400,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13451,Vvar__2___24Anonymous__13452)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13400),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13457] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13457)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13457)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13475] :
( t(Vvar__1___24Anonymous__13475,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13475,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13475)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13475),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13475),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13478] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13478)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13478)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13480] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13480)
& ? [Vvar__2___24Anonymous__13481] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13481)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13480,Vvar__2___24Anonymous__13481)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13484] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13484)
& ? [Vvar__2___24Anonymous__13485] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13485)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13484,Vvar__2___24Anonymous__13485)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13488] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13488)
& ? [Vvar__2___24Anonymous__13489] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13489)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13488,Vvar__2___24Anonymous__13489)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13492] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13492)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13492)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13494] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13494)
& ? [Vvar__2___24Anonymous__13495] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13495)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13494,Vvar__2___24Anonymous__13495)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13498] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13498)
& ? [Vvar__2___24Anonymous__13499] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13499)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13498,Vvar__2___24Anonymous__13499)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13531] :
( t(Vvar__1___24Anonymous__13531,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13531,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13531)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13531),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13531),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13534] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13534)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13534)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13536] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13536)
& ? [Vvar__2___24Anonymous__13537] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13537)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13536,Vvar__2___24Anonymous__13537)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13540] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13540)
& ? [Vvar__2___24Anonymous__13541] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13541)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13540,Vvar__2___24Anonymous__13541)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13544] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13544)
& ? [Vvar__2___24Anonymous__13545] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13545)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13544,Vvar__2___24Anonymous__13545)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13548] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13548)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13548)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13550] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13550)
& ? [Vvar__2___24Anonymous__13551] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13551)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13550,Vvar__2___24Anonymous__13551)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13554] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13554)
& ? [Vvar__2___24Anonymous__13555] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13555)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13554,Vvar__2___24Anonymous__13555)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13587] :
( t(Vvar__1___24Anonymous__13587,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13587,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13587)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13587),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13587),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13590] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13590)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13590)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13592] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13592)
& ? [Vvar__2___24Anonymous__13593] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13593)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13592,Vvar__2___24Anonymous__13593)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13596] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13596)
& ? [Vvar__2___24Anonymous__13597] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13597)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13596,Vvar__2___24Anonymous__13597)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13600] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13600)
& ? [Vvar__2___24Anonymous__13601] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13601)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13600,Vvar__2___24Anonymous__13601)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13604] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13604)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13604)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13606] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13606)
& ? [Vvar__2___24Anonymous__13607] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13607)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13606,Vvar__2___24Anonymous__13607)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13610] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13610)
& ? [Vvar__2___24Anonymous__13611] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13611)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13610,Vvar__2___24Anonymous__13611)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13643] :
( t(Vvar__1___24Anonymous__13643,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13643,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13643)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13643),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13643),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13646] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13646)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13646)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13648] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13648)
& ? [Vvar__2___24Anonymous__13649] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13649)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13648,Vvar__2___24Anonymous__13649)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13652] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13652)
& ? [Vvar__2___24Anonymous__13653] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13653)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13652,Vvar__2___24Anonymous__13653)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13656] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13656)
& ? [Vvar__2___24Anonymous__13657] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13657)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13656,Vvar__2___24Anonymous__13657)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13660] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13660)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13660)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13662] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13662)
& ? [Vvar__2___24Anonymous__13663] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13663)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13662,Vvar__2___24Anonymous__13663)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13666] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13666)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13666)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13684] :
( t(Vvar__1___24Anonymous__13684,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13684,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13684)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13684),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13684),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13687] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13687)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13687)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13689] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13689)
& ? [Vvar__2___24Anonymous__13690] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13690)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13689,Vvar__2___24Anonymous__13690)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13693] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13693)
& ? [Vvar__2___24Anonymous__13694] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13694)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13693,Vvar__2___24Anonymous__13694)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13697] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13697)
& ? [Vvar__2___24Anonymous__13698] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13698)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13697,Vvar__2___24Anonymous__13698)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13701] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13701)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13701)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13703] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13703)
& ? [Vvar__2___24Anonymous__13704] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13704)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13703,Vvar__2___24Anonymous__13704)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13707] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13707)
& ? [Vvar__2___24Anonymous__13708] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13708)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13707,Vvar__2___24Anonymous__13708)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13740] :
( t(Vvar__1___24Anonymous__13740,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13740,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13740)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13740),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13740),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13743] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13743)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13743)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13745] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13745)
& ? [Vvar__2___24Anonymous__13746] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13746)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13745,Vvar__2___24Anonymous__13746)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13749] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13749)
& ? [Vvar__2___24Anonymous__13750] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13750)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13749,Vvar__2___24Anonymous__13750)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13753] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13753)
& ? [Vvar__2___24Anonymous__13754] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13754)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13753,Vvar__2___24Anonymous__13754)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13757] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13757)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13757)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13759] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13759)
& ? [Vvar__2___24Anonymous__13760] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13760)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13759,Vvar__2___24Anonymous__13760)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__e,V14__e_27] :
( cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__e,V14__e_27)
<=> ! [V15__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V15__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V15__l,V13__e)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V15__l,V14__e_27))) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.NPEmul',axiom,
! [V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V6__x)
=> ( ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14473] :
( t(Vvar__1___24Anonymous__14473,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14473,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14473)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14473),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14473,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14473),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14473),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14473),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14477] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14477)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14477)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14479] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14479)
& ? [Vvar__2___24Anonymous__14480] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14480)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14479,Vvar__2___24Anonymous__14480)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14483] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14483)
& ? [Vvar__2___24Anonymous__14484] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14484)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14483,Vvar__2___24Anonymous__14484)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14487] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14487)
& ? [Vvar__2___24Anonymous__14488] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14488)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14487,Vvar__2___24Anonymous__14488)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14491] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14491)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14491)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14493] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14493)
& ? [Vvar__2___24Anonymous__14494] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14494)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14493,Vvar__2___24Anonymous__14494)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14501] :
( t(Vvar__1___24Anonymous__14501,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14501,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14501)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14501),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14501,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14501),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14501),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14501),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14505] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14505)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14505)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14507] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14507)
& ? [Vvar__2___24Anonymous__14508] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14508)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14507,Vvar__2___24Anonymous__14508)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14511] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14511)
& ? [Vvar__2___24Anonymous__14512] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14512)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14511,Vvar__2___24Anonymous__14512)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14515] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14515)
& ? [Vvar__2___24Anonymous__14516] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14516)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14515,Vvar__2___24Anonymous__14516)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14519] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14519)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14519)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14521] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14521)
& ? [Vvar__2___24Anonymous__14522] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14522)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14521,Vvar__2___24Anonymous__14522)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14525] :
( t(Vvar__1___24Anonymous__14525,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14525)
& ( ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14558] :
( t(Vvar__1___24Anonymous__14558,V0__C)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14558)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,happ(happ(V3__cmul,Vvar__1___24Anonymous__14525),Vvar__1___24Anonymous__14558)) )
| ? [Vvar__1___24Anonymous__14560] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14560)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14560)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14564] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14564)
& ? [Vvar__2___24Anonymous__14565] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14565)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14564,Vvar__2___24Anonymous__14565)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14572] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14572)
& ? [Vvar__2___24Anonymous__14573] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14573)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14572,Vvar__2___24Anonymous__14573)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14580] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14580)
& ? [Vvar__2___24Anonymous__14581] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14581)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14580,Vvar__2___24Anonymous__14581)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14588] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14588)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14588)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14592] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14592)
& ? [Vvar__2___24Anonymous__14593] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14593)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14592,Vvar__2___24Anonymous__14593)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14525,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14525),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14600] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14600)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14600)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14619] :
( t(Vvar__1___24Anonymous__14619,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14619,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14619)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14619),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14619,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14619),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14619),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14619),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14623)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14623)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14625] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14625)
& ? [Vvar__2___24Anonymous__14626] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14626)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14625,Vvar__2___24Anonymous__14626)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14629] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14629)
& ? [Vvar__2___24Anonymous__14630] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14630)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14629,Vvar__2___24Anonymous__14630)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14633] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14633)
& ? [Vvar__2___24Anonymous__14634] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14634)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14633,Vvar__2___24Anonymous__14634)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14637] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14637)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14637)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14639] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14639)
& ? [Vvar__2___24Anonymous__14640] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14640)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14639,Vvar__2___24Anonymous__14640)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14643] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14643)
& ? [Vvar__2___24Anonymous__14644] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14644)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14643,Vvar__2___24Anonymous__14644)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14678] :
( t(Vvar__1___24Anonymous__14678,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14678,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14678)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14678),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14678,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14678),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14678),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14678),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14682] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14682)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14682)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14684] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14684)
& ? [Vvar__2___24Anonymous__14685] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14685)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14684,Vvar__2___24Anonymous__14685)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14688] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14688)
& ? [Vvar__2___24Anonymous__14689] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14689)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14688,Vvar__2___24Anonymous__14689)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14692] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14692)
& ? [Vvar__2___24Anonymous__14693] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14693)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14692,Vvar__2___24Anonymous__14693)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14696] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14696)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14696)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14698] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14698)
& ? [Vvar__2___24Anonymous__14699] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14699)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14698,Vvar__2___24Anonymous__14699)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14702] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14702)
& ? [Vvar__2___24Anonymous__14703] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14703)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14702,Vvar__2___24Anonymous__14703)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14737] :
( t(Vvar__1___24Anonymous__14737,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14737,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14737)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14737),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14737,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14737),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14737),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14737),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14741] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14741)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14741)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14743] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14743)
& ? [Vvar__2___24Anonymous__14744] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14744)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14743,Vvar__2___24Anonymous__14744)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14747] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14747)
& ? [Vvar__2___24Anonymous__14748] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14748)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14747,Vvar__2___24Anonymous__14748)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14751] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14751)
& ? [Vvar__2___24Anonymous__14752] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14752)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14751,Vvar__2___24Anonymous__14752)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14755] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14755)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14755)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14757] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14757)
& ? [Vvar__2___24Anonymous__14758] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14758)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14757,Vvar__2___24Anonymous__14758)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14761] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14761)
& ? [Vvar__2___24Anonymous__14762] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14762)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14761,Vvar__2___24Anonymous__14762)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14796] :
( t(Vvar__1___24Anonymous__14796,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14796,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14796)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14796),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14796,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14796),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14796),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14796),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14800] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14800)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14800)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14802] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14802)
& ? [Vvar__2___24Anonymous__14803] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14803)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14802,Vvar__2___24Anonymous__14803)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14806] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14806)
& ? [Vvar__2___24Anonymous__14807] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14807)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14806,Vvar__2___24Anonymous__14807)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14810] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14810)
& ? [Vvar__2___24Anonymous__14811] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14811)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14810,Vvar__2___24Anonymous__14811)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14814] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14814)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14814)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14816] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14816)
& ? [Vvar__2___24Anonymous__14817] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14817)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14816,Vvar__2___24Anonymous__14817)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14820] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14820)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14820)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14839] :
( t(Vvar__1___24Anonymous__14839,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14839,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14839)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14839),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14839,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14839),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14839),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14839),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14843] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14843)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14843)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14845] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14845)
& ? [Vvar__2___24Anonymous__14846] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14846)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14845,Vvar__2___24Anonymous__14846)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14849] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14849)
& ? [Vvar__2___24Anonymous__14850] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14850)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14849,Vvar__2___24Anonymous__14850)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14853] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14853)
& ? [Vvar__2___24Anonymous__14854] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14854)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14853,Vvar__2___24Anonymous__14854)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14857] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14857)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14857)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14859] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14859)
& ? [Vvar__2___24Anonymous__14860] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14860)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14859,Vvar__2___24Anonymous__14860)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14863] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14863)
& ? [Vvar__2___24Anonymous__14864] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14864)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14863,Vvar__2___24Anonymous__14864)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14900] :
( t(Vvar__1___24Anonymous__14900,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14900,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14900)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14900),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__14900,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14900),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14900),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__14900),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14904] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14904)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14904)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14906] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14906)
& ? [Vvar__2___24Anonymous__14907] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14907)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14906,Vvar__2___24Anonymous__14907)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14910] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14910)
& ? [Vvar__2___24Anonymous__14911] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14911)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14910,Vvar__2___24Anonymous__14911)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14914] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14914)
& ? [Vvar__2___24Anonymous__14915] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14915)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14914,Vvar__2___24Anonymous__14915)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__14918] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14918)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14918)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__14920] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14920)
& ? [Vvar__2___24Anonymous__14921] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14921)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14864)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14921)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14920,Vvar__2___24Anonymous__14921)
& ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vvar__2___24Anonymous__14864,Vvar__2___24Anonymous__14921) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eField__theory_2eNPEpow___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,Vvar__1___24Anonymous__14863,Vvar__1___24Anonymous__14920),Vvar__2___24Anonymous__14864) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vvar__2___24Anonymous__14864,Vvar__2___24Anonymous__14921) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__14344] :
( t(Vvar__1___24Anonymous__14344,V0__C)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14344)
& 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__14344)) )
| ? [Vvar__1___24Anonymous__14346] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14346)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14346)
& 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__14348] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14348)
& ? [Vvar__2___24Anonymous__14349] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14349)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14348,Vvar__2___24Anonymous__14349)
& 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__14352] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14352)
& ? [Vvar__2___24Anonymous__14353] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14353)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14352,Vvar__2___24Anonymous__14353)
& 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__14356] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14356)
& ? [Vvar__2___24Anonymous__14357] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14357)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14356,Vvar__2___24Anonymous__14357)
& 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__14360] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14360)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14360)
& 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__14362] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14362)
& ? [Vvar__2___24Anonymous__14363] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14363)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14362,Vvar__2___24Anonymous__14363)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.NPEsub',axiom,
! [V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e1)
=> ( ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13853] :
( t(Vvar__1___24Anonymous__13853,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13853,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13853)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13853),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13853),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13856] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13856)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13856)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13858] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13858)
& ? [Vvar__2___24Anonymous__13859] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13859)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13858,Vvar__2___24Anonymous__13859)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13862] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13862)
& ? [Vvar__2___24Anonymous__13863] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13863)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13862,Vvar__2___24Anonymous__13863)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13866] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13866)
& ? [Vvar__2___24Anonymous__13867] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13867)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13866,Vvar__2___24Anonymous__13867)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13870] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13870)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13870)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13872] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13872)
& ? [Vvar__2___24Anonymous__13873] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13873)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13872,Vvar__2___24Anonymous__13873)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13880] :
( t(Vvar__1___24Anonymous__13880,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13880,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13880)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13880),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13880),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13883] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13883)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13883)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13885] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13885)
& ? [Vvar__2___24Anonymous__13886] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13886)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13885,Vvar__2___24Anonymous__13886)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13889] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13889)
& ? [Vvar__2___24Anonymous__13890] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13890)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13889,Vvar__2___24Anonymous__13890)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13893] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13893)
& ? [Vvar__2___24Anonymous__13894] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13894)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13893,Vvar__2___24Anonymous__13894)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13897] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13897)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13897)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13899] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13899)
& ? [Vvar__2___24Anonymous__13900] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13900)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13899,Vvar__2___24Anonymous__13900)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13903] :
( t(Vvar__1___24Anonymous__13903,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13903)
& ( ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13903,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13903,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13928] :
( t(Vvar__1___24Anonymous__13928,V0__C)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13928)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,happ(happ(V2__csub,Vvar__1___24Anonymous__13903),Vvar__1___24Anonymous__13928)) )
| ? [Vvar__1___24Anonymous__13930] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13930)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13903,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13930)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13933] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13933)
& ? [Vvar__2___24Anonymous__13934] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13934)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13903,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13933,Vvar__2___24Anonymous__13934)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13939] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13939)
& ? [Vvar__2___24Anonymous__13940] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13940)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13903,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13939,Vvar__2___24Anonymous__13940)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13945] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13945)
& ? [Vvar__2___24Anonymous__13946] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13946)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13903,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13945,Vvar__2___24Anonymous__13946)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13951] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13951)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13903,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13951)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13954] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13954)
& ? [Vvar__2___24Anonymous__13955] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13955)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13903,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13954,Vvar__2___24Anonymous__13955)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V5__e2) )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13903),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13960] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13960)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13960)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13978] :
( t(Vvar__1___24Anonymous__13978,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__13978,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__13978)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13978),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__13978),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__13981] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13981)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__13981)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13983] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13983)
& ? [Vvar__2___24Anonymous__13984] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13984)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__13983,Vvar__2___24Anonymous__13984)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13987] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13987)
& ? [Vvar__2___24Anonymous__13988] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13988)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__13987,Vvar__2___24Anonymous__13988)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13991] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13991)
& ? [Vvar__2___24Anonymous__13992] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__13992)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__13991,Vvar__2___24Anonymous__13992)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__13995] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13995)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__13995)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__13997] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__13997)
& ? [Vvar__2___24Anonymous__13998] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13998)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__13997,Vvar__2___24Anonymous__13998)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14001] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14001)
& ? [Vvar__2___24Anonymous__14002] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14002)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14001,Vvar__2___24Anonymous__14002)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14034] :
( t(Vvar__1___24Anonymous__14034,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__14034,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14034)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__14034),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__14034),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14037] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14037)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14037)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14039] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14039)
& ? [Vvar__2___24Anonymous__14040] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14040)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14039,Vvar__2___24Anonymous__14040)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14043] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14043)
& ? [Vvar__2___24Anonymous__14044] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14044)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14043,Vvar__2___24Anonymous__14044)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14047] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14047)
& ? [Vvar__2___24Anonymous__14048] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14048)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14047,Vvar__2___24Anonymous__14048)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14051] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14051)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14051)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14053] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14053)
& ? [Vvar__2___24Anonymous__14054] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14054)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14053,Vvar__2___24Anonymous__14054)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14057] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14057)
& ? [Vvar__2___24Anonymous__14058] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14058)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14057,Vvar__2___24Anonymous__14058)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14090] :
( t(Vvar__1___24Anonymous__14090,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__14090,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14090)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__14090),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__14090),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14093] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14093)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14093)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14095] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14095)
& ? [Vvar__2___24Anonymous__14096] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14096)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14095,Vvar__2___24Anonymous__14096)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14099] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14099)
& ? [Vvar__2___24Anonymous__14100] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14100)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14099,Vvar__2___24Anonymous__14100)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14103] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14103)
& ? [Vvar__2___24Anonymous__14104] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14104)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14103,Vvar__2___24Anonymous__14104)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14107] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14107)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14107)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14109] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14109)
& ? [Vvar__2___24Anonymous__14110] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14110)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14109,Vvar__2___24Anonymous__14110)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14113] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14113)
& ? [Vvar__2___24Anonymous__14114] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14114)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14113,Vvar__2___24Anonymous__14114)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14146] :
( t(Vvar__1___24Anonymous__14146,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__14146,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14146)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__14146),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__14146),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14149] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14149)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14149)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14151] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14151)
& ? [Vvar__2___24Anonymous__14152] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14152)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14151,Vvar__2___24Anonymous__14152)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14155] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14155)
& ? [Vvar__2___24Anonymous__14156] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14156)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14155,Vvar__2___24Anonymous__14156)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14159] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14159)
& ? [Vvar__2___24Anonymous__14160] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14160)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14159,Vvar__2___24Anonymous__14160)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14163] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14163)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14163)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14165] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14165)
& ? [Vvar__2___24Anonymous__14166] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14166)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14165,Vvar__2___24Anonymous__14166)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14169] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14169)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14169)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14187] :
( t(Vvar__1___24Anonymous__14187,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__14187,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14187)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__14187),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__14187),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14190] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14190)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14190)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14192] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14192)
& ? [Vvar__2___24Anonymous__14193] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14193)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14192,Vvar__2___24Anonymous__14193)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14196] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14196)
& ? [Vvar__2___24Anonymous__14197] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14197)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14196,Vvar__2___24Anonymous__14197)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14200] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14200)
& ? [Vvar__2___24Anonymous__14201] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14201)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14200,Vvar__2___24Anonymous__14201)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14204] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14204)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14204)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14206] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14206)
& ? [Vvar__2___24Anonymous__14207] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14207)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14206,Vvar__2___24Anonymous__14207)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14210] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14210)
& ? [Vvar__2___24Anonymous__14211] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14211)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14210,Vvar__2___24Anonymous__14211)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14243] :
( t(Vvar__1___24Anonymous__14243,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__14243,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__14243)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__14243),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__14243),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14246] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14246)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__14246)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14248] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14248)
& ? [Vvar__2___24Anonymous__14249] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14249)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__14248,Vvar__2___24Anonymous__14249)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14252] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14252)
& ? [Vvar__2___24Anonymous__14253] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14253)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__14252,Vvar__2___24Anonymous__14253)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14256] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14256)
& ? [Vvar__2___24Anonymous__14257] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14257)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__14256,Vvar__2___24Anonymous__14257)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__14260] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14260)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__14260)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__14262] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__14262)
& ? [Vvar__2___24Anonymous__14263] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14263)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__14262,Vvar__2___24Anonymous__14263)
& cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V2__csub,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.PCond',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__le)
=> ( ( V15__le = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__1075] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__1075)
& ? [Vvar__2___24Anonymous__1076] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__1076)
& ( 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__1076)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__1075,Vvar__2___24Anonymous__1076)
& ( ( Vvar__2___24Anonymous__1076 = 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__1075)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__1087] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__1087)
& ? [Vvar__2___24Anonymous__1088] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__1088)
& Vvar__2___24Anonymous__1076 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__1087,Vvar__2___24Anonymous__1088)
& ( 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__1075)),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__1076) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__15722] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__15722)
& ? [Vvar__2__denum__15723] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__15723)
& ? [Vvar__3__condition__15724] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__15724)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__15722,Vvar__2__denum__15723,Vvar__3__condition__15724)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__15724 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__15713] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__15713)
& ? [Vvar__2__denum__15714] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__15714)
& ? [Vvar__3__condition__15715] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__15715)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__15713,Vvar__2__denum__15714,Vvar__3__condition__15715)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__15714 ) ) ) ) ) ).
fof('$_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_2427568___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('$_def_Coq.setoid_ring.Field_theory.display_pow_linear',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den] : cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear___24a20(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den) = c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2428165___24a20(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den) ).
fof('$_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__15702] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__15702)
& ? [Vvar__2__denum__15703] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__15703)
& ? [Vvar__3__condition__15704] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__15704)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__15702,Vvar__2__denum__15703,Vvar__3__condition__15704)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__15702 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_common',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__15758] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__15758)
& ? [Vvar__2__rsplit__common__15759] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__15759)
& ? [Vvar__3__rsplit__right__15760] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__15760)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__15758,Vvar__2__rsplit__common__15759,Vvar__3__rsplit__right__15760)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,V1__r) = Vvar__2__rsplit__common__15759 ) ) ) ) ) ).
fof('$_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__15747] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__15747)
& ? [Vvar__2__rsplit__common__15748] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__15748)
& ? [Vvar__3__rsplit__right__15749] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__15749)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__15747,Vvar__2__rsplit__common__15748,Vvar__3__rsplit__right__15749)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,V1__r) = Vvar__1__rsplit__left__15747 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__15767] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__15767)
& ? [Vvar__2__rsplit__common__15768] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__15768)
& ? [Vvar__3__rsplit__right__15769] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__15769)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__15767,Vvar__2__rsplit__common__15768,Vvar__3__rsplit__right__15769)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,V1__r) = Vvar__3__rsplit__right__15769 ) ) ) ) ) ).
fof('$_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('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
! [Vvar__55015] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__55015)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__55015) ) ).
fof('$_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__28747] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28747)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28747)
& 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__28747) ) ) ) ) ).
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__55020] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__55020)
& ? [Vvar__2___24Anonymous__55021] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__55021)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__55020)
=> ( V8__w = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__55020,Vvar__2___24Anonymous__55021)
& ( ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__55021)
=> ( Vvar__1___24Anonymous__55020 = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( Vvar__2___24Anonymous__55021 = 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__55020) )
| ? [Vvar__1___24Anonymous__55042] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__55042)
& ? [Vvar__2___24Anonymous__55043] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__55043)
& Vvar__2___24Anonymous__55021 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__55042,Vvar__2___24Anonymous__55043)
& 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__55021)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__55045] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55045)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__55021)
=> ( Vvar__1___24Anonymous__55020 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55045)
& ( ( Vvar__2___24Anonymous__55021 = 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__55020) )
| ? [Vvar__1___24Anonymous__55052] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__55052)
& ? [Vvar__2___24Anonymous__55053] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__55053)
& Vvar__2___24Anonymous__55021 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__55052,Vvar__2___24Anonymous__55053)
& 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__55020)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,Vvar__2___24Anonymous__55021)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__54973] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54973)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54973)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54973)
& ( ? [Vvar__0___24Anonymous__54977] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54977)
& Vvar__0___24Anonymous__54973 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54977)
& 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__54973))) )
| ? [Vvar__0___24Anonymous__54978] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54978)
& Vvar__0___24Anonymous__54973 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54978)
& 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__54973))) )
| ( Vvar__0___24Anonymous__54973 = 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__54979] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54979)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54979)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54979)
& ( ? [Vvar__0___24Anonymous__54983] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54983)
& Vvar__0___24Anonymous__54979 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54983)
& 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__54979)) )
| ? [Vvar__0___24Anonymous__54984] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54984)
& Vvar__0___24Anonymous__54979 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54984)
& 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__54979)) )
| ( Vvar__0___24Anonymous__54979 = 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('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__17373] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17373)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17373)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__17373) )
| ? [Vvar__0___24Anonymous__17374] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17374)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17374)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__17374)) ) ) ) ) ).
fof('$_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__17426] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17426)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17426)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__17427] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17427)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17427)
& 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__17427)) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.triv_div',axiom,
! [V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y] :
( cType___24t(V0__C)
=> ( c_24__type__13765___24t(V0__C,V3__ceqb)
=> ( t(V4__x,V0__C)
=> ( t(V5__y,V0__C)
=> ( ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V2__cI,V1__cO) )
| ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V1__cO,V4__x) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.setoid_ring.Ring_polynom.Mphi',axiom,
! [V0__R,V1__rO,V2__rI,V3__rmul,V5__l,V6__M] :
( cType___24t(V0__R)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V6__M)
=> ( ( V6__M = cCoq_2esetoid__ring_2eRing__polynom_2emon0
& cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,V5__l,V6__M) = V2__rI )
| ? [Vvar__0___24Anonymous__48080] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48080)
& ? [Vvar__1___24Anonymous__48081] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__48081)
& V6__M = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__48080,Vvar__1___24Anonymous__48081)
& cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,V5__l,V6__M) = cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__R,Vvar__0___24Anonymous__48080,V5__l),Vvar__1___24Anonymous__48081) ) )
| ? [Vvar__0___24Anonymous__48083] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48083)
& ? [Vvar__1___24Anonymous__48084] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__48084)
& V6__M = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__48083,Vvar__1___24Anonymous__48084)
& cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,V5__l,V6__M) = happ(happ(V3__rmul,cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,cCoq_2eLists_2eList_2etl___24a2(V0__R,V5__l),Vvar__1___24Anonymous__48084)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V3__rmul,cCoq_2eLists_2eList_2ehd___24a3(V0__R,V1__rO,V5__l),Vvar__0___24Anonymous__48083)) ) ) ) ) ) ).
fof('$_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__2558] :
( t(Vvar__1___24Anonymous__2558,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__2558)
& 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__2558) )
| ? [Vvar__1___24Anonymous__2560] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2560)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__2560)
& 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__2560,V13__l) )
| ? [Vvar__1___24Anonymous__2562] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__2562)
& ? [Vvar__2___24Anonymous__2563] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__2563)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__2562,Vvar__2___24Anonymous__2563)
& 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__2562)),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__2563)) ) )
| ? [Vvar__1___24Anonymous__2566] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__2566)
& ? [Vvar__2___24Anonymous__2567] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__2567)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__2566,Vvar__2___24Anonymous__2567)
& 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__2566)),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__2567)) ) )
| ? [Vvar__1___24Anonymous__2570] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__2570)
& ? [Vvar__2___24Anonymous__2571] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__2571)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__2570,Vvar__2___24Anonymous__2571)
& 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__2570)),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__2571)) ) )
| ? [Vvar__1___24Anonymous__2574] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__2574)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__2574)
& 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__2574)) )
| ? [Vvar__1___24Anonymous__2576] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__2576)
& ? [Vvar__2___24Anonymous__2577] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2577)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__2576,Vvar__2___24Anonymous__2577)
& 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__2576)),happ(V10__Cp__phi,Vvar__2___24Anonymous__2577)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.PaddC',axiom,
! [V0__C,V1__cadd,V3__P,V4__c] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V3__P)
=> ( ? [Vvar__1___24Anonymous__45781] :
( t(Vvar__1___24Anonymous__45781,V0__C)
& V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__45781)
& cCoq_2esetoid__ring_2eRing__polynom_2ePaddC___24a4(V0__C,V1__cadd,V3__P,V4__c) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,happ(happ(V1__cadd,Vvar__1___24Anonymous__45781),V4__c)) )
| ? [Vvar__1___24Anonymous__45783] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__45783)
& ? [Vvar__2___24Anonymous__45784] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__45784)
& V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__45783,Vvar__2___24Anonymous__45784)
& cCoq_2esetoid__ring_2eRing__polynom_2ePaddC___24a4(V0__C,V1__cadd,V3__P,V4__c) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__45783,cCoq_2esetoid__ring_2eRing__polynom_2ePaddC___24a4(V0__C,V1__cadd,Vvar__2___24Anonymous__45784,V4__c)) ) )
| ? [Vvar__1___24Anonymous__45787] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__45787)
& ? [Vvar__2___24Anonymous__45788] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__45788)
& ? [Vvar__3___24Anonymous__45789] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__45789)
& V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__45787,Vvar__2___24Anonymous__45788,Vvar__3___24Anonymous__45789)
& cCoq_2esetoid__ring_2eRing__polynom_2ePaddC___24a4(V0__C,V1__cadd,V3__P,V4__c) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__45787,Vvar__2___24Anonymous__45788,cCoq_2esetoid__ring_2eRing__polynom_2ePaddC___24a4(V0__C,V1__cadd,Vvar__3___24Anonymous__45789,V4__c)) ) ) ) ) ) ) ).
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__17907] :
( t(Vvar__1___24Anonymous__17907,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__17907)
& ( ? [Vvar__1___24Anonymous__17917] :
( t(Vvar__1___24Anonymous__17917,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__17917)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__17907),Vvar__1___24Anonymous__17917) )
| ? [Vvar__1___24Anonymous__17919] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17919)
& ? [Vvar__2___24Anonymous__17920] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__17920)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__17919,Vvar__2___24Anonymous__17920)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__17923] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17923)
& ? [Vvar__2___24Anonymous__17924] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17924)
& ? [Vvar__3___24Anonymous__17925] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__17925)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__17923,Vvar__2___24Anonymous__17924,Vvar__3___24Anonymous__17925)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__17930] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17930)
& ? [Vvar__2___24Anonymous__17931] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__17931)
& ( 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__17930,Vvar__2___24Anonymous__17931)
& ( ? [Vvar__1___24Anonymous__17951] :
( t(Vvar__1___24Anonymous__17951,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__17951)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__17953] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17953)
& ? [Vvar__2___24Anonymous__17954] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__17954)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17930)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17953)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__17953,Vvar__2___24Anonymous__17954)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__17930,Vvar__1___24Anonymous__17953) = 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__17931,Vvar__2___24Anonymous__17954) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__17930,Vvar__1___24Anonymous__17953) = 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__17930,Vvar__1___24Anonymous__17953) = 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__17959] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17959)
& ? [Vvar__2___24Anonymous__17960] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17960)
& ? [Vvar__3___24Anonymous__17961] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__17961)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__17959,Vvar__2___24Anonymous__17960,Vvar__3___24Anonymous__17961)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__17966] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17966)
& ? [Vvar__2___24Anonymous__17967] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17967)
& ? [Vvar__3___24Anonymous__17968] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__17968)
& ( 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__17966,Vvar__2___24Anonymous__17967,Vvar__3___24Anonymous__17968)
& ( ? [Vvar__1___24Anonymous__18001] :
( t(Vvar__1___24Anonymous__18001,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__18001)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__18003] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__18003)
& ? [Vvar__2___24Anonymous__18004] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__18004)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__18003,Vvar__2___24Anonymous__18004)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__18007] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__18007)
& ? [Vvar__2___24Anonymous__18008] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__18008)
& ? [Vvar__3___24Anonymous__18009] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__18009)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17967)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__18008)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__18007,Vvar__2___24Anonymous__18008,Vvar__3___24Anonymous__18009)
& ( ( cType___24t(V0__C)
=> ( c_24__type__13765___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17966)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__18007)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__17967,Vvar__2___24Anonymous__18008) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__17966,Vvar__1___24Anonymous__18007) = 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__17968,Vvar__3___24Anonymous__18009) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__17966,Vvar__1___24Anonymous__18007) = 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__17967,Vvar__2___24Anonymous__18008) = 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__17967,Vvar__2___24Anonymous__18008) = 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.PmulC',axiom,
! [V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__P,V6__c] :
( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(V6__c,V0__C)
=> ( ( happ(happ(V4__ceqb,V6__c),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing__polynom_2ePmulC___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__P,V6__c) = cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V0__C,V1__cO) )
| ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13765___24t(V0__C,V4__ceqb)
=> ( t(V6__c,V0__C)
=> ( happ(happ(V4__ceqb,V6__c),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,V6__c),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing__polynom_2ePmulC___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__P,V6__c) = V5__P )
| ( happ(happ(V4__ceqb,V6__c),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eRing__polynom_2ePmulC___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__P,V6__c) = cCoq_2esetoid__ring_2eRing__polynom_2ePmulC__aux___24a6(V0__C,V1__cO,V3__cmul,V4__ceqb,V5__P,V6__c) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.PmulC_aux',axiom,
! [V0__C,V1__cO,V2__cmul,V3__ceqb,V5__P,V6__c] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V5__P)
=> ( ? [Vvar__1___24Anonymous__46252] :
( t(Vvar__1___24Anonymous__46252,V0__C)
& V5__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__46252)
& cCoq_2esetoid__ring_2eRing__polynom_2ePmulC__aux___24a6(V0__C,V1__cO,V2__cmul,V3__ceqb,V5__P,V6__c) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,happ(happ(V2__cmul,Vvar__1___24Anonymous__46252),V6__c)) )
| ? [Vvar__1___24Anonymous__46254] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__46254)
& ? [Vvar__2___24Anonymous__46255] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__46255)
& V5__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__46254,Vvar__2___24Anonymous__46255)
& cCoq_2esetoid__ring_2eRing__polynom_2ePmulC__aux___24a6(V0__C,V1__cO,V2__cmul,V3__ceqb,V5__P,V6__c) = cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,Vvar__1___24Anonymous__46254,cCoq_2esetoid__ring_2eRing__polynom_2ePmulC__aux___24a6(V0__C,V1__cO,V2__cmul,V3__ceqb,Vvar__2___24Anonymous__46255,V6__c)) ) )
| ? [Vvar__1___24Anonymous__46258] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__46258)
& ? [Vvar__2___24Anonymous__46259] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__46259)
& ? [Vvar__3___24Anonymous__46260] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__46260)
& V5__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__46258,Vvar__2___24Anonymous__46259,Vvar__3___24Anonymous__46260)
& cCoq_2esetoid__ring_2eRing__polynom_2ePmulC__aux___24a6(V0__C,V1__cO,V2__cmul,V3__ceqb,V5__P,V6__c) = cCoq_2esetoid__ring_2eRing__polynom_2emkPX___24a6(V0__C,V1__cO,V3__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2ePmulC__aux___24a6(V0__C,V1__cO,V2__cmul,V3__ceqb,Vvar__1___24Anonymous__46258,V6__c),Vvar__2___24Anonymous__46259,cCoq_2esetoid__ring_2eRing__polynom_2ePmulC__aux___24a6(V0__C,V1__cO,V2__cmul,V3__ceqb,Vvar__3___24Anonymous__46260,V6__c)) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Popp',axiom,
! [V0__C,V1__copp,V3__P] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V3__P)
=> ( ? [Vvar__1___24Anonymous__45759] :
( t(Vvar__1___24Anonymous__45759,V0__C)
& V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__45759)
& cCoq_2esetoid__ring_2eRing__polynom_2ePopp___24a3(V0__C,V1__copp,V3__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,happ(V1__copp,Vvar__1___24Anonymous__45759)) )
| ? [Vvar__1___24Anonymous__45761] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__45761)
& ? [Vvar__2___24Anonymous__45762] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__45762)
& V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__45761,Vvar__2___24Anonymous__45762)
& cCoq_2esetoid__ring_2eRing__polynom_2ePopp___24a3(V0__C,V1__copp,V3__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__45761,cCoq_2esetoid__ring_2eRing__polynom_2ePopp___24a3(V0__C,V1__copp,Vvar__2___24Anonymous__45762)) ) )
| ? [Vvar__1___24Anonymous__45765] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__45765)
& ? [Vvar__2___24Anonymous__45766] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__45766)
& ? [Vvar__3___24Anonymous__45767] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__45767)
& V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__45765,Vvar__2___24Anonymous__45766,Vvar__3___24Anonymous__45767)
& cCoq_2esetoid__ring_2eRing__polynom_2ePopp___24a3(V0__C,V1__copp,V3__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2ePopp___24a3(V0__C,V1__copp,Vvar__1___24Anonymous__45765),Vvar__2___24Anonymous__45766,cCoq_2esetoid__ring_2eRing__polynom_2ePopp___24a3(V0__C,V1__copp,Vvar__3___24Anonymous__45767)) ) ) ) ) ) ) ).
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__18060] :
( t(Vvar__1___24Anonymous__18060,V4__C)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V4__C,Vvar__1___24Anonymous__18060)
& 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__18060) )
| ? [Vvar__1___24Anonymous__18062] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__18062)
& ? [Vvar__2___24Anonymous__18063] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__2___24Anonymous__18063)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V4__C,Vvar__1___24Anonymous__18062,Vvar__2___24Anonymous__18063)
& 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__18062,V7__l),Vvar__2___24Anonymous__18063) ) )
| ? [Vvar__1___24Anonymous__18066] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__1___24Anonymous__18066)
& ? [Vvar__2___24Anonymous__18067] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__18067)
& ? [Vvar__3___24Anonymous__18068] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__3___24Anonymous__18068)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V4__C,Vvar__1___24Anonymous__18066,Vvar__2___24Anonymous__18067,Vvar__3___24Anonymous__18068)
& 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__18066)),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__18067))),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__18068)) ) ) ) ) ) ) ) ).
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__19023___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__19024___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__19025___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Ppow_pos',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__ceqb,V6__subst__l,V8__res,V9__P,V10__p] :
( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V10__p)
=> ( ? [Vvar__0___24Anonymous__49519] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__49519)
& V10__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__49519)
& cCoq_2esetoid__ring_2eRing__polynom_2ePpow__pos___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__ceqb,V6__subst__l,V8__res,V9__P,V10__p) = happ(V6__subst__l,cCoq_2esetoid__ring_2eRing__polynom_2ePmul___24a8(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2ePpow__pos___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__ceqb,V6__subst__l,cCoq_2esetoid__ring_2eRing__polynom_2ePpow__pos___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__ceqb,V6__subst__l,V8__res,V9__P,Vvar__0___24Anonymous__49519),V9__P,Vvar__0___24Anonymous__49519),V9__P)) )
| ? [Vvar__0___24Anonymous__49520] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__49520)
& V10__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__49520)
& cCoq_2esetoid__ring_2eRing__polynom_2ePpow__pos___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__ceqb,V6__subst__l,V8__res,V9__P,V10__p) = cCoq_2esetoid__ring_2eRing__polynom_2ePpow__pos___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__ceqb,V6__subst__l,cCoq_2esetoid__ring_2eRing__polynom_2ePpow__pos___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__ceqb,V6__subst__l,V8__res,V9__P,Vvar__0___24Anonymous__49520),V9__P,Vvar__0___24Anonymous__49520) )
| ( V10__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2ePpow__pos___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__ceqb,V6__subst__l,V8__res,V9__P,V10__p) = happ(V6__subst__l,cCoq_2esetoid__ring_2eRing__polynom_2ePmul___24a8(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__ceqb,V8__res,V9__P)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.PsubC',axiom,
! [V0__C,V1__csub,V3__P,V4__c] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V3__P)
=> ( ? [Vvar__1___24Anonymous__45810] :
( t(Vvar__1___24Anonymous__45810,V0__C)
& V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__45810)
& cCoq_2esetoid__ring_2eRing__polynom_2ePsubC___24a4(V0__C,V1__csub,V3__P,V4__c) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,happ(happ(V1__csub,Vvar__1___24Anonymous__45810),V4__c)) )
| ? [Vvar__1___24Anonymous__45812] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__45812)
& ? [Vvar__2___24Anonymous__45813] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__45813)
& V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__45812,Vvar__2___24Anonymous__45813)
& cCoq_2esetoid__ring_2eRing__polynom_2ePsubC___24a4(V0__C,V1__csub,V3__P,V4__c) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__45812,cCoq_2esetoid__ring_2eRing__polynom_2ePsubC___24a4(V0__C,V1__csub,Vvar__2___24Anonymous__45813,V4__c)) ) )
| ? [Vvar__1___24Anonymous__45816] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__45816)
& ? [Vvar__2___24Anonymous__45817] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__45817)
& ? [Vvar__3___24Anonymous__45818] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__45818)
& V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__45816,Vvar__2___24Anonymous__45817,Vvar__3___24Anonymous__45818)
& cCoq_2esetoid__ring_2eRing__polynom_2ePsubC___24a4(V0__C,V1__csub,V3__P,V4__c) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__45816,Vvar__2___24Anonymous__45817,cCoq_2esetoid__ring_2eRing__polynom_2ePsubC___24a4(V0__C,V1__csub,Vvar__3___24Anonymous__45818,V4__c)) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.add_pow_list',axiom,
! [V0__R,V1__r,V2__n,V3__l] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( ( V2__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list___24a4(V0__R,V1__r,V2__n,V3__l) = V3__l )
| ? [Vvar__0___24Anonymous__51413] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__51413)
& V2__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__51413)
& cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list___24a4(V0__R,V1__r,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,V1__r,Vvar__0___24Anonymous__51413),V3__l) ) ) ) ) ).
fof('$_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__18376] :
( 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__18376)
& ? [Vvar__2___24Anonymous__18377] :
( 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__18377)
& ( 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__18376)
=> ( 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__18376,Vvar__2___24Anonymous__18377)
& ? [Vvar__2___24Anonymous__18395] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__2___24Anonymous__18395)
& ? [Vvar__3___24Anonymous__18396] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__3___24Anonymous__18396)
& ( 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__18377)
=> ( Vvar__1___24Anonymous__18376 = 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__18395,Vvar__3___24Anonymous__18396)
& ( ( Vvar__2___24Anonymous__18377 = 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__18395)),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__18396))) ) )
| ? [Vvar__1___24Anonymous__18407] :
( 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__18407)
& ? [Vvar__2___24Anonymous__18408] :
( 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__18408)
& Vvar__2___24Anonymous__18377 = 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__18407,Vvar__2___24Anonymous__18408)
& ( 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__18395)),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__18396)))
& 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__18377) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkPinj',axiom,
! [V0__C,V1__j,V2__P] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V2__P)
=> ( ? [Vvar__1___24Anonymous__45692] :
( t(Vvar__1___24Anonymous__45692,V0__C)
& V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__45692)
& cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = V2__P )
| ? [Vvar__1___24Anonymous__45694] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__45694)
& ? [Vvar__2___24Anonymous__45695] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__45695)
& V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__45694,Vvar__2___24Anonymous__45695)
& cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__j,Vvar__1___24Anonymous__45694),Vvar__2___24Anonymous__45695) ) )
| ? [Vvar__1___24Anonymous__45698] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__45698)
& ? [Vvar__2___24Anonymous__45699] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__45699)
& ? [Vvar__3___24Anonymous__45700] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__45700)
& V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__45698,Vvar__2___24Anonymous__45699,Vvar__3___24Anonymous__45700)
& cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,V1__j,V2__P) ) ) ) ) ) ) ).
fof('$_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__46637] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46637)
& ? [Vvar__1___24Anonymous__46638] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__46638)
& V1__M = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__46637,Vvar__1___24Anonymous__46638)
& 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__46640] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46640)
& ? [Vvar__1___24Anonymous__46641] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__46641)
& V1__M = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__46640,Vvar__1___24Anonymous__46641)
& cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V0__j,V1__M) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mk_X',axiom,
! [V0__C,V1__cO,V2__cI,V3__j] : cCoq_2esetoid__ring_2eRing__polynom_2emk__X___24a4(V0__C,V1__cO,V2__cI,V3__j) = cCoq_2esetoid__ring_2eRing__polynom_2emkPinj__pred___24a3(V0__C,V3__j,cCoq_2esetoid__ring_2eRing__polynom_2emkX___24a3(V0__C,V1__cO,V2__cI)) ).
fof('$_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__18639] :
( 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__18639)
& ? [Vvar__2___24Anonymous__18640] :
( 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__18640)
& ( 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__18639)
=> ( 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__18639,Vvar__2___24Anonymous__18640)
& ? [Vvar__2___24Anonymous__18656] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__18656)
& ? [Vvar__3___24Anonymous__18657] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__18657)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__1293___24t(V0__C,V3__cadd)
=> ( c_24__type__1293___24t(V0__C,V4__cmul)
=> ( c_24__type__1293___24t(V0__C,V5__csub)
=> ( c_24__type__1302___24t(V0__C,V6__copp)
=> ( c_24__type__13765___24t(V0__C,V7__ceqb)
=> ( c_24__type__18370___24t(V0__C,V8__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__18656)
=> ( Vvar__1___24Anonymous__18639 = 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__18656,Vvar__3___24Anonymous__18657)
& ( ? [Vvar__1___24Anonymous__18665] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__18665)
& 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__18656)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__18665)
& 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__18665,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__18657)),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__18640)) )
| ( 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__18656)) = 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__18640) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkadd_mult',axiom,
! [V0__R,V1__rI,V2__radd,V3__rsub,V4__C,V5__cI,V6__ceqb,V7__phi,V8__get__sign,V9__mkpow,V10__mkmult__pow,V11__rP,V12__c,V13__lm] :
( cType___24t(V0__R)
=> ( cType___24t(V4__C)
=> ( c_24__type__19645___24t(V0__R,V4__C,V8__get__sign)
=> ( t(V12__c,V4__C)
=> ( ? [Vvar__1___24Anonymous__51195] :
( t(Vvar__1___24Anonymous__51195,V4__C)
& happ(V8__get__sign,V12__c) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V4__C,Vvar__1___24Anonymous__51195)
& cCoq_2esetoid__ring_2eRing__polynom_2emkadd__mult___24a14(V0__R,V1__rI,V2__radd,V3__rsub,V4__C,V5__cI,V6__ceqb,V7__phi,V8__get__sign,V9__mkpow,V10__mkmult__pow,V11__rP,V12__c,V13__lm) = happ(happ(V3__rsub,V11__rP),cCoq_2esetoid__ring_2eRing__polynom_2emkmult__c__pos___24a10(V0__R,V1__rI,V4__C,V5__cI,V6__ceqb,V7__phi,V9__mkpow,V10__mkmult__pow,Vvar__1___24Anonymous__51195,V13__lm)) )
| ( happ(V8__get__sign,V12__c) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V4__C)
& cCoq_2esetoid__ring_2eRing__polynom_2emkadd__mult___24a14(V0__R,V1__rI,V2__radd,V3__rsub,V4__C,V5__cI,V6__ceqb,V7__phi,V8__get__sign,V9__mkpow,V10__mkmult__pow,V11__rP,V12__c,V13__lm) = happ(happ(V2__radd,V11__rP),cCoq_2esetoid__ring_2eRing__polynom_2emkmult__c__pos___24a10(V0__R,V1__rI,V4__C,V5__cI,V6__ceqb,V7__phi,V9__mkpow,V10__mkmult__pow,V12__c,V13__lm)) ) ) ) ) ) ) ).
fof('$_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__35919] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35919)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35919)
& 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__35919),V4__x,Vvar__0___24Anonymous__35919) )
| ? [Vvar__0___24Anonymous__35920] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35920)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35920)
& 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__35920),V4__x,Vvar__0___24Anonymous__35920) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkmult_rec',axiom,
! [V0__R,V1__mkmult__pow,V3__r,V4__lm] :
( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),V4__lm)
=> ( ( V4__lm = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive))
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec___24a4(V0__R,V1__mkmult__pow,V3__r,V4__lm) = V3__r )
| ? [Vvar__1___24Anonymous__55419] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__55419)
& ? [Vvar__2___24Anonymous__55420] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__2___24Anonymous__55420)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__55419)
=> ( V4__lm = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__1___24Anonymous__55419,Vvar__2___24Anonymous__55420)
& ? [Vvar__2___24Anonymous__55432] :
( t(Vvar__2___24Anonymous__55432,V0__R)
& ? [Vvar__3___24Anonymous__55433] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3___24Anonymous__55433)
& Vvar__1___24Anonymous__55419 = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__2___24Anonymous__55432,Vvar__3___24Anonymous__55433)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec___24a4(V0__R,V1__mkmult__pow,V3__r,V4__lm) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec___24a4(V0__R,V1__mkmult__pow,happ(happ(happ(V1__mkmult__pow,V3__r),Vvar__2___24Anonymous__55432),Vvar__3___24Anonymous__55433),Vvar__2___24Anonymous__55420) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkopp_pow',axiom,
! [V0__R,V1__rmul,V2__ropp,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> ( ? [Vvar__0___24Anonymous__53217] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__53217)
& V4__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__53217)
& cCoq_2esetoid__ring_2eRing__polynom_2emkopp__pow___24a5(V0__R,V1__rmul,V2__ropp,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(V2__ropp,V3__x),V3__x,cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__53217)) )
| ? [Vvar__0___24Anonymous__53218] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__53218)
& V4__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__53218)
& cCoq_2esetoid__ring_2eRing__polynom_2emkopp__pow___24a5(V0__R,V1__rmul,V2__ropp,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(V2__ropp,V3__x),V3__x,cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__53218)) )
| ( V4__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkopp__pow___24a5(V0__R,V1__rmul,V2__ropp,V3__x,V4__p) = happ(V2__ropp,V3__x) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkpow',axiom,
! [V0__R,V1__rmul,V2__x,V3__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__53206] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__53206)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__53206)
& cCoq_2esetoid__ring_2eRing__polynom_2emkpow___24a4(V0__R,V1__rmul,V2__x,V3__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V2__x,V2__x,cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__53206)) )
| ? [Vvar__0___24Anonymous__53207] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__53207)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__53207)
& cCoq_2esetoid__ring_2eRing__polynom_2emkpow___24a4(V0__R,V1__rmul,V2__x,V3__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V2__x,V2__x,cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__53207)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkpow___24a4(V0__R,V1__rmul,V2__x,V3__p) = V2__x ) ) ) ) ).
fof('$_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__18220___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.r_list_pow',axiom,
! [V0__R,V1__rI,V2__rmul,V4__l] :
( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive))
& cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,V4__l) = V1__rI )
| ? [Vvar__1___24Anonymous__52808] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__52808)
& ? [Vvar__2___24Anonymous__52809] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__2___24Anonymous__52809)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__52808)
=> ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__1___24Anonymous__52808,Vvar__2___24Anonymous__52809)
& ? [Vvar__2___24Anonymous__52821] :
( t(Vvar__2___24Anonymous__52821,V0__R)
& ? [Vvar__3___24Anonymous__52822] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3___24Anonymous__52822)
& Vvar__1___24Anonymous__52808 = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__2___24Anonymous__52821,Vvar__3___24Anonymous__52822)
& cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,V4__l) = happ(happ(V2__rmul,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,Vvar__2___24Anonymous__52821,Vvar__3___24Anonymous__52822)),cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,Vvar__2___24Anonymous__52809)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.zmon_pred',axiom,
! [V0__j,V1__M] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__j)
=> ( ? [Vvar__0___24Anonymous__46644] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46644)
& V0__j = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__46644)
& cCoq_2esetoid__ring_2eRing__polynom_2ezmon__pred___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__j),V1__M) )
| ? [Vvar__0___24Anonymous__46645] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46645)
& V0__j = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__46645)
& cCoq_2esetoid__ring_2eRing__polynom_2ezmon__pred___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__j),V1__M) )
| ( V0__j = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2ezmon__pred___24a2(V0__j,V1__M) = V1__M ) ) ) ).
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('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__19743] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19743)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19743)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__19743) ) ) ) ) ).
fof('$_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__35940] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35940)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35940)
& 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__35941__35944___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__35940)),c_24__let__var__6__p__35941__35944___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__35940))) )
| ? [Vvar__0___24Anonymous__35942] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35942)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35942)
& 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__35943__35945___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__35942)),c_24__let__var__6__p__35943__35945___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__35942)) )
| ( 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('$_def_list_utils.concat',axiom,
! [V0__T] : clist__utils_2econcat___24a1(V0__T) = cCoq_2eLists_2eList_2efold__right___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2eapp___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T)) ).
fof('$_def_list_utils.count',axiom,
! [V0__X,V1__p,V3__l] :
( cType___24t(V0__X)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__X)
& clist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__61566] :
( t(Vvar__1___24Anonymous__61566,V0__X)
& ? [Vvar__2___24Anonymous__61567] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,Vvar__2___24Anonymous__61567)
& ( cType___24t(V0__X)
=> ( c_24__type__193___24t(V0__X,V1__p)
=> ( t(Vvar__1___24Anonymous__61566,V0__X)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__X,Vvar__1___24Anonymous__61566,Vvar__2___24Anonymous__61567)
& ( ( happ(V1__p,Vvar__1___24Anonymous__61566) = cCoq_2eInit_2eDatatypes_2etrue
& clist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(clist__utils_2ecount___24a3(V0__X,V1__p,Vvar__2___24Anonymous__61567)) )
| ( happ(V1__p,Vvar__1___24Anonymous__61566) = cCoq_2eInit_2eDatatypes_2efalse
& clist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = clist__utils_2ecount___24a3(V0__X,V1__p,Vvar__2___24Anonymous__61567) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__27004,Vvar__1___24Anonymous__27005,Vvar__0__P__27006,Vvar__1___24Anonymous__27007] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__27004) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__27006) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__26642,Vvar__1___24Anonymous__26643,Vvar__2___24Anonymous__26644] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__26642,Vvar__1___24Anonymous__26643,Vvar__2___24Anonymous__26644) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__5] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__21,Vvar__1___24Anonymous__22,Vvar__0__A__23] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__21,Vvar__1___24Anonymous__22) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__23) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__979,Vvar__1__B__980,Vvar__2___24Anonymous__981,Vvar__0__A__982,Vvar__1__B__983,Vvar__2___24Anonymous__984] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__979,Vvar__1__B__980,Vvar__2___24Anonymous__981) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__982,Vvar__1__B__983,Vvar__2___24Anonymous__984) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__41,Vvar__0__A__42,Vvar__1___24Anonymous__43,Vvar__2___24Anonymous__44] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__41) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__42,Vvar__1___24Anonymous__43,Vvar__2___24Anonymous__44) ).
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__25652,Vvar__1__B__25653,Vvar__2___24Anonymous__25654,Vvar__0__A__25655,Vvar__1__B__25656,Vvar__2___24Anonymous__25657] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__25652,Vvar__1__B__25653,Vvar__2___24Anonymous__25654) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__25655,Vvar__1__B__25656) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__25612,Vvar__1__B__25613,Vvar__2___24Anonymous__25614,Vvar__0__A__25615,Vvar__1__B__25616,Vvar__2___24Anonymous__25617] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__25612,Vvar__1__B__25613) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__25615,Vvar__1__B__25616) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__963] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__963) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__4851] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4851) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__4829,Vvar__0___24Anonymous__4830] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4829) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__4830) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__64366] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__64366) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__36503,Vvar__1___24Anonymous__36504] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__36503,Vvar__1___24Anonymous__36504) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__25754,Vvar__0__A__25755,Vvar__1__h__25756,Vvar__2__n__25757,Vvar__3___24Anonymous__25758] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__25754) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__25755,Vvar__1__h__25756,Vvar__2__n__25757,Vvar__3___24Anonymous__25758) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__27184,Vvar__1___24Anonymous__27185,Vvar__0__C__27186,Vvar__1___24Anonymous__27187] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__27184,Vvar__1___24Anonymous__27185) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__27186,Vvar__1___24Anonymous__27187) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__1045,Vvar__1___24Anonymous__1046,Vvar__0__C__1047,Vvar__1___24Anonymous__1048,Vvar__2___24Anonymous__1049] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__1045,Vvar__1___24Anonymous__1046) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__1047,Vvar__1___24Anonymous__1048,Vvar__2___24Anonymous__1049) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__27235,Vvar__1___24Anonymous__27236] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__27235,Vvar__1___24Anonymous__27236) ).
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__2256,Vvar__1___24Anonymous__2257,Vvar__0__C__2258,Vvar__1___24Anonymous__2259] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__2256,Vvar__1___24Anonymous__2257) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__2258,Vvar__1___24Anonymous__2259) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__3506,Vvar__1__TX__3507,Vvar__2__AA__3508,Vvar__3__AF__3509,Vvar__0__TA__3510,Vvar__1__TX__3511,Vvar__2__AA__3512,Vvar__3__AF__3513] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__3506,Vvar__1__TX__3507,Vvar__2__AA__3508,Vvar__3__AF__3509) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__3510,Vvar__1__TX__3511,Vvar__2__AA__3512,Vvar__3__AF__3513) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__36653,Vvar__1___24Anonymous__36654] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__36653,Vvar__1___24Anonymous__36654) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__15341,Vvar__0__C__15342] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__15341) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__15342) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__2511,Vvar__0__C__2512] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2511) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2512) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__17881,Vvar__1___24Anonymous__17882,Vvar__0__C__17883,Vvar__1___24Anonymous__17884,Vvar__2___24Anonymous__17885] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__17881,Vvar__1___24Anonymous__17882) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__17883,Vvar__1___24Anonymous__17884,Vvar__2___24Anonymous__17885) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__18047,Vvar__1___24Anonymous__18048] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__18047,Vvar__1___24Anonymous__18048) ).
fof('$_fix_2027_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__2027__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__2031] :
( t(Vvar__1___24Anonymous__2031,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__2032] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__2032)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__2031,Vvar__2___24Anonymous__2032)
& c_24__fix__2027__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__2031,c_24__fix__2027__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__2032,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_26516_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__26531] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26531)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26531)
& ( ? [Vvar__0___24Anonymous__26535] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26535)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26535)
& c_24__fix__26516__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__26516__1__add__carry___24a2(Vvar__0___24Anonymous__26531,Vvar__0___24Anonymous__26535)) )
| ? [Vvar__0___24Anonymous__26536] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26536)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26536)
& c_24__fix__26516__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__26516__1__add__carry___24a2(Vvar__0___24Anonymous__26531,Vvar__0___24Anonymous__26536)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__26516__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__26531)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__26537] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26537)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26537)
& ( ? [Vvar__0___24Anonymous__26541] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26541)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26541)
& c_24__fix__26516__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__26516__1__add__carry___24a2(Vvar__0___24Anonymous__26537,Vvar__0___24Anonymous__26541)) )
| ? [Vvar__0___24Anonymous__26542] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26542)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26542)
& c_24__fix__26516__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__26537,Vvar__0___24Anonymous__26542)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__26516__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__26537)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__26543] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26543)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26543)
& c_24__fix__26516__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__26543)) )
| ? [Vvar__0___24Anonymous__26544] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26544)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26544)
& c_24__fix__26516__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__26544)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__26516__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_fix_36598_v_CANONICAL_2',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ( ( Vv__CANONICAL__4 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__36598__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__5 )
| ? [Vvar__1__h__36603] :
( t(Vvar__1__h__36603,Vv__CANONICAL__0)
& ? [Vvar__2__n__36604] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__36604)
& ? [Vvar__3___24Anonymous__36605] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vvar__2__n__36604,Vvar__3___24Anonymous__36605)
& Vv__CANONICAL__4 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vvar__1__h__36603,Vvar__2__n__36604,Vvar__3___24Anonymous__36605)
& c_24__fix__36598__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1__h__36603,c_24__fix__36598__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2__n__36604,Vvar__3___24Anonymous__36605,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__27012,Vvar__0__P__27013,Vvar__1___24Anonymous__27014,Vvar__1___24Anonymous__27015] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__27012) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__27013)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__27012 = Vvar__0__P__27013 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__27008,Vvar__0__P__27009,Vvar__1___24Anonymous__27010,Vvar__1___24Anonymous__27011] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__27008) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__27009)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__27008 = Vvar__0__P__27009 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__26645,Vvar__0___24Anonymous__26646,Vvar__1___24Anonymous__26647,Vvar__1___24Anonymous__26648,Vvar__2___24Anonymous__26649,Vvar__2___24Anonymous__26650] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__26645,Vvar__1___24Anonymous__26647,Vvar__2___24Anonymous__26649) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__26646,Vvar__1___24Anonymous__26648,Vvar__2___24Anonymous__26650)
=> ( Vvar__2___24Anonymous__26649 = Vvar__2___24Anonymous__26650
& Vvar__1___24Anonymous__26647 = Vvar__1___24Anonymous__26648
& Vvar__0___24Anonymous__26645 = Vvar__0___24Anonymous__26646 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__28,Vvar__0__A__29] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__28) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__29)
=> Vvar__0__A__28 = Vvar__0__A__29 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__6,Vvar__0___24Anonymous__7] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7)
=> Vvar__0___24Anonymous__6 = Vvar__0___24Anonymous__7 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__24,Vvar__0__A__25,Vvar__1___24Anonymous__26,Vvar__1___24Anonymous__27] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__24,Vvar__1___24Anonymous__26) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__25,Vvar__1___24Anonymous__27)
=> ( Vvar__1___24Anonymous__26 = Vvar__1___24Anonymous__27
& Vvar__0__A__24 = Vvar__0__A__25 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__47,Vvar__0__A__48,Vvar__1___24Anonymous__49,Vvar__1___24Anonymous__50,Vvar__2___24Anonymous__51,Vvar__2___24Anonymous__52] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__47,Vvar__1___24Anonymous__49,Vvar__2___24Anonymous__51) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__48,Vvar__1___24Anonymous__50,Vvar__2___24Anonymous__52)
=> ( Vvar__2___24Anonymous__51 = Vvar__2___24Anonymous__52
& Vvar__1___24Anonymous__49 = Vvar__1___24Anonymous__50
& Vvar__0__A__47 = Vvar__0__A__48 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__985,Vvar__0__A__986,Vvar__1__B__987,Vvar__1__B__988,Vvar__2___24Anonymous__989,Vvar__2___24Anonymous__990] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__985,Vvar__1__B__987,Vvar__2___24Anonymous__989) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__986,Vvar__1__B__988,Vvar__2___24Anonymous__990)
=> ( Vvar__2___24Anonymous__989 = Vvar__2___24Anonymous__990
& Vvar__1__B__987 = Vvar__1__B__988
& Vvar__0__A__985 = Vvar__0__A__986 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__991,Vvar__0__A__992,Vvar__1__B__993,Vvar__1__B__994,Vvar__2___24Anonymous__995,Vvar__2___24Anonymous__996] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__991,Vvar__1__B__993,Vvar__2___24Anonymous__995) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__992,Vvar__1__B__994,Vvar__2___24Anonymous__996)
=> ( Vvar__2___24Anonymous__995 = Vvar__2___24Anonymous__996
& Vvar__1__B__993 = Vvar__1__B__994
& Vvar__0__A__991 = Vvar__0__A__992 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__45,Vvar__0__A__46] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__45) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__46)
=> Vvar__0__A__45 = Vvar__0__A__46 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__1005,Vvar__0__A__1006,Vvar__1__B__1007,Vvar__1__B__1008,Vvar__2___24Anonymous__1009,Vvar__2___24Anonymous__1010,Vvar__3___24Anonymous__1011,Vvar__3___24Anonymous__1012] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1005,Vvar__1__B__1007,Vvar__2___24Anonymous__1009,Vvar__3___24Anonymous__1011) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1006,Vvar__1__B__1008,Vvar__2___24Anonymous__1010,Vvar__3___24Anonymous__1012)
=> ( Vvar__3___24Anonymous__1011 = Vvar__3___24Anonymous__1012
& Vvar__2___24Anonymous__1009 = Vvar__2___24Anonymous__1010
& Vvar__1__B__1007 = Vvar__1__B__1008
& Vvar__0__A__1005 = Vvar__0__A__1006 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__902,Vvar__0__A__903,Vvar__1__P__904,Vvar__1__P__905,Vvar__2__x__906,Vvar__2__x__907,Vvar__3___24Anonymous__908,Vvar__3___24Anonymous__909] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__902,Vvar__1__P__904,Vvar__2__x__906) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__903,Vvar__1__P__905,Vvar__2__x__907)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__906 = Vvar__2__x__907
& Vvar__1__P__904 = Vvar__1__P__905
& Vvar__0__A__902 = Vvar__0__A__903 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__943,Vvar__0__A__944,Vvar__1__P__945,Vvar__1__P__946,Vvar__2__x__947,Vvar__2__x__948,Vvar__3___24Anonymous__949,Vvar__3___24Anonymous__950] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__943,Vvar__1__P__945,Vvar__2__x__947,Vvar__3___24Anonymous__949) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__944,Vvar__1__P__946,Vvar__2__x__948,Vvar__3___24Anonymous__950)
=> ( Vvar__3___24Anonymous__949 = Vvar__3___24Anonymous__950
& Vvar__2__x__947 = Vvar__2__x__948
& Vvar__1__P__945 = Vvar__1__P__946
& Vvar__0__A__943 = Vvar__0__A__944 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__25658,Vvar__0__A__25659,Vvar__1__B__25660,Vvar__1__B__25661,Vvar__2___24Anonymous__25662,Vvar__2___24Anonymous__25663] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__25658,Vvar__1__B__25660,Vvar__2___24Anonymous__25662) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__25659,Vvar__1__B__25661,Vvar__2___24Anonymous__25663)
=> ( Vvar__2___24Anonymous__25662 = Vvar__2___24Anonymous__25663
& Vvar__1__B__25660 = Vvar__1__B__25661
& Vvar__0__A__25658 = Vvar__0__A__25659 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__25664,Vvar__0__A__25665,Vvar__1__B__25666,Vvar__1__B__25667,Vvar__2___24Anonymous__25668,Vvar__2___24Anonymous__25669] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__25664,Vvar__1__B__25666) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__25665,Vvar__1__B__25667)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__25666 = Vvar__1__B__25667
& Vvar__0__A__25664 = Vvar__0__A__25665 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__25618,Vvar__0__A__25619,Vvar__1__B__25620,Vvar__1__B__25621,Vvar__2___24Anonymous__25622,Vvar__2___24Anonymous__25623] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__25618,Vvar__1__B__25620) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__25619,Vvar__1__B__25621)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__25620 = Vvar__1__B__25621
& Vvar__0__A__25618 = Vvar__0__A__25619 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__25624,Vvar__0__A__25625,Vvar__1__B__25626,Vvar__1__B__25627,Vvar__2___24Anonymous__25628,Vvar__2___24Anonymous__25629] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__25624,Vvar__1__B__25626) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__25625,Vvar__1__B__25627)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__25626 = Vvar__1__B__25627
& Vvar__0__A__25624 = Vvar__0__A__25625 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__964,Vvar__0___24Anonymous__965] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__964) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__965)
=> Vvar__0___24Anonymous__964 = Vvar__0___24Anonymous__965 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__4854,Vvar__0___24Anonymous__4855] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4854) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4855)
=> Vvar__0___24Anonymous__4854 = Vvar__0___24Anonymous__4855 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__4852,Vvar__0___24Anonymous__4853] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4852) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4853)
=> Vvar__0___24Anonymous__4852 = Vvar__0___24Anonymous__4853 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__4831,Vvar__0___24Anonymous__4832] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4831) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4832)
=> Vvar__0___24Anonymous__4831 = Vvar__0___24Anonymous__4832 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__4833,Vvar__0___24Anonymous__4834] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__4833) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__4834)
=> Vvar__0___24Anonymous__4833 = Vvar__0___24Anonymous__4834 ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__64367,Vvar__0___24Anonymous__64368] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__64367) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__64368)
=> Vvar__0___24Anonymous__64367 = Vvar__0___24Anonymous__64368 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__17769,Vvar__0__Qnum__17770,Vvar__1__Qden__17771,Vvar__1__Qden__17772] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__17769,Vvar__1__Qden__17771) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__17770,Vvar__1__Qden__17772)
=> ( Vvar__1__Qden__17771 = Vvar__1__Qden__17772
& Vvar__0__Qnum__17769 = Vvar__0__Qnum__17770 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__4775,Vvar__0___24Anonymous__4776,Vvar__1___24Anonymous__4777,Vvar__1___24Anonymous__4778,Vvar__2___24Anonymous__4779,Vvar__2___24Anonymous__4780,Vvar__3___24Anonymous__4781,Vvar__3___24Anonymous__4782,Vvar__4___24Anonymous__4783,Vvar__4___24Anonymous__4784,Vvar__5___24Anonymous__4785,Vvar__5___24Anonymous__4786,Vvar__6___24Anonymous__4787,Vvar__6___24Anonymous__4788,Vvar__7___24Anonymous__4789,Vvar__7___24Anonymous__4790] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4775,Vvar__1___24Anonymous__4777,Vvar__2___24Anonymous__4779,Vvar__3___24Anonymous__4781,Vvar__4___24Anonymous__4783,Vvar__5___24Anonymous__4785,Vvar__6___24Anonymous__4787,Vvar__7___24Anonymous__4789) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4776,Vvar__1___24Anonymous__4778,Vvar__2___24Anonymous__4780,Vvar__3___24Anonymous__4782,Vvar__4___24Anonymous__4784,Vvar__5___24Anonymous__4786,Vvar__6___24Anonymous__4788,Vvar__7___24Anonymous__4790)
=> ( Vvar__7___24Anonymous__4789 = Vvar__7___24Anonymous__4790
& Vvar__6___24Anonymous__4787 = Vvar__6___24Anonymous__4788
& Vvar__5___24Anonymous__4785 = Vvar__5___24Anonymous__4786
& Vvar__4___24Anonymous__4783 = Vvar__4___24Anonymous__4784
& Vvar__3___24Anonymous__4781 = Vvar__3___24Anonymous__4782
& Vvar__2___24Anonymous__4779 = Vvar__2___24Anonymous__4780
& Vvar__1___24Anonymous__4777 = Vvar__1___24Anonymous__4778
& Vvar__0___24Anonymous__4775 = Vvar__0___24Anonymous__4776 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__36505,Vvar__0___24Anonymous__36506,Vvar__1___24Anonymous__36507,Vvar__1___24Anonymous__36508] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__36505,Vvar__1___24Anonymous__36507) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__36506,Vvar__1___24Anonymous__36508)
=> ( Vvar__1___24Anonymous__36507 = Vvar__1___24Anonymous__36508
& Vvar__0___24Anonymous__36505 = Vvar__0___24Anonymous__36506 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__25761,Vvar__0__A__25762,Vvar__1__h__25763,Vvar__1__h__25764,Vvar__2__n__25765,Vvar__2__n__25766,Vvar__3___24Anonymous__25767,Vvar__3___24Anonymous__25768] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__25761,Vvar__1__h__25763,Vvar__2__n__25765,Vvar__3___24Anonymous__25767) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__25762,Vvar__1__h__25764,Vvar__2__n__25766,Vvar__3___24Anonymous__25768)
=> ( Vvar__3___24Anonymous__25767 = Vvar__3___24Anonymous__25768
& Vvar__2__n__25765 = Vvar__2__n__25766
& Vvar__1__h__25763 = Vvar__1__h__25764
& Vvar__0__A__25761 = Vvar__0__A__25762 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__25759,Vvar__0__A__25760] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__25759) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__25760)
=> Vvar__0__A__25759 = Vvar__0__A__25760 ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__27192,Vvar__0__C__27193,Vvar__1___24Anonymous__27194,Vvar__1___24Anonymous__27195] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__27192,Vvar__1___24Anonymous__27194) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__27193,Vvar__1___24Anonymous__27195)
=> ( Vvar__1___24Anonymous__27194 = Vvar__1___24Anonymous__27195
& Vvar__0__C__27192 = Vvar__0__C__27193 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__27196,Vvar__0__C__27197,Vvar__1___24Anonymous__27198,Vvar__1___24Anonymous__27199,Vvar__2___24Anonymous__27200,Vvar__2___24Anonymous__27201] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__27196,Vvar__1___24Anonymous__27198,Vvar__2___24Anonymous__27200) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__27197,Vvar__1___24Anonymous__27199,Vvar__2___24Anonymous__27201)
=> ( Vvar__2___24Anonymous__27200 = Vvar__2___24Anonymous__27201
& Vvar__1___24Anonymous__27198 = Vvar__1___24Anonymous__27199
& Vvar__0__C__27196 = Vvar__0__C__27197 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__27188,Vvar__0__C__27189,Vvar__1___24Anonymous__27190,Vvar__1___24Anonymous__27191] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__27188,Vvar__1___24Anonymous__27190) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__27189,Vvar__1___24Anonymous__27191)
=> ( Vvar__1___24Anonymous__27190 = Vvar__1___24Anonymous__27191
& Vvar__0__C__27188 = Vvar__0__C__27189 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__27208,Vvar__0__C__27209,Vvar__1___24Anonymous__27210,Vvar__1___24Anonymous__27211,Vvar__2___24Anonymous__27212,Vvar__2___24Anonymous__27213] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__27208,Vvar__1___24Anonymous__27210,Vvar__2___24Anonymous__27212) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__27209,Vvar__1___24Anonymous__27211,Vvar__2___24Anonymous__27213)
=> ( Vvar__2___24Anonymous__27212 = Vvar__2___24Anonymous__27213
& Vvar__1___24Anonymous__27210 = Vvar__1___24Anonymous__27211
& Vvar__0__C__27208 = Vvar__0__C__27209 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__27214,Vvar__0__C__27215,Vvar__1___24Anonymous__27216,Vvar__1___24Anonymous__27217] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__27214,Vvar__1___24Anonymous__27216) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__27215,Vvar__1___24Anonymous__27217)
=> ( Vvar__1___24Anonymous__27216 = Vvar__1___24Anonymous__27217
& Vvar__0__C__27214 = Vvar__0__C__27215 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__27218,Vvar__0__C__27219,Vvar__1___24Anonymous__27220,Vvar__1___24Anonymous__27221,Vvar__2___24Anonymous__27222,Vvar__2___24Anonymous__27223] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__27218,Vvar__1___24Anonymous__27220,Vvar__2___24Anonymous__27222) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__27219,Vvar__1___24Anonymous__27221,Vvar__2___24Anonymous__27223)
=> ( Vvar__2___24Anonymous__27222 = Vvar__2___24Anonymous__27223
& Vvar__1___24Anonymous__27220 = Vvar__1___24Anonymous__27221
& Vvar__0__C__27218 = Vvar__0__C__27219 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__27202,Vvar__0__C__27203,Vvar__1___24Anonymous__27204,Vvar__1___24Anonymous__27205,Vvar__2___24Anonymous__27206,Vvar__2___24Anonymous__27207] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__27202,Vvar__1___24Anonymous__27204,Vvar__2___24Anonymous__27206) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__27203,Vvar__1___24Anonymous__27205,Vvar__2___24Anonymous__27207)
=> ( Vvar__2___24Anonymous__27206 = Vvar__2___24Anonymous__27207
& Vvar__1___24Anonymous__27204 = Vvar__1___24Anonymous__27205
& Vvar__0__C__27202 = Vvar__0__C__27203 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__1060,Vvar__0__C__1061,Vvar__1___24Anonymous__1062,Vvar__1___24Anonymous__1063,Vvar__2___24Anonymous__1064,Vvar__2___24Anonymous__1065,Vvar__3___24Anonymous__1066,Vvar__3___24Anonymous__1067] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__1060,Vvar__1___24Anonymous__1062,Vvar__2___24Anonymous__1064,Vvar__3___24Anonymous__1066) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__1061,Vvar__1___24Anonymous__1063,Vvar__2___24Anonymous__1065,Vvar__3___24Anonymous__1067)
=> ( Vvar__3___24Anonymous__1066 = Vvar__3___24Anonymous__1067
& Vvar__2___24Anonymous__1064 = Vvar__2___24Anonymous__1065
& Vvar__1___24Anonymous__1062 = Vvar__1___24Anonymous__1063
& Vvar__0__C__1060 = Vvar__0__C__1061 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__1050,Vvar__0__C__1051,Vvar__1___24Anonymous__1052,Vvar__1___24Anonymous__1053] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__1050,Vvar__1___24Anonymous__1052) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__1051,Vvar__1___24Anonymous__1053)
=> ( Vvar__1___24Anonymous__1052 = Vvar__1___24Anonymous__1053
& Vvar__0__C__1050 = Vvar__0__C__1051 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__1054,Vvar__0__C__1055,Vvar__1___24Anonymous__1056,Vvar__1___24Anonymous__1057,Vvar__2___24Anonymous__1058,Vvar__2___24Anonymous__1059] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__1054,Vvar__1___24Anonymous__1056,Vvar__2___24Anonymous__1058) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__1055,Vvar__1___24Anonymous__1057,Vvar__2___24Anonymous__1059)
=> ( Vvar__2___24Anonymous__1058 = Vvar__2___24Anonymous__1059
& Vvar__1___24Anonymous__1056 = Vvar__1___24Anonymous__1057
& Vvar__0__C__1054 = Vvar__0__C__1055 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__27241,Vvar__0___24Anonymous__27242,Vvar__1___24Anonymous__27243,Vvar__1___24Anonymous__27244] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__27241,Vvar__1___24Anonymous__27243) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__27242,Vvar__1___24Anonymous__27244)
=> ( Vvar__1___24Anonymous__27243 = Vvar__1___24Anonymous__27244
& Vvar__0___24Anonymous__27241 = Vvar__0___24Anonymous__27242 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__27237,Vvar__0___24Anonymous__27238,Vvar__1___24Anonymous__27239,Vvar__1___24Anonymous__27240] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__27237,Vvar__1___24Anonymous__27239) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__27238,Vvar__1___24Anonymous__27240)
=> ( Vvar__1___24Anonymous__27239 = Vvar__1___24Anonymous__27240
& Vvar__0___24Anonymous__27237 = Vvar__0___24Anonymous__27238 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__30287,Vvar__0__r__30288] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__30287) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__30288)
=> Vvar__0__r__30287 = Vvar__0__r__30288 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__30275,Vvar__0__r1__30276,Vvar__1__r2__30277,Vvar__1__r2__30278] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__30275,Vvar__1__r2__30277) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__30276,Vvar__1__r2__30278)
=> ( Vvar__1__r2__30277 = Vvar__1__r2__30278
& Vvar__0__r1__30275 = Vvar__0__r1__30276 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__30279,Vvar__0__r1__30280,Vvar__1__r2__30281,Vvar__1__r2__30282] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__30279,Vvar__1__r2__30281) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__30280,Vvar__1__r2__30282)
=> ( Vvar__1__r2__30281 = Vvar__1__r2__30282
& Vvar__0__r1__30279 = Vvar__0__r1__30280 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__30289,Vvar__0__r__30290] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__30289) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__30290)
=> Vvar__0__r__30289 = Vvar__0__r__30290 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__30271,Vvar__0__r1__30272,Vvar__1__r2__30273,Vvar__1__r2__30274] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__30271,Vvar__1__r2__30273) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__30272,Vvar__1__r2__30274)
=> ( Vvar__1__r2__30273 = Vvar__1__r2__30274
& Vvar__0__r1__30271 = Vvar__0__r1__30272 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__30283,Vvar__0__r1__30284,Vvar__1__z__30285,Vvar__1__z__30286] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__30283,Vvar__1__z__30285) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__30284,Vvar__1__z__30286)
=> ( Vvar__1__z__30285 = Vvar__1__z__30286
& Vvar__0__r1__30283 = Vvar__0__r1__30284 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__30267,Vvar__0__r__30268] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__30267) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__30268)
=> Vvar__0__r__30267 = Vvar__0__r__30268 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__30269,Vvar__0__r__30270] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__30269) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__30270)
=> Vvar__0__r__30269 = Vvar__0__r__30270 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__35666,Vvar__0__T__35667,Vvar__1__Flhs__35668,Vvar__1__Flhs__35669,Vvar__2__Fop__35670,Vvar__2__Fop__35671,Vvar__3__Frhs__35672,Vvar__3__Frhs__35673] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__35666,Vvar__1__Flhs__35668,Vvar__2__Fop__35670,Vvar__3__Frhs__35672) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__35667,Vvar__1__Flhs__35669,Vvar__2__Fop__35671,Vvar__3__Frhs__35673)
=> ( Vvar__3__Frhs__35672 = Vvar__3__Frhs__35673
& Vvar__2__Fop__35670 = Vvar__2__Fop__35671
& Vvar__1__Flhs__35668 = Vvar__1__Flhs__35669
& Vvar__0__T__35666 = Vvar__0__T__35667 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__2280,Vvar__0__C__2281,Vvar__1___24Anonymous__2282,Vvar__1___24Anonymous__2283,Vvar__2___24Anonymous__2284,Vvar__2___24Anonymous__2285] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__2280,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2284) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__2281,Vvar__1___24Anonymous__2283,Vvar__2___24Anonymous__2285)
=> ( Vvar__2___24Anonymous__2284 = Vvar__2___24Anonymous__2285
& Vvar__1___24Anonymous__2282 = Vvar__1___24Anonymous__2283
& Vvar__0__C__2280 = Vvar__0__C__2281 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__2286,Vvar__0__C__2287,Vvar__1___24Anonymous__2288,Vvar__1___24Anonymous__2289] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__2286,Vvar__1___24Anonymous__2288) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__2287,Vvar__1___24Anonymous__2289)
=> ( Vvar__1___24Anonymous__2288 = Vvar__1___24Anonymous__2289
& Vvar__0__C__2286 = Vvar__0__C__2287 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__2260,Vvar__0__C__2261,Vvar__1___24Anonymous__2262,Vvar__1___24Anonymous__2263] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__2260,Vvar__1___24Anonymous__2262) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__2261,Vvar__1___24Anonymous__2263)
=> ( Vvar__1___24Anonymous__2262 = Vvar__1___24Anonymous__2263
& Vvar__0__C__2260 = Vvar__0__C__2261 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__2268,Vvar__0__C__2269,Vvar__1___24Anonymous__2270,Vvar__1___24Anonymous__2271,Vvar__2___24Anonymous__2272,Vvar__2___24Anonymous__2273] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__2268,Vvar__1___24Anonymous__2270,Vvar__2___24Anonymous__2272) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__2269,Vvar__1___24Anonymous__2271,Vvar__2___24Anonymous__2273)
=> ( Vvar__2___24Anonymous__2272 = Vvar__2___24Anonymous__2273
& Vvar__1___24Anonymous__2270 = Vvar__1___24Anonymous__2271
& Vvar__0__C__2268 = Vvar__0__C__2269 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__2274,Vvar__0__C__2275,Vvar__1___24Anonymous__2276,Vvar__1___24Anonymous__2277,Vvar__2___24Anonymous__2278,Vvar__2___24Anonymous__2279] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__2274,Vvar__1___24Anonymous__2276,Vvar__2___24Anonymous__2278) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__2275,Vvar__1___24Anonymous__2277,Vvar__2___24Anonymous__2279)
=> ( Vvar__2___24Anonymous__2278 = Vvar__2___24Anonymous__2279
& Vvar__1___24Anonymous__2276 = Vvar__1___24Anonymous__2277
& Vvar__0__C__2274 = Vvar__0__C__2275 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__2264,Vvar__0__C__2265,Vvar__1___24Anonymous__2266,Vvar__1___24Anonymous__2267] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__2264,Vvar__1___24Anonymous__2266) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__2265,Vvar__1___24Anonymous__2267)
=> ( Vvar__1___24Anonymous__2266 = Vvar__1___24Anonymous__2267
& Vvar__0__C__2264 = Vvar__0__C__2265 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__2290,Vvar__0__C__2291] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__2290) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__2291)
=> Vvar__0__C__2290 = Vvar__0__C__2291 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__3540,Vvar__0__TA__3541,Vvar__1__TX__3542,Vvar__1__TX__3543,Vvar__2__AA__3544,Vvar__2__AA__3545,Vvar__3__AF__3546,Vvar__3__AF__3547,Vvar__4___24Anonymous__3548,Vvar__4___24Anonymous__3549,Vvar__5___24Anonymous__3550,Vvar__5___24Anonymous__3551] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__3540,Vvar__1__TX__3542,Vvar__2__AA__3544,Vvar__3__AF__3546,Vvar__4___24Anonymous__3548,Vvar__5___24Anonymous__3550) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__3541,Vvar__1__TX__3543,Vvar__2__AA__3545,Vvar__3__AF__3547,Vvar__4___24Anonymous__3549,Vvar__5___24Anonymous__3551)
=> ( Vvar__5___24Anonymous__3550 = Vvar__5___24Anonymous__3551
& Vvar__4___24Anonymous__3548 = Vvar__4___24Anonymous__3549
& Vvar__3__AF__3546 = Vvar__3__AF__3547
& Vvar__2__AA__3544 = Vvar__2__AA__3545
& Vvar__1__TX__3542 = Vvar__1__TX__3543
& Vvar__0__TA__3540 = Vvar__0__TA__3541 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__3552,Vvar__0__TA__3553,Vvar__1__TX__3554,Vvar__1__TX__3555,Vvar__2__AA__3556,Vvar__2__AA__3557,Vvar__3__AF__3558,Vvar__3__AF__3559,Vvar__4___24Anonymous__3560,Vvar__4___24Anonymous__3561,Vvar__5___24Anonymous__3562,Vvar__5___24Anonymous__3563] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__3552,Vvar__1__TX__3554,Vvar__2__AA__3556,Vvar__3__AF__3558,Vvar__4___24Anonymous__3560,Vvar__5___24Anonymous__3562) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__3553,Vvar__1__TX__3555,Vvar__2__AA__3557,Vvar__3__AF__3559,Vvar__4___24Anonymous__3561,Vvar__5___24Anonymous__3563)
=> ( Vvar__5___24Anonymous__3562 = Vvar__5___24Anonymous__3563
& Vvar__4___24Anonymous__3560 = Vvar__4___24Anonymous__3561
& Vvar__3__AF__3558 = Vvar__3__AF__3559
& Vvar__2__AA__3556 = Vvar__2__AA__3557
& Vvar__1__TX__3554 = Vvar__1__TX__3555
& Vvar__0__TA__3552 = Vvar__0__TA__3553 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__3564,Vvar__0__TA__3565,Vvar__1__TX__3566,Vvar__1__TX__3567,Vvar__2__AA__3568,Vvar__2__AA__3569,Vvar__3__AF__3570,Vvar__3__AF__3571,Vvar__4___24Anonymous__3572,Vvar__4___24Anonymous__3573,Vvar__5___24Anonymous__3574,Vvar__5___24Anonymous__3575] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__3564,Vvar__1__TX__3566,Vvar__2__AA__3568,Vvar__3__AF__3570,Vvar__4___24Anonymous__3572,Vvar__5___24Anonymous__3574) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__3565,Vvar__1__TX__3567,Vvar__2__AA__3569,Vvar__3__AF__3571,Vvar__4___24Anonymous__3573,Vvar__5___24Anonymous__3575)
=> ( Vvar__5___24Anonymous__3574 = Vvar__5___24Anonymous__3575
& Vvar__4___24Anonymous__3572 = Vvar__4___24Anonymous__3573
& Vvar__3__AF__3570 = Vvar__3__AF__3571
& Vvar__2__AA__3568 = Vvar__2__AA__3569
& Vvar__1__TX__3566 = Vvar__1__TX__3567
& Vvar__0__TA__3564 = Vvar__0__TA__3565 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__3522,Vvar__0__TA__3523,Vvar__1__TX__3524,Vvar__1__TX__3525,Vvar__2__AA__3526,Vvar__2__AA__3527,Vvar__3__AF__3528,Vvar__3__AF__3529] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__3522,Vvar__1__TX__3524,Vvar__2__AA__3526,Vvar__3__AF__3528) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__3523,Vvar__1__TX__3525,Vvar__2__AA__3527,Vvar__3__AF__3529)
=> ( Vvar__3__AF__3528 = Vvar__3__AF__3529
& Vvar__2__AA__3526 = Vvar__2__AA__3527
& Vvar__1__TX__3524 = Vvar__1__TX__3525
& Vvar__0__TA__3522 = Vvar__0__TA__3523 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__3586,Vvar__0__TA__3587,Vvar__1__TX__3588,Vvar__1__TX__3589,Vvar__2__AA__3590,Vvar__2__AA__3591,Vvar__3__AF__3592,Vvar__3__AF__3593,Vvar__4___24Anonymous__3594,Vvar__4___24Anonymous__3595,Vvar__5___24Anonymous__3596,Vvar__5___24Anonymous__3597,Vvar__6___24Anonymous__3598,Vvar__6___24Anonymous__3599] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__3586,Vvar__1__TX__3588,Vvar__2__AA__3590,Vvar__3__AF__3592,Vvar__4___24Anonymous__3594,Vvar__5___24Anonymous__3596,Vvar__6___24Anonymous__3598) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__3587,Vvar__1__TX__3589,Vvar__2__AA__3591,Vvar__3__AF__3593,Vvar__4___24Anonymous__3595,Vvar__5___24Anonymous__3597,Vvar__6___24Anonymous__3599)
=> ( Vvar__6___24Anonymous__3598 = Vvar__6___24Anonymous__3599
& Vvar__5___24Anonymous__3596 = Vvar__5___24Anonymous__3597
& Vvar__4___24Anonymous__3594 = Vvar__4___24Anonymous__3595
& Vvar__3__AF__3592 = Vvar__3__AF__3593
& Vvar__2__AA__3590 = Vvar__2__AA__3591
& Vvar__1__TX__3588 = Vvar__1__TX__3589
& Vvar__0__TA__3586 = Vvar__0__TA__3587 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__3576,Vvar__0__TA__3577,Vvar__1__TX__3578,Vvar__1__TX__3579,Vvar__2__AA__3580,Vvar__2__AA__3581,Vvar__3__AF__3582,Vvar__3__AF__3583,Vvar__4___24Anonymous__3584,Vvar__4___24Anonymous__3585] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__3576,Vvar__1__TX__3578,Vvar__2__AA__3580,Vvar__3__AF__3582,Vvar__4___24Anonymous__3584) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__3577,Vvar__1__TX__3579,Vvar__2__AA__3581,Vvar__3__AF__3583,Vvar__4___24Anonymous__3585)
=> ( Vvar__4___24Anonymous__3584 = Vvar__4___24Anonymous__3585
& Vvar__3__AF__3582 = Vvar__3__AF__3583
& Vvar__2__AA__3580 = Vvar__2__AA__3581
& Vvar__1__TX__3578 = Vvar__1__TX__3579
& Vvar__0__TA__3576 = Vvar__0__TA__3577 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__3514,Vvar__0__TA__3515,Vvar__1__TX__3516,Vvar__1__TX__3517,Vvar__2__AA__3518,Vvar__2__AA__3519,Vvar__3__AF__3520,Vvar__3__AF__3521] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__3514,Vvar__1__TX__3516,Vvar__2__AA__3518,Vvar__3__AF__3520) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__3515,Vvar__1__TX__3517,Vvar__2__AA__3519,Vvar__3__AF__3521)
=> ( Vvar__3__AF__3520 = Vvar__3__AF__3521
& Vvar__2__AA__3518 = Vvar__2__AA__3519
& Vvar__1__TX__3516 = Vvar__1__TX__3517
& Vvar__0__TA__3514 = Vvar__0__TA__3515 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__3530,Vvar__0__TA__3531,Vvar__1__TX__3532,Vvar__1__TX__3533,Vvar__2__AA__3534,Vvar__2__AA__3535,Vvar__3__AF__3536,Vvar__3__AF__3537,Vvar__4___24Anonymous__3538,Vvar__4___24Anonymous__3539] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__3530,Vvar__1__TX__3532,Vvar__2__AA__3534,Vvar__3__AF__3536,Vvar__4___24Anonymous__3538) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__3531,Vvar__1__TX__3533,Vvar__2__AA__3535,Vvar__3__AF__3537,Vvar__4___24Anonymous__3539)
=> ( Vvar__4___24Anonymous__3538 = Vvar__4___24Anonymous__3539
& Vvar__3__AF__3536 = Vvar__3__AF__3537
& Vvar__2__AA__3534 = Vvar__2__AA__3535
& Vvar__1__TX__3532 = Vvar__1__TX__3533
& Vvar__0__TA__3530 = Vvar__0__TA__3531 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__36659,Vvar__0___24Anonymous__36660,Vvar__1___24Anonymous__36661,Vvar__1___24Anonymous__36662] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__36659,Vvar__1___24Anonymous__36661) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__36660,Vvar__1___24Anonymous__36662)
=> ( Vvar__1___24Anonymous__36661 = Vvar__1___24Anonymous__36662
& Vvar__0___24Anonymous__36659 = Vvar__0___24Anonymous__36660 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__36663,Vvar__0___24Anonymous__36664,Vvar__1___24Anonymous__36665,Vvar__1___24Anonymous__36666,Vvar__2___24Anonymous__36667,Vvar__2___24Anonymous__36668] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__36663,Vvar__1___24Anonymous__36665,Vvar__2___24Anonymous__36667) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__36664,Vvar__1___24Anonymous__36666,Vvar__2___24Anonymous__36668)
=> ( Vvar__2___24Anonymous__36667 = Vvar__2___24Anonymous__36668
& Vvar__1___24Anonymous__36665 = Vvar__1___24Anonymous__36666
& Vvar__0___24Anonymous__36663 = Vvar__0___24Anonymous__36664 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__36655,Vvar__0___24Anonymous__36656,Vvar__1___24Anonymous__36657,Vvar__1___24Anonymous__36658] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__36655,Vvar__1___24Anonymous__36657) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__36656,Vvar__1___24Anonymous__36658)
=> ( Vvar__1___24Anonymous__36657 = Vvar__1___24Anonymous__36658
& Vvar__0___24Anonymous__36655 = Vvar__0___24Anonymous__36656 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__15345,Vvar__0__C__15346] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__15345) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__15346)
=> Vvar__0__C__15345 = Vvar__0__C__15346 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__15343,Vvar__0__C__15344] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__15343) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__15344)
=> Vvar__0__C__15343 = Vvar__0__C__15344 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__15351,Vvar__0__C__15352,Vvar__1___24Anonymous__15353,Vvar__1___24Anonymous__15354] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__15351,Vvar__1___24Anonymous__15353) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__15352,Vvar__1___24Anonymous__15354)
=> ( Vvar__1___24Anonymous__15353 = Vvar__1___24Anonymous__15354
& Vvar__0__C__15351 = Vvar__0__C__15352 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__15355,Vvar__0__C__15356,Vvar__1___24Anonymous__15357,Vvar__1___24Anonymous__15358,Vvar__2___24Anonymous__15359,Vvar__2___24Anonymous__15360] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__15355,Vvar__1___24Anonymous__15357,Vvar__2___24Anonymous__15359) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__15356,Vvar__1___24Anonymous__15358,Vvar__2___24Anonymous__15360)
=> ( Vvar__2___24Anonymous__15359 = Vvar__2___24Anonymous__15360
& Vvar__1___24Anonymous__15357 = Vvar__1___24Anonymous__15358
& Vvar__0__C__15355 = Vvar__0__C__15356 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__15347,Vvar__0__C__15348,Vvar__1___24Anonymous__15349,Vvar__1___24Anonymous__15350] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__15347,Vvar__1___24Anonymous__15349) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__15348,Vvar__1___24Anonymous__15350)
=> ( Vvar__1___24Anonymous__15349 = Vvar__1___24Anonymous__15350
& Vvar__0__C__15347 = Vvar__0__C__15348 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__15381,Vvar__0__C__15382,Vvar__1___24Anonymous__15383,Vvar__1___24Anonymous__15384,Vvar__2___24Anonymous__15385,Vvar__2___24Anonymous__15386] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__15381,Vvar__1___24Anonymous__15383,Vvar__2___24Anonymous__15385) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__15382,Vvar__1___24Anonymous__15384,Vvar__2___24Anonymous__15386)
=> ( Vvar__2___24Anonymous__15385 = Vvar__2___24Anonymous__15386
& Vvar__1___24Anonymous__15383 = Vvar__1___24Anonymous__15384
& Vvar__0__C__15381 = Vvar__0__C__15382 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__15377,Vvar__0__C__15378,Vvar__1___24Anonymous__15379,Vvar__1___24Anonymous__15380] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__15377,Vvar__1___24Anonymous__15379) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__15378,Vvar__1___24Anonymous__15380)
=> ( Vvar__1___24Anonymous__15379 = Vvar__1___24Anonymous__15380
& Vvar__0__C__15377 = Vvar__0__C__15378 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__15367,Vvar__0__C__15368,Vvar__1___24Anonymous__15369,Vvar__1___24Anonymous__15370,Vvar__2___24Anonymous__15371,Vvar__2___24Anonymous__15372] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__15367,Vvar__1___24Anonymous__15369,Vvar__2___24Anonymous__15371) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__15368,Vvar__1___24Anonymous__15370,Vvar__2___24Anonymous__15372)
=> ( Vvar__2___24Anonymous__15371 = Vvar__2___24Anonymous__15372
& Vvar__1___24Anonymous__15369 = Vvar__1___24Anonymous__15370
& Vvar__0__C__15367 = Vvar__0__C__15368 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__15373,Vvar__0__C__15374,Vvar__1___24Anonymous__15375,Vvar__1___24Anonymous__15376] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__15373,Vvar__1___24Anonymous__15375) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__15374,Vvar__1___24Anonymous__15376)
=> ( Vvar__1___24Anonymous__15375 = Vvar__1___24Anonymous__15376
& Vvar__0__C__15373 = Vvar__0__C__15374 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__15387,Vvar__0__C__15388,Vvar__1___24Anonymous__15389,Vvar__1___24Anonymous__15390,Vvar__2___24Anonymous__15391,Vvar__2___24Anonymous__15392] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__15387,Vvar__1___24Anonymous__15389,Vvar__2___24Anonymous__15391) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__15388,Vvar__1___24Anonymous__15390,Vvar__2___24Anonymous__15392)
=> ( Vvar__2___24Anonymous__15391 = Vvar__2___24Anonymous__15392
& Vvar__1___24Anonymous__15389 = Vvar__1___24Anonymous__15390
& Vvar__0__C__15387 = Vvar__0__C__15388 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__15361,Vvar__0__C__15362,Vvar__1___24Anonymous__15363,Vvar__1___24Anonymous__15364,Vvar__2___24Anonymous__15365,Vvar__2___24Anonymous__15366] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__15361,Vvar__1___24Anonymous__15363,Vvar__2___24Anonymous__15365) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__15362,Vvar__1___24Anonymous__15364,Vvar__2___24Anonymous__15366)
=> ( Vvar__2___24Anonymous__15365 = Vvar__2___24Anonymous__15366
& Vvar__1___24Anonymous__15363 = Vvar__1___24Anonymous__15364
& Vvar__0__C__15361 = Vvar__0__C__15362 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__15684,Vvar__0__C__15685,Vvar__1__num__15686,Vvar__1__num__15687,Vvar__2__denum__15688,Vvar__2__denum__15689,Vvar__3__condition__15690,Vvar__3__condition__15691] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__15684,Vvar__1__num__15686,Vvar__2__denum__15688,Vvar__3__condition__15690) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__15685,Vvar__1__num__15687,Vvar__2__denum__15689,Vvar__3__condition__15691)
=> ( Vvar__3__condition__15690 = Vvar__3__condition__15691
& Vvar__2__denum__15688 = Vvar__2__denum__15689
& Vvar__1__num__15686 = Vvar__1__num__15687
& Vvar__0__C__15684 = Vvar__0__C__15685 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__15737,Vvar__0__C__15738,Vvar__1__rsplit__left__15739,Vvar__1__rsplit__left__15740,Vvar__2__rsplit__common__15741,Vvar__2__rsplit__common__15742,Vvar__3__rsplit__right__15743,Vvar__3__rsplit__right__15744] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__15737,Vvar__1__rsplit__left__15739,Vvar__2__rsplit__common__15741,Vvar__3__rsplit__right__15743) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__15738,Vvar__1__rsplit__left__15740,Vvar__2__rsplit__common__15742,Vvar__3__rsplit__right__15744)
=> ( Vvar__3__rsplit__right__15743 = Vvar__3__rsplit__right__15744
& Vvar__2__rsplit__common__15741 = Vvar__2__rsplit__common__15742
& Vvar__1__rsplit__left__15739 = Vvar__1__rsplit__left__15740
& Vvar__0__C__15737 = Vvar__0__C__15738 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__2515,Vvar__0__C__2516] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2515) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2516)
=> Vvar__0__C__2515 = Vvar__0__C__2516 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__2513,Vvar__0__C__2514] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2513) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2514)
=> Vvar__0__C__2513 = Vvar__0__C__2514 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__2521,Vvar__0__C__2522,Vvar__1___24Anonymous__2523,Vvar__1___24Anonymous__2524] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2521,Vvar__1___24Anonymous__2523) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2522,Vvar__1___24Anonymous__2524)
=> ( Vvar__1___24Anonymous__2523 = Vvar__1___24Anonymous__2524
& Vvar__0__C__2521 = Vvar__0__C__2522 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__2525,Vvar__0__C__2526,Vvar__1___24Anonymous__2527,Vvar__1___24Anonymous__2528,Vvar__2___24Anonymous__2529,Vvar__2___24Anonymous__2530] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2525,Vvar__1___24Anonymous__2527,Vvar__2___24Anonymous__2529) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2526,Vvar__1___24Anonymous__2528,Vvar__2___24Anonymous__2530)
=> ( Vvar__2___24Anonymous__2529 = Vvar__2___24Anonymous__2530
& Vvar__1___24Anonymous__2527 = Vvar__1___24Anonymous__2528
& Vvar__0__C__2525 = Vvar__0__C__2526 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__2517,Vvar__0__C__2518,Vvar__1___24Anonymous__2519,Vvar__1___24Anonymous__2520] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2517,Vvar__1___24Anonymous__2519) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2518,Vvar__1___24Anonymous__2520)
=> ( Vvar__1___24Anonymous__2519 = Vvar__1___24Anonymous__2520
& Vvar__0__C__2517 = Vvar__0__C__2518 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__2537,Vvar__0__C__2538,Vvar__1___24Anonymous__2539,Vvar__1___24Anonymous__2540,Vvar__2___24Anonymous__2541,Vvar__2___24Anonymous__2542] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2537,Vvar__1___24Anonymous__2539,Vvar__2___24Anonymous__2541) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2538,Vvar__1___24Anonymous__2540,Vvar__2___24Anonymous__2542)
=> ( Vvar__2___24Anonymous__2541 = Vvar__2___24Anonymous__2542
& Vvar__1___24Anonymous__2539 = Vvar__1___24Anonymous__2540
& Vvar__0__C__2537 = Vvar__0__C__2538 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__2543,Vvar__0__C__2544,Vvar__1___24Anonymous__2545,Vvar__1___24Anonymous__2546] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2543,Vvar__1___24Anonymous__2545) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2544,Vvar__1___24Anonymous__2546)
=> ( Vvar__1___24Anonymous__2545 = Vvar__1___24Anonymous__2546
& Vvar__0__C__2543 = Vvar__0__C__2544 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__2547,Vvar__0__C__2548,Vvar__1___24Anonymous__2549,Vvar__1___24Anonymous__2550,Vvar__2___24Anonymous__2551,Vvar__2___24Anonymous__2552] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2547,Vvar__1___24Anonymous__2549,Vvar__2___24Anonymous__2551) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2548,Vvar__1___24Anonymous__2550,Vvar__2___24Anonymous__2552)
=> ( Vvar__2___24Anonymous__2551 = Vvar__2___24Anonymous__2552
& Vvar__1___24Anonymous__2549 = Vvar__1___24Anonymous__2550
& Vvar__0__C__2547 = Vvar__0__C__2548 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__2531,Vvar__0__C__2532,Vvar__1___24Anonymous__2533,Vvar__1___24Anonymous__2534,Vvar__2___24Anonymous__2535,Vvar__2___24Anonymous__2536] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2531,Vvar__1___24Anonymous__2533,Vvar__2___24Anonymous__2535) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2532,Vvar__1___24Anonymous__2534,Vvar__2___24Anonymous__2536)
=> ( Vvar__2___24Anonymous__2535 = Vvar__2___24Anonymous__2536
& Vvar__1___24Anonymous__2533 = Vvar__1___24Anonymous__2534
& Vvar__0__C__2531 = Vvar__0__C__2532 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__17896,Vvar__0__C__17897,Vvar__1___24Anonymous__17898,Vvar__1___24Anonymous__17899,Vvar__2___24Anonymous__17900,Vvar__2___24Anonymous__17901,Vvar__3___24Anonymous__17902,Vvar__3___24Anonymous__17903] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__17896,Vvar__1___24Anonymous__17898,Vvar__2___24Anonymous__17900,Vvar__3___24Anonymous__17902) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__17897,Vvar__1___24Anonymous__17899,Vvar__2___24Anonymous__17901,Vvar__3___24Anonymous__17903)
=> ( Vvar__3___24Anonymous__17902 = Vvar__3___24Anonymous__17903
& Vvar__2___24Anonymous__17900 = Vvar__2___24Anonymous__17901
& Vvar__1___24Anonymous__17898 = Vvar__1___24Anonymous__17899
& Vvar__0__C__17896 = Vvar__0__C__17897 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__17886,Vvar__0__C__17887,Vvar__1___24Anonymous__17888,Vvar__1___24Anonymous__17889] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__17886,Vvar__1___24Anonymous__17888) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__17887,Vvar__1___24Anonymous__17889)
=> ( Vvar__1___24Anonymous__17888 = Vvar__1___24Anonymous__17889
& Vvar__0__C__17886 = Vvar__0__C__17887 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__17890,Vvar__0__C__17891,Vvar__1___24Anonymous__17892,Vvar__1___24Anonymous__17893,Vvar__2___24Anonymous__17894,Vvar__2___24Anonymous__17895] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__17890,Vvar__1___24Anonymous__17892,Vvar__2___24Anonymous__17894) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__17891,Vvar__1___24Anonymous__17893,Vvar__2___24Anonymous__17895)
=> ( Vvar__2___24Anonymous__17894 = Vvar__2___24Anonymous__17895
& Vvar__1___24Anonymous__17892 = Vvar__1___24Anonymous__17893
& Vvar__0__C__17890 = Vvar__0__C__17891 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__18053,Vvar__0___24Anonymous__18054,Vvar__1___24Anonymous__18055,Vvar__1___24Anonymous__18056] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__18053,Vvar__1___24Anonymous__18055) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__18054,Vvar__1___24Anonymous__18056)
=> ( Vvar__1___24Anonymous__18055 = Vvar__1___24Anonymous__18056
& Vvar__0___24Anonymous__18053 = Vvar__0___24Anonymous__18054 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__18049,Vvar__0___24Anonymous__18050,Vvar__1___24Anonymous__18051,Vvar__1___24Anonymous__18052] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__18049,Vvar__1___24Anonymous__18051) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__18050,Vvar__1___24Anonymous__18052)
=> ( Vvar__1___24Anonymous__18051 = Vvar__1___24Anonymous__18052
& Vvar__0___24Anonymous__18049 = Vvar__0___24Anonymous__18050 ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__26994,Vvar__1___24Anonymous__26995,VX26996] :
( cProp___24t(Vvar__0__P__26994)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__26995)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__26994,Vvar__1___24Anonymous__26995,VX26996)
=> ( ( p(Vvar__0__P__26994)
& Vvar__1___24Anonymous__26995 = cCoq_2eInit_2eDatatypes_2etrue
& VX26996 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__26994) )
| ( ~ p(Vvar__0__P__26994)
& Vvar__1___24Anonymous__26995 = cCoq_2eInit_2eDatatypes_2efalse
& VX26996 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__26994) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX26638] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX26638)
=> ( VX26638 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__26639] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__26639)
& ? [Vvar__1___24Anonymous__26640] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__26640)
& ? [Vvar__2___24Anonymous__26641] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__26641)
& VX26638 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__26639,Vvar__1___24Anonymous__26640,Vvar__2___24Anonymous__26641) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX27016] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX27016)
=> ( VX27016 = cCoq_2eInit_2eByte_2ex00
| VX27016 = cCoq_2eInit_2eByte_2ex01
| VX27016 = cCoq_2eInit_2eByte_2ex02
| VX27016 = cCoq_2eInit_2eByte_2ex03
| VX27016 = cCoq_2eInit_2eByte_2ex04
| VX27016 = cCoq_2eInit_2eByte_2ex05
| VX27016 = cCoq_2eInit_2eByte_2ex06
| VX27016 = cCoq_2eInit_2eByte_2ex07
| VX27016 = cCoq_2eInit_2eByte_2ex08
| VX27016 = cCoq_2eInit_2eByte_2ex09
| VX27016 = cCoq_2eInit_2eByte_2ex0a
| VX27016 = cCoq_2eInit_2eByte_2ex0b
| VX27016 = cCoq_2eInit_2eByte_2ex0c
| VX27016 = cCoq_2eInit_2eByte_2ex0d
| VX27016 = cCoq_2eInit_2eByte_2ex0e
| VX27016 = cCoq_2eInit_2eByte_2ex0f
| VX27016 = cCoq_2eInit_2eByte_2ex10
| VX27016 = cCoq_2eInit_2eByte_2ex11
| VX27016 = cCoq_2eInit_2eByte_2ex12
| VX27016 = cCoq_2eInit_2eByte_2ex13
| VX27016 = cCoq_2eInit_2eByte_2ex14
| VX27016 = cCoq_2eInit_2eByte_2ex15
| VX27016 = cCoq_2eInit_2eByte_2ex16
| VX27016 = cCoq_2eInit_2eByte_2ex17
| VX27016 = cCoq_2eInit_2eByte_2ex18
| VX27016 = cCoq_2eInit_2eByte_2ex19
| VX27016 = cCoq_2eInit_2eByte_2ex1a
| VX27016 = cCoq_2eInit_2eByte_2ex1b
| VX27016 = cCoq_2eInit_2eByte_2ex1c
| VX27016 = cCoq_2eInit_2eByte_2ex1d
| VX27016 = cCoq_2eInit_2eByte_2ex1e
| VX27016 = cCoq_2eInit_2eByte_2ex1f
| VX27016 = cCoq_2eInit_2eByte_2ex20
| VX27016 = cCoq_2eInit_2eByte_2ex21
| VX27016 = cCoq_2eInit_2eByte_2ex22
| VX27016 = cCoq_2eInit_2eByte_2ex23
| VX27016 = cCoq_2eInit_2eByte_2ex24
| VX27016 = cCoq_2eInit_2eByte_2ex25
| VX27016 = cCoq_2eInit_2eByte_2ex26
| VX27016 = cCoq_2eInit_2eByte_2ex27
| VX27016 = cCoq_2eInit_2eByte_2ex28
| VX27016 = cCoq_2eInit_2eByte_2ex29
| VX27016 = cCoq_2eInit_2eByte_2ex2a
| VX27016 = cCoq_2eInit_2eByte_2ex2b
| VX27016 = cCoq_2eInit_2eByte_2ex2c
| VX27016 = cCoq_2eInit_2eByte_2ex2d
| VX27016 = cCoq_2eInit_2eByte_2ex2e
| VX27016 = cCoq_2eInit_2eByte_2ex2f
| VX27016 = cCoq_2eInit_2eByte_2ex30
| VX27016 = cCoq_2eInit_2eByte_2ex31
| VX27016 = cCoq_2eInit_2eByte_2ex32
| VX27016 = cCoq_2eInit_2eByte_2ex33
| VX27016 = cCoq_2eInit_2eByte_2ex34
| VX27016 = cCoq_2eInit_2eByte_2ex35
| VX27016 = cCoq_2eInit_2eByte_2ex36
| VX27016 = cCoq_2eInit_2eByte_2ex37
| VX27016 = cCoq_2eInit_2eByte_2ex38
| VX27016 = cCoq_2eInit_2eByte_2ex39
| VX27016 = cCoq_2eInit_2eByte_2ex3a
| VX27016 = cCoq_2eInit_2eByte_2ex3b
| VX27016 = cCoq_2eInit_2eByte_2ex3c
| VX27016 = cCoq_2eInit_2eByte_2ex3d
| VX27016 = cCoq_2eInit_2eByte_2ex3e
| VX27016 = cCoq_2eInit_2eByte_2ex3f
| VX27016 = cCoq_2eInit_2eByte_2ex40
| VX27016 = cCoq_2eInit_2eByte_2ex41
| VX27016 = cCoq_2eInit_2eByte_2ex42
| VX27016 = cCoq_2eInit_2eByte_2ex43
| VX27016 = cCoq_2eInit_2eByte_2ex44
| VX27016 = cCoq_2eInit_2eByte_2ex45
| VX27016 = cCoq_2eInit_2eByte_2ex46
| VX27016 = cCoq_2eInit_2eByte_2ex47
| VX27016 = cCoq_2eInit_2eByte_2ex48
| VX27016 = cCoq_2eInit_2eByte_2ex49
| VX27016 = cCoq_2eInit_2eByte_2ex4a
| VX27016 = cCoq_2eInit_2eByte_2ex4b
| VX27016 = cCoq_2eInit_2eByte_2ex4c
| VX27016 = cCoq_2eInit_2eByte_2ex4d
| VX27016 = cCoq_2eInit_2eByte_2ex4e
| VX27016 = cCoq_2eInit_2eByte_2ex4f
| VX27016 = cCoq_2eInit_2eByte_2ex50
| VX27016 = cCoq_2eInit_2eByte_2ex51
| VX27016 = cCoq_2eInit_2eByte_2ex52
| VX27016 = cCoq_2eInit_2eByte_2ex53
| VX27016 = cCoq_2eInit_2eByte_2ex54
| VX27016 = cCoq_2eInit_2eByte_2ex55
| VX27016 = cCoq_2eInit_2eByte_2ex56
| VX27016 = cCoq_2eInit_2eByte_2ex57
| VX27016 = cCoq_2eInit_2eByte_2ex58
| VX27016 = cCoq_2eInit_2eByte_2ex59
| VX27016 = cCoq_2eInit_2eByte_2ex5a
| VX27016 = cCoq_2eInit_2eByte_2ex5b
| VX27016 = cCoq_2eInit_2eByte_2ex5c
| VX27016 = cCoq_2eInit_2eByte_2ex5d
| VX27016 = cCoq_2eInit_2eByte_2ex5e
| VX27016 = cCoq_2eInit_2eByte_2ex5f
| VX27016 = cCoq_2eInit_2eByte_2ex60
| VX27016 = cCoq_2eInit_2eByte_2ex61
| VX27016 = cCoq_2eInit_2eByte_2ex62
| VX27016 = cCoq_2eInit_2eByte_2ex63
| VX27016 = cCoq_2eInit_2eByte_2ex64
| VX27016 = cCoq_2eInit_2eByte_2ex65
| VX27016 = cCoq_2eInit_2eByte_2ex66
| VX27016 = cCoq_2eInit_2eByte_2ex67
| VX27016 = cCoq_2eInit_2eByte_2ex68
| VX27016 = cCoq_2eInit_2eByte_2ex69
| VX27016 = cCoq_2eInit_2eByte_2ex6a
| VX27016 = cCoq_2eInit_2eByte_2ex6b
| VX27016 = cCoq_2eInit_2eByte_2ex6c
| VX27016 = cCoq_2eInit_2eByte_2ex6d
| VX27016 = cCoq_2eInit_2eByte_2ex6e
| VX27016 = cCoq_2eInit_2eByte_2ex6f
| VX27016 = cCoq_2eInit_2eByte_2ex70
| VX27016 = cCoq_2eInit_2eByte_2ex71
| VX27016 = cCoq_2eInit_2eByte_2ex72
| VX27016 = cCoq_2eInit_2eByte_2ex73
| VX27016 = cCoq_2eInit_2eByte_2ex74
| VX27016 = cCoq_2eInit_2eByte_2ex75
| VX27016 = cCoq_2eInit_2eByte_2ex76
| VX27016 = cCoq_2eInit_2eByte_2ex77
| VX27016 = cCoq_2eInit_2eByte_2ex78
| VX27016 = cCoq_2eInit_2eByte_2ex79
| VX27016 = cCoq_2eInit_2eByte_2ex7a
| VX27016 = cCoq_2eInit_2eByte_2ex7b
| VX27016 = cCoq_2eInit_2eByte_2ex7c
| VX27016 = cCoq_2eInit_2eByte_2ex7d
| VX27016 = cCoq_2eInit_2eByte_2ex7e
| VX27016 = cCoq_2eInit_2eByte_2ex7f
| VX27016 = cCoq_2eInit_2eByte_2ex80
| VX27016 = cCoq_2eInit_2eByte_2ex81
| VX27016 = cCoq_2eInit_2eByte_2ex82
| VX27016 = cCoq_2eInit_2eByte_2ex83
| VX27016 = cCoq_2eInit_2eByte_2ex84
| VX27016 = cCoq_2eInit_2eByte_2ex85
| VX27016 = cCoq_2eInit_2eByte_2ex86
| VX27016 = cCoq_2eInit_2eByte_2ex87
| VX27016 = cCoq_2eInit_2eByte_2ex88
| VX27016 = cCoq_2eInit_2eByte_2ex89
| VX27016 = cCoq_2eInit_2eByte_2ex8a
| VX27016 = cCoq_2eInit_2eByte_2ex8b
| VX27016 = cCoq_2eInit_2eByte_2ex8c
| VX27016 = cCoq_2eInit_2eByte_2ex8d
| VX27016 = cCoq_2eInit_2eByte_2ex8e
| VX27016 = cCoq_2eInit_2eByte_2ex8f
| VX27016 = cCoq_2eInit_2eByte_2ex90
| VX27016 = cCoq_2eInit_2eByte_2ex91
| VX27016 = cCoq_2eInit_2eByte_2ex92
| VX27016 = cCoq_2eInit_2eByte_2ex93
| VX27016 = cCoq_2eInit_2eByte_2ex94
| VX27016 = cCoq_2eInit_2eByte_2ex95
| VX27016 = cCoq_2eInit_2eByte_2ex96
| VX27016 = cCoq_2eInit_2eByte_2ex97
| VX27016 = cCoq_2eInit_2eByte_2ex98
| VX27016 = cCoq_2eInit_2eByte_2ex99
| VX27016 = cCoq_2eInit_2eByte_2ex9a
| VX27016 = cCoq_2eInit_2eByte_2ex9b
| VX27016 = cCoq_2eInit_2eByte_2ex9c
| VX27016 = cCoq_2eInit_2eByte_2ex9d
| VX27016 = cCoq_2eInit_2eByte_2ex9e
| VX27016 = cCoq_2eInit_2eByte_2ex9f
| VX27016 = cCoq_2eInit_2eByte_2exa0
| VX27016 = cCoq_2eInit_2eByte_2exa1
| VX27016 = cCoq_2eInit_2eByte_2exa2
| VX27016 = cCoq_2eInit_2eByte_2exa3
| VX27016 = cCoq_2eInit_2eByte_2exa4
| VX27016 = cCoq_2eInit_2eByte_2exa5
| VX27016 = cCoq_2eInit_2eByte_2exa6
| VX27016 = cCoq_2eInit_2eByte_2exa7
| VX27016 = cCoq_2eInit_2eByte_2exa8
| VX27016 = cCoq_2eInit_2eByte_2exa9
| VX27016 = cCoq_2eInit_2eByte_2exaa
| VX27016 = cCoq_2eInit_2eByte_2exab
| VX27016 = cCoq_2eInit_2eByte_2exac
| VX27016 = cCoq_2eInit_2eByte_2exad
| VX27016 = cCoq_2eInit_2eByte_2exae
| VX27016 = cCoq_2eInit_2eByte_2exaf
| VX27016 = cCoq_2eInit_2eByte_2exb0
| VX27016 = cCoq_2eInit_2eByte_2exb1
| VX27016 = cCoq_2eInit_2eByte_2exb2
| VX27016 = cCoq_2eInit_2eByte_2exb3
| VX27016 = cCoq_2eInit_2eByte_2exb4
| VX27016 = cCoq_2eInit_2eByte_2exb5
| VX27016 = cCoq_2eInit_2eByte_2exb6
| VX27016 = cCoq_2eInit_2eByte_2exb7
| VX27016 = cCoq_2eInit_2eByte_2exb8
| VX27016 = cCoq_2eInit_2eByte_2exb9
| VX27016 = cCoq_2eInit_2eByte_2exba
| VX27016 = cCoq_2eInit_2eByte_2exbb
| VX27016 = cCoq_2eInit_2eByte_2exbc
| VX27016 = cCoq_2eInit_2eByte_2exbd
| VX27016 = cCoq_2eInit_2eByte_2exbe
| VX27016 = cCoq_2eInit_2eByte_2exbf
| VX27016 = cCoq_2eInit_2eByte_2exc0
| VX27016 = cCoq_2eInit_2eByte_2exc1
| VX27016 = cCoq_2eInit_2eByte_2exc2
| VX27016 = cCoq_2eInit_2eByte_2exc3
| VX27016 = cCoq_2eInit_2eByte_2exc4
| VX27016 = cCoq_2eInit_2eByte_2exc5
| VX27016 = cCoq_2eInit_2eByte_2exc6
| VX27016 = cCoq_2eInit_2eByte_2exc7
| VX27016 = cCoq_2eInit_2eByte_2exc8
| VX27016 = cCoq_2eInit_2eByte_2exc9
| VX27016 = cCoq_2eInit_2eByte_2exca
| VX27016 = cCoq_2eInit_2eByte_2excb
| VX27016 = cCoq_2eInit_2eByte_2excc
| VX27016 = cCoq_2eInit_2eByte_2excd
| VX27016 = cCoq_2eInit_2eByte_2exce
| VX27016 = cCoq_2eInit_2eByte_2excf
| VX27016 = cCoq_2eInit_2eByte_2exd0
| VX27016 = cCoq_2eInit_2eByte_2exd1
| VX27016 = cCoq_2eInit_2eByte_2exd2
| VX27016 = cCoq_2eInit_2eByte_2exd3
| VX27016 = cCoq_2eInit_2eByte_2exd4
| VX27016 = cCoq_2eInit_2eByte_2exd5
| VX27016 = cCoq_2eInit_2eByte_2exd6
| VX27016 = cCoq_2eInit_2eByte_2exd7
| VX27016 = cCoq_2eInit_2eByte_2exd8
| VX27016 = cCoq_2eInit_2eByte_2exd9
| VX27016 = cCoq_2eInit_2eByte_2exda
| VX27016 = cCoq_2eInit_2eByte_2exdb
| VX27016 = cCoq_2eInit_2eByte_2exdc
| VX27016 = cCoq_2eInit_2eByte_2exdd
| VX27016 = cCoq_2eInit_2eByte_2exde
| VX27016 = cCoq_2eInit_2eByte_2exdf
| VX27016 = cCoq_2eInit_2eByte_2exe0
| VX27016 = cCoq_2eInit_2eByte_2exe1
| VX27016 = cCoq_2eInit_2eByte_2exe2
| VX27016 = cCoq_2eInit_2eByte_2exe3
| VX27016 = cCoq_2eInit_2eByte_2exe4
| VX27016 = cCoq_2eInit_2eByte_2exe5
| VX27016 = cCoq_2eInit_2eByte_2exe6
| VX27016 = cCoq_2eInit_2eByte_2exe7
| VX27016 = cCoq_2eInit_2eByte_2exe8
| VX27016 = cCoq_2eInit_2eByte_2exe9
| VX27016 = cCoq_2eInit_2eByte_2exea
| VX27016 = cCoq_2eInit_2eByte_2exeb
| VX27016 = cCoq_2eInit_2eByte_2exec
| VX27016 = cCoq_2eInit_2eByte_2exed
| VX27016 = cCoq_2eInit_2eByte_2exee
| VX27016 = cCoq_2eInit_2eByte_2exef
| VX27016 = cCoq_2eInit_2eByte_2exf0
| VX27016 = cCoq_2eInit_2eByte_2exf1
| VX27016 = cCoq_2eInit_2eByte_2exf2
| VX27016 = cCoq_2eInit_2eByte_2exf3
| VX27016 = cCoq_2eInit_2eByte_2exf4
| VX27016 = cCoq_2eInit_2eByte_2exf5
| VX27016 = cCoq_2eInit_2eByte_2exf6
| VX27016 = cCoq_2eInit_2eByte_2exf7
| VX27016 = cCoq_2eInit_2eByte_2exf8
| VX27016 = cCoq_2eInit_2eByte_2exf9
| VX27016 = cCoq_2eInit_2eByte_2exfa
| VX27016 = cCoq_2eInit_2eByte_2exfb
| VX27016 = cCoq_2eInit_2eByte_2exfc
| VX27016 = cCoq_2eInit_2eByte_2exfd
| VX27016 = cCoq_2eInit_2eByte_2exfe
| VX27016 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__27017,Vvar__1__Q__27018,Vvar__2___24Anonymous__27019] :
( cProp___24t(Vvar__0__P__27017)
=> ( cProp___24t(Vvar__1__Q__27018)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__27019)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__27017,Vvar__1__Q__27018,Vvar__2___24Anonymous__27019)
=> ( ( p(Vvar__0__P__27017)
& Vvar__2___24Anonymous__27019 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__27018)
& Vvar__2___24Anonymous__27019 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__27038,Vvar__1__Plt__27039,Vvar__2__Pgt__27040,Vvar__3___24Anonymous__27041] :
( cProp___24t(Vvar__0__Peq__27038)
=> ( cProp___24t(Vvar__1__Plt__27039)
=> ( cProp___24t(Vvar__2__Pgt__27040)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__27041)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__27038,Vvar__1__Plt__27039,Vvar__2__Pgt__27040,Vvar__3___24Anonymous__27041)
=> ( ( p(Vvar__0__Peq__27038)
& Vvar__3___24Anonymous__27041 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__27039)
& Vvar__3___24Anonymous__27041 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__27040)
& Vvar__3___24Anonymous__27041 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX160] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX160)
=> ( VX160 = cCoq_2eInit_2eDatatypes_2etrue
| VX160 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX27037] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX27037)
=> ( VX27037 = cCoq_2eInit_2eDatatypes_2eEq
| VX27037 = cCoq_2eInit_2eDatatypes_2eLt
| VX27037 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__35,VX36] :
( cType___24t(Vvar__0__A__35)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35,VX36)
=> ( VX36 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__35)
| ? [Vvar__1___24Anonymous__39] :
( t(Vvar__1___24Anonymous__39,Vvar__0__A__35)
& ? [Vvar__2___24Anonymous__40] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35,Vvar__2___24Anonymous__40)
& VX36 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__35,Vvar__1___24Anonymous__39,Vvar__2___24Anonymous__40) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX3)
=> ( VX3 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4)
& VX3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__14,VX15] :
( cType___24t(Vvar__0__A__14)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__14,VX15)
=> ( ? [Vvar__1___24Anonymous__17] :
( t(Vvar__1___24Anonymous__17,Vvar__0__A__14)
& VX15 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__14,Vvar__1___24Anonymous__17) )
| VX15 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__14) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__997,Vvar__1__B__998,VX999] :
( cType___24t(Vvar__0__A__997)
=> ( cType___24t(Vvar__1__B__998)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__997,Vvar__1__B__998,VX999)
=> ? [Vvar__2___24Anonymous__1002] :
( t(Vvar__2___24Anonymous__1002,Vvar__0__A__997)
& ? [Vvar__3___24Anonymous__1003] :
( t(Vvar__3___24Anonymous__1003,Vvar__1__B__998)
& VX999 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__997,Vvar__1__B__998,Vvar__2___24Anonymous__1002,Vvar__3___24Anonymous__1003) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__967,Vvar__1__B__968,VX969] :
( cType___24t(Vvar__0__A__967)
=> ( cType___24t(Vvar__1__B__968)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__967,Vvar__1__B__968,VX969)
=> ( ? [Vvar__2___24Anonymous__972] :
( t(Vvar__2___24Anonymous__972,Vvar__0__A__967)
& VX969 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__967,Vvar__1__B__968,Vvar__2___24Anonymous__972) )
| ? [Vvar__2___24Anonymous__975] :
( t(Vvar__2___24Anonymous__975,Vvar__1__B__968)
& VX969 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__967,Vvar__1__B__968,Vvar__2___24Anonymous__975) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX966] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX966)
=> VX966 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__149,Vvar__1___24Anonymous__150] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__149)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__150)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__149,Vvar__1___24Anonymous__150))
=> ( Vvar__1___24Anonymous__150 = Vvar__0__n__149
| ? [Vvar__1__m__154] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__154)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__149,Vvar__1__m__154))
& Vvar__1___24Anonymous__150 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__154) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__881,Vvar__1__P__882,VX885] :
( cType___24t(Vvar__0__A__881)
=> ( c_24__type__895___24t(Vvar__0__A__881,Vvar__1__P__882,Vvar__1__P__882)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__881,Vvar__1__P__882,VX885)
=> ? [Vvar__2__x__890] :
( t(Vvar__2__x__890,Vvar__0__A__881)
& p(happ(Vvar__1__P__882,Vvar__2__x__890))
& VX885 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__881,Vvar__1__P__882,Vvar__2__x__890) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__920,Vvar__1__P__921,VX924] :
( cType___24t(Vvar__0__A__920)
=> ( c_24__type__934___24t(Vvar__0__A__920,Vvar__1__P__921,Vvar__1__P__921)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__920,Vvar__1__P__921,VX924)
=> ? [Vvar__2__x__929] :
( t(Vvar__2__x__929,Vvar__0__A__920)
& ? [Vvar__3___24Anonymous__930] :
( t(Vvar__3___24Anonymous__930,happ(Vvar__1__P__921,Vvar__2__x__929))
& VX924 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__920,Vvar__1__P__921,Vvar__2__x__929,Vvar__3___24Anonymous__930) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__25600,Vvar__1__B__25601,VX25602] :
( cProp___24t(Vvar__0__A__25600)
=> ( cProp___24t(Vvar__1__B__25601)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__25600,Vvar__1__B__25601,VX25602)
=> ( ( p(Vvar__0__A__25600)
& VX25602 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__25600,Vvar__1__B__25601) )
| ( p(Vvar__1__B__25601)
& VX25602 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__25600,Vvar__1__B__25601) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__25640,Vvar__1__B__25641,VX25642] :
( cType___24t(Vvar__0__A__25640)
=> ( cProp___24t(Vvar__1__B__25641)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__25640,Vvar__1__B__25641,VX25642)
=> ( ? [Vvar__2___24Anonymous__25645] :
( t(Vvar__2___24Anonymous__25645,Vvar__0__A__25640)
& VX25642 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__25640,Vvar__1__B__25641,Vvar__2___24Anonymous__25645) )
| ( p(Vvar__1__B__25641)
& VX25642 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__25640,Vvar__1__B__25641) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__617,Vvar__1__a__618,Vvar__2___24Anonymous__619,Vvar__3___24Anonymous__620] :
( cType___24t(Vvar__0__A__617)
=> ( t(Vvar__1__a__618,Vvar__0__A__617)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__617,Vvar__2___24Anonymous__619)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__617,Vvar__3___24Anonymous__620)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__617,Vvar__1__a__618,Vvar__2___24Anonymous__619,Vvar__3___24Anonymous__620)
=> ( ? [Vvar__2__l__624] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__617,Vvar__2__l__624)
& Vvar__3___24Anonymous__620 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__617,Vvar__1__a__618,Vvar__2__l__624)
& Vvar__2___24Anonymous__619 = Vvar__2__l__624 )
| ? [Vvar__2__x__627] :
( t(Vvar__2__x__627,Vvar__0__A__617)
& ? [Vvar__3__l__628] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__617,Vvar__3__l__628)
& ? [Vvar__4__l_27__629] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__617,Vvar__4__l_27__629)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__617,Vvar__1__a__618,Vvar__3__l__628,Vvar__4__l_27__629)
& Vvar__3___24Anonymous__620 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__617,Vvar__2__x__627,Vvar__4__l_27__629)
& Vvar__2___24Anonymous__619 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__617,Vvar__2__x__627,Vvar__3__l__628) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__29013,Vvar__1__P__29014,Vvar__2___24Anonymous__29017] :
( cType___24t(Vvar__0__A__29013)
=> ( c_24__type__29037___24t(Vvar__0__A__29013,Vvar__1__P__29014,Vvar__2___24Anonymous__29017,Vvar__1__P__29014)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29013,Vvar__2___24Anonymous__29017)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__29013,Vvar__1__P__29014,Vvar__2___24Anonymous__29017)
=> ( ? [Vvar__2__x__29023] :
( t(Vvar__2__x__29023,Vvar__0__A__29013)
& ? [Vvar__3__l__29024] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29013,Vvar__3__l__29024)
& p(happ(Vvar__1__P__29014,Vvar__2__x__29023))
& Vvar__2___24Anonymous__29017 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29013,Vvar__2__x__29023,Vvar__3__l__29024) ) )
| ? [Vvar__2__x__29030] :
( t(Vvar__2__x__29030,Vvar__0__A__29013)
& ? [Vvar__3__l__29031] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29013,Vvar__3__l__29031)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__29013,Vvar__1__P__29014,Vvar__3__l__29031)
& Vvar__2___24Anonymous__29017 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29013,Vvar__2__x__29030,Vvar__3__l__29031) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__1461,Vvar__1__P__1462,Vvar__2___24Anonymous__1465] :
( cType___24t(Vvar__0__A__1461)
=> ( c_24__type__1483___24t(Vvar__0__A__1461,Vvar__1__P__1462,Vvar__2___24Anonymous__1465,Vvar__1__P__1462)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1461,Vvar__2___24Anonymous__1465)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__1461,Vvar__1__P__1462,Vvar__2___24Anonymous__1465)
=> ( Vvar__2___24Anonymous__1465 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1461)
| ? [Vvar__2__x__1475] :
( t(Vvar__2__x__1475,Vvar__0__A__1461)
& ? [Vvar__3__l__1476] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1461,Vvar__3__l__1476)
& p(happ(Vvar__1__P__1462,Vvar__2__x__1475))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__1461,Vvar__1__P__1462,Vvar__3__l__1476)
& Vvar__2___24Anonymous__1465 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1461,Vvar__2__x__1475,Vvar__3__l__1476) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__651,Vvar__1__B__652,Vvar__2__R__653,Vvar__3___24Anonymous__658,Vvar__4___24Anonymous__659] :
( cType___24t(Vvar__0__A__651)
=> ( cType___24t(Vvar__1__B__652)
=> ( c_24__type__696___24t(Vvar__0__A__651,Vvar__1__B__652,Vvar__2__R__653,Vvar__3___24Anonymous__658,Vvar__4___24Anonymous__659,Vvar__2__R__653)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__651,Vvar__3___24Anonymous__658)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__652,Vvar__4___24Anonymous__659)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__651,Vvar__1__B__652,Vvar__2__R__653,Vvar__3___24Anonymous__658,Vvar__4___24Anonymous__659)
=> ( ( Vvar__4___24Anonymous__659 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__652)
& Vvar__3___24Anonymous__658 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__651) )
| ? [Vvar__3__x__675] :
( t(Vvar__3__x__675,Vvar__0__A__651)
& ? [Vvar__4__y__676] :
( t(Vvar__4__y__676,Vvar__1__B__652)
& ? [Vvar__5__l__677] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__651,Vvar__5__l__677)
& ? [Vvar__6__l_27__678] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__652,Vvar__6__l_27__678)
& p(happ(happ(Vvar__2__R__653,Vvar__3__x__675),Vvar__4__y__676))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__651,Vvar__1__B__652,Vvar__2__R__653,Vvar__5__l__677,Vvar__6__l_27__678)
& Vvar__4___24Anonymous__659 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__652,Vvar__4__y__676,Vvar__6__l_27__678)
& Vvar__3___24Anonymous__658 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__651,Vvar__3__x__675,Vvar__5__l__677) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__1491,Vvar__1__R__1492,Vvar__2___24Anonymous__1497] :
( cType___24t(Vvar__0__A__1491)
=> ( c_24__type__1524___24t(Vvar__0__A__1491,Vvar__1__R__1492,Vvar__2___24Anonymous__1497,Vvar__1__R__1492)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1491,Vvar__2___24Anonymous__1497)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__1491,Vvar__1__R__1492,Vvar__2___24Anonymous__1497)
=> ( Vvar__2___24Anonymous__1497 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1491)
| ? [Vvar__2__a__1511] :
( t(Vvar__2__a__1511,Vvar__0__A__1491)
& ? [Vvar__3__l__1512] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1491,Vvar__3__l__1512)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__1491,happ(Vvar__1__R__1492,Vvar__2__a__1511),Vvar__3__l__1512)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__1491,Vvar__1__R__1492,Vvar__3__l__1512)
& Vvar__2___24Anonymous__1497 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1491,Vvar__2__a__1511,Vvar__3__l__1512) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__642,Vvar__1___24Anonymous__643] :
( cType___24t(Vvar__0__A__642)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__642,Vvar__1___24Anonymous__643)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__642,Vvar__1___24Anonymous__643))
=> ( Vvar__1___24Anonymous__643 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__642)
| ? [Vvar__1__x__647] :
( t(Vvar__1__x__647,Vvar__0__A__642)
& ? [Vvar__2__l__648] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__642,Vvar__2__l__648)
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__642,Vvar__1__x__647,Vvar__2__l__648))
& p(cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__642,Vvar__2__l__648))
& Vvar__1___24Anonymous__643 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__642,Vvar__1__x__647,Vvar__2__l__648) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__758,Vvar__1__eqA__759,Vvar__2__x__764,Vvar__3___24Anonymous__765] :
( cType___24t(Vvar__0__A__758)
=> ( c_24__type__798___24t(Vvar__0__A__758,Vvar__1__eqA__759,Vvar__2__x__764,Vvar__3___24Anonymous__765,Vvar__1__eqA__759)
=> ( t(Vvar__2__x__764,Vvar__0__A__758)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__758,Vvar__3___24Anonymous__765)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__758,Vvar__1__eqA__759,Vvar__2__x__764,Vvar__3___24Anonymous__765)
=> ( ? [Vvar__3__y__774] :
( t(Vvar__3__y__774,Vvar__0__A__758)
& ? [Vvar__4__l__775] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__758,Vvar__4__l__775)
& p(happ(happ(Vvar__1__eqA__759,Vvar__2__x__764),Vvar__3__y__774))
& Vvar__3___24Anonymous__765 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__758,Vvar__3__y__774,Vvar__4__l__775) ) )
| ? [Vvar__3__y__784] :
( t(Vvar__3__y__784,Vvar__0__A__758)
& ? [Vvar__4__l__785] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__758,Vvar__4__l__785)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__758,Vvar__1__eqA__759,Vvar__2__x__764,Vvar__4__l__785)
& Vvar__3___24Anonymous__765 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__758,Vvar__3__y__784,Vvar__4__l__785) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__2780,Vvar__1__eqA__2781,Vvar__2___24Anonymous__2786] :
( cType___24t(Vvar__0__A__2780)
=> ( c_24__type__2813___24t(Vvar__0__A__2780,Vvar__1__eqA__2781,Vvar__2___24Anonymous__2786,Vvar__1__eqA__2781)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2780,Vvar__2___24Anonymous__2786)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__2780,Vvar__1__eqA__2781,Vvar__2___24Anonymous__2786)
=> ( Vvar__2___24Anonymous__2786 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2780)
| ? [Vvar__2__x__2800] :
( t(Vvar__2__x__2800,Vvar__0__A__2780)
& ? [Vvar__3__l__2801] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2780,Vvar__3__l__2801)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__2780,Vvar__1__eqA__2781,Vvar__2__x__2800,Vvar__3__l__2801)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__2780,Vvar__1__eqA__2781,Vvar__3__l__2801)
& Vvar__2___24Anonymous__2786 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2780,Vvar__2__x__2800,Vvar__3__l__2801) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__2818,Vvar__1__eqA__2819,Vvar__2___24Anonymous__2824,Vvar__3___24Anonymous__2825] :
( cType___24t(Vvar__0__A__2818)
=> ( c_24__type__2856___24t(Vvar__0__A__2818,Vvar__1__eqA__2819,Vvar__2___24Anonymous__2824,Vvar__3___24Anonymous__2825,Vvar__1__eqA__2819)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2818,Vvar__2___24Anonymous__2824)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2818,Vvar__3___24Anonymous__2825)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__2818,Vvar__1__eqA__2819,Vvar__2___24Anonymous__2824,Vvar__3___24Anonymous__2825)
=> ( ( Vvar__3___24Anonymous__2825 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2818)
& Vvar__2___24Anonymous__2824 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2818) )
| ? [Vvar__2__x__2839] :
( t(Vvar__2__x__2839,Vvar__0__A__2818)
& ? [Vvar__3__x_27__2840] :
( t(Vvar__3__x_27__2840,Vvar__0__A__2818)
& ? [Vvar__4__l__2841] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2818,Vvar__4__l__2841)
& ? [Vvar__5__l_27__2842] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2818,Vvar__5__l_27__2842)
& p(happ(happ(Vvar__1__eqA__2819,Vvar__2__x__2839),Vvar__3__x_27__2840))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__2818,Vvar__1__eqA__2819,Vvar__4__l__2841,Vvar__5__l_27__2842)
& Vvar__3___24Anonymous__2825 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2818,Vvar__3__x_27__2840,Vvar__5__l_27__2842)
& Vvar__2___24Anonymous__2824 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2818,Vvar__2__x__2839,Vvar__4__l__2841) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX961] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX961)
=> ( VX961 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__962] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__962)
& VX961 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__962) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX4845] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX4845)
=> ( VX4845 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__4846] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4846)
& VX4845 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4846) )
| ? [Vvar__0___24Anonymous__4847] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4847)
& VX4845 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4847) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX4824] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX4824)
=> ( ? [Vvar__0___24Anonymous__4825] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4825)
& VX4824 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4825) )
| ? [Vvar__0___24Anonymous__4826] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4826)
& VX4824 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__4826) )
| VX4824 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX64363] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX64363)
=> ( VX64363 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__64364] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64364)
& VX64363 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__64364) )
| VX64363 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX17766] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX17766)
=> ? [Vvar__0__Qnum__17767] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__17767)
& ? [Vvar__1__Qden__17768] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__17768)
& VX17766 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__17767,Vvar__1__Qden__17768) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__1601,Vvar__1__leA__1602,Vvar__2___24Anonymous__1607] :
( cType___24t(Vvar__0__A__1601)
=> ( c_24__type__1697___24t(Vvar__0__A__1601,Vvar__1__leA__1602,Vvar__2___24Anonymous__1607,Vvar__1__leA__1602)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1601,Vvar__2___24Anonymous__1607)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__1601,Vvar__1__leA__1602,Vvar__2___24Anonymous__1607)
=> ( Vvar__2___24Anonymous__1607 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1601)
| ? [Vvar__2__x__1621] :
( t(Vvar__2__x__1621,Vvar__0__A__1601)
& Vvar__2___24Anonymous__1607 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1601,Vvar__2__x__1621,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1601)) )
| ? [Vvar__2__x__1628] :
( t(Vvar__2__x__1628,Vvar__0__A__1601)
& ? [Vvar__3__y__1629] :
( t(Vvar__3__y__1629,Vvar__0__A__1601)
& ? [Vvar__4__l__1630] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1601,Vvar__4__l__1630)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__1601,Vvar__1__leA__1602,Vvar__2__x__1628,Vvar__3__y__1629)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__1601,Vvar__1__leA__1602,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__1601,Vvar__4__l__1630,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1601,Vvar__3__y__1629,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1601))))
& Vvar__2___24Anonymous__1607 = c_24__case__Coq_2eInit_2eDatatypes_2elist_241895___24a6(Vvar__0__A__1601,Vvar__1__leA__1602,Vvar__2___24Anonymous__1607,Vvar__2__x__1628,Vvar__3__y__1629,Vvar__4__l__1630) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__30316,Vvar__1__leA__30317,Vvar__2___24Anonymous__30322,Vvar__3___24Anonymous__30323] :
( cType___24t(Vvar__0__A__30316)
=> ( c_24__type__30365___24t(Vvar__0__A__30316,Vvar__1__leA__30317,Vvar__2___24Anonymous__30322,Vvar__3___24Anonymous__30323,Vvar__1__leA__30317)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30316,Vvar__2___24Anonymous__30322)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30316,Vvar__3___24Anonymous__30323)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__30316,Vvar__1__leA__30317,Vvar__2___24Anonymous__30322,Vvar__3___24Anonymous__30323)
=> ( ? [Vvar__2__a__30331] :
( t(Vvar__2__a__30331,Vvar__0__A__30316)
& ? [Vvar__3__x__30332] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30316,Vvar__3__x__30332)
& Vvar__3___24Anonymous__30323 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30316,Vvar__2__a__30331,Vvar__3__x__30332)
& Vvar__2___24Anonymous__30322 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30316) ) )
| ? [Vvar__2__a__30339] :
( t(Vvar__2__a__30339,Vvar__0__A__30316)
& ? [Vvar__3__b__30340] :
( t(Vvar__3__b__30340,Vvar__0__A__30316)
& p(happ(happ(Vvar__1__leA__30317,Vvar__2__a__30339),Vvar__3__b__30340))
& ? [Vvar__5__x__30342] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30316,Vvar__5__x__30342)
& ? [Vvar__6__y__30343] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30316,Vvar__6__y__30343)
& Vvar__3___24Anonymous__30323 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30316,Vvar__3__b__30340,Vvar__6__y__30343)
& Vvar__2___24Anonymous__30322 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30316,Vvar__2__a__30339,Vvar__5__x__30342) ) ) ) )
| ? [Vvar__2__a__30350] :
( t(Vvar__2__a__30350,Vvar__0__A__30316)
& ? [Vvar__3__x__30351] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30316,Vvar__3__x__30351)
& ? [Vvar__4__y__30352] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30316,Vvar__4__y__30352)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__30316,Vvar__1__leA__30317,Vvar__3__x__30351,Vvar__4__y__30352)
& Vvar__3___24Anonymous__30323 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30316,Vvar__2__a__30350,Vvar__4__y__30352)
& Vvar__2___24Anonymous__30322 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30316,Vvar__2__a__30350,Vvar__3__x__30351) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__1588,Vvar__1__R__1589,Vvar__2__x__1590,Vvar__3___24Anonymous__1591] :
( cType___24t(Vvar__0__A__1588)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__1588,Vvar__1__R__1589)
=> ( t(Vvar__2__x__1590,Vvar__0__A__1588)
=> ( t(Vvar__3___24Anonymous__1591,Vvar__0__A__1588)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__1588,Vvar__1__R__1589,Vvar__2__x__1590,Vvar__3___24Anonymous__1591)
=> ( ? [Vvar__3__y__1596] :
( t(Vvar__3__y__1596,Vvar__0__A__1588)
& p(happ(happ(Vvar__1__R__1589,Vvar__2__x__1590),Vvar__3__y__1596))
& Vvar__3___24Anonymous__1591 = Vvar__3__y__1596 )
| Vvar__3___24Anonymous__1591 = Vvar__2__x__1590 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Permutation.Permutation',axiom,
! [Vvar__0__A__720,Vvar__1___24Anonymous__721,Vvar__2___24Anonymous__722] :
( cType___24t(Vvar__0__A__720)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__720,Vvar__1___24Anonymous__721)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__720,Vvar__2___24Anonymous__722)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__720,Vvar__1___24Anonymous__721,Vvar__2___24Anonymous__722)
=> ( ( Vvar__2___24Anonymous__722 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__720)
& Vvar__1___24Anonymous__721 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__720) )
| ? [Vvar__1__x__726] :
( t(Vvar__1__x__726,Vvar__0__A__720)
& ? [Vvar__2__l__727] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__720,Vvar__2__l__727)
& ? [Vvar__3__l_27__728] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__720,Vvar__3__l_27__728)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__720,Vvar__2__l__727,Vvar__3__l_27__728)
& Vvar__2___24Anonymous__722 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__720,Vvar__1__x__726,Vvar__3__l_27__728)
& Vvar__1___24Anonymous__721 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__720,Vvar__1__x__726,Vvar__2__l__727) ) ) )
| ? [Vvar__1__x__731] :
( t(Vvar__1__x__731,Vvar__0__A__720)
& ? [Vvar__2__y__732] :
( t(Vvar__2__y__732,Vvar__0__A__720)
& ? [Vvar__3__l__733] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__720,Vvar__3__l__733)
& Vvar__2___24Anonymous__722 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__720,Vvar__1__x__731,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__720,Vvar__2__y__732,Vvar__3__l__733))
& Vvar__1___24Anonymous__721 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__720,Vvar__2__y__732,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__720,Vvar__1__x__731,Vvar__3__l__733)) ) ) )
| ? [Vvar__1__l__735] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__720,Vvar__1__l__735)
& ? [Vvar__2__l_27__736] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__720,Vvar__2__l_27__736)
& ? [Vvar__3__l_27_27__737] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__720,Vvar__3__l_27_27__737)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__720,Vvar__1__l__735,Vvar__2__l_27__736)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__720,Vvar__2__l_27__736,Vvar__3__l_27_27__737)
& Vvar__2___24Anonymous__722 = Vvar__3__l_27_27__737
& Vvar__1___24Anonymous__721 = Vvar__1__l__735 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__298,Vvar__1__R__299,Vvar__2__a__304,Vvar__3___24Anonymous__305] :
( cType___24t(Vvar__0__A__298)
=> ( c_24__type__335___24t(Vvar__0__A__298,Vvar__1__R__299,Vvar__2__a__304,Vvar__3___24Anonymous__305,Vvar__1__R__299)
=> ( t(Vvar__2__a__304,Vvar__0__A__298)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__298,Vvar__3___24Anonymous__305)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__298,Vvar__1__R__299,Vvar__2__a__304,Vvar__3___24Anonymous__305)
=> ( Vvar__3___24Anonymous__305 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__298)
| ? [Vvar__3__b__321] :
( t(Vvar__3__b__321,Vvar__0__A__298)
& ? [Vvar__4__l__322] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__298,Vvar__4__l__322)
& p(happ(happ(Vvar__1__R__299,Vvar__2__a__304),Vvar__3__b__321))
& Vvar__3___24Anonymous__305 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__298,Vvar__3__b__321,Vvar__4__l__322) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__36416,Vvar__1__R__36417,Vvar__2___24Anonymous__36422] :
( cType___24t(Vvar__0__A__36416)
=> ( c_24__type__36457___24t(Vvar__0__A__36416,Vvar__1__R__36417,Vvar__2___24Anonymous__36422,Vvar__1__R__36417)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36416,Vvar__2___24Anonymous__36422)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__36416,Vvar__1__R__36417,Vvar__2___24Anonymous__36422)
=> ( Vvar__2___24Anonymous__36422 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36416)
| ? [Vvar__2__a__36436] :
( t(Vvar__2__a__36436,Vvar__0__A__36416)
& Vvar__2___24Anonymous__36422 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36416,Vvar__2__a__36436,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36416)) )
| ? [Vvar__2__a__36443] :
( t(Vvar__2__a__36443,Vvar__0__A__36416)
& ? [Vvar__3__b__36444] :
( t(Vvar__3__b__36444,Vvar__0__A__36416)
& ? [Vvar__4__l__36445] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36416,Vvar__4__l__36445)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__36416,Vvar__1__R__36417,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36416,Vvar__3__b__36444,Vvar__4__l__36445))
& p(happ(happ(Vvar__1__R__36417,Vvar__2__a__36443),Vvar__3__b__36444))
& Vvar__2___24Anonymous__36422 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36416,Vvar__2__a__36443,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36416,Vvar__3__b__36444,Vvar__4__l__36445)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__337,Vvar__1__R__338,Vvar__2___24Anonymous__343] :
( cType___24t(Vvar__0__A__337)
=> ( c_24__type__370___24t(Vvar__0__A__337,Vvar__1__R__338,Vvar__2___24Anonymous__343,Vvar__1__R__338)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__337,Vvar__2___24Anonymous__343)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__337,Vvar__1__R__338,Vvar__2___24Anonymous__343)
=> ( Vvar__2___24Anonymous__343 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__337)
| ? [Vvar__2__a__357] :
( t(Vvar__2__a__357,Vvar__0__A__337)
& ? [Vvar__3__l__358] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__337,Vvar__3__l__358)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__337,Vvar__1__R__338,Vvar__3__l__358)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__337,Vvar__1__R__338,Vvar__2__a__357,Vvar__3__l__358)
& Vvar__2___24Anonymous__343 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__337,Vvar__2__a__357,Vvar__3__l__358) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__36459,Vvar__1__R__36460,Vvar__2___24Anonymous__36465] :
( cType___24t(Vvar__0__A__36459)
=> ( c_24__type__36492___24t(Vvar__0__A__36459,Vvar__1__R__36460,Vvar__2___24Anonymous__36465,Vvar__1__R__36460)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36459,Vvar__2___24Anonymous__36465)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__36459,Vvar__1__R__36460,Vvar__2___24Anonymous__36465)
=> ( Vvar__2___24Anonymous__36465 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36459)
| ? [Vvar__2__a__36479] :
( t(Vvar__2__a__36479,Vvar__0__A__36459)
& ? [Vvar__3__l__36480] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36459,Vvar__3__l__36480)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__36459,Vvar__1__R__36460,Vvar__3__l__36480)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__36459,happ(Vvar__1__R__36460,Vvar__2__a__36479),Vvar__3__l__36480)
& Vvar__2___24Anonymous__36465 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36459,Vvar__2__a__36479,Vvar__3__l__36480) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX4766] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX4766)
=> ? [Vvar__0___24Anonymous__4767] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__4767)
& ? [Vvar__1___24Anonymous__4768] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__4768)
& ? [Vvar__2___24Anonymous__4769] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__4769)
& ? [Vvar__3___24Anonymous__4770] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__4770)
& ? [Vvar__4___24Anonymous__4771] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__4771)
& ? [Vvar__5___24Anonymous__4772] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__4772)
& ? [Vvar__6___24Anonymous__4773] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__4773)
& ? [Vvar__7___24Anonymous__4774] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__4774)
& VX4766 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4767,Vvar__1___24Anonymous__4768,Vvar__2___24Anonymous__4769,Vvar__3___24Anonymous__4770,Vvar__4___24Anonymous__4771,Vvar__5___24Anonymous__4772,Vvar__6___24Anonymous__4773,Vvar__7___24Anonymous__4774) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX36500] :
( cCoq_2eStrings_2eString_2estring___24t(VX36500)
=> ( VX36500 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__36501] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__36501)
& ? [Vvar__1___24Anonymous__36502] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__36502)
& VX36500 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__36501,Vvar__1___24Anonymous__36502) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX45536] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX45536)
=> ( VX45536 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX45536 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX45536 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__25743,Vvar__1___24Anonymous__25744,VX25745] :
( cType___24t(Vvar__0__A__25743)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__25744)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__25743,Vvar__1___24Anonymous__25744,VX25745)
=> ( ( Vvar__1___24Anonymous__25744 = cCoq_2eInit_2eDatatypes_2eO
& VX25745 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__25743) )
| ? [Vvar__1__h__25748] :
( t(Vvar__1__h__25748,Vvar__0__A__25743)
& ? [Vvar__2__n__25749] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__25749)
& ? [Vvar__3___24Anonymous__25750] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__25743,Vvar__2__n__25749,Vvar__3___24Anonymous__25750)
& Vvar__1___24Anonymous__25744 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__25749)
& VX25745 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__25743,Vvar__1__h__25748,Vvar__2__n__25749,Vvar__3___24Anonymous__25750) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX27224] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX27224)
=> ( VX27224 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__27225] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27225)
& ? [Vvar__1___24Anonymous__27226] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__27226)
& VX27224 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__27225,Vvar__1___24Anonymous__27226) ) )
| ? [Vvar__0___24Anonymous__27227] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27227)
& ? [Vvar__1___24Anonymous__27228] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__27228)
& VX27224 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__27227,Vvar__1___24Anonymous__27228) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__27060,VX27061] :
( cType___24t(Vvar__0__C__27060)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__27060,VX27061)
=> ( ? [Vvar__1___24Anonymous__27063] :
( t(Vvar__1___24Anonymous__27063,Vvar__0__C__27060)
& VX27061 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__27060,Vvar__1___24Anonymous__27063) )
| ? [Vvar__1___24Anonymous__27065] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__27065)
& VX27061 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__27060,Vvar__1___24Anonymous__27065) )
| ? [Vvar__1___24Anonymous__27067] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__27060,Vvar__1___24Anonymous__27067)
& ? [Vvar__2___24Anonymous__27068] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__27060,Vvar__2___24Anonymous__27068)
& VX27061 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__27060,Vvar__1___24Anonymous__27067,Vvar__2___24Anonymous__27068) ) )
| ? [Vvar__1___24Anonymous__27070] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__27060,Vvar__1___24Anonymous__27070)
& ? [Vvar__2___24Anonymous__27071] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__27060,Vvar__2___24Anonymous__27071)
& VX27061 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__27060,Vvar__1___24Anonymous__27070,Vvar__2___24Anonymous__27071) ) )
| ? [Vvar__1___24Anonymous__27073] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__27060,Vvar__1___24Anonymous__27073)
& ? [Vvar__2___24Anonymous__27074] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__27060,Vvar__2___24Anonymous__27074)
& VX27061 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__27060,Vvar__1___24Anonymous__27073,Vvar__2___24Anonymous__27074) ) )
| ? [Vvar__1___24Anonymous__27076] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__27060,Vvar__1___24Anonymous__27076)
& VX27061 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__27060,Vvar__1___24Anonymous__27076) )
| ? [Vvar__1___24Anonymous__27078] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__27060,Vvar__1___24Anonymous__27078)
& ? [Vvar__2___24Anonymous__27079] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__27079)
& VX27061 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__27060,Vvar__1___24Anonymous__27078,Vvar__2___24Anonymous__27079) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__1021,VX1022] :
( cType___24t(Vvar__0__C__1021)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__1021,VX1022)
=> ( ? [Vvar__1___24Anonymous__1024] :
( t(Vvar__1___24Anonymous__1024,Vvar__0__C__1021)
& VX1022 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__1021,Vvar__1___24Anonymous__1024) )
| ? [Vvar__1___24Anonymous__1026] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1026)
& ? [Vvar__2___24Anonymous__1027] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__1021,Vvar__2___24Anonymous__1027)
& VX1022 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__1021,Vvar__1___24Anonymous__1026,Vvar__2___24Anonymous__1027) ) )
| ? [Vvar__1___24Anonymous__1029] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__1021,Vvar__1___24Anonymous__1029)
& ? [Vvar__2___24Anonymous__1030] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1030)
& ? [Vvar__3___24Anonymous__1031] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__1021,Vvar__3___24Anonymous__1031)
& VX1022 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__1021,Vvar__1___24Anonymous__1029,Vvar__2___24Anonymous__1030,Vvar__3___24Anonymous__1031) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__29065,Vvar__1__rO__29066,Vvar__2__rI__29067,Vvar__3__rplus__29068,Vvar__4__rtimes__29073,Vvar__5__rminus__29078,Vvar__6__ropp__29083,Vvar__7__req__29086,Vvar__8__rle__29091,Vvar__9__rlt__29096] :
( cType___24t(Vvar__0__R__29065)
=> ( t(Vvar__1__rO__29066,Vvar__0__R__29065)
=> ( t(Vvar__2__rI__29067,Vvar__0__R__29065)
=> ( c_24__type__29497___24t(Vvar__0__R__29065,Vvar__1__rO__29066,Vvar__2__rI__29067,Vvar__3__rplus__29068,Vvar__4__rtimes__29073,Vvar__5__rminus__29078,Vvar__6__ropp__29083,Vvar__7__req__29086,Vvar__8__rle__29091,Vvar__9__rlt__29096,Vvar__3__rplus__29068)
=> ( c_24__type__29598___24t(Vvar__0__R__29065,Vvar__1__rO__29066,Vvar__2__rI__29067,Vvar__3__rplus__29068,Vvar__4__rtimes__29073,Vvar__5__rminus__29078,Vvar__6__ropp__29083,Vvar__7__req__29086,Vvar__8__rle__29091,Vvar__9__rlt__29096,Vvar__4__rtimes__29073)
=> ( c_24__type__29699___24t(Vvar__0__R__29065,Vvar__1__rO__29066,Vvar__2__rI__29067,Vvar__3__rplus__29068,Vvar__4__rtimes__29073,Vvar__5__rminus__29078,Vvar__6__ropp__29083,Vvar__7__req__29086,Vvar__8__rle__29091,Vvar__9__rlt__29096,Vvar__5__rminus__29078)
=> ( c_24__type__29789___24t(Vvar__0__R__29065,Vvar__1__rO__29066,Vvar__2__rI__29067,Vvar__3__rplus__29068,Vvar__4__rtimes__29073,Vvar__5__rminus__29078,Vvar__6__ropp__29083,Vvar__7__req__29086,Vvar__8__rle__29091,Vvar__9__rlt__29096,Vvar__6__ropp__29083)
=> ( c_24__type__29890___24t(Vvar__0__R__29065,Vvar__1__rO__29066,Vvar__2__rI__29067,Vvar__3__rplus__29068,Vvar__4__rtimes__29073,Vvar__5__rminus__29078,Vvar__6__ropp__29083,Vvar__7__req__29086,Vvar__8__rle__29091,Vvar__9__rlt__29096,Vvar__7__req__29086)
=> ( c_24__type__29991___24t(Vvar__0__R__29065,Vvar__1__rO__29066,Vvar__2__rI__29067,Vvar__3__rplus__29068,Vvar__4__rtimes__29073,Vvar__5__rminus__29078,Vvar__6__ropp__29083,Vvar__7__req__29086,Vvar__8__rle__29091,Vvar__9__rlt__29096,Vvar__8__rle__29091)
=> ( c_24__type__30092___24t(Vvar__0__R__29065,Vvar__1__rO__29066,Vvar__2__rI__29067,Vvar__3__rplus__29068,Vvar__4__rtimes__29073,Vvar__5__rminus__29078,Vvar__6__ropp__29083,Vvar__7__req__29086,Vvar__8__rle__29091,Vvar__9__rlt__29096,Vvar__9__rlt__29096)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__29065,Vvar__1__rO__29066,Vvar__2__rI__29067,Vvar__3__rplus__29068,Vvar__4__rtimes__29073,Vvar__5__rminus__29078,Vvar__6__ropp__29083,Vvar__7__req__29086,Vvar__8__rle__29091,Vvar__9__rlt__29096)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__29065,Vvar__7__req__29086)
& ! [Vvar__var__var__var__var__11__x1__29140__29146__29251__29257__29263] :
( t(Vvar__var__var__var__var__11__x1__29140__29146__29251__29257__29263,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__12__x2__29141__29147__29252__29258__29264] :
( t(Vvar__var__var__var__var__12__x2__29141__29147__29252__29258__29264,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__7__req__29086,Vvar__var__var__var__var__11__x1__29140__29146__29251__29257__29263),Vvar__var__var__var__var__12__x2__29141__29147__29252__29258__29264))
=> ! [Vvar__var__var__var__var__14__y1__29142__29148__29253__29259__29265] :
( t(Vvar__var__var__var__var__14__y1__29142__29148__29253__29259__29265,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__15__y2__29143__29149__29254__29260__29266] :
( t(Vvar__var__var__var__var__15__y2__29143__29149__29254__29260__29266,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__7__req__29086,Vvar__var__var__var__var__14__y1__29142__29148__29253__29259__29265),Vvar__var__var__var__var__15__y2__29143__29149__29254__29260__29266))
=> p(happ(happ(Vvar__7__req__29086,happ(happ(Vvar__3__rplus__29068,Vvar__var__var__var__var__11__x1__29140__29146__29251__29257__29263),Vvar__var__var__var__var__14__y1__29142__29148__29253__29259__29265)),happ(happ(Vvar__3__rplus__29068,Vvar__var__var__var__var__12__x2__29141__29147__29252__29258__29264),Vvar__var__var__var__var__15__y2__29143__29149__29254__29260__29266))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__29153__29159__29269__29275__29281] :
( t(Vvar__var__var__var__var__12__x1__29153__29159__29269__29275__29281,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__13__x2__29154__29160__29270__29276__29282] :
( t(Vvar__var__var__var__var__13__x2__29154__29160__29270__29276__29282,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__7__req__29086,Vvar__var__var__var__var__12__x1__29153__29159__29269__29275__29281),Vvar__var__var__var__var__13__x2__29154__29160__29270__29276__29282))
=> ! [Vvar__var__var__var__var__15__y1__29155__29161__29271__29277__29283] :
( t(Vvar__var__var__var__var__15__y1__29155__29161__29271__29277__29283,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__16__y2__29156__29162__29272__29278__29284] :
( t(Vvar__var__var__var__var__16__y2__29156__29162__29272__29278__29284,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__7__req__29086,Vvar__var__var__var__var__15__y1__29155__29161__29271__29277__29283),Vvar__var__var__var__var__16__y2__29156__29162__29272__29278__29284))
=> p(happ(happ(Vvar__7__req__29086,happ(happ(Vvar__4__rtimes__29073,Vvar__var__var__var__var__12__x1__29153__29159__29269__29275__29281),Vvar__var__var__var__var__15__y1__29155__29161__29271__29277__29283)),happ(happ(Vvar__4__rtimes__29073,Vvar__var__var__var__var__13__x2__29154__29160__29270__29276__29282),Vvar__var__var__var__var__16__y2__29156__29162__29272__29278__29284))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__29166__29169__29287__29290__29293] :
( t(Vvar__var__var__var__var__13__x1__29166__29169__29287__29290__29293,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__14__x2__29167__29170__29288__29291__29294] :
( t(Vvar__var__var__var__var__14__x2__29167__29170__29288__29291__29294,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__7__req__29086,Vvar__var__var__var__var__13__x1__29166__29169__29287__29290__29293),Vvar__var__var__var__var__14__x2__29167__29170__29288__29291__29294))
=> p(happ(happ(Vvar__7__req__29086,happ(Vvar__6__ropp__29083,Vvar__var__var__var__var__13__x1__29166__29169__29287__29290__29293)),happ(Vvar__6__ropp__29083,Vvar__var__var__var__var__14__x2__29167__29170__29288__29291__29294))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__29173__29179__29296__29302__29308] :
( t(Vvar__var__var__var__var__14__x1__29173__29179__29296__29302__29308,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__15__x2__29174__29180__29297__29303__29309] :
( t(Vvar__var__var__var__var__15__x2__29174__29180__29297__29303__29309,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__7__req__29086,Vvar__var__var__var__var__14__x1__29173__29179__29296__29302__29308),Vvar__var__var__var__var__15__x2__29174__29180__29297__29303__29309))
=> ! [Vvar__var__var__var__var__17__y1__29175__29181__29298__29304__29310] :
( t(Vvar__var__var__var__var__17__y1__29175__29181__29298__29304__29310,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__18__y2__29176__29182__29299__29305__29311] :
( t(Vvar__var__var__var__var__18__y2__29176__29182__29299__29305__29311,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__7__req__29086,Vvar__var__var__var__var__17__y1__29175__29181__29298__29304__29310),Vvar__var__var__var__var__18__y2__29176__29182__29299__29305__29311))
=> ( p(happ(happ(Vvar__8__rle__29091,Vvar__var__var__var__var__14__x1__29173__29179__29296__29302__29308),Vvar__var__var__var__var__17__y1__29175__29181__29298__29304__29310))
<=> p(happ(happ(Vvar__8__rle__29091,Vvar__var__var__var__var__15__x2__29174__29180__29297__29303__29309),Vvar__var__var__var__var__18__y2__29176__29182__29299__29305__29311)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__29186__29192__29314__29320__29326] :
( t(Vvar__var__var__var__var__15__x1__29186__29192__29314__29320__29326,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__16__x2__29187__29193__29315__29321__29327] :
( t(Vvar__var__var__var__var__16__x2__29187__29193__29315__29321__29327,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__7__req__29086,Vvar__var__var__var__var__15__x1__29186__29192__29314__29320__29326),Vvar__var__var__var__var__16__x2__29187__29193__29315__29321__29327))
=> ! [Vvar__var__var__var__var__18__y1__29188__29194__29316__29322__29328] :
( t(Vvar__var__var__var__var__18__y1__29188__29194__29316__29322__29328,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__19__y2__29189__29195__29317__29323__29329] :
( t(Vvar__var__var__var__var__19__y2__29189__29195__29317__29323__29329,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__7__req__29086,Vvar__var__var__var__var__18__y1__29188__29194__29316__29322__29328),Vvar__var__var__var__var__19__y2__29189__29195__29317__29323__29329))
=> ( p(happ(happ(Vvar__9__rlt__29096,Vvar__var__var__var__var__15__x1__29186__29192__29314__29320__29326),Vvar__var__var__var__var__18__y1__29188__29194__29316__29322__29328))
<=> p(happ(happ(Vvar__9__rlt__29096,Vvar__var__var__var__var__16__x2__29187__29193__29315__29321__29327),Vvar__var__var__var__var__19__y2__29189__29195__29317__29323__29329)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__29065,Vvar__1__rO__29066,Vvar__2__rI__29067,Vvar__3__rplus__29068,Vvar__4__rtimes__29073,Vvar__5__rminus__29078,Vvar__6__ropp__29083,Vvar__7__req__29086)
& ! [Vvar__var__var__var__17__n__29200__29201__29332__29333] :
( t(Vvar__var__var__var__17__n__29200__29201__29332__29333,Vvar__0__R__29065)
=> p(happ(happ(Vvar__8__rle__29091,Vvar__var__var__var__17__n__29200__29201__29332__29333),Vvar__var__var__var__17__n__29200__29201__29332__29333)) )
& ! [Vvar__var__var__var__var__18__n__29203__29207__29334__29338__29342] :
( t(Vvar__var__var__var__var__18__n__29203__29207__29334__29338__29342,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__19__m__29204__29208__29335__29339__29343] :
( t(Vvar__var__var__var__var__19__m__29204__29208__29335__29339__29343,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__8__rle__29091,Vvar__var__var__var__var__18__n__29203__29207__29334__29338__29342),Vvar__var__var__var__var__19__m__29204__29208__29335__29339__29343))
=> ( p(happ(happ(Vvar__8__rle__29091,Vvar__var__var__var__var__19__m__29204__29208__29335__29339__29343),Vvar__var__var__var__var__18__n__29203__29207__29334__29338__29342))
=> p(happ(happ(Vvar__7__req__29086,Vvar__var__var__var__var__18__n__29203__29207__29334__29338__29342),Vvar__var__var__var__var__19__m__29204__29208__29335__29339__29343)) ) ) ) )
& ! [Vvar__var__var__var__19__n__29212__29217__29346__29351] :
( t(Vvar__var__var__var__19__n__29212__29217__29346__29351,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__20__m__29213__29218__29347__29352] :
( t(Vvar__var__var__var__20__m__29213__29218__29347__29352,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__21__p__29214__29219__29348__29353] :
( t(Vvar__var__var__var__21__p__29214__29219__29348__29353,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__8__rle__29091,Vvar__var__var__var__19__n__29212__29217__29346__29351),Vvar__var__var__var__20__m__29213__29218__29347__29352))
=> ( p(happ(happ(Vvar__8__rle__29091,Vvar__var__var__var__20__m__29213__29218__29347__29352),Vvar__var__var__var__21__p__29214__29219__29348__29353))
=> p(happ(happ(Vvar__8__rle__29091,Vvar__var__var__var__19__n__29212__29217__29346__29351),Vvar__var__var__var__21__p__29214__29219__29348__29353)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__29223__29225__29356__29358__29360__29362] :
( t(Vvar__var__var__var__var__var__20__n__29223__29225__29356__29358__29360__29362,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__var__21__m__29224__29226__29357__29359__29361__29363] :
( t(Vvar__var__var__var__var__var__21__m__29224__29226__29357__29359__29361__29363,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__9__rlt__29096,Vvar__var__var__var__var__var__20__n__29223__29225__29356__29358__29360__29362),Vvar__var__var__var__var__var__21__m__29224__29226__29357__29359__29361__29363))
<=> ( p(happ(happ(Vvar__8__rle__29091,Vvar__var__var__var__var__var__20__n__29223__29225__29356__29358__29360__29362),Vvar__var__var__var__var__var__21__m__29224__29226__29357__29359__29361__29363))
& ~ p(happ(happ(Vvar__7__req__29086,Vvar__var__var__var__var__var__20__n__29223__29225__29356__29358__29360__29362),Vvar__var__var__var__var__var__21__m__29224__29226__29357__29359__29361__29363)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__29228__29230__29364__29366__29368] :
( t(Vvar__var__var__var__var__21__n__29228__29230__29364__29366__29368,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__22__m__29229__29231__29365__29367__29369] :
( t(Vvar__var__var__var__var__22__m__29229__29231__29365__29367__29369,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__9__rlt__29096,Vvar__var__var__var__var__21__n__29228__29230__29364__29366__29368),Vvar__var__var__var__var__22__m__29229__29231__29365__29367__29369))
| p(happ(happ(Vvar__7__req__29086,Vvar__var__var__var__var__21__n__29228__29230__29364__29366__29368),Vvar__var__var__var__var__22__m__29229__29231__29365__29367__29369))
| p(happ(happ(Vvar__9__rlt__29096,Vvar__var__var__var__var__22__m__29229__29231__29365__29367__29369),Vvar__var__var__var__var__21__n__29228__29230__29364__29366__29368)) ) ) )
& ! [Vvar__var__var__var__var__22__n__29233__29237__29370__29374__29378] :
( t(Vvar__var__var__var__var__22__n__29233__29237__29370__29374__29378,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__23__m__29234__29238__29371__29375__29379] :
( t(Vvar__var__var__var__var__23__m__29234__29238__29371__29375__29379,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__24__p__29235__29239__29372__29376__29380] :
( t(Vvar__var__var__var__var__24__p__29235__29239__29372__29376__29380,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__8__rle__29091,Vvar__var__var__var__var__22__n__29233__29237__29370__29374__29378),Vvar__var__var__var__var__23__m__29234__29238__29371__29375__29379))
=> p(happ(happ(Vvar__8__rle__29091,happ(happ(Vvar__3__rplus__29068,Vvar__var__var__var__var__24__p__29235__29239__29372__29376__29380),Vvar__var__var__var__var__22__n__29233__29237__29370__29374__29378)),happ(happ(Vvar__3__rplus__29068,Vvar__var__var__var__var__24__p__29235__29239__29372__29376__29380),Vvar__var__var__var__var__23__m__29234__29238__29371__29375__29379))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__29242__29246__29382__29386__29390__29394] :
( t(Vvar__var__var__var__var__var__23__n__29242__29246__29382__29386__29390__29394,Vvar__0__R__29065)
=> ! [Vvar__var__var__var__var__var__24__m__29243__29247__29383__29387__29391__29395] :
( t(Vvar__var__var__var__var__var__24__m__29243__29247__29383__29387__29391__29395,Vvar__0__R__29065)
=> ( p(happ(happ(Vvar__9__rlt__29096,Vvar__1__rO__29066),Vvar__var__var__var__var__var__23__n__29242__29246__29382__29386__29390__29394))
=> ( p(happ(happ(Vvar__9__rlt__29096,Vvar__1__rO__29066),Vvar__var__var__var__var__var__24__m__29243__29247__29383__29387__29391__29395))
=> p(happ(happ(Vvar__9__rlt__29096,Vvar__1__rO__29066),happ(happ(Vvar__4__rtimes__29073,Vvar__var__var__var__var__var__23__n__29242__29246__29382__29386__29390__29394),Vvar__var__var__var__var__var__24__m__29243__29247__29383__29387__29391__29395))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__29086,Vvar__1__rO__29066),Vvar__2__rI__29067))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX30146] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX30146)
=> ( VX30146 = cCoq_2emicromega_2eRMicromega_2eC0
| VX30146 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__30147] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__30147)
& VX30146 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__30147) )
| ? [Vvar__0__r__30148] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__30148)
& VX30146 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__30148) )
| ? [Vvar__0__r1__30149] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__30149)
& ? [Vvar__1__r2__30150] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__30150)
& VX30146 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__30149,Vvar__1__r2__30150) ) )
| ? [Vvar__0__r1__30151] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__30151)
& ? [Vvar__1__r2__30152] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__30152)
& VX30146 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__30151,Vvar__1__r2__30152) ) )
| ? [Vvar__0__r1__30153] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__30153)
& ? [Vvar__1__r2__30154] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__30154)
& VX30146 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__30153,Vvar__1__r2__30154) ) )
| ? [Vvar__0__r1__30155] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__30155)
& ? [Vvar__1__z__30156] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__30156)
& VX30146 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__30155,Vvar__1__z__30156) ) )
| ? [Vvar__0__r__30157] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__30157)
& VX30146 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__30157) )
| ? [Vvar__0__r__30158] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__30158)
& VX30146 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__30158) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__35660,VX35661] :
( cType___24t(Vvar__0__T__35660)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__35660,VX35661)
=> ? [Vvar__1__Flhs__35663] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__35660,Vvar__1__Flhs__35663)
& ? [Vvar__2__Fop__35664] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__35664)
& ? [Vvar__3__Frhs__35665] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__35660,Vvar__3__Frhs__35665)
& VX35661 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__35660,Vvar__1__Flhs__35663,Vvar__2__Fop__35664,Vvar__3__Frhs__35665) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX2145] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX2145)
=> ( VX2145 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX2145 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX2145 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX2145 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX55414] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX55414)
=> ( VX55414 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX55414 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX55414 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX55414 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX55414 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX55414 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__2146,VX2147] :
( cType___24t(Vvar__0__C__2146)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__2146,VX2147)
=> ( ? [Vvar__1___24Anonymous__2149] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__2149)
& VX2147 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__2146,Vvar__1___24Anonymous__2149) )
| ? [Vvar__1___24Anonymous__2151] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__2146,Vvar__1___24Anonymous__2151)
& VX2147 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__2146,Vvar__1___24Anonymous__2151) )
| ? [Vvar__1___24Anonymous__2153] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__2146,Vvar__1___24Anonymous__2153)
& ? [Vvar__2___24Anonymous__2154] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__2146,Vvar__2___24Anonymous__2154)
& VX2147 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__2146,Vvar__1___24Anonymous__2153,Vvar__2___24Anonymous__2154) ) )
| ? [Vvar__1___24Anonymous__2156] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__2146,Vvar__1___24Anonymous__2156)
& ? [Vvar__2___24Anonymous__2157] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__2146,Vvar__2___24Anonymous__2157)
& VX2147 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__2146,Vvar__1___24Anonymous__2156,Vvar__2___24Anonymous__2157) ) )
| ? [Vvar__1___24Anonymous__2159] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__2146,Vvar__1___24Anonymous__2159)
& ? [Vvar__2___24Anonymous__2160] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__2146,Vvar__2___24Anonymous__2160)
& VX2147 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__2146,Vvar__1___24Anonymous__2159,Vvar__2___24Anonymous__2160) ) )
| ? [Vvar__1___24Anonymous__2162] :
( t(Vvar__1___24Anonymous__2162,Vvar__0__C__2146)
& VX2147 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__2146,Vvar__1___24Anonymous__2162) )
| VX2147 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__2146) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436] :
( cType___24t(Vvar__0__R__30367)
=> ( t(Vvar__1__rO__30368,Vvar__0__R__30367)
=> ( t(Vvar__2__rI__30369,Vvar__0__R__30367)
=> ( c_24__type__30900___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__3__rplus__30370)
=> ( c_24__type__31246___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__4__rtimes__30375)
=> ( c_24__type__31592___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__5__rminus__30380)
=> ( c_24__type__31915___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__6__ropp__30385)
=> ( c_24__type__32261___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__7__req__30388)
=> ( c_24__type__32607___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__8__rle__30393)
=> ( cType___24t(Vvar__9__C__30398)
=> ( t(Vvar__10__cO__30399,Vvar__9__C__30398)
=> ( t(Vvar__11__cI__30400,Vvar__9__C__30398)
=> ( c_24__type__32953___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__12__cplus__30401)
=> ( c_24__type__33299___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__13__ctimes__30406)
=> ( c_24__type__33645___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__14__cminus__30411)
=> ( c_24__type__33968___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__15__copp__30416)
=> ( c_24__type__34314___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__16__ceqb__30419)
=> ( c_24__type__34660___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__17__cleb__30424)
=> ( c_24__type__34983___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__18__phi__30429)
=> ( cType___24t(Vvar__19__E__30432)
=> ( c_24__type__35306___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__20__pow__phi__30433)
=> ( c_24__type__35652___24t(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436,Vvar__21__rpow__30436)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__8__rle__30393,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__17__cleb__30424,Vvar__18__phi__30429,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__30367,Vvar__1__rO__30368,Vvar__2__rI__30369,Vvar__3__rplus__30370,Vvar__4__rtimes__30375,Vvar__5__rminus__30380,Vvar__6__ropp__30385,Vvar__7__req__30388,Vvar__9__C__30398,Vvar__10__cO__30399,Vvar__11__cI__30400,Vvar__12__cplus__30401,Vvar__13__ctimes__30406,Vvar__14__cminus__30411,Vvar__15__copp__30416,Vvar__16__ceqb__30419,Vvar__18__phi__30429)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__30367,Vvar__2__rI__30369,Vvar__4__rtimes__30375,Vvar__7__req__30388,Vvar__19__E__30432,Vvar__20__pow__phi__30433,Vvar__21__rpow__30436)
& ! [Vvar__var__var__var__var__var__24__x__30519__30522__30532__30535__30538__30541] :
( t(Vvar__var__var__var__var__var__24__x__30519__30522__30532__30535__30538__30541,Vvar__9__C__30398)
=> ! [Vvar__var__var__var__var__var__25__y__30520__30523__30533__30536__30539__30542] :
( t(Vvar__var__var__var__var__var__25__y__30520__30523__30533__30536__30539__30542,Vvar__9__C__30398)
=> ( happ(happ(Vvar__16__ceqb__30419,Vvar__var__var__var__var__var__24__x__30519__30522__30532__30535__30538__30541),Vvar__var__var__var__var__var__25__y__30520__30523__30533__30536__30539__30542) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__30388,happ(Vvar__18__phi__30429,Vvar__var__var__var__var__var__24__x__30519__30522__30532__30535__30538__30541)),happ(Vvar__18__phi__30429,Vvar__var__var__var__var__var__25__y__30520__30523__30533__30536__30539__30542))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__30526__30529__30544__30547__30550__30553] :
( t(Vvar__var__var__var__var__var__25__x__30526__30529__30544__30547__30550__30553,Vvar__9__C__30398)
=> ! [Vvar__var__var__var__var__var__26__y__30527__30530__30545__30548__30551__30554] :
( t(Vvar__var__var__var__var__var__26__y__30527__30530__30545__30548__30551__30554,Vvar__9__C__30398)
=> ( happ(happ(Vvar__17__cleb__30424,Vvar__var__var__var__var__var__25__x__30526__30529__30544__30547__30550__30553),Vvar__var__var__var__var__var__26__y__30527__30530__30545__30548__30551__30554) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__30393,happ(Vvar__18__phi__30429,Vvar__var__var__var__var__var__25__x__30526__30529__30544__30547__30550__30553)),happ(Vvar__18__phi__30429,Vvar__var__var__var__var__var__26__y__30527__30530__30545__30548__30551__30554))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,VX3161] :
( cType___24t(Vvar__0__TA__3157)
=> ( cType___24t(Vvar__1__TX__3158)
=> ( cType___24t(Vvar__2__AA__3159)
=> ( cType___24t(Vvar__3__AF__3160)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,VX3161)
=> ( VX3161 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160)
| VX3161 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160)
| ? [Vvar__4___24Anonymous__3174] :
( t(Vvar__4___24Anonymous__3174,Vvar__1__TX__3158)
& VX3161 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__4___24Anonymous__3174) )
| ? [Vvar__4___24Anonymous__3179] :
( t(Vvar__4___24Anonymous__3179,Vvar__0__TA__3157)
& ? [Vvar__5___24Anonymous__3180] :
( t(Vvar__5___24Anonymous__3180,Vvar__2__AA__3159)
& VX3161 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__4___24Anonymous__3179,Vvar__5___24Anonymous__3180) ) )
| ? [Vvar__4___24Anonymous__3185] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__4___24Anonymous__3185)
& ? [Vvar__5___24Anonymous__3186] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__5___24Anonymous__3186)
& VX3161 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__4___24Anonymous__3185,Vvar__5___24Anonymous__3186) ) )
| ? [Vvar__4___24Anonymous__3191] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__4___24Anonymous__3191)
& ? [Vvar__5___24Anonymous__3192] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__5___24Anonymous__3192)
& VX3161 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__4___24Anonymous__3191,Vvar__5___24Anonymous__3192) ) )
| ? [Vvar__4___24Anonymous__3197] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__4___24Anonymous__3197)
& VX3161 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__4___24Anonymous__3197) )
| ? [Vvar__4___24Anonymous__3202] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__4___24Anonymous__3202)
& ? [Vvar__5___24Anonymous__3203] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__3160,Vvar__5___24Anonymous__3203)
& ? [Vvar__6___24Anonymous__3204] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__6___24Anonymous__3204)
& VX3161 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__3157,Vvar__1__TX__3158,Vvar__2__AA__3159,Vvar__3__AF__3160,Vvar__4___24Anonymous__3202,Vvar__5___24Anonymous__3203,Vvar__6___24Anonymous__3204) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX36626] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX36626)
=> ( VX36626 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__36627] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__36627)
& ? [Vvar__1___24Anonymous__36628] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__36628)
& VX36626 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__36627,Vvar__1___24Anonymous__36628) ) )
| ? [Vvar__0___24Anonymous__36629] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__36629)
& ? [Vvar__1___24Anonymous__36630] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__36630)
& VX36626 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__36629,Vvar__1___24Anonymous__36630) ) )
| ? [Vvar__0___24Anonymous__36631] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__36631)
& ? [Vvar__1___24Anonymous__36632] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__36632)
& ? [Vvar__2___24Anonymous__36633] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__36633)
& VX36626 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__36631,Vvar__1___24Anonymous__36632,Vvar__2___24Anonymous__36633) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__15066,VX15067] :
( cType___24t(Vvar__0__C__15066)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15066,VX15067)
=> ( VX15067 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__15066)
| VX15067 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__15066)
| ? [Vvar__1___24Anonymous__15071] :
( t(Vvar__1___24Anonymous__15071,Vvar__0__C__15066)
& VX15067 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__15066,Vvar__1___24Anonymous__15071) )
| ? [Vvar__1___24Anonymous__15073] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15073)
& VX15067 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__15066,Vvar__1___24Anonymous__15073) )
| ? [Vvar__1___24Anonymous__15075] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15066,Vvar__1___24Anonymous__15075)
& ? [Vvar__2___24Anonymous__15076] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15066,Vvar__2___24Anonymous__15076)
& VX15067 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__15066,Vvar__1___24Anonymous__15075,Vvar__2___24Anonymous__15076) ) )
| ? [Vvar__1___24Anonymous__15078] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15066,Vvar__1___24Anonymous__15078)
& ? [Vvar__2___24Anonymous__15079] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15066,Vvar__2___24Anonymous__15079)
& VX15067 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__15066,Vvar__1___24Anonymous__15078,Vvar__2___24Anonymous__15079) ) )
| ? [Vvar__1___24Anonymous__15081] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15066,Vvar__1___24Anonymous__15081)
& ? [Vvar__2___24Anonymous__15082] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15066,Vvar__2___24Anonymous__15082)
& VX15067 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__15066,Vvar__1___24Anonymous__15081,Vvar__2___24Anonymous__15082) ) )
| ? [Vvar__1___24Anonymous__15084] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15066,Vvar__1___24Anonymous__15084)
& VX15067 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__15066,Vvar__1___24Anonymous__15084) )
| ? [Vvar__1___24Anonymous__15086] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15066,Vvar__1___24Anonymous__15086)
& VX15067 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__15066,Vvar__1___24Anonymous__15086) )
| ? [Vvar__1___24Anonymous__15088] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15066,Vvar__1___24Anonymous__15088)
& ? [Vvar__2___24Anonymous__15089] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15066,Vvar__2___24Anonymous__15089)
& VX15067 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__15066,Vvar__1___24Anonymous__15088,Vvar__2___24Anonymous__15089) ) )
| ? [Vvar__1___24Anonymous__15091] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15066,Vvar__1___24Anonymous__15091)
& ? [Vvar__2___24Anonymous__15092] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__15092)
& VX15067 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__15066,Vvar__1___24Anonymous__15091,Vvar__2___24Anonymous__15092) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__12137,Vvar__1__rO__12138,Vvar__2__rI__12139,Vvar__3__radd__12140,Vvar__4__rmul__12145,Vvar__5__rsub__12150,Vvar__6__ropp__12155,Vvar__7__rdiv__12158,Vvar__8__rinv__12163,Vvar__9__req__12166] :
( cType___24t(Vvar__0__R__12137)
=> ( t(Vvar__1__rO__12138,Vvar__0__R__12137)
=> ( t(Vvar__2__rI__12139,Vvar__0__R__12137)
=> ( c_24__type__12331___24t(Vvar__0__R__12137,Vvar__1__rO__12138,Vvar__2__rI__12139,Vvar__3__radd__12140,Vvar__4__rmul__12145,Vvar__5__rsub__12150,Vvar__6__ropp__12155,Vvar__7__rdiv__12158,Vvar__8__rinv__12163,Vvar__9__req__12166,Vvar__3__radd__12140)
=> ( c_24__type__12424___24t(Vvar__0__R__12137,Vvar__1__rO__12138,Vvar__2__rI__12139,Vvar__3__radd__12140,Vvar__4__rmul__12145,Vvar__5__rsub__12150,Vvar__6__ropp__12155,Vvar__7__rdiv__12158,Vvar__8__rinv__12163,Vvar__9__req__12166,Vvar__4__rmul__12145)
=> ( c_24__type__12517___24t(Vvar__0__R__12137,Vvar__1__rO__12138,Vvar__2__rI__12139,Vvar__3__radd__12140,Vvar__4__rmul__12145,Vvar__5__rsub__12150,Vvar__6__ropp__12155,Vvar__7__rdiv__12158,Vvar__8__rinv__12163,Vvar__9__req__12166,Vvar__5__rsub__12150)
=> ( c_24__type__12599___24t(Vvar__0__R__12137,Vvar__1__rO__12138,Vvar__2__rI__12139,Vvar__3__radd__12140,Vvar__4__rmul__12145,Vvar__5__rsub__12150,Vvar__6__ropp__12155,Vvar__7__rdiv__12158,Vvar__8__rinv__12163,Vvar__9__req__12166,Vvar__6__ropp__12155)
=> ( c_24__type__12692___24t(Vvar__0__R__12137,Vvar__1__rO__12138,Vvar__2__rI__12139,Vvar__3__radd__12140,Vvar__4__rmul__12145,Vvar__5__rsub__12150,Vvar__6__ropp__12155,Vvar__7__rdiv__12158,Vvar__8__rinv__12163,Vvar__9__req__12166,Vvar__7__rdiv__12158)
=> ( c_24__type__12774___24t(Vvar__0__R__12137,Vvar__1__rO__12138,Vvar__2__rI__12139,Vvar__3__radd__12140,Vvar__4__rmul__12145,Vvar__5__rsub__12150,Vvar__6__ropp__12155,Vvar__7__rdiv__12158,Vvar__8__rinv__12163,Vvar__9__req__12166,Vvar__8__rinv__12163)
=> ( c_24__type__12867___24t(Vvar__0__R__12137,Vvar__1__rO__12138,Vvar__2__rI__12139,Vvar__3__radd__12140,Vvar__4__rmul__12145,Vvar__5__rsub__12150,Vvar__6__ropp__12155,Vvar__7__rdiv__12158,Vvar__8__rinv__12163,Vvar__9__req__12166,Vvar__9__req__12166)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__12137,Vvar__1__rO__12138,Vvar__2__rI__12139,Vvar__3__radd__12140,Vvar__4__rmul__12145,Vvar__5__rsub__12150,Vvar__6__ropp__12155,Vvar__7__rdiv__12158,Vvar__8__rinv__12163,Vvar__9__req__12166)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__12137,Vvar__1__rO__12138,Vvar__2__rI__12139,Vvar__3__radd__12140,Vvar__4__rmul__12145,Vvar__5__rsub__12150,Vvar__6__ropp__12155,Vvar__9__req__12166)
& ~ p(happ(happ(Vvar__9__req__12166,Vvar__2__rI__12139),Vvar__1__rO__12138))
& ! [Vvar__var__var__var__var__var__var__12__p__12209__12211__12218__12220__12222__12224__12226] :
( t(Vvar__var__var__var__var__var__var__12__p__12209__12211__12218__12220__12222__12224__12226,Vvar__0__R__12137)
=> ! [Vvar__var__var__var__var__var__var__13__q__12210__12212__12219__12221__12223__12225__12227] :
( t(Vvar__var__var__var__var__var__var__13__q__12210__12212__12219__12221__12223__12225__12227,Vvar__0__R__12137)
=> p(happ(happ(Vvar__9__req__12166,happ(happ(Vvar__7__rdiv__12158,Vvar__var__var__var__var__var__var__12__p__12209__12211__12218__12220__12222__12224__12226),Vvar__var__var__var__var__var__var__13__q__12210__12212__12219__12221__12223__12225__12227)),happ(happ(Vvar__4__rmul__12145,Vvar__var__var__var__var__var__var__12__p__12209__12211__12218__12220__12222__12224__12226),happ(Vvar__8__rinv__12163,Vvar__var__var__var__var__var__var__13__q__12210__12212__12219__12221__12223__12225__12227)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__12214__12216__12228__12230__12232__12234__12236__12238] :
( t(Vvar__var__var__var__var__var__var__var__13__p__12214__12216__12228__12230__12232__12234__12236__12238,Vvar__0__R__12137)
=> ( ~ p(happ(happ(Vvar__9__req__12166,Vvar__var__var__var__var__var__var__var__13__p__12214__12216__12228__12230__12232__12234__12236__12238),Vvar__1__rO__12138))
=> p(happ(happ(Vvar__9__req__12166,happ(happ(Vvar__4__rmul__12145,happ(Vvar__8__rinv__12163,Vvar__var__var__var__var__var__var__var__13__p__12214__12216__12228__12230__12232__12234__12236__12238)),Vvar__var__var__var__var__var__var__var__13__p__12214__12216__12228__12230__12232__12234__12236__12238)),Vvar__2__rI__12139)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__15678,VX15679] :
( cType___24t(Vvar__0__C__15678)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__15678,VX15679)
=> ? [Vvar__1__num__15681] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15678,Vvar__1__num__15681)
& ? [Vvar__2__denum__15682] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15678,Vvar__2__denum__15682)
& ? [Vvar__3__condition__15683] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__15678),Vvar__3__condition__15683)
& VX15679 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__15678,Vvar__1__num__15681,Vvar__2__denum__15682,Vvar__3__condition__15683) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__15731,VX15732] :
( cType___24t(Vvar__0__C__15731)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__15731,VX15732)
=> ? [Vvar__1__rsplit__left__15734] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15731,Vvar__1__rsplit__left__15734)
& ? [Vvar__2__rsplit__common__15735] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15731,Vvar__2__rsplit__common__15735)
& ? [Vvar__3__rsplit__right__15736] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15731,Vvar__3__rsplit__right__15736)
& VX15732 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__15731,Vvar__1__rsplit__left__15734,Vvar__2__rsplit__common__15735,Vvar__3__rsplit__right__15736) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX18036] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX18036)
=> ( VX18036 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__18037] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18037)
& ? [Vvar__1___24Anonymous__18038] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__18038)
& VX18036 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__18037,Vvar__1___24Anonymous__18038) ) )
| ? [Vvar__0___24Anonymous__18039] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18039)
& ? [Vvar__1___24Anonymous__18040] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__18040)
& VX18036 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__18039,Vvar__1___24Anonymous__18040) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__2331,VX2332] :
( cType___24t(Vvar__0__C__2331)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2331,VX2332)
=> ( VX2332 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2331)
| VX2332 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2331)
| ? [Vvar__1___24Anonymous__2336] :
( t(Vvar__1___24Anonymous__2336,Vvar__0__C__2331)
& VX2332 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2331,Vvar__1___24Anonymous__2336) )
| ? [Vvar__1___24Anonymous__2338] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2338)
& VX2332 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2331,Vvar__1___24Anonymous__2338) )
| ? [Vvar__1___24Anonymous__2340] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2331,Vvar__1___24Anonymous__2340)
& ? [Vvar__2___24Anonymous__2341] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2331,Vvar__2___24Anonymous__2341)
& VX2332 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2331,Vvar__1___24Anonymous__2340,Vvar__2___24Anonymous__2341) ) )
| ? [Vvar__1___24Anonymous__2343] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2331,Vvar__1___24Anonymous__2343)
& ? [Vvar__2___24Anonymous__2344] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2331,Vvar__2___24Anonymous__2344)
& VX2332 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2331,Vvar__1___24Anonymous__2343,Vvar__2___24Anonymous__2344) ) )
| ? [Vvar__1___24Anonymous__2346] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2331,Vvar__1___24Anonymous__2346)
& ? [Vvar__2___24Anonymous__2347] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2331,Vvar__2___24Anonymous__2347)
& VX2332 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2331,Vvar__1___24Anonymous__2346,Vvar__2___24Anonymous__2347) ) )
| ? [Vvar__1___24Anonymous__2349] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2331,Vvar__1___24Anonymous__2349)
& VX2332 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2331,Vvar__1___24Anonymous__2349) )
| ? [Vvar__1___24Anonymous__2351] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2331,Vvar__1___24Anonymous__2351)
& ? [Vvar__2___24Anonymous__2352] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2352)
& VX2332 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2331,Vvar__1___24Anonymous__2351,Vvar__2___24Anonymous__2352) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__17857,VX17858] :
( cType___24t(Vvar__0__C__17857)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__17857,VX17858)
=> ( ? [Vvar__1___24Anonymous__17860] :
( t(Vvar__1___24Anonymous__17860,Vvar__0__C__17857)
& VX17858 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__17857,Vvar__1___24Anonymous__17860) )
| ? [Vvar__1___24Anonymous__17862] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17862)
& ? [Vvar__2___24Anonymous__17863] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__17857,Vvar__2___24Anonymous__17863)
& VX17858 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__17857,Vvar__1___24Anonymous__17862,Vvar__2___24Anonymous__17863) ) )
| ? [Vvar__1___24Anonymous__17865] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__17857,Vvar__1___24Anonymous__17865)
& ? [Vvar__2___24Anonymous__17866] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17866)
& ? [Vvar__3___24Anonymous__17867] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__17857,Vvar__3___24Anonymous__17867)
& VX17858 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__17857,Vvar__1___24Anonymous__17865,Vvar__2___24Anonymous__17866,Vvar__3___24Anonymous__17867) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__20053,Vvar__1__rO__20054,Vvar__2__rI__20055,Vvar__3__radd__20056,Vvar__4__rmul__20061,Vvar__5__rsub__20066,Vvar__6__ropp__20071,Vvar__7__req__20074] :
( cType___24t(Vvar__0__R__20053)
=> ( t(Vvar__1__rO__20054,Vvar__0__R__20053)
=> ( t(Vvar__2__rI__20055,Vvar__0__R__20053)
=> ( c_24__type__20302___24t(Vvar__0__R__20053,Vvar__1__rO__20054,Vvar__2__rI__20055,Vvar__3__radd__20056,Vvar__4__rmul__20061,Vvar__5__rsub__20066,Vvar__6__ropp__20071,Vvar__7__req__20074,Vvar__3__radd__20056)
=> ( c_24__type__20365___24t(Vvar__0__R__20053,Vvar__1__rO__20054,Vvar__2__rI__20055,Vvar__3__radd__20056,Vvar__4__rmul__20061,Vvar__5__rsub__20066,Vvar__6__ropp__20071,Vvar__7__req__20074,Vvar__4__rmul__20061)
=> ( c_24__type__20428___24t(Vvar__0__R__20053,Vvar__1__rO__20054,Vvar__2__rI__20055,Vvar__3__radd__20056,Vvar__4__rmul__20061,Vvar__5__rsub__20066,Vvar__6__ropp__20071,Vvar__7__req__20074,Vvar__5__rsub__20066)
=> ( c_24__type__20482___24t(Vvar__0__R__20053,Vvar__1__rO__20054,Vvar__2__rI__20055,Vvar__3__radd__20056,Vvar__4__rmul__20061,Vvar__5__rsub__20066,Vvar__6__ropp__20071,Vvar__7__req__20074,Vvar__6__ropp__20071)
=> ( c_24__type__20545___24t(Vvar__0__R__20053,Vvar__1__rO__20054,Vvar__2__rI__20055,Vvar__3__radd__20056,Vvar__4__rmul__20061,Vvar__5__rsub__20066,Vvar__6__ropp__20071,Vvar__7__req__20074,Vvar__7__req__20074)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__20053,Vvar__1__rO__20054,Vvar__2__rI__20055,Vvar__3__radd__20056,Vvar__4__rmul__20061,Vvar__5__rsub__20066,Vvar__6__ropp__20071,Vvar__7__req__20074)
=> ( ! [Vvar__var__var__var__var__var__8__x__20107__20108__20161__20162__20163__20164] :
( t(Vvar__var__var__var__var__var__8__x__20107__20108__20161__20162__20163__20164,Vvar__0__R__20053)
=> p(happ(happ(Vvar__7__req__20074,happ(happ(Vvar__3__radd__20056,Vvar__1__rO__20054),Vvar__var__var__var__var__var__8__x__20107__20108__20161__20162__20163__20164)),Vvar__var__var__var__var__var__8__x__20107__20108__20161__20162__20163__20164)) )
& ! [Vvar__var__var__var__var__9__x__20110__20112__20165__20167__20169] :
( t(Vvar__var__var__var__var__9__x__20110__20112__20165__20167__20169,Vvar__0__R__20053)
=> ! [Vvar__var__var__var__var__10__y__20111__20113__20166__20168__20170] :
( t(Vvar__var__var__var__var__10__y__20111__20113__20166__20168__20170,Vvar__0__R__20053)
=> p(happ(happ(Vvar__7__req__20074,happ(happ(Vvar__3__radd__20056,Vvar__var__var__var__var__9__x__20110__20112__20165__20167__20169),Vvar__var__var__var__var__10__y__20111__20113__20166__20168__20170)),happ(happ(Vvar__3__radd__20056,Vvar__var__var__var__var__10__y__20111__20113__20166__20168__20170),Vvar__var__var__var__var__9__x__20110__20112__20165__20167__20169))) ) )
& ! [Vvar__var__var__var__var__10__x__20115__20118__20171__20174__20177] :
( t(Vvar__var__var__var__var__10__x__20115__20118__20171__20174__20177,Vvar__0__R__20053)
=> ! [Vvar__var__var__var__var__11__y__20116__20119__20172__20175__20178] :
( t(Vvar__var__var__var__var__11__y__20116__20119__20172__20175__20178,Vvar__0__R__20053)
=> ! [Vvar__var__var__var__var__12__z__20117__20120__20173__20176__20179] :
( t(Vvar__var__var__var__var__12__z__20117__20120__20173__20176__20179,Vvar__0__R__20053)
=> p(happ(happ(Vvar__7__req__20074,happ(happ(Vvar__3__radd__20056,Vvar__var__var__var__var__10__x__20115__20118__20171__20174__20177),happ(happ(Vvar__3__radd__20056,Vvar__var__var__var__var__11__y__20116__20119__20172__20175__20178),Vvar__var__var__var__var__12__z__20117__20120__20173__20176__20179))),happ(happ(Vvar__3__radd__20056,happ(happ(Vvar__3__radd__20056,Vvar__var__var__var__var__10__x__20115__20118__20171__20174__20177),Vvar__var__var__var__var__11__y__20116__20119__20172__20175__20178)),Vvar__var__var__var__var__12__z__20117__20120__20173__20176__20179))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__20122__20123__20180__20181__20182__20183] :
( t(Vvar__var__var__var__var__var__11__x__20122__20123__20180__20181__20182__20183,Vvar__0__R__20053)
=> p(happ(happ(Vvar__7__req__20074,happ(happ(Vvar__4__rmul__20061,Vvar__2__rI__20055),Vvar__var__var__var__var__var__11__x__20122__20123__20180__20181__20182__20183)),Vvar__var__var__var__var__var__11__x__20122__20123__20180__20181__20182__20183)) )
& ! [Vvar__var__var__var__var__var__12__x__20125__20126__20184__20185__20186__20187] :
( t(Vvar__var__var__var__var__var__12__x__20125__20126__20184__20185__20186__20187,Vvar__0__R__20053)
=> p(happ(happ(Vvar__7__req__20074,happ(happ(Vvar__4__rmul__20061,Vvar__1__rO__20054),Vvar__var__var__var__var__var__12__x__20125__20126__20184__20185__20186__20187)),Vvar__1__rO__20054)) )
& ! [Vvar__var__var__var__var__13__x__20128__20130__20188__20190__20192] :
( t(Vvar__var__var__var__var__13__x__20128__20130__20188__20190__20192,Vvar__0__R__20053)
=> ! [Vvar__var__var__var__var__14__y__20129__20131__20189__20191__20193] :
( t(Vvar__var__var__var__var__14__y__20129__20131__20189__20191__20193,Vvar__0__R__20053)
=> p(happ(happ(Vvar__7__req__20074,happ(happ(Vvar__4__rmul__20061,Vvar__var__var__var__var__13__x__20128__20130__20188__20190__20192),Vvar__var__var__var__var__14__y__20129__20131__20189__20191__20193)),happ(happ(Vvar__4__rmul__20061,Vvar__var__var__var__var__14__y__20129__20131__20189__20191__20193),Vvar__var__var__var__var__13__x__20128__20130__20188__20190__20192))) ) )
& ! [Vvar__var__var__var__var__14__x__20133__20136__20194__20197__20200] :
( t(Vvar__var__var__var__var__14__x__20133__20136__20194__20197__20200,Vvar__0__R__20053)
=> ! [Vvar__var__var__var__var__15__y__20134__20137__20195__20198__20201] :
( t(Vvar__var__var__var__var__15__y__20134__20137__20195__20198__20201,Vvar__0__R__20053)
=> ! [Vvar__var__var__var__var__16__z__20135__20138__20196__20199__20202] :
( t(Vvar__var__var__var__var__16__z__20135__20138__20196__20199__20202,Vvar__0__R__20053)
=> p(happ(happ(Vvar__7__req__20074,happ(happ(Vvar__4__rmul__20061,Vvar__var__var__var__var__14__x__20133__20136__20194__20197__20200),happ(happ(Vvar__4__rmul__20061,Vvar__var__var__var__var__15__y__20134__20137__20195__20198__20201),Vvar__var__var__var__var__16__z__20135__20138__20196__20199__20202))),happ(happ(Vvar__4__rmul__20061,happ(happ(Vvar__4__rmul__20061,Vvar__var__var__var__var__14__x__20133__20136__20194__20197__20200),Vvar__var__var__var__var__15__y__20134__20137__20195__20198__20201)),Vvar__var__var__var__var__16__z__20135__20138__20196__20199__20202))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__20140__20143__20203__20206__20209__20212] :
( t(Vvar__var__var__var__var__var__15__x__20140__20143__20203__20206__20209__20212,Vvar__0__R__20053)
=> ! [Vvar__var__var__var__var__var__16__y__20141__20144__20204__20207__20210__20213] :
( t(Vvar__var__var__var__var__var__16__y__20141__20144__20204__20207__20210__20213,Vvar__0__R__20053)
=> ! [Vvar__var__var__var__var__var__17__z__20142__20145__20205__20208__20211__20214] :
( t(Vvar__var__var__var__var__var__17__z__20142__20145__20205__20208__20211__20214,Vvar__0__R__20053)
=> p(happ(happ(Vvar__7__req__20074,happ(happ(Vvar__4__rmul__20061,happ(happ(Vvar__3__radd__20056,Vvar__var__var__var__var__var__15__x__20140__20143__20203__20206__20209__20212),Vvar__var__var__var__var__var__16__y__20141__20144__20204__20207__20210__20213)),Vvar__var__var__var__var__var__17__z__20142__20145__20205__20208__20211__20214)),happ(happ(Vvar__3__radd__20056,happ(happ(Vvar__4__rmul__20061,Vvar__var__var__var__var__var__15__x__20140__20143__20203__20206__20209__20212),Vvar__var__var__var__var__var__17__z__20142__20145__20205__20208__20211__20214)),happ(happ(Vvar__4__rmul__20061,Vvar__var__var__var__var__var__16__y__20141__20144__20204__20207__20210__20213),Vvar__var__var__var__var__var__17__z__20142__20145__20205__20208__20211__20214)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__20147__20149__20215__20217__20219__20221] :
( t(Vvar__var__var__var__var__var__16__x__20147__20149__20215__20217__20219__20221,Vvar__0__R__20053)
=> ! [Vvar__var__var__var__var__var__17__y__20148__20150__20216__20218__20220__20222] :
( t(Vvar__var__var__var__var__var__17__y__20148__20150__20216__20218__20220__20222,Vvar__0__R__20053)
=> p(happ(happ(Vvar__7__req__20074,happ(Vvar__6__ropp__20071,happ(happ(Vvar__4__rmul__20061,Vvar__var__var__var__var__var__16__x__20147__20149__20215__20217__20219__20221),Vvar__var__var__var__var__var__17__y__20148__20150__20216__20218__20220__20222))),happ(happ(Vvar__4__rmul__20061,happ(Vvar__6__ropp__20071,Vvar__var__var__var__var__var__16__x__20147__20149__20215__20217__20219__20221)),Vvar__var__var__var__var__var__17__y__20148__20150__20216__20218__20220__20222))) ) )
& ! [Vvar__var__var__var__var__var__17__x__20152__20154__20223__20225__20227__20229] :
( t(Vvar__var__var__var__var__var__17__x__20152__20154__20223__20225__20227__20229,Vvar__0__R__20053)
=> ! [Vvar__var__var__var__var__var__18__y__20153__20155__20224__20226__20228__20230] :
( t(Vvar__var__var__var__var__var__18__y__20153__20155__20224__20226__20228__20230,Vvar__0__R__20053)
=> p(happ(happ(Vvar__7__req__20074,happ(Vvar__6__ropp__20071,happ(happ(Vvar__3__radd__20056,Vvar__var__var__var__var__var__17__x__20152__20154__20223__20225__20227__20229),Vvar__var__var__var__var__var__18__y__20153__20155__20224__20226__20228__20230))),happ(happ(Vvar__3__radd__20056,happ(Vvar__6__ropp__20071,Vvar__var__var__var__var__var__17__x__20152__20154__20223__20225__20227__20229)),happ(Vvar__6__ropp__20071,Vvar__var__var__var__var__var__18__y__20153__20155__20224__20226__20228__20230)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__20157__20159__20231__20233__20235__20237__20239] :
( t(Vvar__var__var__var__var__var__var__18__x__20157__20159__20231__20233__20235__20237__20239,Vvar__0__R__20053)
=> ! [Vvar__var__var__var__var__var__var__19__y__20158__20160__20232__20234__20236__20238__20240] :
( t(Vvar__var__var__var__var__var__var__19__y__20158__20160__20232__20234__20236__20238__20240,Vvar__0__R__20053)
=> p(happ(happ(Vvar__7__req__20074,happ(happ(Vvar__5__rsub__20066,Vvar__var__var__var__var__var__var__18__x__20157__20159__20231__20233__20235__20237__20239),Vvar__var__var__var__var__var__var__19__y__20158__20160__20232__20234__20236__20238__20240)),happ(happ(Vvar__3__radd__20056,Vvar__var__var__var__var__var__var__18__x__20157__20159__20231__20233__20235__20237__20239),happ(Vvar__6__ropp__20071,Vvar__var__var__var__var__var__var__19__y__20158__20160__20232__20234__20236__20238__20240)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__24691,Vvar__1__req__24692,Vvar__2__C__24697,Vvar__3__cadd__24698,Vvar__4__cmul__24703,Vvar__5__phi__24708,Vvar__6__cdiv__24711] :
( cType___24t(Vvar__0__R__24691)
=> ( c_24__type__24831___24t(Vvar__0__R__24691,Vvar__1__req__24692,Vvar__2__C__24697,Vvar__3__cadd__24698,Vvar__4__cmul__24703,Vvar__5__phi__24708,Vvar__6__cdiv__24711,Vvar__1__req__24692)
=> ( cType___24t(Vvar__2__C__24697)
=> ( c_24__type__24881___24t(Vvar__0__R__24691,Vvar__1__req__24692,Vvar__2__C__24697,Vvar__3__cadd__24698,Vvar__4__cmul__24703,Vvar__5__phi__24708,Vvar__6__cdiv__24711,Vvar__3__cadd__24698)
=> ( c_24__type__24931___24t(Vvar__0__R__24691,Vvar__1__req__24692,Vvar__2__C__24697,Vvar__3__cadd__24698,Vvar__4__cmul__24703,Vvar__5__phi__24708,Vvar__6__cdiv__24711,Vvar__4__cmul__24703)
=> ( c_24__type__24973___24t(Vvar__0__R__24691,Vvar__1__req__24692,Vvar__2__C__24697,Vvar__3__cadd__24698,Vvar__4__cmul__24703,Vvar__5__phi__24708,Vvar__6__cdiv__24711,Vvar__5__phi__24708)
=> ( c_24__type__25023___24t(Vvar__0__R__24691,Vvar__1__req__24692,Vvar__2__C__24697,Vvar__3__cadd__24698,Vvar__4__cmul__24703,Vvar__5__phi__24708,Vvar__6__cdiv__24711,Vvar__6__cdiv__24711)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__24691,Vvar__1__req__24692,Vvar__2__C__24697,Vvar__3__cadd__24698,Vvar__4__cmul__24703,Vvar__5__phi__24708,Vvar__6__cdiv__24711)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__24743__24748__24753__24758__24763__24768__24773__24778] :
( t(Vvar__var__var__var__var__var__var__var__7__a__24743__24748__24753__24758__24763__24768__24773__24778,Vvar__2__C__24697)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__24744__24749__24754__24759__24764__24769__24774__24779] :
( t(Vvar__var__var__var__var__var__var__var__8__b__24744__24749__24754__24759__24764__24769__24774__24779,Vvar__2__C__24697)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2425086___24a9(Vvar__0__R__24691,Vvar__1__req__24692,Vvar__2__C__24697,Vvar__3__cadd__24698,Vvar__4__cmul__24703,Vvar__5__phi__24708,Vvar__6__cdiv__24711,Vvar__var__var__var__var__var__var__var__7__a__24743__24748__24753__24758__24763__24768__24773__24778,Vvar__var__var__var__var__var__var__var__8__b__24744__24749__24754__24759__24764__24769__24774__24779) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__25128,Vvar__1__rI__25129,Vvar__2__rmul__25130,Vvar__3__req__25135,Vvar__4__Cpow__25140,Vvar__5__Cp__phi__25141,Vvar__6__rpow__25144] :
( cType___24t(Vvar__0__R__25128)
=> ( t(Vvar__1__rI__25129,Vvar__0__R__25128)
=> ( c_24__type__25230___24t(Vvar__0__R__25128,Vvar__1__rI__25129,Vvar__2__rmul__25130,Vvar__3__req__25135,Vvar__4__Cpow__25140,Vvar__5__Cp__phi__25141,Vvar__6__rpow__25144,Vvar__2__rmul__25130)
=> ( c_24__type__25274___24t(Vvar__0__R__25128,Vvar__1__rI__25129,Vvar__2__rmul__25130,Vvar__3__req__25135,Vvar__4__Cpow__25140,Vvar__5__Cp__phi__25141,Vvar__6__rpow__25144,Vvar__3__req__25135)
=> ( cType___24t(Vvar__4__Cpow__25140)
=> ( c_24__type__25310___24t(Vvar__0__R__25128,Vvar__1__rI__25129,Vvar__2__rmul__25130,Vvar__3__req__25135,Vvar__4__Cpow__25140,Vvar__5__Cp__phi__25141,Vvar__6__rpow__25144,Vvar__5__Cp__phi__25141)
=> ( c_24__type__25354___24t(Vvar__0__R__25128,Vvar__1__rI__25129,Vvar__2__rmul__25130,Vvar__3__req__25135,Vvar__4__Cpow__25140,Vvar__5__Cp__phi__25141,Vvar__6__rpow__25144,Vvar__6__rpow__25144)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__25128,Vvar__1__rI__25129,Vvar__2__rmul__25130,Vvar__3__req__25135,Vvar__4__Cpow__25140,Vvar__5__Cp__phi__25141,Vvar__6__rpow__25144)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__25172__25174__25176__25178__25180__25182__25184__25186] :
( t(Vvar__var__var__var__var__var__var__var__7__r__25172__25174__25176__25178__25180__25182__25184__25186,Vvar__0__R__25128)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__25173__25175__25177__25179__25181__25183__25185__25187] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__25173__25175__25177__25179__25181__25183__25185__25187)
=> p(happ(happ(Vvar__3__req__25135,happ(happ(Vvar__6__rpow__25144,Vvar__var__var__var__var__var__var__var__7__r__25172__25174__25176__25178__25180__25182__25184__25186),happ(Vvar__5__Cp__phi__25141,Vvar__var__var__var__var__var__var__var__8__n__25173__25175__25177__25179__25181__25183__25185__25187))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__25128,Vvar__1__rI__25129,Vvar__2__rmul__25130,Vvar__var__var__var__var__var__var__var__7__r__25172__25174__25176__25178__25180__25182__25184__25186,Vvar__var__var__var__var__var__var__var__8__n__25173__25175__25177__25179__25181__25183__25185__25187))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__20647,Vvar__1__radd__20648,Vvar__2__rmul__20653,Vvar__3__ropp__20658,Vvar__4__req__20661] :
( cType___24t(Vvar__0__R__20647)
=> ( c_24__type__20752___24t(Vvar__0__R__20647,Vvar__1__radd__20648,Vvar__2__rmul__20653,Vvar__3__ropp__20658,Vvar__4__req__20661,Vvar__1__radd__20648)
=> ( c_24__type__20782___24t(Vvar__0__R__20647,Vvar__1__radd__20648,Vvar__2__rmul__20653,Vvar__3__ropp__20658,Vvar__4__req__20661,Vvar__2__rmul__20653)
=> ( c_24__type__20806___24t(Vvar__0__R__20647,Vvar__1__radd__20648,Vvar__2__rmul__20653,Vvar__3__ropp__20658,Vvar__4__req__20661,Vvar__3__ropp__20658)
=> ( c_24__type__20836___24t(Vvar__0__R__20647,Vvar__1__radd__20648,Vvar__2__rmul__20653,Vvar__3__ropp__20658,Vvar__4__req__20661,Vvar__4__req__20661)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__20647,Vvar__1__radd__20648,Vvar__2__rmul__20653,Vvar__3__ropp__20658,Vvar__4__req__20661)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__20866___24a5(Vvar__0__R__20647,Vvar__1__radd__20648,Vvar__2__rmul__20653,Vvar__3__ropp__20658,Vvar__4__req__20661),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__20647,c_24__type__20890___24a5(Vvar__0__R__20647,Vvar__1__radd__20648,Vvar__2__rmul__20653,Vvar__3__ropp__20658,Vvar__4__req__20661),Vvar__4__req__20661,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__20647,Vvar__0__R__20647,Vvar__4__req__20661,Vvar__4__req__20661)),Vvar__1__radd__20648)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__20923___24a5(Vvar__0__R__20647,Vvar__1__radd__20648,Vvar__2__rmul__20653,Vvar__3__ropp__20658,Vvar__4__req__20661),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__20647,c_24__type__20947___24a5(Vvar__0__R__20647,Vvar__1__radd__20648,Vvar__2__rmul__20653,Vvar__3__ropp__20658,Vvar__4__req__20661),Vvar__4__req__20661,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__20647,Vvar__0__R__20647,Vvar__4__req__20661,Vvar__4__req__20661)),Vvar__2__rmul__20653)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__20974___24a5(Vvar__0__R__20647,Vvar__1__radd__20648,Vvar__2__rmul__20653,Vvar__3__ropp__20658,Vvar__4__req__20661),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__20647,Vvar__0__R__20647,Vvar__4__req__20661,Vvar__4__req__20661),Vvar__3__ropp__20658)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086] :
( cType___24t(Vvar__0__R__22034)
=> ( t(Vvar__1__rO__22035,Vvar__0__R__22034)
=> ( t(Vvar__2__rI__22036,Vvar__0__R__22034)
=> ( c_24__type__22430___24t(Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086,Vvar__3__radd__22037)
=> ( c_24__type__22643___24t(Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086,Vvar__4__rmul__22042)
=> ( c_24__type__22856___24t(Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086,Vvar__5__rsub__22047)
=> ( c_24__type__23051___24t(Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086,Vvar__6__ropp__22052)
=> ( c_24__type__23264___24t(Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086,Vvar__7__req__22055)
=> ( cType___24t(Vvar__8__C__22060)
=> ( t(Vvar__9__cO__22061,Vvar__8__C__22060)
=> ( t(Vvar__10__cI__22062,Vvar__8__C__22060)
=> ( c_24__type__23477___24t(Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086,Vvar__11__cadd__22063)
=> ( c_24__type__23690___24t(Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086,Vvar__12__cmul__22068)
=> ( c_24__type__23903___24t(Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086,Vvar__13__csub__22073)
=> ( c_24__type__24098___24t(Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086,Vvar__14__copp__22078)
=> ( c_24__type__24311___24t(Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086,Vvar__15__ceqb__22081)
=> ( c_24__type__24506___24t(Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086,Vvar__16__phi__22086)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__22034,Vvar__1__rO__22035,Vvar__2__rI__22036,Vvar__3__radd__22037,Vvar__4__rmul__22042,Vvar__5__rsub__22047,Vvar__6__ropp__22052,Vvar__7__req__22055,Vvar__8__C__22060,Vvar__9__cO__22061,Vvar__10__cI__22062,Vvar__11__cadd__22063,Vvar__12__cmul__22068,Vvar__13__csub__22073,Vvar__14__copp__22078,Vvar__15__ceqb__22081,Vvar__16__phi__22086)
=> ( p(happ(happ(Vvar__7__req__22055,happ(Vvar__16__phi__22086,Vvar__9__cO__22061)),Vvar__1__rO__22035))
& p(happ(happ(Vvar__7__req__22055,happ(Vvar__16__phi__22086,Vvar__10__cI__22062)),Vvar__2__rI__22036))
& ! [Vvar__var__var__var__var__var__var__19__x__22148__22150__22172__22174__22176__22178__22180] :
( t(Vvar__var__var__var__var__var__var__19__x__22148__22150__22172__22174__22176__22178__22180,Vvar__8__C__22060)
=> ! [Vvar__var__var__var__var__var__var__20__y__22149__22151__22173__22175__22177__22179__22181] :
( t(Vvar__var__var__var__var__var__var__20__y__22149__22151__22173__22175__22177__22179__22181,Vvar__8__C__22060)
=> p(happ(happ(Vvar__7__req__22055,happ(Vvar__16__phi__22086,happ(happ(Vvar__11__cadd__22063,Vvar__var__var__var__var__var__var__19__x__22148__22150__22172__22174__22176__22178__22180),Vvar__var__var__var__var__var__var__20__y__22149__22151__22173__22175__22177__22179__22181))),happ(happ(Vvar__3__radd__22037,happ(Vvar__16__phi__22086,Vvar__var__var__var__var__var__var__19__x__22148__22150__22172__22174__22176__22178__22180)),happ(Vvar__16__phi__22086,Vvar__var__var__var__var__var__var__20__y__22149__22151__22173__22175__22177__22179__22181)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__22153__22155__22182__22184__22186__22188__22190] :
( t(Vvar__var__var__var__var__var__var__20__x__22153__22155__22182__22184__22186__22188__22190,Vvar__8__C__22060)
=> ! [Vvar__var__var__var__var__var__var__21__y__22154__22156__22183__22185__22187__22189__22191] :
( t(Vvar__var__var__var__var__var__var__21__y__22154__22156__22183__22185__22187__22189__22191,Vvar__8__C__22060)
=> p(happ(happ(Vvar__7__req__22055,happ(Vvar__16__phi__22086,happ(happ(Vvar__13__csub__22073,Vvar__var__var__var__var__var__var__20__x__22153__22155__22182__22184__22186__22188__22190),Vvar__var__var__var__var__var__var__21__y__22154__22156__22183__22185__22187__22189__22191))),happ(happ(Vvar__5__rsub__22047,happ(Vvar__16__phi__22086,Vvar__var__var__var__var__var__var__20__x__22153__22155__22182__22184__22186__22188__22190)),happ(Vvar__16__phi__22086,Vvar__var__var__var__var__var__var__21__y__22154__22156__22183__22185__22187__22189__22191)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__22158__22160__22192__22194__22196__22198__22200] :
( t(Vvar__var__var__var__var__var__var__21__x__22158__22160__22192__22194__22196__22198__22200,Vvar__8__C__22060)
=> ! [Vvar__var__var__var__var__var__var__22__y__22159__22161__22193__22195__22197__22199__22201] :
( t(Vvar__var__var__var__var__var__var__22__y__22159__22161__22193__22195__22197__22199__22201,Vvar__8__C__22060)
=> p(happ(happ(Vvar__7__req__22055,happ(Vvar__16__phi__22086,happ(happ(Vvar__12__cmul__22068,Vvar__var__var__var__var__var__var__21__x__22158__22160__22192__22194__22196__22198__22200),Vvar__var__var__var__var__var__var__22__y__22159__22161__22193__22195__22197__22199__22201))),happ(happ(Vvar__4__rmul__22042,happ(Vvar__16__phi__22086,Vvar__var__var__var__var__var__var__21__x__22158__22160__22192__22194__22196__22198__22200)),happ(Vvar__16__phi__22086,Vvar__var__var__var__var__var__var__22__y__22159__22161__22193__22195__22197__22199__22201)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__22163__22164__22202__22203__22204__22205__22206] :
( t(Vvar__var__var__var__var__var__var__22__x__22163__22164__22202__22203__22204__22205__22206,Vvar__8__C__22060)
=> p(happ(happ(Vvar__7__req__22055,happ(Vvar__16__phi__22086,happ(Vvar__14__copp__22078,Vvar__var__var__var__var__var__var__22__x__22163__22164__22202__22203__22204__22205__22206))),happ(Vvar__6__ropp__22052,happ(Vvar__16__phi__22086,Vvar__var__var__var__var__var__var__22__x__22163__22164__22202__22203__22204__22205__22206)))) )
& ! [Vvar__var__var__var__var__var__23__x__22166__22169__22207__22210__22213__22216] :
( t(Vvar__var__var__var__var__var__23__x__22166__22169__22207__22210__22213__22216,Vvar__8__C__22060)
=> ! [Vvar__var__var__var__var__var__24__y__22167__22170__22208__22211__22214__22217] :
( t(Vvar__var__var__var__var__var__24__y__22167__22170__22208__22211__22214__22217,Vvar__8__C__22060)
=> ( happ(happ(Vvar__15__ceqb__22081,Vvar__var__var__var__var__var__23__x__22166__22169__22207__22210__22213__22216),Vvar__var__var__var__var__var__24__y__22167__22170__22208__22211__22214__22217) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__22055,happ(Vvar__16__phi__22086,Vvar__var__var__var__var__var__23__x__22166__22169__22207__22210__22213__22216)),happ(Vvar__16__phi__22086,Vvar__var__var__var__var__var__24__y__22167__22170__22208__22211__22214__22217))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__63352,Vvar__1__rO__63353,Vvar__2__rI__63354,Vvar__3__radd__63355,Vvar__4__rmul__63360,Vvar__5__rsub__63365,Vvar__6__ropp__63370,Vvar__7__req__63373] :
( cType___24t(Vvar__0__R__63352)
=> ( t(Vvar__1__rO__63353,Vvar__0__R__63352)
=> ( t(Vvar__2__rI__63354,Vvar__0__R__63352)
=> ( c_24__type__63576___24t(Vvar__0__R__63352,Vvar__1__rO__63353,Vvar__2__rI__63354,Vvar__3__radd__63355,Vvar__4__rmul__63360,Vvar__5__rsub__63365,Vvar__6__ropp__63370,Vvar__7__req__63373,Vvar__3__radd__63355)
=> ( c_24__type__63639___24t(Vvar__0__R__63352,Vvar__1__rO__63353,Vvar__2__rI__63354,Vvar__3__radd__63355,Vvar__4__rmul__63360,Vvar__5__rsub__63365,Vvar__6__ropp__63370,Vvar__7__req__63373,Vvar__4__rmul__63360)
=> ( c_24__type__63702___24t(Vvar__0__R__63352,Vvar__1__rO__63353,Vvar__2__rI__63354,Vvar__3__radd__63355,Vvar__4__rmul__63360,Vvar__5__rsub__63365,Vvar__6__ropp__63370,Vvar__7__req__63373,Vvar__5__rsub__63365)
=> ( c_24__type__63756___24t(Vvar__0__R__63352,Vvar__1__rO__63353,Vvar__2__rI__63354,Vvar__3__radd__63355,Vvar__4__rmul__63360,Vvar__5__rsub__63365,Vvar__6__ropp__63370,Vvar__7__req__63373,Vvar__6__ropp__63370)
=> ( c_24__type__63819___24t(Vvar__0__R__63352,Vvar__1__rO__63353,Vvar__2__rI__63354,Vvar__3__radd__63355,Vvar__4__rmul__63360,Vvar__5__rsub__63365,Vvar__6__ropp__63370,Vvar__7__req__63373,Vvar__7__req__63373)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__63352,Vvar__1__rO__63353,Vvar__2__rI__63354,Vvar__3__radd__63355,Vvar__4__rmul__63360,Vvar__5__rsub__63365,Vvar__6__ropp__63370,Vvar__7__req__63373)
=> ( ! [Vvar__var__var__var__var__var__8__x__63406__63407__63450__63451__63452__63453] :
( t(Vvar__var__var__var__var__var__8__x__63406__63407__63450__63451__63452__63453,Vvar__0__R__63352)
=> p(happ(happ(Vvar__7__req__63373,happ(happ(Vvar__3__radd__63355,Vvar__1__rO__63353),Vvar__var__var__var__var__var__8__x__63406__63407__63450__63451__63452__63453)),Vvar__var__var__var__var__var__8__x__63406__63407__63450__63451__63452__63453)) )
& ! [Vvar__var__var__var__var__9__x__63409__63411__63454__63456__63458] :
( t(Vvar__var__var__var__var__9__x__63409__63411__63454__63456__63458,Vvar__0__R__63352)
=> ! [Vvar__var__var__var__var__10__y__63410__63412__63455__63457__63459] :
( t(Vvar__var__var__var__var__10__y__63410__63412__63455__63457__63459,Vvar__0__R__63352)
=> p(happ(happ(Vvar__7__req__63373,happ(happ(Vvar__3__radd__63355,Vvar__var__var__var__var__9__x__63409__63411__63454__63456__63458),Vvar__var__var__var__var__10__y__63410__63412__63455__63457__63459)),happ(happ(Vvar__3__radd__63355,Vvar__var__var__var__var__10__y__63410__63412__63455__63457__63459),Vvar__var__var__var__var__9__x__63409__63411__63454__63456__63458))) ) )
& ! [Vvar__var__var__var__var__10__x__63414__63417__63460__63463__63466] :
( t(Vvar__var__var__var__var__10__x__63414__63417__63460__63463__63466,Vvar__0__R__63352)
=> ! [Vvar__var__var__var__var__11__y__63415__63418__63461__63464__63467] :
( t(Vvar__var__var__var__var__11__y__63415__63418__63461__63464__63467,Vvar__0__R__63352)
=> ! [Vvar__var__var__var__var__12__z__63416__63419__63462__63465__63468] :
( t(Vvar__var__var__var__var__12__z__63416__63419__63462__63465__63468,Vvar__0__R__63352)
=> p(happ(happ(Vvar__7__req__63373,happ(happ(Vvar__3__radd__63355,Vvar__var__var__var__var__10__x__63414__63417__63460__63463__63466),happ(happ(Vvar__3__radd__63355,Vvar__var__var__var__var__11__y__63415__63418__63461__63464__63467),Vvar__var__var__var__var__12__z__63416__63419__63462__63465__63468))),happ(happ(Vvar__3__radd__63355,happ(happ(Vvar__3__radd__63355,Vvar__var__var__var__var__10__x__63414__63417__63460__63463__63466),Vvar__var__var__var__var__11__y__63415__63418__63461__63464__63467)),Vvar__var__var__var__var__12__z__63416__63419__63462__63465__63468))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__63421__63422__63469__63470__63471__63472] :
( t(Vvar__var__var__var__var__var__11__x__63421__63422__63469__63470__63471__63472,Vvar__0__R__63352)
=> p(happ(happ(Vvar__7__req__63373,happ(happ(Vvar__4__rmul__63360,Vvar__2__rI__63354),Vvar__var__var__var__var__var__11__x__63421__63422__63469__63470__63471__63472)),Vvar__var__var__var__var__var__11__x__63421__63422__63469__63470__63471__63472)) )
& ! [Vvar__var__var__var__var__12__x__63424__63426__63473__63475__63477] :
( t(Vvar__var__var__var__var__12__x__63424__63426__63473__63475__63477,Vvar__0__R__63352)
=> ! [Vvar__var__var__var__var__13__y__63425__63427__63474__63476__63478] :
( t(Vvar__var__var__var__var__13__y__63425__63427__63474__63476__63478,Vvar__0__R__63352)
=> p(happ(happ(Vvar__7__req__63373,happ(happ(Vvar__4__rmul__63360,Vvar__var__var__var__var__12__x__63424__63426__63473__63475__63477),Vvar__var__var__var__var__13__y__63425__63427__63474__63476__63478)),happ(happ(Vvar__4__rmul__63360,Vvar__var__var__var__var__13__y__63425__63427__63474__63476__63478),Vvar__var__var__var__var__12__x__63424__63426__63473__63475__63477))) ) )
& ! [Vvar__var__var__var__var__13__x__63429__63432__63479__63482__63485] :
( t(Vvar__var__var__var__var__13__x__63429__63432__63479__63482__63485,Vvar__0__R__63352)
=> ! [Vvar__var__var__var__var__14__y__63430__63433__63480__63483__63486] :
( t(Vvar__var__var__var__var__14__y__63430__63433__63480__63483__63486,Vvar__0__R__63352)
=> ! [Vvar__var__var__var__var__15__z__63431__63434__63481__63484__63487] :
( t(Vvar__var__var__var__var__15__z__63431__63434__63481__63484__63487,Vvar__0__R__63352)
=> p(happ(happ(Vvar__7__req__63373,happ(happ(Vvar__4__rmul__63360,Vvar__var__var__var__var__13__x__63429__63432__63479__63482__63485),happ(happ(Vvar__4__rmul__63360,Vvar__var__var__var__var__14__y__63430__63433__63480__63483__63486),Vvar__var__var__var__var__15__z__63431__63434__63481__63484__63487))),happ(happ(Vvar__4__rmul__63360,happ(happ(Vvar__4__rmul__63360,Vvar__var__var__var__var__13__x__63429__63432__63479__63482__63485),Vvar__var__var__var__var__14__y__63430__63433__63480__63483__63486)),Vvar__var__var__var__var__15__z__63431__63434__63481__63484__63487))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__63436__63439__63488__63491__63494__63497] :
( t(Vvar__var__var__var__var__var__14__x__63436__63439__63488__63491__63494__63497,Vvar__0__R__63352)
=> ! [Vvar__var__var__var__var__var__15__y__63437__63440__63489__63492__63495__63498] :
( t(Vvar__var__var__var__var__var__15__y__63437__63440__63489__63492__63495__63498,Vvar__0__R__63352)
=> ! [Vvar__var__var__var__var__var__16__z__63438__63441__63490__63493__63496__63499] :
( t(Vvar__var__var__var__var__var__16__z__63438__63441__63490__63493__63496__63499,Vvar__0__R__63352)
=> p(happ(happ(Vvar__7__req__63373,happ(happ(Vvar__4__rmul__63360,happ(happ(Vvar__3__radd__63355,Vvar__var__var__var__var__var__14__x__63436__63439__63488__63491__63494__63497),Vvar__var__var__var__var__var__15__y__63437__63440__63489__63492__63495__63498)),Vvar__var__var__var__var__var__16__z__63438__63441__63490__63493__63496__63499)),happ(happ(Vvar__3__radd__63355,happ(happ(Vvar__4__rmul__63360,Vvar__var__var__var__var__var__14__x__63436__63439__63488__63491__63494__63497),Vvar__var__var__var__var__var__16__z__63438__63441__63490__63493__63496__63499)),happ(happ(Vvar__4__rmul__63360,Vvar__var__var__var__var__var__15__y__63437__63440__63489__63492__63495__63498),Vvar__var__var__var__var__var__16__z__63438__63441__63490__63493__63496__63499)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__63443__63445__63500__63502__63504__63506__63508] :
( t(Vvar__var__var__var__var__var__var__15__x__63443__63445__63500__63502__63504__63506__63508,Vvar__0__R__63352)
=> ! [Vvar__var__var__var__var__var__var__16__y__63444__63446__63501__63503__63505__63507__63509] :
( t(Vvar__var__var__var__var__var__var__16__y__63444__63446__63501__63503__63505__63507__63509,Vvar__0__R__63352)
=> p(happ(happ(Vvar__7__req__63373,happ(happ(Vvar__5__rsub__63365,Vvar__var__var__var__var__var__var__15__x__63443__63445__63500__63502__63504__63506__63508),Vvar__var__var__var__var__var__var__16__y__63444__63446__63501__63503__63505__63507__63509)),happ(happ(Vvar__3__radd__63355,Vvar__var__var__var__var__var__var__15__x__63443__63445__63500__63502__63504__63506__63508),happ(Vvar__6__ropp__63370,Vvar__var__var__var__var__var__var__16__y__63444__63446__63501__63503__63505__63507__63509)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__63448__63449__63510__63511__63512__63513__63514] :
( t(Vvar__var__var__var__var__var__var__16__x__63448__63449__63510__63511__63512__63513__63514,Vvar__0__R__63352)
=> p(happ(happ(Vvar__7__req__63373,happ(happ(Vvar__3__radd__63355,Vvar__var__var__var__var__var__var__16__x__63448__63449__63510__63511__63512__63513__63514),happ(Vvar__6__ropp__63370,Vvar__var__var__var__var__var__var__16__x__63448__63449__63510__63511__63512__63513__63514))),Vvar__1__rO__63353)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__24592,Vvar__1__copp__24593,Vvar__2__ceqb__24596,Vvar__3__get__sign__24601] :
( cType___24t(Vvar__0__C__24592)
=> ( c_24__type__24648___24t(Vvar__0__C__24592,Vvar__1__copp__24593,Vvar__2__ceqb__24596,Vvar__3__get__sign__24601,Vvar__1__copp__24593)
=> ( c_24__type__24667___24t(Vvar__0__C__24592,Vvar__1__copp__24593,Vvar__2__ceqb__24596,Vvar__3__get__sign__24601,Vvar__2__ceqb__24596)
=> ( c_24__type__24681___24t(Vvar__0__C__24592,Vvar__1__copp__24593,Vvar__2__ceqb__24596,Vvar__3__get__sign__24601,Vvar__3__get__sign__24601)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__24592,Vvar__1__copp__24593,Vvar__2__ceqb__24596,Vvar__3__get__sign__24601)
=> ( ! [Vvar__var__var__var__var__var__4__c__24618__24621__24624__24627__24630__24633] :
( t(Vvar__var__var__var__var__var__4__c__24618__24621__24624__24627__24630__24633,Vvar__0__C__24592)
=> ! [Vvar__var__var__var__var__var__5__c_27__24619__24622__24625__24628__24631__24634] :
( t(Vvar__var__var__var__var__var__5__c_27__24619__24622__24625__24628__24631__24634,Vvar__0__C__24592)
=> ( happ(Vvar__3__get__sign__24601,Vvar__var__var__var__var__var__4__c__24618__24621__24624__24627__24630__24633) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__24592,Vvar__var__var__var__var__var__5__c_27__24619__24622__24625__24628__24631__24634)
=> happ(happ(Vvar__2__ceqb__24596,Vvar__var__var__var__var__var__4__c__24618__24621__24624__24627__24630__24633),happ(Vvar__1__copp__24593,Vvar__var__var__var__var__var__5__c_27__24619__24622__24625__24628__24631__24634)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__36012,Vvar__1__radd__36013,Vvar__2__rmul__36018,Vvar__3__req__36023] :
( cType___24t(Vvar__0__R__36012)
=> ( c_24__type__36098___24t(Vvar__0__R__36012,Vvar__1__radd__36013,Vvar__2__rmul__36018,Vvar__3__req__36023,Vvar__1__radd__36013)
=> ( c_24__type__36121___24t(Vvar__0__R__36012,Vvar__1__radd__36013,Vvar__2__rmul__36018,Vvar__3__req__36023,Vvar__2__rmul__36018)
=> ( c_24__type__36144___24t(Vvar__0__R__36012,Vvar__1__radd__36013,Vvar__2__rmul__36018,Vvar__3__req__36023,Vvar__3__req__36023)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__36012,Vvar__1__radd__36013,Vvar__2__rmul__36018,Vvar__3__req__36023)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__36167___24a4(Vvar__0__R__36012,Vvar__1__radd__36013,Vvar__2__rmul__36018,Vvar__3__req__36023),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__36012,c_24__type__36185___24a4(Vvar__0__R__36012,Vvar__1__radd__36013,Vvar__2__rmul__36018,Vvar__3__req__36023),Vvar__3__req__36023,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__36012,Vvar__0__R__36012,Vvar__3__req__36023,Vvar__3__req__36023)),Vvar__1__radd__36013)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__36211___24a4(Vvar__0__R__36012,Vvar__1__radd__36013,Vvar__2__rmul__36018,Vvar__3__req__36023),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__36012,c_24__type__36229___24a4(Vvar__0__R__36012,Vvar__1__radd__36013,Vvar__2__rmul__36018,Vvar__3__req__36023),Vvar__3__req__36023,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__36012,Vvar__0__R__36012,Vvar__3__req__36023,Vvar__3__req__36023)),Vvar__2__rmul__36018)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_lam_1442',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1442___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_18220',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__18220___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__18148___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('$_lam_28964',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__28964___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1) ).
fof('$_lam_37672',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__37672___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_37680',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__37680___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_37688',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__37688___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_37696',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__37696___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_41468',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__41468___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eNat_2emax___24a2(cCoq_2emicromega_2eZMicromega_2ebdepth___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ).
fof('$_lam_55146',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__55146___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_55166',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__55166___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('$_lam_56020',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__56020___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_56026',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__56026___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_57888',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__57888___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eLists_2eList_2emap___24a4(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),c_24__lam__57893___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__2) ).
fof('$_lam_57893',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__57893___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4),Vv__CANONICAL__3) ).
fof('$_lam_60320',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__60320___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_63024',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__63024___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('$_prop_28838',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__28838___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> cCoq_2eLists_2eList_2enth___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ).
fof('$_prop_28904',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__28904___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__2 ) ).
fof('$_prop_28905',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__28905___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__2 ) ).
fof('$_prop_28906',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__28906___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_28907',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__28907___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_28908',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__28908___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_28909',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__28909___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_28947',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__28947___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__2 = Vv__CANONICAL__3 ) ).
fof('$_prop_28948',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__28948___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__2 != Vv__CANONICAL__3 ) ).
fof('$_prop_28956',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__28956___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__2 = Vv__CANONICAL__3 ) ).
fof('$_prop_28957',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__28957___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__2 != Vv__CANONICAL__3 ) ).
fof('$_prop_29057',axiom,
! [V0__A,V1__x,V2__y] :
( p(c_24__prop__29057___24a3(V0__A,V1__x,V2__y))
<=> V1__x = V2__y ) ).
fof('$_prop_36721',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__36721___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_36741',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__36741___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_36887',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__36887___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ).
fof('$_prop_36912',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__36892] :
( p(c_24__prop__36912___24a3(V0__A,V3__x,Vvar__1___24Anonymous__36892))
<=> V3__x = Vvar__1___24Anonymous__36892 ) ).
fof('$_prop_36913',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__36892] :
( p(c_24__prop__36913___24a3(V0__A,V3__x,Vvar__1___24Anonymous__36892))
<=> V3__x != Vvar__1___24Anonymous__36892 ) ).
fof('$_prop_36914',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__36892] :
( p(c_24__prop__36914___24a3(V0__A,V3__x,Vvar__1___24Anonymous__36892))
<=> V3__x = Vvar__1___24Anonymous__36892 ) ).
fof('$_prop_36915',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__36892] :
( p(c_24__prop__36915___24a3(V0__A,V3__x,Vvar__1___24Anonymous__36892))
<=> V3__x != Vvar__1___24Anonymous__36892 ) ).
fof('$_prop_36964',axiom,
! [V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945] :
( p(c_24__prop__36964___24a3(V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945)) ) ).
fof('$_prop_36976',axiom,
! [V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945] :
( p(c_24__prop__36976___24a3(V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__36944,Vvar__2___24Anonymous__36945)) ) ).
fof('$_prop_38634',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__38634___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_38635',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__38635___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_38644',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__38644___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_38645',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__38645___24a2(V0__x,V1__y))
<=> V0__x != V1__y ) ).
fof('$_prop_38646',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__38646___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_38647',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__38647___24a2(V0__x,V1__y))
<=> V0__x != V1__y ) ).
fof('$_prop_54967',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__54967___24a2(V0__A,V1__B))
<=> ( p(V0__A)
| p(V1__B) ) ) ).
fof('$_prop_54968',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__54968___24a2(V0__A,V1__B))
<=> ( p(V0__A)
& p(V1__B) ) ) ).
fof('$_prop_55585',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__55585___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('$_prop_55586',axiom,
! [V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__55541] :
( p(c_24__prop__55586___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__55541))
<=> ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__55541)) ) ).
fof('$_prop_55587',axiom,
! [V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__55541] :
( p(c_24__prop__55587___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__55541))
<=> ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__55541)) ) ).
fof('$_prop_55620',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__55620___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_57643',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2] :
( p(c_24__prop__57643___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2))
<=> ~ p(cCoq_2eLists_2eList_2eNoDup___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ).
fof('$_prop_60316',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__60316___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_prop_60335',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__60335___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(cCoq_2eLists_2eList_2eincl___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ).
fof('$_prop_61211',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__61211___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_61224',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__61224___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('$_type_10',axiom,
! [Vvar__11] :
( c_24__type__10___24t(Vvar__11)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__11,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1019',axiom,
! [Vvar__1020] :
( c_24__type__1019___24t(Vvar__1020)
<=> ! [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__1020,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1069',axiom,
! [Vvar__1070] :
( c_24__type__1069___24t(Vvar__1070)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__1070,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_111',axiom,
! [Vvar__112] :
( c_24__type__111___24t(Vvar__112)
<=> ! [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__112,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_12122',axiom,
! [Vvar__12123] :
( c_24__type__12122___24t(Vvar__12123)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__12123,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_12134',axiom,
! [Vvar__12135] :
( c_24__type__12134___24t(Vvar__12135)
<=> ! [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__12135,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_12331',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__12332] :
( c_24__type__12331___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__12332)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12332,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12424',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__12425] :
( c_24__type__12424___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__12425)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12425,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12517',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__12518] :
( c_24__type__12517___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__12518)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12518,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12599',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__12600] :
( c_24__type__12599___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__12600)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__12600,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_12692',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__12693] :
( c_24__type__12692___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__12693)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12693,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12774',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__12775] :
( c_24__type__12774___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__12775)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__12775,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_12867',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__12868] :
( c_24__type__12867___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__12868)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__12868,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_1288',axiom,
! [Vvar__1289] :
( c_24__type__1288___24t(Vvar__1289)
<=> ! [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__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1314___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1323___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__1289,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),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('$_type_1293',axiom,
! [Vv__CANONICAL__0,Vvar__1294] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vvar__1294)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1294,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1302',axiom,
! [Vv__CANONICAL__0,Vvar__1303] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vvar__1303)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__1303,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_1309',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1310] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1310)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__1310,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_1314',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1315] :
( c_24__type__1314___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1315)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__1315,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_13163',axiom,
! [Vvar__13164] :
( c_24__type__13163___24t(Vvar__13164)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1314___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1323___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__13164,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1323',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1324] :
( c_24__type__1323___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1324)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__1324,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13247',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13248] :
( c_24__type__13247___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13248)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__13248,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13252',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13253] :
( c_24__type__13252___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13253)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> t(happ(Vvar__13253,Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ).
fof('$_type_133',axiom,
! [Vvar__134] :
( c_24__type__133___24t(Vvar__134)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__134,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_13765',axiom,
! [Vv__CANONICAL__0,Vvar__13766] :
( c_24__type__13765___24t(Vv__CANONICAL__0,Vvar__13766)
<=> ! [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__13766,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_138',axiom,
! [Vvar__139] :
( c_24__type__138___24t(Vvar__139)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__139,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13839',axiom,
! [Vvar__13840] :
( c_24__type__13839___24t(Vvar__13840)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13765___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__13840,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_1390',axiom,
! [Vvar__1391] :
( c_24__type__1390___24t(Vvar__1391)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1394___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__1391,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1394',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1395] :
( c_24__type__1394___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1395)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(Vvar__1395,Vv__CANONICAL__2)) ) ) ).
fof('$_type_1426',axiom,
! [Vvar__1427] :
( c_24__type__1426___24t(Vvar__1427)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__193___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(happ(happ(Vvar__1427,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14369',axiom,
! [Vvar__14370] :
( c_24__type__14369___24t(Vvar__14370)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1302___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__14370,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1449',axiom,
! [Vvar__1450] :
( c_24__type__1449___24t(Vvar__1450)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__1450,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1454',axiom,
! [Vvar__1455] :
( c_24__type__1454___24t(Vvar__1455)
<=> ! [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__1455,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1459',axiom,
! [Vvar__1460] :
( c_24__type__1459___24t(Vvar__1460)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,happ(happ(Vvar__1460,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_147',axiom,
! [Vv__CANONICAL__0,Vvar__148] :
( c_24__type__147___24t(Vv__CANONICAL__0,Vvar__148)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__148,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_1483',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1484] :
( c_24__type__1483___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1484)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1484,Vv__CANONICAL__3)) ) ) ).
fof('$_type_15058',axiom,
! [Vvar__15059] :
( c_24__type__15058___24t(Vvar__15059)
<=> ! [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__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13765___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_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(Vvar__15059,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_1524',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1525] :
( c_24__type__1524___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1525)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1525,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_1546',axiom,
! [Vv__CANONICAL__0,Vvar__1547] :
( c_24__type__1546___24t(Vv__CANONICAL__0,Vvar__1547)
<=> ! [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__1547,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_1549',axiom,
! [Vv__CANONICAL__0,Vvar__1550] :
( c_24__type__1549___24t(Vv__CANONICAL__0,Vvar__1550)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__1550,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1554',axiom,
! [Vv__CANONICAL__0,Vvar__1555] :
( c_24__type__1554___24t(Vv__CANONICAL__0,Vvar__1555)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__1555,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_15650',axiom,
! [Vvar__15651] :
( c_24__type__15650___24t(Vvar__15651)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1314___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__1323___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__9,Vv__CANONICAL__15)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__15651,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_15698',axiom,
! [Vvar__15699] :
( c_24__type__15698___24t(Vvar__15699)
<=> ! [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__15699,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_157',axiom,
! [Vvar__158] :
( c_24__type__157___24t(Vvar__158)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__158,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15709',axiom,
! [Vvar__15710] :
( c_24__type__15709___24t(Vvar__15710)
<=> ! [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__15710,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15729',axiom,
! [Vvar__15730] :
( c_24__type__15729___24t(Vvar__15730)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__15730,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15754',axiom,
! [Vvar__15755] :
( c_24__type__15754___24t(Vvar__15755)
<=> ! [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__15755,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1580',axiom,
! [Vvar__1581] :
( c_24__type__1580___24t(Vvar__1581)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__271___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__1581,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_15811',axiom,
! [Vvar__15812] :
( c_24__type__15811___24t(Vvar__15812)
<=> ! [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__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13765___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__15812,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_15841',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15842] :
( c_24__type__15841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15842)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__15842,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_15860',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15861] :
( c_24__type__15860___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15861)
<=> ! [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__15861,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_162',axiom,
! [Vvar__163] :
( c_24__type__162___24t(Vvar__163)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__163,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16422',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__16423] :
( c_24__type__16422___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__16423)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__16423,Vv__CANONICAL__3)) ) ) ).
fof('$_type_165',axiom,
! [Vvar__166] :
( c_24__type__165___24t(Vvar__166)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__166,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1697',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1698] :
( c_24__type__1697___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1698)
<=> ! [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__1698,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_17417',axiom,
! [Vvar__17418] :
( c_24__type__17417___24t(Vvar__17418)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__17418,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_17428',axiom,
! [Vvar__17429] :
( c_24__type__17428___24t(Vvar__17429)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__17429,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17444',axiom,
! [Vvar__17445] :
( c_24__type__17444___24t(Vvar__17445)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__17445,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17446',axiom,
! [Vvar__17447] :
( c_24__type__17446___24t(Vvar__17447)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__17447,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17473',axiom,
! [Vvar__17474] :
( c_24__type__17473___24t(Vvar__17474)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13765___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__17474,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_17519',axiom,
! [Vv__CANONICAL__0,Vvar__17520] :
( c_24__type__17519___24t(Vv__CANONICAL__0,Vvar__17520)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__17520,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_17671',axiom,
! [Vvar__17672] :
( c_24__type__17671___24t(Vvar__17672)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__17672,Vv__CANONICAL__0)) ) ) ).
fof('$_type_177',axiom,
! [Vvar__178] :
( c_24__type__177___24t(Vvar__178)
<=> ! [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__178,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17774',axiom,
! [Vvar__17775] :
( c_24__type__17774___24t(Vvar__17775)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__17775,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17777',axiom,
! [Vvar__17778] :
( c_24__type__17777___24t(Vvar__17778)
<=> ! [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__17778,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17783',axiom,
! [Vvar__17784] :
( c_24__type__17783___24t(Vvar__17784)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__17784,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17809',axiom,
! [Vvar__17810] :
( c_24__type__17809___24t(Vvar__17810)
<=> ! [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__17810,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17812',axiom,
! [Vvar__17813] :
( c_24__type__17812___24t(Vvar__17813)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__17813,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17818',axiom,
! [Vvar__17819] :
( c_24__type__17818___24t(Vvar__17819)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__17819,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18031',axiom,
! [Vvar__18032] :
( c_24__type__18031___24t(Vvar__18032)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__18032,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_18117',axiom,
! [Vvar__18118] :
( c_24__type__18117___24t(Vvar__18118)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1309___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__18118,Vv__CANONICAL__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('$_type_18127',axiom,
! [Vvar__18128] :
( c_24__type__18127___24t(Vvar__18128)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__18128,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18130',axiom,
! [Vvar__18131] :
( c_24__type__18130___24t(Vvar__18131)
<=> ! [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__18131,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18133',axiom,
! [Vvar__18134] :
( c_24__type__18133___24t(Vvar__18134)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__18134,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18138',axiom,
! [Vvar__18139] :
( c_24__type__18138___24t(Vvar__18139)
<=> ! [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__18139,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_18352',axiom,
! [Vvar__18353] :
( c_24__type__18352___24t(Vvar__18353)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__13765___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__18370___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__18353,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_18370',axiom,
! [Vv__CANONICAL__0,Vvar__18371] :
( c_24__type__18370___24t(Vv__CANONICAL__0,Vvar__18371)
<=> ! [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__18371,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_18608',axiom,
! [Vvar__18609] :
( c_24__type__18608___24t(Vvar__18609)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1314___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1323___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8)),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__18609,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_18793',axiom,
! [Vvar__18794] :
( c_24__type__18793___24t(Vvar__18794)
<=> ! [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__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__13765___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__18370___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__18794,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_19',axiom,
! [Vvar__20] :
( c_24__type__19___24t(Vvar__20)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__20,Vv__CANONICAL__0)) ) ) ).
fof('$_type_190',axiom,
! [Vvar__191] :
( c_24__type__190___24t(Vvar__191)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__193___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__191,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_193',axiom,
! [Vv__CANONICAL__0,Vvar__194] :
( c_24__type__193___24t(Vv__CANONICAL__0,Vvar__194)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__194,Vv__CANONICAL__1)) ) ) ).
fof('$_type_19303',axiom,
! [Vvar__19304] :
( c_24__type__19303___24t(Vvar__19304)
<=> ! [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__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___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__15860___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__1314___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__1323___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__16422___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__19304,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),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('$_type_19645',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__19646] :
( c_24__type__19645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__19646)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__19646,Vv__CANONICAL__2)) ) ) ).
fof('$_type_19759',axiom,
! [Vvar__19760] :
( c_24__type__19759___24t(Vvar__19760)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1293___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__19760,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_20302',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20303] :
( c_24__type__20302___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20303)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20303,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20365',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__20366] :
( c_24__type__20365___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__20366)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20366,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20428',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20429] :
( c_24__type__20428___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20429)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20429,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20482',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__20483] :
( c_24__type__20482___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__20483)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__20483,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_20545',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20546] :
( c_24__type__20545___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20546)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__20546,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_20752',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20753] :
( c_24__type__20752___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20753)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20753,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20782',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20783] :
( c_24__type__20782___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20783)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20783,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20806',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20807] :
( c_24__type__20806___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20807)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__20807,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_20836',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20837] :
( c_24__type__20836___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20837)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__20837,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_20866',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20867] :
( c_24__type__20866___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20867)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20867,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20890',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20891] :
( c_24__type__20890___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20891)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__20891,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_20923',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20924] :
( c_24__type__20923___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20924)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20924,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20947',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20948] :
( c_24__type__20947___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20948)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__20948,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_20974',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20975] :
( c_24__type__20974___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20975)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__20975,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_222',axiom,
! [Vvar__223] :
( c_24__type__222___24t(Vvar__223)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__193___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__223,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22430',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__22431] :
( c_24__type__22430___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__22431)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22431,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22643',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__22644] :
( c_24__type__22643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__22644)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22644,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22856',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__22857] :
( c_24__type__22856___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__22857)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22857,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23051',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23052] :
( c_24__type__23051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23052)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__23052,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_2314',axiom,
! [Vvar__2315] :
( c_24__type__2314___24t(Vvar__2315)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,happ(happ(Vvar__2315,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23264',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23265] :
( c_24__type__23264___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23265)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23265,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_23477',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__23478] :
( c_24__type__23477___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__23478)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__23478,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_23690',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23691] :
( c_24__type__23690___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23691)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__23691,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_239',axiom,
! [Vvar__240] :
( c_24__type__239___24t(Vvar__240)
<=> ! [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__240,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23903',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23904] :
( c_24__type__23903___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23904)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__23904,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_24098',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__24099] :
( c_24__type__24098___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__24099)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__24099,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_24311',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__24312] :
( c_24__type__24311___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__24312)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__24312,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_24506',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__24507] :
( c_24__type__24506___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__24507)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__24507,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_24648',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24649] :
( c_24__type__24648___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24649)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__24649,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_24667',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24668] :
( c_24__type__24667___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24668)
<=> ! [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__24668,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_24681',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24682] :
( c_24__type__24681___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24682)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__24682,Vv__CANONICAL__4)) ) ) ).
fof('$_type_24831',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24832] :
( c_24__type__24831___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24832)
<=> ! [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__24832,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_24881',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24882] :
( c_24__type__24881___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24882)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__24882,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_24931',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24932] :
( c_24__type__24931___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24932)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__24932,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_24973',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24974] :
( c_24__type__24973___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24974)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__24974,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_25023',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25024] :
( c_24__type__25023___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25024)
<=> ! [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__25024,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_25099',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25100] :
( c_24__type__25099___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25100)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__25100,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_25107',axiom,
! [Vvar__25108] :
( c_24__type__25107___24t(Vvar__25108)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25108,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25230',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25231] :
( c_24__type__25230___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25231)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25231,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25274',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25275] :
( c_24__type__25274___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25275)
<=> ! [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__25275,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_25310',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25311] :
( c_24__type__25310___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25311)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__25311,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_25354',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25355] :
( c_24__type__25354___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25355)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__25355,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25366',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25367] :
( c_24__type__25366___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25367)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__25367,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_25402',axiom,
! [Vvar__25403] :
( c_24__type__25402___24t(Vvar__25403)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1293___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__25403,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_25522',axiom,
! [Vvar__25523] :
( c_24__type__25522___24t(Vvar__25523)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__25523,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25591',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25592] :
( c_24__type__25591___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25592)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__25592,Vv__CANONICAL__2)) ) ) ).
fof('$_type_25597',axiom,
! [Vvar__25598] :
( c_24__type__25597___24t(Vvar__25598)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__271___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__25598,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_25610',axiom,
! [Vvar__25611] :
( c_24__type__25610___24t(Vvar__25611)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__25611,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25633',axiom,
! [Vvar__25634] :
( c_24__type__25633___24t(Vvar__25634)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__25634,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_25638',axiom,
! [Vvar__25639] :
( c_24__type__25638___24t(Vvar__25639)
<=> ! [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__25639,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_25650',axiom,
! [Vvar__25651] :
( c_24__type__25650___24t(Vvar__25651)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__25651,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25673',axiom,
! [Vvar__25674] :
( c_24__type__25673___24t(Vvar__25674)
<=> ! [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__25674,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_25678',axiom,
! [Vvar__25679] :
( c_24__type__25678___24t(Vvar__25679)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__25679,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_25731',axiom,
! [Vvar__25732] :
( c_24__type__25731___24t(Vvar__25732)
<=> ! [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__703___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__25732,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_25752',axiom,
! [Vvar__25753] :
( c_24__type__25752___24t(Vvar__25753)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__25753,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25769',axiom,
! [Vvar__25770] :
( c_24__type__25769___24t(Vvar__25770)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__25770,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25777',axiom,
! [Vvar__25778] :
( c_24__type__25777___24t(Vvar__25778)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),happ(happ(happ(happ(Vvar__25778,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_259',axiom,
! [Vv__CANONICAL__0,Vvar__260] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vvar__260)
<=> ! [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__260,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_26065',axiom,
! [Vvar__26066] :
( c_24__type__26065___24t(Vvar__26066)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__26066,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26414',axiom,
! [Vvar__26415] :
( c_24__type__26414___24t(Vvar__26415)
<=> ! [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__26415,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26423',axiom,
! [Vvar__26424] :
( c_24__type__26423___24t(Vvar__26424)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__26424,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26430',axiom,
! [Vvar__26431] :
( c_24__type__26430___24t(Vvar__26431)
<=> ! [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__26431,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26546',axiom,
! [Vvar__26547] :
( c_24__type__26546___24t(Vvar__26547)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__26547,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26671',axiom,
! [Vvar__26672] :
( c_24__type__26671___24t(Vvar__26672)
<=> ! [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__26672,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26852',axiom,
! [Vvar__26853] :
( c_24__type__26852___24t(Vvar__26853)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__26853,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26867',axiom,
! [Vvar__26868] :
( c_24__type__26867___24t(Vvar__26868)
<=> ! [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__26868,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26871',axiom,
! [Vvar__26872] :
( c_24__type__26871___24t(Vvar__26872)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__26872,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26902',axiom,
! [Vvar__26903] :
( c_24__type__26902___24t(Vvar__26903)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__26903,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26905',axiom,
! [Vvar__26906] :
( c_24__type__26905___24t(Vvar__26906)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__26906,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26972',axiom,
! [Vvar__26973] :
( c_24__type__26972___24t(Vvar__26973)
<=> ! [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__26973,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26981',axiom,
! [Vvar__26982] :
( c_24__type__26981___24t(Vvar__26982)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__26982,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_26992',axiom,
! [Vvar__26993] :
( c_24__type__26992___24t(Vvar__26993)
<=> ! [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__26993,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_27002',axiom,
! [Vvar__27003] :
( c_24__type__27002___24t(Vvar__27003)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__27003,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27030',axiom,
! [Vvar__27031] :
( c_24__type__27030___24t(Vvar__27031)
<=> ! [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__27031,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_27035',axiom,
! [Vvar__27036] :
( c_24__type__27035___24t(Vvar__27036)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__27036,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_27055',axiom,
! [Vvar__27056] :
( c_24__type__27055___24t(Vvar__27056)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__27056,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27058',axiom,
! [Vv__CANONICAL__0,Vvar__27059] :
( c_24__type__27058___24t(Vv__CANONICAL__0,Vvar__27059)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__27059,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_271',axiom,
! [Vv__CANONICAL__0,Vvar__272] :
( c_24__type__271___24t(Vv__CANONICAL__0,Vvar__272)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__272,Vv__CANONICAL__1)) ) ) ).
fof('$_type_27291',axiom,
! [Vvar__27292] :
( c_24__type__27291___24t(Vvar__27292)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__27292,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27294',axiom,
! [Vvar__27295] :
( c_24__type__27294___24t(Vvar__27295)
<=> ! [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__27295,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27299',axiom,
! [Vvar__27300] :
( c_24__type__27299___24t(Vvar__27300)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__27300,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_27308',axiom,
! [Vvar__27309] :
( c_24__type__27308___24t(Vvar__27309)
<=> ! [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__27309,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27317',axiom,
! [Vvar__27318] :
( c_24__type__27317___24t(Vvar__27318)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__27318,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2744',axiom,
! [Vvar__2745] :
( c_24__type__2744___24t(Vvar__2745)
<=> ! [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__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__1314___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1323___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__2745,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),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_27821',axiom,
! [Vvar__27822] :
( c_24__type__27821___24t(Vvar__27822)
<=> ! [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__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1293___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__15860___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__19645___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__27822,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),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_2813',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2814] :
( c_24__type__2813___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2814)
<=> ! [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__2814,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_28188',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28189] :
( c_24__type__28188___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28189)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__28189,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_28524',axiom,
! [Vvar__28525] :
( c_24__type__28524___24t(Vvar__28525)
<=> ! [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__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1293___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__15860___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cType___24t(Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__1314___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__1323___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( c_24__type__16422___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__28525,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),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('$_type_2856',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__2857] :
( c_24__type__2856___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__2857)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__2857,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_28575',axiom,
! [Vvar__28576] :
( c_24__type__28575___24t(Vvar__28576)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__28580___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__28576,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_28580',axiom,
! [Vv__CANONICAL__0,Vvar__28581] :
( c_24__type__28580___24t(Vv__CANONICAL__0,Vvar__28581)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__28581,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_28702',axiom,
! [Vvar__28703] :
( c_24__type__28702___24t(Vvar__28703)
<=> ! [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__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__13765___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__18370___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__28703,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),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('$_type_28725',axiom,
! [Vvar__28726] :
( c_24__type__28725___24t(Vvar__28726)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__539___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__28726,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_28735',axiom,
! [Vvar__28736] :
( c_24__type__28735___24t(Vvar__28736)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__28736,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28737',axiom,
! [Vvar__28738] :
( c_24__type__28737___24t(Vvar__28738)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__28738,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28741',axiom,
! [Vvar__28742] :
( c_24__type__28741___24t(Vvar__28742)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__28742,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28779',axiom,
! [Vvar__28780] :
( c_24__type__28779___24t(Vvar__28780)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__28780,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_28796',axiom,
! [Vvar__28797] :
( c_24__type__28796___24t(Vvar__28797)
<=> ! [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__28797,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_28828',axiom,
! [Vvar__28829] :
( c_24__type__28828___24t(Vvar__28829)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__28829,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_28836',axiom,
! [Vvar__28837] :
( c_24__type__28836___24t(Vvar__28837)
<=> ! [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__28838___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(happ(happ(Vvar__28837,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_28849',axiom,
! [Vvar__28850] :
( c_24__type__28849___24t(Vvar__28850)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__28850,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_28902',axiom,
! [Vv__CANONICAL__0,Vvar__28903] :
( c_24__type__28902___24t(Vv__CANONICAL__0,Vvar__28903)
<=> ! [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__28904___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__28905___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(Vvar__28903,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_28919',axiom,
! [Vvar__28920] :
( c_24__type__28919___24t(Vvar__28920)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__28902___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__28920,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2892',axiom,
! [Vv__CANONICAL__0,Vvar__2893] :
( c_24__type__2892___24t(Vv__CANONICAL__0,Vvar__2893)
<=> ! [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__2893,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_28945',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28946] :
( c_24__type__28945___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28946)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__28947___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__28948___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__28946,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_28954',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28955] :
( c_24__type__28954___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28955)
<=> ! [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__28956___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__28957___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__28955,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_28982',axiom,
! [Vvar__28983] :
( c_24__type__28982___24t(Vvar__28983)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__193___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__28983,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_29037',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29038] :
( c_24__type__29037___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29038)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__29038,Vv__CANONICAL__3)) ) ) ).
fof('$_type_29045',axiom,
! [Vvar__29046] :
( c_24__type__29045___24t(Vvar__29046)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__29046,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_29055',axiom,
! [Vvar__29056] :
( c_24__type__29055___24t(Vvar__29056)
<=> ! [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__29056,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_29497',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__29498] :
( c_24__type__29497___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__29498)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29498,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2954',axiom,
! [Vvar__2955] :
( c_24__type__2954___24t(Vvar__2955)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__259___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2964___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__615___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__2955,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_29598',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__29599] :
( c_24__type__29598___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__29599)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29599,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2964',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2965] :
( c_24__type__2964___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2965)
<=> ! [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__2965,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_29699',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__29700] :
( c_24__type__29699___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__29700)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29700,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29789',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__29790] :
( c_24__type__29789___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__29790)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__29790,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_29890',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__29891] :
( c_24__type__29890___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__29891)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__29891,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_29991',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__29992] :
( c_24__type__29991___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__29992)
<=> ! [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__29992,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_30092',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__30093] :
( c_24__type__30092___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__30093)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30093,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_30144',axiom,
! [Vv__CANONICAL__0,Vvar__30145] :
( c_24__type__30144___24t(Vv__CANONICAL__0,Vvar__30145)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__30145,Vv__CANONICAL__1)) ) ) ).
fof('$_type_30292',axiom,
! [Vvar__30293] :
( c_24__type__30292___24t(Vvar__30293)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__30293,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30311',axiom,
! [Vvar__30312] :
( c_24__type__30311___24t(Vvar__30312)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__271___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__30312,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30365',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30366] :
( c_24__type__30365___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30366)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30366,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_30900',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__30901] :
( c_24__type__30900___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__30901)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30901,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31',axiom,
! [Vvar__32] :
( c_24__type__31___24t(Vvar__32)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__32,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31246',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__31247] :
( c_24__type__31246___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__31247)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31247,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31592',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__31593] :
( c_24__type__31592___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__31593)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31593,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31915',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__31916] :
( c_24__type__31915___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__31916)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__31916,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_3211',axiom,
! [Vvar__3212] :
( c_24__type__3211___24t(Vvar__3212)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__3212,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_32261',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__32262] :
( c_24__type__32261___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__32262)
<=> ! [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__32262,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_32607',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__32608] :
( c_24__type__32607___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__32608)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__32608,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_32953',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__32954] :
( c_24__type__32953___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__32954)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__32954,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_33',axiom,
! [Vvar__34] :
( c_24__type__33___24t(Vvar__34)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__34,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33299',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__33300] :
( c_24__type__33299___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__33300)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__33300,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_335',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__336] :
( c_24__type__335___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__336)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__336,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_33645',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__33646] :
( c_24__type__33645___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__33646)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__33646,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_33968',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__33969] :
( c_24__type__33968___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__33969)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__33969,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_34314',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__34315] :
( c_24__type__34314___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__34315)
<=> ! [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__34315,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_34660',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__34661] :
( c_24__type__34660___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__34661)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__34661,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_34983',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__34984] :
( c_24__type__34983___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__34984)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__34984,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_35306',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__35307] :
( c_24__type__35306___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__35307)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__35307,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_35652',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__35653] :
( c_24__type__35652___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__35653)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__35653,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35703',axiom,
! [Vvar__35704] :
( c_24__type__35703___24t(Vvar__35704)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__35704,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35708',axiom,
! [Vvar__35709] :
( c_24__type__35708___24t(Vvar__35709)
<=> ! [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__35709,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35716',axiom,
! [Vvar__35717] :
( c_24__type__35716___24t(Vvar__35717)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__35717,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_35720',axiom,
! [Vvar__35721] :
( c_24__type__35720___24t(Vvar__35721)
<=> ! [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__35721,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35786',axiom,
! [Vvar__35787] :
( c_24__type__35786___24t(Vvar__35787)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__5,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__5,Vv__CANONICAL__8)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__35787,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_35911',axiom,
! [Vvar__35912] :
( c_24__type__35911___24t(Vvar__35912)
<=> ! [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__35912,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35916',axiom,
! [Vvar__35917] :
( c_24__type__35916___24t(Vvar__35917)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__35917,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35934',axiom,
! [Vvar__35935] :
( c_24__type__35934___24t(Vvar__35935)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1293___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__35935,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_35955',axiom,
! [Vvar__35956] :
( c_24__type__35955___24t(Vvar__35956)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__35956,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_36098',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36099] :
( c_24__type__36098___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36099)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36099,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36121',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36122] :
( c_24__type__36121___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36122)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36122,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36144',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36145] :
( c_24__type__36144___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36145)
<=> ! [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__36145,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_36167',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36168] :
( c_24__type__36167___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36168)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36168,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36185',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36186] :
( c_24__type__36185___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36186)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__36186,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_36211',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36212] :
( c_24__type__36211___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36212)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36212,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36229',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36230] :
( c_24__type__36229___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36230)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__36230,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_36457',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36458] :
( c_24__type__36457___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36458)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__36458,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_36492',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36493] :
( c_24__type__36492___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36493)
<=> ! [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__36493,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_36496',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__36497] :
( c_24__type__36496___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__36497)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__36497,Vv__CANONICAL__2)) ) ) ).
fof('$_type_36510',axiom,
! [Vvar__36511] :
( c_24__type__36510___24t(Vvar__36511)
<=> ! [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__36511,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36534',axiom,
! [Vvar__36535] :
( c_24__type__36534___24t(Vvar__36535)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__703___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__36535,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_36612',axiom,
! [Vvar__36613] :
( c_24__type__36612___24t(Vvar__36613)
<=> ! [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__36613,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_36621',axiom,
! [Vvar__36622] :
( c_24__type__36621___24t(Vvar__36622)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36624___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__36622,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_36624',axiom,
! [Vv__CANONICAL__0,Vvar__36625] :
( c_24__type__36624___24t(Vv__CANONICAL__0,Vvar__36625)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__36625,Vv__CANONICAL__1)) ) ) ).
fof('$_type_3669',axiom,
! [Vvar__3670] :
( c_24__type__3669___24t(Vvar__3670)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__3670,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36690',axiom,
! [Vvar__36691] :
( c_24__type__36690___24t(Vvar__36691)
<=> ! [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__36691,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_36693',axiom,
! [Vvar__36694] :
( c_24__type__36693___24t(Vvar__36694)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__36694,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36719',axiom,
! [Vvar__36720] :
( c_24__type__36719___24t(Vvar__36720)
<=> ! [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__36720,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36725',axiom,
! [Vvar__36726] :
( c_24__type__36725___24t(Vvar__36726)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__36726,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_36734',axiom,
! [Vvar__36735] :
( c_24__type__36734___24t(Vvar__36735)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(happ(Vvar__36735,Vv__CANONICAL__0)) ) ) ).
fof('$_type_36882',axiom,
! [Vvar__36883] :
( c_24__type__36882___24t(Vvar__36883)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__28902___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eLists_2eList_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__36887___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(happ(happ(Vvar__36883,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_36925',axiom,
! [Vvar__36926] :
( c_24__type__36925___24t(Vvar__36926)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__28902___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__36926,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_36983',axiom,
! [Vvar__36984] :
( c_24__type__36983___24t(Vvar__36984)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__28902___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__36984,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_370',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__371] :
( c_24__type__370___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__371)
<=> ! [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__371,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_37054',axiom,
! [Vvar__37055] :
( c_24__type__37054___24t(Vvar__37055)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),happ(happ(happ(Vvar__37055,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37344',axiom,
! [Vvar__37345] :
( c_24__type__37344___24t(Vvar__37345)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__3,Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__37345,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('$_type_37556',axiom,
! [Vvar__37557] :
( c_24__type__37556___24t(Vvar__37557)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__13765___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(happ(Vvar__37557,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_37655',axiom,
! [Vvar__37656] :
( c_24__type__37655___24t(Vvar__37656)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__3,Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__37656,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('$_type_37739',axiom,
! [Vvar__37740] :
( c_24__type__37739___24t(Vvar__37740)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__37740,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_37865',axiom,
! [Vvar__37866] :
( c_24__type__37865___24t(Vvar__37866)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(Vv__CANONICAL__7,Vv__CANONICAL__10)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__37866,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),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('$_type_37885',axiom,
! [Vvar__37886] :
( c_24__type__37885___24t(Vvar__37886)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__37886,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37888',axiom,
! [Vvar__37889] :
( c_24__type__37888___24t(Vvar__37889)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__37889,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37893',axiom,
! [Vvar__37894] :
( c_24__type__37893___24t(Vvar__37894)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__37894,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37898',axiom,
! [Vvar__37899] :
( c_24__type__37898___24t(Vvar__37899)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__37899,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37904',axiom,
! [Vvar__37905] :
( c_24__type__37904___24t(Vvar__37905)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__37905,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37906',axiom,
! [Vvar__37907] :
( c_24__type__37906___24t(Vvar__37907)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(Vvar__37907,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37937',axiom,
! [Vvar__37938] :
( c_24__type__37937___24t(Vvar__37938)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__37941___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__37938,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_37941',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__37942] :
( c_24__type__37941___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__37942)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__37942,Vv__CANONICAL__2)) ) ) ).
fof('$_type_37975',axiom,
! [Vvar__37976] :
( c_24__type__37975___24t(Vvar__37976)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__37984___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(Vvar__37976,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_37984',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__37985] :
( c_24__type__37984___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__37985)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__2,happ(happ(Vvar__37985,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_382',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__383] :
( c_24__type__382___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__383)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__383,Vv__CANONICAL__2)) ) ) ).
fof('$_type_38632',axiom,
! [Vvar__38633] :
( c_24__type__38632___24t(Vvar__38633)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__38634___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__38635___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__38633,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38649',axiom,
! [Vvar__38650] :
( c_24__type__38649___24t(Vvar__38650)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__38650,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38673',axiom,
! [Vvar__38674] :
( c_24__type__38673___24t(Vvar__38674)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,happ(Vvar__38674,Vv__CANONICAL__0)) ) ) ).
fof('$_type_407',axiom,
! [Vvar__408] :
( c_24__type__407___24t(Vvar__408)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__410___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__3] :
( c_24__type__422___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__408,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_410',axiom,
! [Vv__CANONICAL__0,Vvar__411] :
( c_24__type__410___24t(Vv__CANONICAL__0,Vvar__411)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__411,Vv__CANONICAL__1)) ) ) ).
fof('$_type_41446',axiom,
! [Vvar__41447] :
( c_24__type__41446___24t(Vvar__41447)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(happ(happ(happ(Vvar__41447,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_41469',axiom,
! [Vvar__41470] :
( c_24__type__41469___24t(Vvar__41470)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__41470,Vv__CANONICAL__0)) ) ) ).
fof('$_type_41967',axiom,
! [Vvar__41968] :
( c_24__type__41967___24t(Vvar__41968)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__41968,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_422',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__423] :
( c_24__type__422___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__423)
<=> ! [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__423,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_42498',axiom,
! [Vvar__42499] :
( c_24__type__42498___24t(Vvar__42499)
<=> ! [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__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__259___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__15841___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__15841___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__15841___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__876___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__15860___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( c_24__type__1309___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__42499,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),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_42610',axiom,
! [Vvar__42611] :
( c_24__type__42610___24t(Vvar__42611)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__42614___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__42621___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__42628___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__42611,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('$_type_42614',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42615] :
( c_24__type__42614___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42615)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__42615,Vv__CANONICAL__2)) ) ) ).
fof('$_type_42621',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42622] :
( c_24__type__42621___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42622)
<=> ( p(Vv__CANONICAL__0)
=> t(Vvar__42622,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_42628',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42629] :
( c_24__type__42628___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42629)
<=> ( p(Vv__CANONICAL__1)
=> t(Vvar__42629,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_42660',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42661] :
( c_24__type__42660___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42661)
<=> ! [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__42661,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_42684',axiom,
! [Vvar__42685] :
( c_24__type__42684___24t(Vvar__42685)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__42660___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(happ(happ(Vvar__42685,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_42759',axiom,
! [Vvar__42760] :
( c_24__type__42759___24t(Vvar__42760)
<=> ! [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__42760,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44132',axiom,
! [Vvar__44133] :
( c_24__type__44132___24t(Vvar__44133)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(Vvar__44133,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44163',axiom,
! [Vvar__44164] :
( c_24__type__44163___24t(Vvar__44164)
<=> ! [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__44164,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_446',axiom,
! [Vvar__447] :
( c_24__type__446___24t(Vvar__447)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__447,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_45678',axiom,
! [Vv__CANONICAL__0,Vvar__45679] :
( c_24__type__45678___24t(Vv__CANONICAL__0,Vvar__45679)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__45679,Vv__CANONICAL__1)) ) ) ).
fof('$_type_45775',axiom,
! [Vvar__45776] :
( c_24__type__45775___24t(Vvar__45776)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__45776,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_45802',axiom,
! [Vvar__45803] :
( c_24__type__45802___24t(Vvar__45803)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1293___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] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__45803,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_46291',axiom,
! [Vvar__46292] :
( c_24__type__46291___24t(Vvar__46292)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13765___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__46292,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_46342',axiom,
! [Vvar__46343] :
( c_24__type__46342___24t(Vvar__46343)
<=> ! [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__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13765___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(Vvar__46343,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_468',axiom,
! [Vvar__469] :
( c_24__type__468___24t(Vvar__469)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__469,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4752',axiom,
! [Vvar__4753] :
( c_24__type__4752___24t(Vvar__4753)
<=> ! [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__4753,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_48073',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__48074] :
( c_24__type__48073___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__48074)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> t(happ(happ(Vvar__48074,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_48077',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__48078] :
( c_24__type__48077___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__48078)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(Vvar__48078,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_48108',axiom,
! [Vvar__48109] :
( c_24__type__48108___24t(Vvar__48109)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__48109,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_4822',axiom,
! [Vvar__4823] :
( c_24__type__4822___24t(Vvar__4823)
<=> ! [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__4823,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4835',axiom,
! [Vvar__4836] :
( c_24__type__4835___24t(Vvar__4836)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__4836,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4837',axiom,
! [Vvar__4838] :
( c_24__type__4837___24t(Vvar__4838)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4838,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4843',axiom,
! [Vvar__4844] :
( c_24__type__4843___24t(Vvar__4844)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__4844,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4856',axiom,
! [Vvar__4857] :
( c_24__type__4856___24t(Vvar__4857)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__4857,Vv__CANONICAL__0)) ) ) ).
fof('$_type_49479',axiom,
! [Vvar__49480] :
( c_24__type__49479___24t(Vvar__49480)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__49480,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_49599',axiom,
! [Vvar__49600] :
( c_24__type__49599___24t(Vvar__49600)
<=> ! [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__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13765___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__49611___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__9)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__49600,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_49611',axiom,
! [Vv__CANONICAL__0,Vvar__49612] :
( c_24__type__49611___24t(Vv__CANONICAL__0,Vvar__49612)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(Vvar__49612,Vv__CANONICAL__1)) ) ) ).
fof('$_type_51175',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__51176] :
( c_24__type__51175___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__51176)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(Vvar__51176,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_51191',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__51192] :
( c_24__type__51191___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__51192)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(Vvar__51192,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_51382',axiom,
! [Vvar__51383] :
( c_24__type__51382___24t(Vvar__51383)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__6] :
( c_24__type__15860___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1309___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__19645___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__51175___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__51191___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__12] :
( t(Vv__CANONICAL__12,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__51383,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),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('$_type_51420',axiom,
! [Vvar__51421] :
( c_24__type__51420___24t(Vvar__51421)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),happ(happ(happ(happ(Vvar__51421,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_518',axiom,
! [Vvar__519] :
( c_24__type__518___24t(Vvar__519)
<=> ! [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__519,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_52835',axiom,
! [Vvar__52836] :
( c_24__type__52835___24t(Vvar__52836)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__52836,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_53',axiom,
! [Vvar__54] :
( c_24__type__53___24t(Vvar__54)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__54,Vv__CANONICAL__0)) ) ) ).
fof('$_type_53234',axiom,
! [Vvar__53235] :
( c_24__type__53234___24t(Vvar__53235)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__53235,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_535',axiom,
! [Vvar__536] :
( c_24__type__535___24t(Vvar__536)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__539___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__536,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_53596',axiom,
! [Vvar__53597] :
( c_24__type__53596___24t(Vvar__53597)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__271___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__53601___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__53597,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_53601',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__53602] :
( c_24__type__53601___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__53602)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__53602,Vv__CANONICAL__2)) ) ) ).
fof('$_type_539',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__540] :
( c_24__type__539___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__540)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__540,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_54876',axiom,
! [Vvar__54877] :
( c_24__type__54876___24t(Vvar__54877)
<=> ! [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__54877,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_54959',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__54960] :
( c_24__type__54959___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__54960)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__54960,Vv__CANONICAL__2)) ) ) ).
fof('$_type_55007',axiom,
! [Vvar__55008] :
( c_24__type__55007___24t(Vvar__55008)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___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__55008,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_55116',axiom,
! [Vvar__55117] :
( c_24__type__55116___24t(Vvar__55117)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1302___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vv__CANONICAL__7)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__55117,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ).
fof('$_type_55141',axiom,
! [Vvar__55142] :
( c_24__type__55141___24t(Vvar__55142)
<=> ! [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__55142,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55152',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__55153] :
( c_24__type__55152___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__55153)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__55153,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_55247',axiom,
! [Vvar__55248] :
( c_24__type__55247___24t(Vvar__55248)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__271___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__410___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__55266___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__55248,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('$_type_55266',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__55267] :
( c_24__type__55266___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__55267)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(Vvar__55267,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ) ).
fof('$_type_55289',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__55290] :
( c_24__type__55289___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__55290)
<=> ! [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__55290,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_55405',axiom,
! [Vvar__55406] :
( c_24__type__55405___24t(Vvar__55406)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__55406,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55447',axiom,
! [Vvar__55448] :
( c_24__type__55447___24t(Vvar__55448)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__55455___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__55448,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_55455',axiom,
! [Vv__CANONICAL__0,Vvar__55456] :
( c_24__type__55455___24t(Vv__CANONICAL__0,Vvar__55456)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(Vvar__55456,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_55458',axiom,
! [Vvar__55459] :
( c_24__type__55458___24t(Vvar__55459)
<=> ! [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__55459,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55565',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__55566] :
( c_24__type__55565___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__55566)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__55566,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_55574',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__55575] :
( c_24__type__55574___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__55575)
<=> ! [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__55575,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_55583',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__55584] :
( c_24__type__55583___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__55584)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__55585___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__55584,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_55606',axiom,
! [Vvar__55607] :
( c_24__type__55606___24t(Vvar__55607)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__55618___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__55607,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_55618',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__55619] :
( c_24__type__55618___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__55619)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__55620___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__55619,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_55683',axiom,
! [Vvar__55684] :
( c_24__type__55683___24t(Vvar__55684)
<=> ! [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__55684,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_55749',axiom,
! [Vvar__55750] :
( c_24__type__55749___24t(Vvar__55750)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(happ(happ(Vvar__55750,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55752',axiom,
! [Vvar__55753] :
( c_24__type__55752___24t(Vvar__55753)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__55753,Vv__CANONICAL__0)) ) ) ).
fof('$_type_55767',axiom,
! [Vvar__55768] :
( c_24__type__55767___24t(Vvar__55768)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(happ(happ(Vvar__55768,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_56050',axiom,
! [Vvar__56051] :
( c_24__type__56050___24t(Vvar__56051)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1293___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__56051,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_56178',axiom,
! [Vvar__56179] :
( c_24__type__56178___24t(Vvar__56179)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__410___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__4] :
( c_24__type__56213___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__56179,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ) ).
fof('$_type_56213',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__56214] :
( c_24__type__56213___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__56214)
<=> ! [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__56214,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('$_type_56271',axiom,
! [Vvar__56272] :
( c_24__type__56271___24t(Vvar__56272)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__410___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__4] :
( c_24__type__56306___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__56272,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ) ).
fof('$_type_56306',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__56307] :
( c_24__type__56306___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__56307)
<=> ! [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_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))
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)
=> t(happ(happ(happ(Vvar__56307,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('$_type_565',axiom,
! [Vvar__566] :
( c_24__type__565___24t(Vvar__566)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__572___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(happ(Vvar__566,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_572',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__573] :
( c_24__type__572___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__573)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__573,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_57638',axiom,
! [Vvar__57639] :
( c_24__type__57638___24t(Vvar__57639)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__28902___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eLists_2eList_2eNoDup___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),c_24__prop__57643___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),happ(happ(happ(Vvar__57639,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_57900',axiom,
! [Vvar__57901] :
( c_24__type__57900___24t(Vvar__57901)
<=> ! [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_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),happ(happ(happ(happ(Vvar__57901,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_57906',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__57907] :
( c_24__type__57906___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__57907)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(Vvar__57907,Vv__CANONICAL__2)) ) ) ).
fof('$_type_58',axiom,
! [Vvar__59] :
( c_24__type__58___24t(Vvar__59)
<=> ! [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__59,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_58564',axiom,
! [Vvar__58565] :
( c_24__type__58564___24t(Vvar__58565)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,Vv__CANONICAL__0)
=> cCoq_2eStrings_2eString_2estring___24t(happ(Vvar__58565,Vv__CANONICAL__0)) ) ) ).
fof('$_type_601',axiom,
! [Vvar__602] :
( c_24__type__601___24t(Vvar__602)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__608___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__602,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_60314',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__60315] :
( c_24__type__60314___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__60315)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__60316___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(Vvar__60315,Vv__CANONICAL__2)) ) ) ).
fof('$_type_60330',axiom,
! [Vvar__60331] :
( c_24__type__60330___24t(Vvar__60331)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__28902___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)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eLists_2eList_2eincl___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__60335___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(happ(happ(Vvar__60331,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_608',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__609] :
( c_24__type__608___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__609)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__609,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_61',axiom,
! [Vv__CANONICAL__0,Vvar__62] :
( c_24__type__61___24t(Vv__CANONICAL__0,Vvar__62)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__62,Vv__CANONICAL__1)) ) ) ).
fof('$_type_61209',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__61210] :
( c_24__type__61209___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__61210)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__61211___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__61210,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_61222',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__61223] :
( c_24__type__61222___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__61223)
<=> ! [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__61224___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__61223,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_615',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__616] :
( c_24__type__615___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__616)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__616,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_61576',axiom,
! [Vvar__61577] :
( c_24__type__61576___24t(Vvar__61577)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__193___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(Vvar__61577,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_634',axiom,
! [Vv__CANONICAL__0,Vvar__635] :
( c_24__type__634___24t(Vv__CANONICAL__0,Vvar__635)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__635,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_63576',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__63577] :
( c_24__type__63576___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__63577)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__63577,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_63639',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__63640] :
( c_24__type__63639___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__63640)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__63640,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_63702',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__63703] :
( c_24__type__63702___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__63703)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__63703,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_63756',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__63757] :
( c_24__type__63756___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__63757)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__63757,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_63819',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__63820] :
( c_24__type__63819___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__63820)
<=> ! [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__63820,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_64181',axiom,
! [Vvar__64182] :
( c_24__type__64181___24t(Vvar__64182)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__64182,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_696',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__697] :
( c_24__type__696___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__697)
<=> ! [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__697,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_703',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__704] :
( c_24__type__703___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__704)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__704,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_74',axiom,
! [Vvar__75] :
( c_24__type__74___24t(Vvar__75)
<=> ! [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__75,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_798',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__799] :
( c_24__type__798___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__799)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__799,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_8',axiom,
! [Vvar__9] :
( c_24__type__8___24t(Vvar__9)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__9,Vv__CANONICAL__0)) ) ) ).
fof('$_type_809',axiom,
! [Vvar__810] :
( c_24__type__809___24t(Vvar__810)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__259___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__810,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_844',axiom,
! [Vvar__845] :
( c_24__type__844___24t(Vvar__845)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__259___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__615___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__845,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_86',axiom,
! [Vvar__87] :
( c_24__type__86___24t(Vvar__87)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__87,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_862',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__863] :
( c_24__type__862___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__863)
<=> ! [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__863,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_876',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__877] :
( c_24__type__876___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__877)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__877,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_895',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__896] :
( c_24__type__895___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__896)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__896,Vv__CANONICAL__2)) ) ) ).
fof('$_type_899',axiom,
! [Vvar__900] :
( c_24__type__899___24t(Vvar__900)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__271___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__900,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_917',axiom,
! [Vvar__918] :
( c_24__type__917___24t(Vvar__918)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__271___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__918,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_934',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__935] :
( c_24__type__934___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__935)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__935,Vv__CANONICAL__2)) ) ) ).
fof('$_type_938',axiom,
! [Vvar__939] :
( c_24__type__938___24t(Vvar__939)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__941___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__939,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_941',axiom,
! [Vv__CANONICAL__0,Vvar__942] :
( c_24__type__941___24t(Vv__CANONICAL__0,Vvar__942)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__942,Vv__CANONICAL__1)) ) ) ).
fof('$_type_958',axiom,
! [Vvar__959] :
( c_24__type__958___24t(Vvar__959)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__941___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__959,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_977',axiom,
! [Vvar__978] :
( c_24__type__977___24t(Vvar__978)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__978,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
c_24__type__36621___24t(cCoq_2eArith_2eWf__nat_2eltof) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__27002___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__26852___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__36725___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elements',axiom,
c_24__type__38673___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__26671___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev',axiom,
c_24__type__36734___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
c_24__type__55767___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__33___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__8___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__31___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__162___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__86___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__58___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__12122___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.id',axiom,
cCoq_2eInit_2eDatatypes_2eID___24t(cCoq_2eInit_2eDatatypes_2eid) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__27030___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__27035___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__74___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__19___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.list_rec',axiom,
c_24__type__407___24t(cCoq_2eInit_2eDatatypes_2elist__rec) ).
fof('$_typeof_Coq.Init.Datatypes.list_rect',axiom,
c_24__type__407___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__165___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__53___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__19___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__162___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__1019___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__977___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__12134___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__977___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.xorb',axiom,
c_24__type__162___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__138___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__138___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__138___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__138___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__8___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__138___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__157___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__157___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__157___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__917___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__958___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__25673___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__25678___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__25633___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__25597___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__25638___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__899___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__938___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__25610___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
c_24__type__42610___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__25650___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Lists.List.ForallPairs',axiom,
c_24__type__29045___24t(cCoq_2eLists_2eList_2eForallPairs) ).
fof('$_typeof_Coq.Lists.List.Forall_rect',axiom,
c_24__type__55247___24t(cCoq_2eLists_2eList_2eForall__rect) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__177___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.combine',axiom,
c_24__type__1449___24t(cCoq_2eLists_2eList_2ecombine) ).
fof('$_typeof_Coq.Lists.List.concat',axiom,
c_24__type__518___24t(cCoq_2eLists_2eList_2econcat) ).
fof('$_typeof_Coq.Lists.List.count_occ',axiom,
c_24__type__28919___24t(cCoq_2eLists_2eList_2ecount__occ) ).
fof('$_typeof_Coq.Lists.List.existsb',axiom,
c_24__type__190___24t(cCoq_2eLists_2eList_2eexistsb) ).
fof('$_typeof_Coq.Lists.List.filter',axiom,
c_24__type__222___24t(cCoq_2eLists_2eList_2efilter) ).
fof('$_typeof_Coq.Lists.List.find',axiom,
c_24__type__28982___24t(cCoq_2eLists_2eList_2efind) ).
fof('$_typeof_Coq.Lists.List.firstn',axiom,
c_24__type__239___24t(cCoq_2eLists_2eList_2efirstn) ).
fof('$_typeof_Coq.Lists.List.flat_map',axiom,
c_24__type__1390___24t(cCoq_2eLists_2eList_2eflat__map) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__565___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__601___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.forallb',axiom,
c_24__type__190___24t(cCoq_2eLists_2eList_2eforallb) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__28796___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.hd_error',axiom,
c_24__type__55141___24t(cCoq_2eLists_2eList_2ehd__error) ).
fof('$_typeof_Coq.Lists.List.incl',axiom,
c_24__type__1454___24t(cCoq_2eLists_2eList_2eincl) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__446___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.lel',axiom,
c_24__type__1454___24t(cCoq_2eLists_2eList_2elel) ).
fof('$_typeof_Coq.Lists.List.list_power',axiom,
c_24__type__57900___24t(cCoq_2eLists_2eList_2elist__power) ).
fof('$_typeof_Coq.Lists.List.list_prod',axiom,
c_24__type__1449___24t(cCoq_2eLists_2eList_2elist__prod) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__535___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nodup',axiom,
c_24__type__36983___24t(cCoq_2eLists_2eList_2enodup) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__111___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.nth_default',axiom,
c_24__type__28849___24t(cCoq_2eLists_2eList_2enth__default) ).
fof('$_typeof_Coq.Lists.List.nth_error',axiom,
c_24__type__133___24t(cCoq_2eLists_2eList_2enth__error) ).
fof('$_typeof_Coq.Lists.List.nth_in_or_default',axiom,
c_24__type__28836___24t(cCoq_2eLists_2eList_2enth__in__or__default) ).
fof('$_typeof_Coq.Lists.List.nth_ok',axiom,
c_24__type__28828___24t(cCoq_2eLists_2eList_2enth__ok) ).
fof('$_typeof_Coq.Lists.List.partition',axiom,
c_24__type__1426___24t(cCoq_2eLists_2eList_2epartition) ).
fof('$_typeof_Coq.Lists.List.remove',axiom,
c_24__type__36925___24t(cCoq_2eLists_2eList_2eremove) ).
fof('$_typeof_Coq.Lists.List.removelast',axiom,
c_24__type__468___24t(cCoq_2eLists_2eList_2eremovelast) ).
fof('$_typeof_Coq.Lists.List.repeat',axiom,
c_24__type__29055___24t(cCoq_2eLists_2eList_2erepeat) ).
fof('$_typeof_Coq.Lists.List.rev',axiom,
c_24__type__468___24t(cCoq_2eLists_2eList_2erev) ).
fof('$_typeof_Coq.Lists.List.rev\'',axiom,
c_24__type__468___24t(cCoq_2eLists_2eList_2erev_27) ).
fof('$_typeof_Coq.Lists.List.rev_append',axiom,
c_24__type__86___24t(cCoq_2eLists_2eList_2erev__append) ).
fof('$_typeof_Coq.Lists.List.seq',axiom,
c_24__type__1459___24t(cCoq_2eLists_2eList_2eseq) ).
fof('$_typeof_Coq.Lists.List.skipn',axiom,
c_24__type__239___24t(cCoq_2eLists_2eList_2eskipn) ).
fof('$_typeof_Coq.Lists.List.split',axiom,
c_24__type__37054___24t(cCoq_2eLists_2eList_2esplit) ).
fof('$_typeof_Coq.Lists.List.tl',axiom,
c_24__type__468___24t(cCoq_2eLists_2eList_2etl) ).
fof('$_typeof_Coq.Lists.ListDec.In_dec',axiom,
c_24__type__36882___24t(cCoq_2eLists_2eListDec_2eIn__dec) ).
fof('$_typeof_Coq.Lists.ListDec.NoDup_dec',axiom,
c_24__type__57638___24t(cCoq_2eLists_2eListDec_2eNoDup__dec) ).
fof('$_typeof_Coq.Lists.ListDec.decidable_eq',axiom,
c_24__type__28737___24t(cCoq_2eLists_2eListDec_2edecidable__eq) ).
fof('$_typeof_Coq.Lists.ListDec.incl_dec',axiom,
c_24__type__60330___24t(cCoq_2eLists_2eListDec_2eincl__dec) ).
fof('$_typeof_Coq.Lists.SetoidList.equivlistA',axiom,
c_24__type__809___24t(cCoq_2eLists_2eSetoidList_2eequivlistA) ).
fof('$_typeof_Coq.Lists.SetoidList.inclA',axiom,
c_24__type__809___24t(cCoq_2eLists_2eSetoidList_2einclA) ).
fof('$_typeof_Coq.Lists.SetoidList.removeA',axiom,
c_24__type__55606___24t(cCoq_2eLists_2eSetoidList_2eremoveA) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__844___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__844___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__2954___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__2954___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__27055___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.FinFun.Finite',axiom,
c_24__type__28737___24t(cCoq_2eLogic_2eFinFun_2eFinite) ).
fof('$_typeof_Coq.Logic.FinFun.Finite\'',axiom,
c_24__type__28737___24t(cCoq_2eLogic_2eFinFun_2eFinite_27) ).
fof('$_typeof_Coq.Logic.FinFun.Full',axiom,
c_24__type__28735___24t(cCoq_2eLogic_2eFinFun_2eFull) ).
fof('$_typeof_Coq.Logic.FinFun.Injective',axiom,
c_24__type__28725___24t(cCoq_2eLogic_2eFinFun_2eInjective) ).
fof('$_typeof_Coq.Logic.FinFun.Listing',axiom,
c_24__type__28735___24t(cCoq_2eLogic_2eFinFun_2eListing) ).
fof('$_typeof_Coq.Logic.FinFun.Surjective',axiom,
c_24__type__28725___24t(cCoq_2eLogic_2eFinFun_2eSurjective) ).
fof('$_typeof_Coq.Logic.FinFun.bFun',axiom,
c_24__type__28741___24t(cCoq_2eLogic_2eFinFun_2ebFun) ).
fof('$_typeof_Coq.Logic.FinFun.bInjective',axiom,
c_24__type__28741___24t(cCoq_2eLogic_2eFinFun_2ebInjective) ).
fof('$_typeof_Coq.Logic.FinFun.bSurjective',axiom,
c_24__type__28741___24t(cCoq_2eLogic_2eFinFun_2ebSurjective) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__17444___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__26430___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__26414___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__17444___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__26423___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_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__4843___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('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__4856___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__4856___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('$_typeof_Coq.Numbers.BinNums.xI',axiom,
c_24__type__4835___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__4835___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__36719___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__26546___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
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__4835___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__26546___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__4835___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__17783___24t(cCoq_2eQArith_2eQArith__base_2eQdiv) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq',axiom,
c_24__type__17777___24t(cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__17774___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qminus',axiom,
c_24__type__17783___24t(cCoq_2eQArith_2eQArith__base_2eQminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__17818___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__17809___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__17812___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__30292___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__30292___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__17809___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__17809___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__17812___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__17809___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__25522___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__19___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__55458___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Transitive',axiom,
c_24__type__55405___24t(cCoq_2eSets_2eRelations__1_2eTransitive) ).
fof('$_typeof_Coq.Sorting.Sorted.Sorted_rect',axiom,
c_24__type__56178___24t(cCoq_2eSorting_2eSorted_2eSorted__rect) ).
fof('$_typeof_Coq.Sorting.Sorted.StronglySorted_rec',axiom,
c_24__type__56271___24t(cCoq_2eSorting_2eSorted_2eStronglySorted__rec) ).
fof('$_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__36510___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.append',axiom,
c_24__type__64181___24t(cCoq_2eStrings_2eString_2eappend) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Strings.String.string_of_list_ascii',axiom,
c_24__type__58564___24t(cCoq_2eStrings_2eString_2estring__of__list__ascii) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__36719___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_dec',axiom,
c_24__type__38632___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__25777___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__25769___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.of_list',axiom,
c_24__type__42759___24t(cCoq_2eVectors_2eVectorDef_2eof__list) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__25752___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.to_list',axiom,
c_24__type__36612___24t(cCoq_2eVectors_2eVectorDef_2eto__list) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__4822___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__4822___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__4822___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__4822___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__4822___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__26867___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__41967___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gtb',axiom,
c_24__type__26065___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egtb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__26065___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__26867___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__26867___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__26905___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__26902___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__26871___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pos_sub',axiom,
c_24__type__54876___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__26867___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__26972___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__26867___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__26871___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__26065___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength',axiom,
c_24__type__36693___24t(cCoq_2eZArith_2eZcomplements_2eZlength) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength_aux',axiom,
c_24__type__36690___24t(cCoq_2eZArith_2eZcomplements_2eZlength__aux) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__19___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__19___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__1069___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.EnvRing.Pphi',axiom,
c_24__type__37344___24t(cCoq_2emicromega_2eEnvRing_2ePphi) ).
fof('$_typeof_Coq.micromega.QMicromega.QWitness',axiom,
cType___24t(cCoq_2emicromega_2eQMicromega_2eQWitness) ).
fof('$_typeof_Coq.micromega.RMicromega.RWitness',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRWitness) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__1580___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__30311___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__19___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_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__19___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzAdd',axiom,
c_24__type__37898___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
c_24__type__37904___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzIn',axiom,
c_24__type__37885___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzIn) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulC',axiom,
c_24__type__37893___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulE',axiom,
c_24__type__37898___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzSquare',axiom,
c_24__type__37888___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzZ',axiom,
c_24__type__37906___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzZ) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.cltb',axiom,
c_24__type__37556___24t(cCoq_2emicromega_2eRingMicromega_2ecltb) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_nformula',axiom,
c_24__type__37865___24t(cCoq_2emicromega_2eRingMicromega_2eeval__nformula) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
c_24__type__37739___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_pol',axiom,
c_24__type__37655___24t(cCoq_2emicromega_2eRingMicromega_2eeval__pol) ).
fof('$_typeof_Coq.micromega.RingMicromega.ge_bool',axiom,
c_24__type__4752___24t(cCoq_2emicromega_2eRingMicromega_2ege__bool) ).
fof('$_typeof_Coq.micromega.RingMicromega.map_option',axiom,
c_24__type__37937___24t(cCoq_2emicromega_2eRingMicromega_2emap__option) ).
fof('$_typeof_Coq.micromega.RingMicromega.map_option2',axiom,
c_24__type__37975___24t(cCoq_2emicromega_2eRingMicromega_2emap__option2) ).
fof('$_typeof_Coq.micromega.RingMicromega.nhyps_of_psatz',axiom,
c_24__type__2314___24t(cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.psubC',axiom,
c_24__type__56050___24t(cCoq_2emicromega_2eRingMicromega_2epsubC) ).
fof('$_typeof_Coq.micromega.Tauto.BFormula',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eTauto_2eBFormula) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__3211___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.TFormula',axiom,
c_24__type__3211___24t(cCoq_2emicromega_2eTauto_2eTFormula) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__977___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.Tauto.cnf',axiom,
c_24__type__977___24t(cCoq_2emicromega_2eTauto_2ecnf) ).
fof('$_typeof_Coq.micromega.Tauto.cnf_checker',axiom,
c_24__type__42684___24t(cCoq_2emicromega_2eTauto_2ecnf__checker) ).
fof('$_typeof_Coq.micromega.Tauto.cnf_tt',axiom,
c_24__type__3669___24t(cCoq_2emicromega_2eTauto_2ecnf__tt) ).
fof('$_typeof_Coq.micromega.Tauto.cons_id',axiom,
c_24__type__55683___24t(cCoq_2emicromega_2eTauto_2econs__id) ).
fof('$_typeof_Coq.micromega.Tauto.eval_cnf',axiom,
c_24__type__25731___24t(cCoq_2emicromega_2eTauto_2eeval__cnf) ).
fof('$_typeof_Coq.micromega.Tauto.eval_f',axiom,
c_24__type__53596___24t(cCoq_2emicromega_2eTauto_2eeval__f) ).
fof('$_typeof_Coq.micromega.Tauto.eval_tt',axiom,
c_24__type__36534___24t(cCoq_2emicromega_2eTauto_2eeval__tt) ).
fof('$_typeof_Coq.micromega.ZMicromega.CutProof',axiom,
c_24__type__55749___24t(cCoq_2emicromega_2eZMicromega_2eCutProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.DoneProof',axiom,
cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(cCoq_2emicromega_2eZMicromega_2eDoneProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.EnumProof',axiom,
c_24__type__41446___24t(cCoq_2emicromega_2eZMicromega_2eEnumProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.RatProof',axiom,
c_24__type__55749___24t(cCoq_2emicromega_2eZMicromega_2eRatProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.eqb',axiom,
c_24__type__38649___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.MP.to_list',axiom,
c_24__type__38673___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eto__list) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZWitness',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZWitness) ).
fof('$_typeof_Coq.micromega.ZMicromega.bdepth',axiom,
c_24__type__41469___24t(cCoq_2emicromega_2eZMicromega_2ebdepth) ).
fof('$_typeof_Coq.micromega.ZMicromega.make_conj',axiom,
c_24__type__1580___24t(cCoq_2emicromega_2eZMicromega_2emake__conj) ).
fof('$_typeof_Coq.micromega.ZMicromega.make_impl',axiom,
c_24__type__30311___24t(cCoq_2emicromega_2eZMicromega_2emake__impl) ).
fof('$_typeof_Coq.micromega.ZMicromega.valid_cut_sign',axiom,
c_24__type__55752___24t(cCoq_2emicromega_2eZMicromega_2evalid__cut__sign) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
c_24__type__26902___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).
fof('$_typeof_Coq.setoid_ring.BinList.jump',axiom,
c_24__type__26981___24t(cCoq_2esetoid__ring_2eBinList_2ejump) ).
fof('$_typeof_Coq.setoid_ring.BinList.nth',axiom,
c_24__type__26992___24t(cCoq_2esetoid__ring_2eBinList_2enth) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEI',axiom,
c_24__type__44132___24t(cCoq_2esetoid__ring_2eField__theory_2eFEI) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEO',axiom,
c_24__type__44132___24t(cCoq_2esetoid__ring_2eField__theory_2eFEO) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__27294___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__27299___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__27291___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEdiv',axiom,
c_24__type__27299___24t(cCoq_2esetoid__ring_2eField__theory_2eFEdiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__15650___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__27308___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__27299___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEopp',axiom,
c_24__type__27308___24t(cCoq_2esetoid__ring_2eField__theory_2eFEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEpow',axiom,
c_24__type__27317___24t(cCoq_2esetoid__ring_2eField__theory_2eFEpow) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEsub',axiom,
c_24__type__27299___24t(cCoq_2esetoid__ring_2eField__theory_2eFEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__19___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__28575___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons00',axiom,
c_24__type__28702___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons00) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons2',axiom,
c_24__type__28702___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons2) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEadd',axiom,
c_24__type__13839___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
c_24__type__13163___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEmul',axiom,
c_24__type__15058___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEopp',axiom,
c_24__type__14369___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEsub',axiom,
c_24__type__13839___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__1288___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.absurd_PCond',axiom,
c_24__type__44163___24t(cCoq_2esetoid__ring_2eField__theory_2eabsurd__PCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.ceqb_spec\'',axiom,
c_24__type__42498___24t(cCoq_2esetoid__ring_2eField__theory_2eceqb__spec_27) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__15729___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__15709___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.display_linear',axiom,
c_24__type__27821___24t(cCoq_2esetoid__ring_2eField__theory_2edisplay__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.display_pow_linear',axiom,
c_24__type__28524___24t(cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__19___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__15698___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__15709___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__19___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_common',axiom,
c_24__type__15754___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__common) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
c_24__type__15754___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__left) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
c_24__type__15754___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__right) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.split',axiom,
c_24__type__15811___24t(cCoq_2esetoid__ring_2eField__theory_2esplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__17446___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nsub',axiom,
c_24__type__17444___24t(cCoq_2esetoid__ring_2eInitialRing_2eNsub) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__28779___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiNword',axiom,
c_24__type__55116___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__55007___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__17417___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.get_signZ',axiom,
c_24__type__17428___24t(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.triv_div',axiom,
c_24__type__17473___24t(cCoq_2esetoid__ring_2eInitialRing_2etriv__div) ).
fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
c_24__type__162___24t(cCoq_2esetoid__ring_2eRing_2ebool__eq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mphi',axiom,
c_24__type__48108___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.P0',axiom,
c_24__type__35703___24t(cCoq_2esetoid__ring_2eRing__polynom_2eP0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.P1',axiom,
c_24__type__35703___24t(cCoq_2esetoid__ring_2eRing__polynom_2eP1) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__18127___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__18127___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__18133___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__18138___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__18130___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__2744___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__18138___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__35911___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__35916___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__18138___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__19___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__35716___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PaddC',axiom,
c_24__type__45802___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePaddC) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__35703___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__18031___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pequiv',axiom,
c_24__type__35786___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePequiv) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__35708___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PmulC',axiom,
c_24__type__46342___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePmulC) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PmulC_aux',axiom,
c_24__type__46291___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePmulC__aux) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__19___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Popp',axiom,
c_24__type__45775___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi',axiom,
c_24__type__18117___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__19303___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Ppow_pos',axiom,
c_24__type__49599___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePpow__pos) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PsubC',axiom,
c_24__type__45802___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePsubC) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.add_pow_list',axiom,
c_24__type__51420___24t(cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
c_24__type__18608___24t(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkPinj',axiom,
c_24__type__35708___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkPinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkZmon',axiom,
c_24__type__35720___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkZmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_X',axiom,
c_24__type__49479___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__X) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
c_24__type__18793___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkadd_mult',axiom,
c_24__type__51382___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkadd__mult) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__35934___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_rec',axiom,
c_24__type__55447___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkopp_pow',axiom,
c_24__type__53234___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkopp__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkpow',axiom,
c_24__type__35955___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__18352___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.r_list_pow',axiom,
c_24__type__52835___24t(cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.vmon',axiom,
c_24__type__35720___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
c_24__type__35720___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon_pred',axiom,
c_24__type__35720___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon__pred) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__25107___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__25107___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__25402___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
c_24__type__31___24t(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__17446___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__19759___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__35955___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_X',axiom,
cType___24t(cX) ).
fof('$_typeof_l',axiom,
cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(cX),cl) ).
fof('$_typeof_list_utils.concat',axiom,
c_24__type__518___24t(clist__utils_2econcat) ).
fof('$_typeof_list_utils.count',axiom,
c_24__type__61576___24t(clist__utils_2ecount) ).
fof('$_typeof_s',axiom,
cCoq_2eInit_2eDatatypes_2elist___24t(cX,cs) ).
fof('$_typeof_x',axiom,
cX___24t(cx) ).
fof('Coq.Arith.Compare_dec.dec_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Gt.gt_S_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.gt_S_n',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),cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))
=> cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n) ) ) ) ).
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)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.gt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Le.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Le.le_n_0_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( p(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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.Lt.S_pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)
=> V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2epred___24a1(V0__n)) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_or_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.Lt.lt_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Lt.lt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.Max.max_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n))
=> cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.Arith.Max.max_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.Arith.Minus.minus_Sn_m',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n))
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),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.add_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO))
<=> V0__n = cCoq_2eInit_2eDatatypes_2eO ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n))
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_lt_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p))
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO)) ) ).
fof('Coq.Arith.PeanoNat.Nat.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)
<=> p(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
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2esub___24a2(V1__m,V0__n),V0__n) = V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_diag',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,V0__n) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__138,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__8,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_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8,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_2eDatatypes_2eS) ).
fof('Coq.Arith.Plus.le_plus_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m))) ) ) ).
fof('Coq.Arith.Plus.le_plus_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m))) ) ) ).
fof('Coq.Bool.Bool.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.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__61___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__61___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__10___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.Datatypes.prod_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__54959___24t(V0__A,V1__B,V2__P)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V3__a,V4__b))) ) )
=> ! [V4__p] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
=> p(happ(V2__P,V4__p)) ) ) ) ) ) ).
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__147___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Init.Peano.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.Init.Peano.le_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Init.Peano.plus_n_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Init.Peano.plus_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ).
fof('Coq.Init.Specif.sumbool_ind',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__36496___24t(V0__A,V1__B,V2__P)
=> ( ( p(V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l2))) ) ) ) ) ).
fof('Coq.Lists.List.Add_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V3__l,V4__l_27)
=> cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V4__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l)) ) ) ) ).
fof('Coq.Lists.List.Add_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__634___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__634___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_Forall_neg',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
| ~ p(happ(V1__P,V3__x)) ) )
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,c_24__lam__56026___24a2(V0__A,V1__P),V2__l)
<=> ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___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__271___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__271___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__271___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__271___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__271___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__271___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__271___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__271___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__61___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__271___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__61___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__259___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,happ(V1__R,V2__a),V3__l)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V3__l)
=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.FOP_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__259___24t(V0__A,V1__R)
=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.Forall2_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__703___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__703___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__703___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__703___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__703___24t(V0__A,V1__B,V2__R)
=> ! [V3__P] :
( c_24__type__55289___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__703___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__703___24t(V0__A,V1__B,V2__R)
=> ! [V3__P] :
( c_24__type__55289___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__259___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__259___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__259___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__61___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_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__259___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__61___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_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__259___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_Exists_neg',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,c_24__lam__56020___24a2(V0__A,V1__P),V2__l)
<=> ~ cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V2__l) ) ) ) ) ).
fof('Coq.Lists.List.Forall_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(happ(V1__P,V2__x))
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_dec_subproof',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( ~ p(happ(V1__P,V2__a))
=> ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_dec_subproof0',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l_27)
=> ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_forall',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
=> p(happ(V1__P,V3__x)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_impl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__271___24t(V0__A,V2__Q)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(happ(V1__P,V3__a))
=> p(happ(V2__Q,V3__a)) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V4__l)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V2__Q,V4__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__61___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(happ(V1__P,V4__x))
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V5__l)
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l))
=> p(happ(V1__P,V2__a)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_inv_tail',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> ! [V2__x0] :
( t(V2__x0,V0__A)
=> ! [V3__xs] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__xs)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x0,V3__xs))
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__xs) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.Forall_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__61___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(happ(V1__P,V4__x))
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V5__l)
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.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)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l_27))
<=> ( p(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))
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l))) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_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)
=> ( p(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))
& p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_count_occ',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__decA] :
( c_24__type__28902___24t(V0__A,V1__decA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l))
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__decA,V2__l,V3__x),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_count_occ\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__decA] :
( c_24__type__28902___24t(V0__A,V1__decA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(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__decA,V2__l,V3__x) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_incl_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__l_27))
=> p(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__61___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V4__l))
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l))
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l))
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_length_incl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__l_27))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l_27,V1__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_map_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__539___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ).
fof('Coq.Lists.List.NoDup_nodup',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__decA] :
( c_24__type__28902___24t(V0__A,V1__decA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> p(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)
=> ( p(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_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)
=> ( p(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_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)
=> ( p(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_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)
=> ( p(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__61___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V4__l))
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l))
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l))
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.app_assoc',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__m,V3__n)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m),V3__n) ) ) ) ) ).
fof('Coq.Lists.List.app_assoc_reverse',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m),V3__n) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__m,V3__n)) ) ) ) ) ).
fof('Coq.Lists.List.app_comm_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__y)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,V2__y)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V1__x),V2__y) ) ) ) ) ).
fof('Coq.Lists.List.app_cons_not_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__y)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) != cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V2__y)) ) ) ) ) ).
fof('Coq.Lists.List.app_eq_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
=> ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& V2__l_27 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ) ) ).
fof('Coq.Lists.List.app_inj_tail',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__y)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__b,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( V1__x = V2__y
& V3__a = V4__b ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.app_inv_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l1) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V3__l2)
=> V2__l1 = V3__l2 ) ) ) ) ) ).
fof('Coq.Lists.List.app_inv_tail',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V1__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l2,V1__l)
=> V2__l1 = V3__l2 ) ) ) ) ) ).
fof('Coq.Lists.List.app_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27)) ) ) ) ).
fof('Coq.Lists.List.app_nil_end',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> V1__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.app_nil_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),V1__l) = V1__l ) ) ).
fof('Coq.Lists.List.app_nil_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) = V1__l ) ) ).
fof('Coq.Lists.List.app_nth1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,V1__l,V3__d) ) ) ) ) ) ) ).
fof('Coq.Lists.List.concat_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V1__l1)
=> ! [V2__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V2__l2)
=> cCoq_2eLists_2eList_2econcat___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V1__l1,V2__l2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2econcat___24a2(V0__A,V1__l1),cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l2)) ) ) ) ).
fof('Coq.Lists.List.concat_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V2__l)
=> cCoq_2eLists_2eList_2econcat___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V1__x,V2__l)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l)) ) ) ) ).
fof('Coq.Lists.List.concat_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__539___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V3__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,cCoq_2eLists_2eList_2econcat___24a2(V0__A,V3__l)) = cCoq_2eLists_2eList_2econcat___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),cCoq_2eLists_2eList_2emap___24a3(V0__A,V1__B,V2__f),V3__l)) ) ) ) ) ).
fof('Coq.Lists.List.count_occ_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eq__dec] :
( c_24__type__28902___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_2eInit_2ePeano_2egt___24a2(cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V2__l,V3__x),cCoq_2eInit_2eDatatypes_2eO) ) ) ) ) ) ).
fof('Coq.Lists.List.count_occ_cons_neq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eq__dec] :
( c_24__type__28902___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_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__539___24t(V0__A,V1__B,V2__f)
=> ! [V3__decA] :
( c_24__type__28945___24t(V0__A,V1__B,V3__decA)
=> ! [V4__decB] :
( c_24__type__28954___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__28902___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.elements_in_partition',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__193___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l1)
=> ! [V4__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l2)
=> ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V3__l1,V4__l2)
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V6__x,V2__l))
<=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V6__x,V3__l1))
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V6__x,V4__l2)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.existsb_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__193___24t(V0__A,V1__f)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V2__l1),cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l2)) ) ) ) ) ).
fof('Coq.Lists.List.existsb_exists',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__193___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.ext_in_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__539___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__539___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__193___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__193___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__193___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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),V1__n))
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l) = V2__l ) ) ) ) ).
fof('Coq.Lists.List.firstn_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)
=> p(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',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_2elength___24a2(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l)) = cCoq_2eInit_2eNat_2emin___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)) ) ) ) ).
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)
=> ( p(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_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ).
fof('Coq.Lists.List.firstn_skipn',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l),cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,V2__l)) = V2__l ) ) ) ).
fof('Coq.Lists.List.fold_left_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__572___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_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2efold__left___24a5(cCoq_2eInit_2eDatatypes_2enat,V0__A,c_24__lam__28964___24a1(V0__A),V1__l,cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) ) ) ).
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__615___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__63024___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__615___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__1293___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_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__193___24t(V0__A,V1__f)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V2__l1),cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l2)) ) ) ) ) ).
fof('Coq.Lists.List.forallb_forall',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__193___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.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_combine_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l_27)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V1__B)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V4__x,V5__y),cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V2__l,V3__l_27)))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V2__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_combine_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l_27)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V1__B)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V4__x,V5__y),cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V2__l,V3__l_27)))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V5__y,V3__l_27)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,V3__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l))) ) ) ) ) ) ).
fof('Coq.Lists.List.in_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l))) ) ) ) ).
fof('Coq.Lists.List.in_flat_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__1394___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V4__y,cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,V3__l)))
<=> ? [V5__x] :
( t(V5__x,V0__A)
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V3__l))
& p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V4__y,happ(V2__f,V5__x))) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l)))
=> ( V1__a = V2__b
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__539___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__539___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_prod',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l_27)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V1__B)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V2__l))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V5__y,V3__l_27))
=> p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V4__x,V5__y),cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,V2__l,V3__l_27))) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_prod_aux',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V1__B)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V3__y,V4__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V2__x,V3__y),cCoq_2eLists_2eList_2emap___24a4(V1__B,cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),c_24__lam__1442___24a3(V0__A,V1__B,V2__x),V4__l))) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_prod_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l_27)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V1__B)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V4__x,V5__y),cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,V2__l,V3__l_27)))
<=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V2__l))
& p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V5__y,V3__l_27)) ) ) ) ) ) ) ) ) ).
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_seq',axiom,
! [V0__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__len)
=> ! [V1__start] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__start)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2enat,V2__n,cCoq_2eLists_2eList_2eseq___24a2(V1__start,V0__len)))
<=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__start,V2__n))
& cCoq_2eInit_2ePeano_2elt___24a2(V2__n,cCoq_2eInit_2eNat_2eadd___24a2(V1__start,V0__len)) ) ) ) ) ) ).
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.in_split_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),V2__l)
=> ! [V3__p] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V3__p)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),V3__p,V2__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V3__p),cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),cCoq_2eLists_2eList_2esplit___24a3(V0__A,V1__B,V2__l)))) ) ) ) ) ) ).
fof('Coq.Lists.List.in_split_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),V2__l)
=> ! [V3__p] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V3__p)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),V3__p,V2__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V3__p),cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),cCoq_2eLists_2eList_2esplit___24a3(V0__A,V1__B,V2__l)))) ) ) ) ) ) ).
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))
=> ( p(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)
=> p(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)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n))
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__m,V3__n))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m),V3__n)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_appl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__n,V2__m))) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_appr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__m,V3__n))) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V3__m))
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__m))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l),V3__m)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V1__l)) ) ) ).
fof('Coq.Lists.List.incl_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__m))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__m))) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_tran',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m))
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__m,V3__n))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__b] :
( t(V1__b,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V2__l,V3__m)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__b,V3__m)) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_cons_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V3__l,V4__m)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__b,V4__m)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_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__539___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__539___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__539___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__539___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__539___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__539___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__539___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__539___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__539___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__55146___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__539___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__539___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__55152___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__55166___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__539___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.map_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__539___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,cCoq_2eLists_2eList_2erev___24a2(V0__A,V3__l)) = cCoq_2eLists_2eList_2erev___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)) ) ) ) ) ).
fof('Coq.Lists.List.neg_Forall_Exists_neg',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__271___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3___24Anonymous] :
( c_24__type__60314___24t(V0__A,V1__P,V3___24Anonymous)
=> ( ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l)
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,c_24__lam__60320___24a2(V0__A,V1__P),V2__l) ) ) ) ) ) ).
fof('Coq.Lists.List.nil_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) != cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l) ) ) ) ).
fof('Coq.Lists.List.nodup_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__decA] :
( c_24__type__28902___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__28902___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_app1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V3__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))
=> cCoq_2eLists_2eList_2enth__error___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V3__n) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V2__n))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V3__d) = V3__d ) ) ) ) ) ).
fof('Coq.Lists.List.remove_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eq__dec] :
( c_24__type__28902___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.repeat_spec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__y,cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,V1__n)))
=> V3__y = V2__x ) ) ) ) ) ).
fof('Coq.Lists.List.rev_alt',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,V1__l) = cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.rev_app_distr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__y)
=> cCoq_2eLists_2eList_2erev___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,V2__y)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__y),cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__x)) ) ) ) ).
fof('Coq.Lists.List.rev_append_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V1__l,V2__l_27) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l),V2__l_27) ) ) ) ).
fof('Coq.Lists.List.rev_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__61___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__61___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.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_all',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.List.skipn_all2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),V1__n))
=> cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ) ).
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_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_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,V2__l)) = cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),V1__n) ) ) ) ).
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.ListDec.In_decidable',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ).
fof('Coq.Lists.ListDec.NoDup_decidable',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l)) ) ) ) ).
fof('Coq.Lists.ListDec.incl_decidable',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__l_27)) ) ) ) ) ).
fof('Coq.Lists.ListDec.uniquify',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ? [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
& p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l_27))
& p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__l_27)) ) ) ) ) ).
fof('Coq.Lists.ListDec.uniquify_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V1__B)
=> ! [V3__f] :
( c_24__type__539___24t(V0__A,V1__B,V3__f)
=> ! [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(cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__f,V5__l_27)))
& p(cCoq_2eLists_2eList_2eincl___24a3(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__f,V4__l),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__f,V5__l_27))) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_InfA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__ltA] :
( c_24__type__259___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__259___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__259___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__259___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__259___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__259___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__259___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2892___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__61___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__259___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__259___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__259___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__259___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__259___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__259___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__61___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__259___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__259___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__259___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__259___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__61___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__259___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__259___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__259___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__259___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_eqA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__ltA] :
( c_24__type__259___24t(V0__A,V3__ltA)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__259___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__271___24a1(V0__A),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cProp,V1__eqA,c_3c_3d_3e)),V3__ltA)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ( p(happ(happ(V1__eqA,V6__x),V7__y))
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V3__ltA,V7__y,V5__l)
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V3__ltA,V6__x,V5__l) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InfA_ltA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__ltA] :
( c_24__type__259___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_altdef',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V2__l)
<=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,cCoq_2eClasses_2eRelationClasses_2ecomplement___24a2(V0__A,V1__eqA),V2__l) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V4__l_27)
=> ( ! [V7__x] :
( t(V7__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V7__x,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V7__x,V4__l_27)
=> p(c_24False) ) ) )
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___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__259___24t(V0__A,V1__eqA)
=> ! [V2__P] :
( c_24__type__61___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__259___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__259___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_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V3__l_27)))
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.SortA_NoDupA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__ltA] :
( c_24__type__259___24t(V0__A,V3__ltA)
=> ( cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(V0__A,V3__ltA)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__259___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__271___24a1(V0__A),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cProp,V1__eqA,c_3c_3d_3e)),V3__ltA)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V3__ltA,V6__l)
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V6__l) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.SortA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__ltA] :
( c_24__type__259___24t(V0__A,V3__ltA)
=> ! [V4__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
=> ! [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V3__ltA,V4__l1)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V3__ltA,V5__l2)
=> ( ! [V8__x] :
( t(V8__x,V0__A)
=> ! [V9__y] :
( t(V9__y,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V8__x,V4__l1)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V9__y,V5__l2)
=> p(happ(happ(V3__ltA,V8__x),V9__y)) ) ) ) )
=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V3__ltA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,V5__l2)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.app_eqlistA_compat',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1554___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),c_24__type__1549___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA))),cCoq_2eInit_2eDatatypes_2eapp___24a1(V0__A)) ) ) ).
fof('Coq.Lists.SetoidList.eqarefl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___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__259___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__259___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__259___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__259___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__259___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__259___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__259___24t(V0__A,V1__eqA)
=> ! [V2__P] :
( c_24__type__634___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__259___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_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___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_rev_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l1_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V2__l1,V3__l1_27)
=> ! [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
=> ! [V6__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V5__l2,V6__l2_27)
=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l1),V5__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V3__l1_27),V6__l2_27)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ! [V2__P] :
( c_24__type__634___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_app_idem',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V2__l),V2__l) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_app_proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1554___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),c_24__type__1549___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA))),cCoq_2eInit_2eDatatypes_2eapp___24a1(V0__A)) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_cons_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___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__259___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1546___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__1549___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__259___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__259___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__259___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__259___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA)) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_eqlistA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__eqB] :
( c_24__type__862___24t(V0__A,V2__B,V3__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V2__B,V3__eqB)
=> ! [V5__f] :
( c_24__type__615___24t(V0__A,V2__B,V5__f)
=> ! [V6__i] :
( t(V6__i,V2__B)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__615___24a2(V0__A,V2__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__876___24a2(V0__A,V2__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V2__B,V2__B,V3__eqB,V3__eqB)),V5__f)
=> ! [V8__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V8__s)
=> ! [V9__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V9__s_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V8__s,V9__s_27)
=> p(happ(happ(V3__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V2__B,V0__A,V5__f,V6__i,V8__s)),cCoq_2eLists_2eList_2efold__right___24a5(V2__B,V0__A,V5__f,V6__i,V9__s_27))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_eqlistA2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__eqB] :
( c_24__type__862___24t(V0__A,V2__B,V3__eqB)
=> ! [V4__f] :
( c_24__type__615___24t(V0__A,V2__B,V4__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__615___24a2(V0__A,V2__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__876___24a2(V0__A,V2__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V2__B,V2__B,V3__eqB,V3__eqB)),V4__f)
=> ! [V6__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__s)
=> ! [V7__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__s_27)
=> ! [V8__i] :
( t(V8__i,V2__B)
=> ! [V9__j] :
( t(V9__j,V2__B)
=> ( p(happ(happ(V3__eqB,V8__i),V9__j))
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V6__s,V7__s_27)
=> p(happ(happ(V3__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V2__B,V0__A,V4__f,V8__i,V6__s)),cCoq_2eLists_2eList_2efold__right___24a5(V2__B,V0__A,V4__f,V9__j,V7__s_27))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.incl_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___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__259___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__eqA__dec] :
( c_24__type__61209___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_NoDupA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__eqA__dec] :
( c_24__type__61222___24t(V0__A,V1__eqA,V3__eqA__dec)
=> ! [V4__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__s)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V4__s)
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V3__eqA__dec,V5__x,V4__s)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.rev_eqlistA_compat',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__259___24t(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1549___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA)),cCoq_2eLists_2eList_2erev___24a1(V0__A)) ) ) ).
fof('Coq.Logic.Decidable.dec_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__54968___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__54967___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.imp_simp',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( p(V0__A)
=> p(V1__B) )
=> ( ~ p(V0__A)
| p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
& p(V1__B) )
=> ( ~ p(V0__A)
| ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_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.FinFun.Injective_carac',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLogic_2eFinFun_2eListing___24a2(V0__A,V2__l)
=> ! [V4__f] :
( c_24__type__539___24t(V0__A,V1__B,V4__f)
=> ( cCoq_2eLogic_2eFinFun_2eInjective___24a3(V0__A,V1__B,V4__f)
<=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V4__f,V2__l))) ) ) ) ) ) ) ).
fof('Coq.Logic.FinFun.Injective_list_carac',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
=> ! [V3__f] :
( c_24__type__539___24t(V0__A,V1__B,V3__f)
=> ( cCoq_2eLogic_2eFinFun_2eInjective___24a3(V0__A,V1__B,V3__f)
<=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__f,V4__l))) ) ) ) ) ) ) ) ).
fof('Coq.Logic.FinFun.Injective_map_NoDup',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__539___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLogic_2eFinFun_2eInjective___24a3(V0__A,V1__B,V2__f)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l))) ) ) ) ) ) ) ).
fof('Coq.Logic.FinFun.Surjective_list_carac',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__539___24t(V0__A,V1__B,V2__f)
=> ( cCoq_2eLogic_2eFinFun_2eSurjective___24a3(V0__A,V1__B,V2__f)
<=> ! [V3__lB] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__lB)
=> ? [V4__lA] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__lA)
& p(cCoq_2eLists_2eList_2eincl___24a3(V1__B,V3__lB,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__lA))) ) ) ) ) ) ) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__4837___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.add_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__36721___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.peano_ind',axiom,
! [V0__P] :
( c_24__type__4837___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.Relations.Relation_Operators.Lt_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__259___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__259___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__259___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__259___24t(V0__A,V1__leA)
=> ! [V2__P] :
( c_24__type__634___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__259___24t(V0__A,V1__leA)
=> ! [V2__P] :
( c_24__type__634___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.Setoids.Setoid.Build_Setoid_Theory',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__A,V1__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V1__Aeq,V3__x),V3__x)) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> p(happ(happ(V1__Aeq,V4__y),V3__x)) ) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ! [V5__z] :
( t(V5__z,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> ( p(happ(happ(V1__Aeq,V4__y),V5__z))
=> p(happ(happ(V1__Aeq,V3__x),V5__z)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.NoDup_Permutation',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l_27))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V1__l))
<=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V2__l_27)) ) )
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.NoDup_Permutation_bis',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l_27))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__l_27))
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_Add',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l),V3__l_27) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_Add_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l1,V3__l2)
=> ! [V5__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l1_27)
=> ! [V6__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l1_27,V2__l1)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V6__l2_27,V3__l2)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V5__l1_27,V6__l2_27) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_Equivalence',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.Permutation_NoDup',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l_27)) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_NoDup\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__61___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cProp,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),c_3c_3d_3e),cCoq_2eLists_2eList_2eNoDup___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.Permutation_add_inside',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ! [V4__tl] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__tl)
=> ! [V5__tl_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__tl_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l,V3__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V4__tl,V5__tl_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V4__tl)),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l_27,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V5__tl_27))) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ! [V4__m_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__m_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V3__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__m,V4__m_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l_27,V4__m_27)) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1554___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),c_24__type__1549___24a1(V0__A),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A))),cCoq_2eInit_2eDatatypes_2eapp___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.Permutation_app_comm',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l_27,V1__l)) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__tl] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__tl)
=> ! [V3__tl_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__tl_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__tl,V3__tl_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__tl),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V3__tl_27)) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l1)
=> ! [V2__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l2)
=> ! [V3__l3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l3)
=> ! [V4__l4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l4)
=> ! [V5__a] :
( t(V5__a,V0__A)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__a,V2__l2)),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l3,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__a,V4__l4)))
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l1,V2__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l3,V4__l4)) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app_inv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l1),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V3__l2))
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l1,V3__l2) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app_inv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V1__l),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l2,V1__l))
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l1,V3__l2) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_app_tail',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__tl] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__tl)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V3__tl),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l_27,V3__tl)) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1546___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__1549___24a1(V0__A),c_3d___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A))),cCoq_2eInit_2eDatatypes_2econs___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.Permutation_cons_app',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)
=> ! [V4__a] :
( t(V4__a,V0__A)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2))
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V1__l),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V3__l2))) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_cons_app_inv',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)
=> ! [V4__a] :
( t(V4__a,V0__A)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V1__l),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V3__l2)))
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_cons_append',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_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V1__l),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_cons_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V1__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V2__l_27))
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V1__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l_27)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_in\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2892___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__61___24a1(V0__A),c_3d___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cProp,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),c_3c_3d_3e)),cCoq_2eLists_2eList_2eIn___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.Permutation_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__634___24t(V0__A,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V4__l,V5__l_27)
=> ( p(happ(happ(V1__P,V4__l),V5__l_27))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V5__l_27))) ) ) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,V6__l)))) ) ) )
=> ( ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ! [V7__l_27_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V5__l,V6__l_27)
=> ( p(happ(happ(V1__P,V5__l),V6__l_27))
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l_27,V7__l_27_27)
=> ( p(happ(happ(V1__P,V6__l_27),V7__l_27_27))
=> p(happ(happ(V1__P,V5__l),V7__l_27_27)) ) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l,V7__l)
=> p(happ(happ(V1__P,V6__l),V7__l)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_ind_bis',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__634___24t(V0__A,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V4__l,V5__l_27)
=> ( p(happ(happ(V1__P,V4__l),V5__l_27))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V5__l_27))) ) ) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l,V7__l_27)
=> ( p(happ(happ(V1__P,V6__l),V7__l_27))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,V7__l_27)))) ) ) ) ) ) )
=> ( ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ! [V7__l_27_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V5__l,V6__l_27)
=> ( p(happ(happ(V1__P,V5__l),V6__l_27))
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l_27,V7__l_27_27)
=> ( p(happ(happ(V1__P,V6__l_27),V7__l_27_27))
=> p(happ(happ(V1__P,V5__l),V7__l_27_27)) ) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l,V7__l_27)
=> p(happ(happ(V1__P,V6__l),V7__l_27)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_length\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30144___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),cCoq_2eInit_2eDatatypes_2elength___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.Permutation_length_1_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),V2__l)
=> V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_length_2_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a1] :
( t(V1__a1,V0__A)
=> ! [V2__a2] :
( t(V2__a2,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a2,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))),V3__l)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a2,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
| V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a2,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a1,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__539___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V3__l,V4__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l_27)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_map\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__539___24t(V0__A,V1__B,V2__f)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__57906___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V1__B)),cCoq_2eLists_2eList_2emap___24a3(V0__A,V1__B,V2__f)) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_middle',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l1)
=> ! [V2__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l2)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l1,V2__l2)),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V2__l2))) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),V1__l)
=> V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_nil_app_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ~ cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V2__l_27))) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_nil_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_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V1__l)) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V1__l) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l)) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_rev\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1549___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A)),cCoq_2eLists_2eList_2erev___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.Permutation_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__634___24t(V0__A,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V4__l,V5__l_27)
=> ( p(happ(happ(V1__P,V4__l),V5__l_27))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V5__l_27))) ) ) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,V6__l)))) ) ) )
=> ( ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ! [V7__l_27_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V5__l,V6__l_27)
=> ( p(happ(happ(V1__P,V5__l),V6__l_27))
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l_27,V7__l_27_27)
=> ( p(happ(happ(V1__P,V6__l_27),V7__l_27_27))
=> p(happ(happ(V1__P,V5__l),V7__l_27_27)) ) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l,V7__l)
=> p(happ(happ(V1__P,V6__l),V7__l)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l_27,V1__l) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__l_27_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l_27,V3__l_27_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V3__l_27_27) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.perm_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.perm_skip',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l,V3__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V3__l_27)) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.perm_swap',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V3__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__y,V3__l))) ) ) ) ) ).
fof('Coq.Sorting.Permutation.perm_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__l_27_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l_27,V3__l_27_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V3__l_27_27) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.HdRel_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__259___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__259___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__P] :
( c_24__type__61___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__259___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__259___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__259___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__P] :
( c_24__type__61___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__259___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__259___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.LSorted_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__259___24t(V0__A,V1__R)
=> cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Sorting.Sorted.LocallySorted_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__259___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__61___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__259___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V3__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,happ(V1__R,V2__a),V3__l)
=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.SSorted_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__259___24t(V0__A,V1__R)
=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_LocallySorted_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__259___24t(V0__A,V1__R)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V2__l)
<=> cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V0__A,V1__R,V2__l) ) ) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_StronglySorted',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__259___24t(V0__A,V1__R)
=> ( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__A,V1__R)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V3__l)
=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V3__l) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__259___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__259___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))
=> 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__259___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__61___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__259___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_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__259___24t(V0__A,V1__R)
=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__259___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__61___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__259___24t(V0__A,V1__R)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V2__l)
=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V2__l) ) ) ) ) ).
fof('Coq.Sorting.Sorted.StronglySorted_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__259___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__61___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_2eStronglySorted___24a3(V0__A,V1__R,V5__l)
=> ( p(happ(V2__P,V5__l))
=> ( 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)
=> ( 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__259___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__61___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_2eStronglySorted___24a3(V0__A,V1__R,V5__l)
=> ( p(happ(V2__P,V5__l))
=> ( 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)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__36741___24a2(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.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.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.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_2454884___24a2(V0__p,V1__q) ) ) ).
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.Znat.inj_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__y) ) ) ) ).
fof('Coq.ZArith.Znat.inj_gt',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_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_lt',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)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_le_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_lt_ge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zegal_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.auxiliary.Zge_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zgt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zle_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zlt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zne_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.micromega.EnvRing.Psquare_ok',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cadd] :
( c_24__type__15841___24t(V0__R,V11__C,V14__cadd)
=> ! [V15__cmul] :
( c_24__type__15841___24t(V0__R,V11__C,V15__cmul)
=> ! [V16__csub] :
( c_24__type__15841___24t(V0__R,V11__C,V16__csub)
=> ! [V17__copp] :
( c_24__type__876___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__15860___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__phi] :
( c_24__type__1309___24t(V0__R,V11__C,V19__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,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V19__phi)
=> ! [V21__P] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V11__C,V21__P)
=> ! [V22__l] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(V0__R,V22__l)
=> p(happ(happ(V7__req,cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V3__radd,V4__rmul,V11__C,V19__phi,V22__l,cCoq_2emicromega_2eEnvRing_2ePsquare___24a7(V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V18__ceqb,V21__P))),happ(happ(V4__rmul,cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V3__radd,V4__rmul,V11__C,V19__phi,V22__l,V21__P)),cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V3__radd,V4__rmul,V11__C,V19__phi,V22__l,V21__P)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_square_nonneg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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.SORsetoid',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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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__1302___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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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.OrderedRing.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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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.Refl.make_conj_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__271___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__271___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__271___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__271___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__271___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_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__t)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__a)
=> ! [V3__eval] :
( c_24__type__271___24t(V0__A,V3__eval)
=> ( ! [V4__d] :
( t(V4__d,V0__A)
=> ( p(happ(V3__eval,V4__d))
| ~ p(happ(V3__eval,V4__d)) ) )
=> ( ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__t,V2__a))
=> ( ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,V1__t)
| ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,V2__a) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.not_make_conj_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__t] :
( t(V1__t,V0__A)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__a)
=> ! [V3__eval] :
( c_24__type__271___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.Rops_wd',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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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__eq__ext___24a5(V0__R,V3__rplus,V4__rtimes,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.SORrm',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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__15841___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__15841___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__15841___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__876___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__15860___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__15860___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__1309___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__1314___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__1323___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V18__phi) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.cltb_sound',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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cplus] :
( c_24__type__15841___24t(V0__R,V11__C,V14__cplus)
=> ! [V15__ctimes] :
( c_24__type__15841___24t(V0__R,V11__C,V15__ctimes)
=> ! [V16__cminus] :
( c_24__type__15841___24t(V0__R,V11__C,V16__cminus)
=> ! [V17__copp] :
( c_24__type__876___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__15860___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__cleb] :
( c_24__type__15860___24t(V0__R,V11__C,V19__cleb)
=> ! [V20__phi] :
( c_24__type__1309___24t(V0__R,V11__C,V20__phi)
=> ! [V21__E] :
( cType___24t(V21__E)
=> ! [V22__pow__phi] :
( c_24__type__1314___24t(V0__R,V11__C,V21__E,V22__pow__phi)
=> ! [V23__rpow] :
( c_24__type__1323___24t(V0__R,V11__C,V21__E,V23__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V11__C,V12__cO,V13__cI,V14__cplus,V15__ctimes,V16__cminus,V17__copp,V18__ceqb,V19__cleb,V20__phi,V21__E,V22__pow__phi,V23__rpow)
=> ! [V25__x] :
( t(V25__x,V11__C)
=> ! [V26__y] :
( t(V26__y,V11__C)
=> ( cCoq_2emicromega_2eRingMicromega_2ecltb___24a5(V11__C,V18__ceqb,V19__cleb,V25__x,V26__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V9__rlt,happ(V20__phi,V25__x)),happ(V20__phi,V26__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.eval_Psatz_Sound',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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cplus] :
( c_24__type__15841___24t(V0__R,V11__C,V14__cplus)
=> ! [V15__ctimes] :
( c_24__type__15841___24t(V0__R,V11__C,V15__ctimes)
=> ! [V16__cminus] :
( c_24__type__15841___24t(V0__R,V11__C,V16__cminus)
=> ! [V17__copp] :
( c_24__type__876___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__15860___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__cleb] :
( c_24__type__15860___24t(V0__R,V11__C,V19__cleb)
=> ! [V20__phi] :
( c_24__type__1309___24t(V0__R,V11__C,V20__phi)
=> ! [V21__E] :
( cType___24t(V21__E)
=> ! [V22__pow__phi] :
( c_24__type__1314___24t(V0__R,V11__C,V21__E,V22__pow__phi)
=> ! [V23__rpow] :
( c_24__type__1323___24t(V0__R,V11__C,V21__E,V23__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V11__C,V12__cO,V13__cI,V14__cplus,V15__ctimes,V16__cminus,V17__copp,V18__ceqb,V19__cleb,V20__phi,V21__E,V22__pow__phi,V23__rpow)
=> ! [V25__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V11__C),V25__l)
=> ! [V26__env] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(V0__R,V26__env)
=> ( ! [V27__f] :
( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V11__C,V27__f)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V11__C),V27__f,V25__l))
=> cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a11(V0__R,V1__rO,V3__rplus,V4__rtimes,V7__req,V8__rle,V9__rlt,V11__C,V20__phi,V26__env,V27__f) ) )
=> ! [V28__e] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V11__C,V28__e)
=> ! [V29__f] :
( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V11__C,V29__f)
=> ( cCoq_2emicromega_2eRingMicromega_2eeval__Psatz___24a9(V11__C,V12__cO,V13__cI,V14__cplus,V15__ctimes,V18__ceqb,V19__cleb,V25__l,V28__e) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V11__C),V29__f)
=> cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a11(V0__R,V1__rO,V3__rplus,V4__rtimes,V7__req,V8__rle,V9__rlt,V11__C,V20__phi,V26__env,V29__f) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.extract_hyps_app',axiom,
! [V0__C] :
( cType___24t(V0__C)
=> ! [V1__cO] :
( t(V1__cO,V0__C)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C),V2__l)
=> ! [V3__ln1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,V3__ln1)
=> ! [V4__ln2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,V4__ln2)
=> cCoq_2emicromega_2eRingMicromega_2eextract__hyps___24a4(V0__C,V1__cO,V2__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2enat,V3__ln1,V4__ln2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eextract__hyps___24a4(V0__C,V1__cO,V2__l,V3__ln1),cCoq_2emicromega_2eRingMicromega_2eextract__hyps___24a4(V0__C,V1__cO,V2__l,V4__ln2)) ) ) ) ) ) ).
fof('Coq.micromega.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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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.nformula_plus_nformula_correct',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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cplus] :
( c_24__type__15841___24t(V0__R,V11__C,V14__cplus)
=> ! [V15__ctimes] :
( c_24__type__15841___24t(V0__R,V11__C,V15__ctimes)
=> ! [V16__cminus] :
( c_24__type__15841___24t(V0__R,V11__C,V16__cminus)
=> ! [V17__copp] :
( c_24__type__876___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__15860___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__cleb] :
( c_24__type__15860___24t(V0__R,V11__C,V19__cleb)
=> ! [V20__phi] :
( c_24__type__1309___24t(V0__R,V11__C,V20__phi)
=> ! [V21__E] :
( cType___24t(V21__E)
=> ! [V22__pow__phi] :
( c_24__type__1314___24t(V0__R,V11__C,V21__E,V22__pow__phi)
=> ! [V23__rpow] :
( c_24__type__1323___24t(V0__R,V11__C,V21__E,V23__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V11__C,V12__cO,V13__cI,V14__cplus,V15__ctimes,V16__cminus,V17__copp,V18__ceqb,V19__cleb,V20__phi,V21__E,V22__pow__phi,V23__rpow)
=> ! [V25__env] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(V0__R,V25__env)
=> ! [V26__f1] :
( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V11__C,V26__f1)
=> ! [V27__f2] :
( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V11__C,V27__f2)
=> ! [V28__f] :
( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V11__C,V28__f)
=> ( cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a11(V0__R,V1__rO,V3__rplus,V4__rtimes,V7__req,V8__rle,V9__rlt,V11__C,V20__phi,V25__env,V26__f1)
=> ( cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a11(V0__R,V1__rO,V3__rplus,V4__rtimes,V7__req,V8__rle,V9__rlt,V11__C,V20__phi,V25__env,V27__f2)
=> ( cCoq_2emicromega_2eRingMicromega_2enformula__plus__nformula___24a6(V11__C,V12__cO,V14__cplus,V18__ceqb,V26__f1,V27__f2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V11__C),V28__f)
=> cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a11(V0__R,V1__rO,V3__rplus,V4__rtimes,V7__req,V8__rle,V9__rlt,V11__C,V20__phi,V25__env,V28__f) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.rle_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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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__259___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__271___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,cProp,V7__req,c_3c_3d_3e)),V8__rle) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.rlt_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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__259___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__271___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,cProp,V7__req,c_3c_3d_3e)),V9__rlt) ) ) ) ) ) ) ) ) ) ) ) ).
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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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__1302___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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1293___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1293___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__259___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__259___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__539___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_2455702___24a4(V0__A,V1__B,V2__f,V3__l) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.mem_elements',axiom,
! [V0__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V0__x)
=> ! [V1__v] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__v)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__x,V1__v) = cCoq_2eInit_2eDatatypes_2etrue
<=> p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,V0__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V1__v))) ) ) ) ).
fof('Coq.micromega.ZMicromega.in_bdepth',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,V0__l)
=> ! [V1__a] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V1__a)
=> ! [V2__b] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V2__b)
=> ! [V3__y] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V3__y)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2emicromega_2eZMicromega_2eZArithProof,V3__y,V0__l))
=> cCoq_2eArith_2eWf__nat_2eltof___24a4(cCoq_2emicromega_2eZMicromega_2eZArithProof,cCoq_2emicromega_2eZMicromega_2ebdepth,V3__y,cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V1__a,V2__b,V0__l)) ) ) ) ) ) ).
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.OMEGA7',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ! [V3__t] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__t)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__z,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V3__t,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V3__t)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA10',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k1)
=> ! [V6__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__k2)
=> ! [V7__P] :
( c_24__type__17671___24t(V7__P)
=> ( p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V6__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V6__k2)))))
=> p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V6__k2)))) ) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA11',axiom,
! [V0__v1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v1)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k1)
=> ! [V5__P] :
( c_24__type__17671___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V4__k1)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l1,V4__k1),V3__l2))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,V1__c1),V2__l1),V4__k1),V3__l2))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA12',axiom,
! [V0__v2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v2)
=> ! [V1__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c2)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k2)
=> ! [V5__P] :
( c_24__type__17671___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c2,V4__k2)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l2,V4__k2)))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,V1__c2),V3__l2),V4__k2)))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA13',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__17671___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA14',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__17671___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA15',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k2)
=> ! [V6__P] :
( c_24__type__17671___24t(V6__P)
=> ( p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__c1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V5__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V5__k2)))))
=> p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V5__k2)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__17671___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__17671___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__17671___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__17671___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__17671___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__17671___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__17671___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__17671___24t(V2__P)
=> ( p(happ(V2__P,V1__y))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__17671___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.intro_Z',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = V1__y
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.omega.OmegaLemmas.new_var',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& V0__x = V1__y ) ) ).
fof('Coq.setoid_ring.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_succ',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_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__j),V2__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,cCoq_2eNumbers_2eBinNums_2exH,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V1__j,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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1309___24t(V0__R,V9__C,V10__phi)
=> ! [V11__Cpow] :
( cType___24t(V11__Cpow)
=> ! [V12__Cp__phi] :
( c_24__type__1314___24t(V0__R,V9__C,V11__Cpow,V12__Cp__phi)
=> ! [V13__rpow] :
( c_24__type__1323___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.NPEeval_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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1309___24t(V0__R,V9__C,V10__phi)
=> ! [V11__Cpow] :
( cType___24t(V11__Cpow)
=> ! [V12__Cp__phi] :
( c_24__type__1314___24t(V0__R,V9__C,V11__Cpow,V12__Cp__phi)
=> ! [V13__rpow] :
( c_24__type__1323___24t(V0__R,V9__C,V11__Cpow,V13__rpow)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13247___24a3(V0__R,V9__C,V11__Cpow),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__R),c_24__type__13252___24a3(V0__R,V9__C,V11__Cpow),c_3d___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__R)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V9__C),V0__R,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),V7__req)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a12(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__1309___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__1314___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__1323___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__1309___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__1314___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__1323___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__1309___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__1314___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__1323___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__1309___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__1314___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__1323___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__15841___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__15841___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__15841___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__876___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__15860___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1309___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__1314___24t(V0__R,V8__C,V18__Cpow,V19__Cp__phi)
=> ! [V20__rpow] :
( c_24__type__1323___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__15841___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__15841___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__15841___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__876___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__15860___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1309___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.cross_product_eq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ( ~ p(happ(happ(V9__req,V15__b),V1__rO))
=> ( ~ p(happ(happ(V9__req,V17__d),V1__rO))
=> ( p(happ(happ(V9__req,happ(happ(V4__rmul,V14__a),V17__d)),happ(happ(V4__rmul,V16__c),V15__b)))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V14__a),V15__b)),happ(happ(V7__rdiv,V16__c),V17__d))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.field_is_integral_domain',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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.pow_pos_div',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ! [V15__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V15__p)
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> p(happ(happ(V9__req,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,happ(happ(V7__rdiv,V13__a),V14__b),V15__p)),happ(happ(V7__rdiv,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V13__a,V15__p)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V14__b,V15__p)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.pow_pos_nz',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V14__p)
=> ( ~ p(happ(happ(V9__req,V13__x),V1__rO))
=> ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V13__x,V14__p)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.radd_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1302___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__259___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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.rdiv2b',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ! [V15__c] :
( t(V15__c,V0__R)
=> ! [V16__d] :
( t(V16__d,V0__R)
=> ! [V17__e] :
( t(V17__e,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V14__b),V17__e)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V16__d),V17__e)),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V3__radd,happ(happ(V7__rdiv,V13__a),happ(happ(V4__rmul,V14__b),V17__e))),happ(happ(V7__rdiv,V15__c),happ(happ(V4__rmul,V16__d),V17__e)))),happ(happ(V7__rdiv,happ(happ(V3__radd,happ(happ(V4__rmul,V13__a),V16__d)),happ(happ(V4__rmul,V15__c),V14__b))),happ(happ(V4__rmul,V14__b),happ(happ(V4__rmul,V16__d),V17__e))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv3b',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ! [V18__e] :
( t(V18__e,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V15__b),V18__e)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V17__d),V18__e)),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V5__rsub,happ(happ(V7__rdiv,V14__a),happ(happ(V4__rmul,V15__b),V18__e))),happ(happ(V7__rdiv,V16__c),happ(happ(V4__rmul,V17__d),V18__e)))),happ(happ(V7__rdiv,happ(happ(V5__rsub,happ(happ(V4__rmul,V14__a),V17__d)),happ(happ(V4__rmul,V16__c),V15__b))),happ(happ(V4__rmul,V15__b),happ(happ(V4__rmul,V17__d),V18__e))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv4b',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ! [V18__e] :
( t(V18__e,V0__R)
=> ! [V19__f] :
( t(V19__f,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V15__b),V18__e)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V17__d),V19__f)),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(happ(V7__rdiv,happ(happ(V4__rmul,V14__a),V19__f)),happ(happ(V4__rmul,V15__b),V18__e))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V16__c),V18__e)),happ(happ(V4__rmul,V17__d),V19__f)))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V14__a),V16__c)),happ(happ(V4__rmul,V15__b),V17__d)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv5',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> p(happ(happ(V9__req,happ(V6__ropp,happ(happ(V7__rdiv,V13__a),V14__b))),happ(happ(V7__rdiv,happ(V6__ropp,V13__a)),V14__b))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv6',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__a),V1__rO))
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> p(happ(happ(V9__req,happ(V8__rinv,happ(happ(V7__rdiv,V13__a),V14__b))),happ(happ(V7__rdiv,V14__b),V13__a))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv7b',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ! [V18__e] :
( t(V18__e,V0__R)
=> ! [V19__f] :
( t(V19__f,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V15__b),V19__f)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V16__c),V18__e)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V17__d),V19__f)),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,happ(happ(V7__rdiv,happ(happ(V4__rmul,V14__a),V18__e)),happ(happ(V4__rmul,V15__b),V19__f))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V16__c),V18__e)),happ(happ(V4__rmul,V17__d),V19__f)))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V14__a),V17__d)),happ(happ(V4__rmul,V15__b),V16__c)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv8',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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__1302___24t(V0__R,V1__rinv)
=> ! [V2__req] :
( c_24__type__259___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__1302___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1302___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__259___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1302___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__259___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__1302___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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.Field_theory.rsub_ext_Proper',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1293___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1302___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__259___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)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___24a1(V0__R),V9__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V9__req,V9__req)),V5__rsub) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.Ztriv_div_th',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__259___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> ! [V3__zphi] :
( c_24__type__17519___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.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__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1302___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__259___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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.PaddC_ok',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cadd] :
( c_24__type__15841___24t(V0__R,V11__C,V14__cadd)
=> ! [V15__cmul] :
( c_24__type__15841___24t(V0__R,V11__C,V15__cmul)
=> ! [V16__csub] :
( c_24__type__15841___24t(V0__R,V11__C,V16__csub)
=> ! [V17__copp] :
( c_24__type__876___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__15860___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__phi] :
( c_24__type__1309___24t(V0__R,V11__C,V19__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,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V19__phi)
=> ! [V21__c] :
( t(V21__c,V11__C)
=> ! [V22__P] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V11__C,V22__P)
=> ! [V23__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V23__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,cCoq_2esetoid__ring_2eRing__polynom_2ePaddC___24a4(V11__C,V14__cadd,V22__P,V21__c))),happ(happ(V3__radd,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,V22__P)),happ(V19__phi,V21__c)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.Padd_ok',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cadd] :
( c_24__type__15841___24t(V0__R,V11__C,V14__cadd)
=> ! [V15__cmul] :
( c_24__type__15841___24t(V0__R,V11__C,V15__cmul)
=> ! [V16__csub] :
( c_24__type__15841___24t(V0__R,V11__C,V16__csub)
=> ! [V17__copp] :
( c_24__type__876___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__15860___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__phi] :
( c_24__type__1309___24t(V0__R,V11__C,V19__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,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V19__phi)
=> ! [V21__P_27] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V11__C,V21__P_27)
=> ! [V22__P] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V11__C,V22__P)
=> ! [V23__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V23__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,cCoq_2esetoid__ring_2eRing__polynom_2ePadd___24a6(V11__C,V12__cO,V14__cadd,V18__ceqb,V22__P,V21__P_27))),happ(happ(V3__radd,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,V22__P)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,V21__P_27)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.PmulC_aux_ok',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cadd] :
( c_24__type__15841___24t(V0__R,V11__C,V14__cadd)
=> ! [V15__cmul] :
( c_24__type__15841___24t(V0__R,V11__C,V15__cmul)
=> ! [V16__csub] :
( c_24__type__15841___24t(V0__R,V11__C,V16__csub)
=> ! [V17__copp] :
( c_24__type__876___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__15860___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__phi] :
( c_24__type__1309___24t(V0__R,V11__C,V19__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,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V19__phi)
=> ! [V21__c] :
( t(V21__c,V11__C)
=> ! [V22__P] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V11__C,V22__P)
=> ! [V23__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V23__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,cCoq_2esetoid__ring_2eRing__polynom_2ePmulC__aux___24a6(V11__C,V12__cO,V15__cmul,V18__ceqb,V22__P,V21__c))),happ(happ(V4__rmul,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,V22__P)),happ(V19__phi,V21__c)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.PmulC_ok',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cadd] :
( c_24__type__15841___24t(V0__R,V11__C,V14__cadd)
=> ! [V15__cmul] :
( c_24__type__15841___24t(V0__R,V11__C,V15__cmul)
=> ! [V16__csub] :
( c_24__type__15841___24t(V0__R,V11__C,V16__csub)
=> ! [V17__copp] :
( c_24__type__876___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__15860___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__phi] :
( c_24__type__1309___24t(V0__R,V11__C,V19__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,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V19__phi)
=> ! [V21__c] :
( t(V21__c,V11__C)
=> ! [V22__P] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V11__C,V22__P)
=> ! [V23__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V23__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,cCoq_2esetoid__ring_2eRing__polynom_2ePmulC___24a7(V11__C,V12__cO,V13__cI,V15__cmul,V18__ceqb,V22__P,V21__c))),happ(happ(V4__rmul,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,V22__P)),happ(V19__phi,V21__c)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.Pmul_ok',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cadd] :
( c_24__type__15841___24t(V0__R,V11__C,V14__cadd)
=> ! [V15__cmul] :
( c_24__type__15841___24t(V0__R,V11__C,V15__cmul)
=> ! [V16__csub] :
( c_24__type__15841___24t(V0__R,V11__C,V16__csub)
=> ! [V17__copp] :
( c_24__type__876___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__15860___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__phi] :
( c_24__type__1309___24t(V0__R,V11__C,V19__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,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V19__phi)
=> ! [V21__P] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V11__C,V21__P)
=> ! [V22__P_27] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V11__C,V22__P_27)
=> ! [V23__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V23__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,cCoq_2esetoid__ring_2eRing__polynom_2ePmul___24a8(V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V18__ceqb,V21__P,V22__P_27))),happ(happ(V4__rmul,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,V21__P)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,V22__P_27)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.Pol_ind',axiom,
! [V0__C] :
( cType___24t(V0__C)
=> ! [V1__P] :
( c_24__type__45678___24t(V0__C,V1__P)
=> ( ! [V2__c] :
( t(V2__c,V0__C)
=> p(happ(V1__P,cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,V2__c))) )
=> ( ! [V3__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ! [V4__p] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__p)
=> ( p(happ(V1__P,V4__p))
=> p(happ(V1__P,cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,V3__p,V4__p))) ) ) )
=> ( ! [V4__p] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__p)
=> ( p(happ(V1__P,V4__p))
=> ! [V6__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
=> ! [V7__p] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V7__p)
=> ( p(happ(V1__P,V7__p))
=> p(happ(V1__P,cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,V4__p,V6__p,V7__p))) ) ) ) ) )
=> ! [V5__p] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V5__p)
=> p(happ(V1__P,V5__p)) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.Popp_ok',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cadd] :
( c_24__type__15841___24t(V0__R,V11__C,V14__cadd)
=> ! [V15__cmul] :
( c_24__type__15841___24t(V0__R,V11__C,V15__cmul)
=> ! [V16__csub] :
( c_24__type__15841___24t(V0__R,V11__C,V16__csub)
=> ! [V17__copp] :
( c_24__type__876___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__15860___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__phi] :
( c_24__type__1309___24t(V0__R,V11__C,V19__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,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V19__phi)
=> ! [V21__P] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V11__C,V21__P)
=> ! [V22__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V22__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V22__l,cCoq_2esetoid__ring_2eRing__polynom_2ePopp___24a3(V11__C,V17__copp,V21__P))),happ(V6__ropp,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V22__l,V21__P)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__15841___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__15841___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__15841___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__876___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__15860___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1309___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__15841___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__15841___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__15841___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__876___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__15860___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1309___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.Pphi_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__radd] :
( c_24__type__1293___24t(V0__R,V2__radd)
=> ! [V3__rmul] :
( c_24__type__1293___24t(V0__R,V3__rmul)
=> ! [V4__req] :
( c_24__type__259___24t(V0__R,V4__req)
=> ! [V5__C] :
( cType___24t(V5__C)
=> ! [V6__phi] :
( c_24__type__1309___24t(V0__R,V5__C,V6__phi)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__48073___24a2(V0__R,V5__C),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__R),c_24__type__48077___24a2(V0__R,V5__C),c_3d___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__R)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V5__C),V0__R,cCoq_2esetoid__ring_2eRing__polynom_2ePequiv___24a7(V0__R,V1__rO,V2__radd,V3__rmul,V4__req,V5__C,V6__phi),V4__req)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a6(V0__R,V1__rO,V2__radd,V3__rmul,V5__C,V6__phi)) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.PsubC_ok',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cadd] :
( c_24__type__15841___24t(V0__R,V11__C,V14__cadd)
=> ! [V15__cmul] :
( c_24__type__15841___24t(V0__R,V11__C,V15__cmul)
=> ! [V16__csub] :
( c_24__type__15841___24t(V0__R,V11__C,V16__csub)
=> ! [V17__copp] :
( c_24__type__876___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__15860___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__phi] :
( c_24__type__1309___24t(V0__R,V11__C,V19__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,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V19__phi)
=> ! [V21__c] :
( t(V21__c,V11__C)
=> ! [V22__P] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V11__C,V22__P)
=> ! [V23__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V23__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,cCoq_2esetoid__ring_2eRing__polynom_2ePsubC___24a4(V11__C,V16__csub,V22__P,V21__c))),happ(happ(V5__rsub,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,V22__P)),happ(V19__phi,V21__c)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.Psub_ok',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cadd] :
( c_24__type__15841___24t(V0__R,V11__C,V14__cadd)
=> ! [V15__cmul] :
( c_24__type__15841___24t(V0__R,V11__C,V15__cmul)
=> ! [V16__csub] :
( c_24__type__15841___24t(V0__R,V11__C,V16__csub)
=> ! [V17__copp] :
( c_24__type__876___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__15860___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__phi] :
( c_24__type__1309___24t(V0__R,V11__C,V19__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,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V19__phi)
=> ! [V21__P_27] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V11__C,V21__P_27)
=> ! [V22__P] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V11__C,V22__P)
=> ! [V23__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V23__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,cCoq_2esetoid__ring_2eRing__polynom_2ePsub___24a8(V11__C,V12__cO,V14__cadd,V16__csub,V17__copp,V18__ceqb,V22__P,V21__P_27))),happ(happ(V5__rsub,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,V22__P)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V3__radd,V4__rmul,V11__C,V19__phi,V23__l,V21__P_27)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__15841___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__15841___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__15841___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__876___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__15860___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1309___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.local_mkpow_ok',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__259___24t(V0__R,V3__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V3__req)
=> ! [V5__Cpow] :
( cType___24t(V5__Cpow)
=> ! [V6__Cp__phi] :
( c_24__type__25366___24t(V0__R,V5__Cpow,V6__Cp__phi)
=> ! [V7__rpow] :
( c_24__type__572___24t(V0__R,V5__Cpow,V7__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V1__rI,V2__rmul,V3__req,V5__Cpow,V6__Cp__phi,V7__rpow)
=> ! [V9__r] :
( t(V9__r,V0__R)
=> ! [V10__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V10__p)
=> p(happ(happ(V3__req,c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2453203___24a6(V0__R,V5__Cpow,V6__Cp__phi,V7__rpow,V9__r,V10__p)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V9__r,V10__p))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.mkPinj_ok',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__radd] :
( c_24__type__1293___24t(V0__R,V2__radd)
=> ! [V3__rmul] :
( c_24__type__1293___24t(V0__R,V3__rmul)
=> ! [V4__req] :
( c_24__type__259___24t(V0__R,V4__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V4__req)
=> ! [V6__C] :
( cType___24t(V6__C)
=> ! [V7__phi] :
( c_24__type__1309___24t(V0__R,V6__C,V7__phi)
=> ! [V8__j] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V8__j)
=> ! [V9__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V9__l)
=> ! [V10__P] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V6__C,V10__P)
=> p(happ(happ(V4__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V6__C,V7__phi,V9__l,cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V6__C,V8__j,V10__P))),cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V6__C,V7__phi,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__R,V8__j,V9__l),V10__P))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.mkZmon_ok',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rmul] :
( c_24__type__1293___24t(V0__R,V3__rmul)
=> ! [V4__req] :
( c_24__type__259___24t(V0__R,V4__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V4__req)
=> ! [V6__M] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V6__M)
=> ! [V7__j] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V7__j)
=> ! [V8__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V8__l)
=> p(happ(happ(V4__req,cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,V8__l,cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V7__j,V6__M))),cCoq_2esetoid__ring_2eRing__polynom_2eMphi___24a6(V0__R,V1__rO,V2__rI,V3__rmul,V8__l,cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V7__j,V6__M)))) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.mkmult_pow_ok',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V11__p)
=> ! [V12__r] :
( t(V12__r,V0__R)
=> ! [V13__x] :
( t(V13__x,V0__R)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V4__rmul,V12__r,V13__x,V11__p)),happ(happ(V4__rmul,V12__r),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V13__x,V11__p)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.mkopp_pow_ok',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V11__p)
=> ! [V12__x] :
( t(V12__x,V0__R)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2emkopp__pow___24a5(V0__R,V4__rmul,V6__ropp,V12__x,V11__p)),happ(V6__ropp,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V12__x,V11__p)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.mkpow_ok',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V11__p)
=> ! [V12__x] :
( t(V12__x,V0__R)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2emkpow___24a4(V0__R,V4__rmul,V12__x,V11__p)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V12__x,V11__p))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.pow_pos_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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__i] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V12__i)
=> ! [V13__j] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V13__j)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V11__x,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V13__j,V12__i))),happ(happ(V4__rmul,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V11__x,V12__i)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V11__x,V13__j)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.radd_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1302___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__259___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1302___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__259___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1302___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__259___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__1302___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.rsub_ext_Proper',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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V5__rsub) ) ) ) ) ) ) ) ) ) ) ) ).
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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1302___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__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___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.Radd_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1302___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__259___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1302___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__259___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__259___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__req] :
( c_24__type__259___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.div_eucl_th',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__259___24t(V0__R,V1__req)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__cadd] :
( c_24__type__15841___24t(V0__R,V2__C,V3__cadd)
=> ! [V4__cmul] :
( c_24__type__15841___24t(V0__R,V2__C,V4__cmul)
=> ! [V5__phi] :
( c_24__type__1309___24t(V0__R,V2__C,V5__phi)
=> ! [V6__cdiv] :
( c_24__type__25099___24t(V0__R,V2__C,V6__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V0__R,V1__req,V2__C,V3__cadd,V4__cmul,V5__phi,V6__cdiv)
=> ! [V8__a] :
( t(V8__a,V2__C)
=> ! [V9__b] :
( t(V9__b,V2__C)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2453424___24a9(V0__R,V1__req,V2__C,V3__cadd,V4__cmul,V5__phi,V6__cdiv,V8__a,V9__b) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.get_sign_None_th',axiom,
! [V0__C] :
( cType___24t(V0__C)
=> ! [V1__copp] :
( c_24__type__1302___24t(V0__C,V1__copp)
=> ! [V2__ceqb] :
( c_24__type__13765___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__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1302___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__259___24t(V0__R,V4__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1302___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__1293___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1293___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__259___24t(V0__R,V3__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1302___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__15841___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__15841___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__15841___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__876___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__15860___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1309___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__15841___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__15841___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__15841___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__876___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__15860___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1309___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__15841___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__15841___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__15841___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__876___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__15860___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1309___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__15841___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__15841___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__15841___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__876___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__15860___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1309___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__15841___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__15841___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__15841___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__876___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__15860___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1309___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__15841___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__15841___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__15841___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__876___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__15860___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1309___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__1293___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1293___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1293___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1302___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__259___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__15841___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__15841___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__15841___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__876___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__15860___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1309___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__1293___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__259___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__25366___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__572___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('list_utils.In_Permutation',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__61___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cProp,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),c_3c_3d_3e),cCoq_2eLists_2eList_2eIn___24a2(V0__A,V1__x)) ) ) ).
fof('list_utils.In_filter',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__p] :
( c_24__type__193___24t(V0__T,V1__p)
=> ! [V2__t] :
( t(V2__t,V0__T)
=> ( happ(V1__p,V2__t) = cCoq_2eInit_2eDatatypes_2etrue
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V4__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V2__t,V4__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V2__t,cCoq_2eLists_2eList_2efilter___24a3(V0__T,V1__p,V4__l))) ) ) ) ) ) ) ).
fof('list_utils.In_inv_perm',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( t(V1__x,V0__X)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V1__x,V2__l))
=> ? [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V4__l_27)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__X,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__X,V1__x,V4__l_27),V2__l) ) ) ) ) ) ).
fof('list_utils.In_map_inv',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__U] :
( cType___24t(V1__U)
=> ! [V2__f] :
( c_24__type__539___24t(V0__T,V1__U,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V3__l)
=> ! [V4__y] :
( t(V4__y,V1__U)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__U,V4__y,cCoq_2eLists_2eList_2emap___24a4(V0__T,V1__U,V2__f,V3__l)))
=> ? [V6__x] :
( t(V6__x,V0__T)
& happ(V2__f,V6__x) = V4__y
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V6__x,V3__l)) ) ) ) ) ) ) ) ).
fof('list_utils.NoDup_filter',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__p] :
( c_24__type__193___24t(V0__T,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__T,V2__l))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__T,cCoq_2eLists_2eList_2efilter___24a3(V0__T,V1__p,V2__l))) ) ) ) ) ).
fof('list_utils.NoDup_map_inv\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__539___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)))
=> p(cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l)) ) ) ) ) ) ).
fof('list_utils.Permutation_NoDup',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__61___24a1(V0__X),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),cProp,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__X),c_3c_3d_3e),cCoq_2eLists_2eList_2eNoDup___24a1(V0__X)) ) ).
fof('list_utils.Permutation_incl',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V1__a)
=> ! [V2__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__b)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__X,V1__a,V2__b)
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__X,V1__a,V2__b)) ) ) ) ) ).
fof('list_utils.app_nil_r',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__T,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T)) = V1__l ) ) ).
fof('list_utils.concat_app',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V1__x)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V2__y)
=> clist__utils_2econcat___24a2(V0__T,cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V1__x,V2__y)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__T,clist__utils_2econcat___24a2(V0__T,V1__x),clist__utils_2econcat___24a2(V0__T,V2__y)) ) ) ) ).
fof('list_utils.count_0',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__193___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ( ! [V3__x] :
( t(V3__x,V0__X)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V3__x,V2__l))
=> happ(V1__p,V3__x) = cCoq_2eInit_2eDatatypes_2efalse ) )
=> clist__utils_2ecount___24a3(V0__X,V1__p,V2__l) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ).
fof('list_utils.count_app',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__193___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__l_27)
=> clist__utils_2ecount___24a3(V0__X,V1__p,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__X,V2__l,V3__l_27)) = cCoq_2eInit_2eNat_2eadd___24a2(clist__utils_2ecount___24a3(V0__X,V1__p,V2__l),clist__utils_2ecount___24a3(V0__X,V1__p,V3__l_27)) ) ) ) ) ).
fof('list_utils.count_filter_le',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__193___24t(V0__X,V1__p)
=> ! [V2__f] :
( c_24__type__193___24t(V0__X,V2__f)
=> ! [V3__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__x)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(clist__utils_2ecount___24a3(V0__X,V1__p,cCoq_2eLists_2eList_2efilter___24a3(V0__X,V2__f,V3__x)),clist__utils_2ecount___24a3(V0__X,V1__p,V3__x))) ) ) ) ) ).
fof('list_utils.count_le',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__193___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(clist__utils_2ecount___24a3(V0__X,V1__p,V2__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,V2__l))) ) ) ) ).
fof('list_utils.count_lt',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__193___24t(V0__X,V1__p)
=> ! [V2__v] :
( t(V2__v,V0__X)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V2__v,V3__l))
=> ( happ(V1__p,V2__v) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eInit_2ePeano_2elt___24a2(clist__utils_2ecount___24a3(V0__X,V1__p,V3__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,V3__l)) ) ) ) ) ) ) ).
fof('list_utils.count_perm_simple',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__p] :
( c_24__type__193___24t(V0__A,V1__p)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30144___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),clist__utils_2ecount___24a2(V0__A,V1__p)) ) ) ).
fof('list_utils.filter_all',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__193___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ( ! [V3__x] :
( t(V3__x,V0__X)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V3__x,V2__l))
=> happ(V1__p,V3__x) = cCoq_2eInit_2eDatatypes_2etrue ) )
=> cCoq_2eLists_2eList_2efilter___24a3(V0__X,V1__p,V2__l) = V2__l ) ) ) ) ).
fof('list_utils.filter_none',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__193___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ( ! [V3__x] :
( t(V3__x,V0__X)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V3__x,V2__l))
=> happ(V1__p,V3__x) = cCoq_2eInit_2eDatatypes_2efalse ) )
<=> cCoq_2eLists_2eList_2efilter___24a3(V0__X,V1__p,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__X) ) ) ) ) ).
fof('list_utils.filter_preserves_incl',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__193___24t(V0__X,V1__p)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__a)
=> ! [V3__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__b)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__X,V2__a,V3__b))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__X,cCoq_2eLists_2eList_2efilter___24a3(V0__X,V1__p,V2__a),cCoq_2eLists_2eList_2efilter___24a3(V0__X,V1__p,V3__b))) ) ) ) ) ) ).
fof('list_utils.incl_In',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( t(V1__x,V0__X)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V1__x,V2__l))
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V4__l_27)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__X,V2__l,V4__l_27))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V1__x,V4__l_27)) ) ) ) ) ) ) ).
fof('list_utils.incl_filter',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__193___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__X,cCoq_2eLists_2eList_2efilter___24a3(V0__X,V1__p,V2__l),V2__l)) ) ) ) ).
fof('list_utils.incl_in',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)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__T,V1__a,V2__b))
=> ! [V4__x] :
( t(V4__x,V0__T)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V4__x,V1__a))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V4__x,V2__b)) ) ) ) ) ) ) ).
fof('list_utils.incl_map',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__539___24t(V0__X,V1__Y,V2__f)
=> ! [V3__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__a)
=> ! [V4__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V4__b)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__X,V3__a,V4__b))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V1__Y,cCoq_2eLists_2eList_2emap___24a4(V0__X,V1__Y,V2__f,V3__a),cCoq_2eLists_2eList_2emap___24a4(V0__X,V1__Y,V2__f,V4__b))) ) ) ) ) ) ) ).
fof('list_utils.incl_trans',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)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__x,V2__y))
=> ! [V4__z] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__z)
=> ( p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__y,V4__z))
=> p(cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__x,V4__z)) ) ) ) ) ) ) ).
fof('list_utils.length_filter',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__193___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,cCoq_2eLists_2eList_2efilter___24a3(V0__X,V1__p,V2__l)) = clist__utils_2ecount___24a3(V0__X,V1__p,V2__l) ) ) ) ).
fof('list_utils.length_filter_le',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__p] :
( c_24__type__193___24t(V0__T,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__l)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cCoq_2eLists_2eList_2efilter___24a3(V0__T,V1__p,V2__l)),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,V2__l))) ) ) ) ).
fof('list_utils.map_cons',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__U] :
( cType___24t(V1__U)
=> ! [V2__f] :
( c_24__type__539___24t(V0__T,V1__U,V2__f)
=> ! [V3__h] :
( t(V3__h,V0__T)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V4__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__T,V1__U,V2__f,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V3__h,V4__l)) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__U,happ(V2__f,V3__h),cCoq_2eLists_2eList_2emap___24a4(V0__T,V1__U,V2__f,V4__l)) ) ) ) ) ) ).
fof('list_utils.pointwise_eq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__x] :
( c_24__type__539___24t(V0__A,V1__B,V2__x)
=> cCoq_2eClasses_2eMorphisms_2epointwise__relation___24a5(V0__A,V1__B,c_3d___24a1(V1__B),V2__x,V2__x) ) ) ) ).
fof('$adef_$_lam_57893_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__57893,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__57893___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_41468_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__41468,V_24X1),V_24X2) = c_24__lam__41468___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1442_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1442,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1442___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_case_Coq.setoid_ring.Ring_polynom.Pol$27568_$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_2427568,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),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_2427568___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('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
fof('$adef_$_lam_28964_$a1',axiom,
! [V_24X1] : happ(c_24__lam__28964,V_24X1) = c_24__lam__28964___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_$_prop_36914_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36914,V_24X1),V_24X2),V_24X3) = c_24__prop__36914___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEmul_$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_2eNPEmul,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_Coq.ZArith.BinIntDef.Z.of_N_$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('$adef_Coq.Init.Datatypes.BoolSpec_$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_28904_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__28904,V_24X1),V_24X2),V_24X3) = c_24__prop__28904___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.micromega.RingMicromega.eval_pol_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__pol,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.micromega.RingMicromega.psubC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2epsubC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2epsubC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.get_sign_None_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_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_$_prop_55586_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__55586,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__55586___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_37688_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__37688,V_24X1),V_24X2),V_24X3) = c_24__lam__37688___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.List.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_$_prop_28957_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__28957,V_24X1),V_24X2),V_24X3) = c_24__prop__28957___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_prop_36741_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__36741,V_24X1),V_24X2) = c_24__prop__36741___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_36976_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36976,V_24X1),V_24X2),V_24X3) = c_24__prop__36976___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('$adef_$_let_17_lnum_27335_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__lnum__27335,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = c_24__let__17__lnum__27335___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_Coq.Reals.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.micromega.EnvRing.Psquare_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePsquare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eEnvRing_2ePsquare___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_prop_54967_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__54967,V_24X1),V_24X2) = c_24__prop__54967___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PsubC_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePsubC,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePsubC___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.FinFun.bSurjective_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2ebSurjective,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2ebSurjective___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_36913_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36913,V_24X1),V_24X2),V_24X3) = c_24__prop__36913___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.micromega.Tauto.eval_f_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__f,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_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_Coq.Lists.List.fold_right_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2efold__right___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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.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_$_prop_28956_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__28956,V_24X1),V_24X2),V_24X3) = c_24__prop__28956___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('$adef_Coq.Lists.SetoidList.transpose_restr2_$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('$adef_Coq.setoid_ring.Ring_polynom.Popp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePopp,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePopp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PsubC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePsubC,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePsubC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.existsb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eexistsb,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eexistsb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Env.jump_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnv_2ejump,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnv_2ejump___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_60320_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__60320,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__60320___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_36887_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36887,V_24X1),V_24X2),V_24X3) = c_24__prop__36887___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.hd_$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('$adef_$_prop_28947_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__28947,V_24X1),V_24X2),V_24X3) = c_24__prop__28947___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_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_$_lam_63024_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__63024,V_24X1),V_24X2),V_24X3) = c_24__lam__63024___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_37680_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__37680,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__37680___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.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_$_prop_55587_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__55587,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__55587___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.skipn_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eskipn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eskipn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.rev_append_$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('$adef_$_lam_57888_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__57888,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__57888___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.setoid_ring.Ring_polynom.PaddC_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePaddC,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePaddC___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.In_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLists_2eList_2eIn,V_24X1) = cCoq_2eLists_2eList_2eIn___24a1(V_24X1) ).
fof('$adef_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.Lists.List.map_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2emap___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_list_utils.concat_$a1',axiom,
! [V_24X1] : happ(clist__utils_2econcat,V_24X1) = clist__utils_2econcat___24a1(V_24X1) ).
fof('$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_Coq.micromega.Tauto.BFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eTauto_2eBFormula,V_24X1) = cCoq_2emicromega_2eTauto_2eBFormula___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.id_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eid,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eid___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.setoid_ring.Field_theory.NPEadd_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEadd,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_prop_29057_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29057,V_24X1),V_24X2),V_24X3) = c_24__prop__29057___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_36912_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36912,V_24X1),V_24X2),V_24X3) = c_24__prop__36912___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.FinFun.Surjective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eSurjective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eSurjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.eval_cnf_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__cnf,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.micromega.Tauto.TFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.interp_PElist_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.Lists.List.NoDup_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLists_2eList_2eNoDup,V_24X1) = cCoq_2eLists_2eList_2eNoDup___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.elements_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pmul_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePmul,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eRing__polynom_2ePmul___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_$_prop_38644_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38644,V_24X1),V_24X2) = c_24__prop__38644___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.PArith.BinPosDef.Pos.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V_24X1) ).
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('$adef_$_case_Coq.Init.Datatypes.prod$53424_$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_2453424,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_2453424___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_list_utils.concat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(clist__utils_2econcat,V_24X1),V_24X2) = clist__utils_2econcat___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('$adef_$_prop_55620_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__55620,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__55620___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.display_pow_linear_$a20',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20) = cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear___24a20(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkZmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkZmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_56026_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__56026,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__56026___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.micromega.RingMicromega.cltb_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecltb,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2ecltb___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.VectorDef.to_list_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eto__list,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2eto__list___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Strings.String.append_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eappend,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eappend___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_$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_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring.bool_eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing_2ebool__eq,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.equivlistA_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eSetoidList_2eequivlistA,V_24X1),V_24X2) = cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Forall2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eList_2eForall2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRdiv,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Specif.sumbool$28890_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eSpecif_2esumbool_2428890,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_2428890___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Logic.FinFun.bFun_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2ebFun,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2ebFun___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__left,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_60320_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__60320,V_24X1),V_24X2) = c_24__lam__60320___24a2(V_24X1,V_24X2) ).
fof('$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_$_let_var_6_p_35943_35945_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__35943__35945,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__35943__35945___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.micromega.Tauto.cnf_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$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('$adef_Coq.setoid_ring.Ring_polynom.mkPinj_pred_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkPinj__pred,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2emkPinj__pred___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_prop_28948_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__28948,V_24X1),V_24X2),V_24X3) = c_24__prop__28948___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_$_lam_37688_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__37688,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__37688___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_prop_54968_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__54968,V_24X1),V_24X2) = c_24__prop__54968___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_fix_2027_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__2027__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__2027__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.rev\'_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2erev_27,V_24X1),V_24X2) = cCoq_2eLists_2eList_2erev_27___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.negb_$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('$adef_$_let_17_mkopp_pow_19024_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__19024,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__19024___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.Lists.List.combine_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2ecombine,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2ecombine___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.P1_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eP1,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2eP1___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.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.setoid_ring.Ring_polynom.mkmult_c_pos_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__c__pos,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__c__pos___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Lists.List.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_$_let_11_subst_l_18148_$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__18148,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__18148___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.setoid_ring.Field_theory.display_linear_$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('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_37672_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__37672,V_24X1),V_24X2),V_24X3) = c_24__lam__37672___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.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_$_let_var_6_p_35941_35944_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__35941__35944,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__35941__35944___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_pow_$a18',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18) ).
fof('$adef_Coq.Init.Specif.right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.List.ForallPairs_$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('$adef_Coq.micromega.Env.hd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnv_2ehd,V_24X1),V_24X2) = cCoq_2emicromega_2eEnv_2ehd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRplus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sorting.Permutation.Permutation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1) = cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V_24X1) ).
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('$adef_$_prop_61211_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__61211,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__61211___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_case_Coq.Numbers.BinNums.Z$54884_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2454884,V_24X1),V_24X2))
<=> c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2454884___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_18220_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__18220,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__18220___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.setoid_ring.Field_theory.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_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_$_fix_26516_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__26516__1__add__carry,V_24X1),V_24X2) = c_24__fix__26516__1__add__carry___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$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_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) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$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('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec,V_24X1),V_24X2) = cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.nformula_plus_nformula_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2enformula__plus__nformula,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2enformula__plus__nformula___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('$adef_Coq.Sorting.Permutation.Permutation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb___24a2(V_24X1,V_24X2) ).
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('$adef_list_utils.count_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(clist__utils_2ecount,V_24X1),V_24X2) = clist__utils_2ecount___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('$adef_Coq.setoid_ring.Ring_polynom.Pequiv_$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_2eRing__polynom_2ePequiv,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eRing__polynom_2ePequiv___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_Coq.Classes.Morphisms.pointwise_relation_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2epointwise__relation,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eClasses_2eMorphisms_2epointwise__relation___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_Coq.micromega.Env.tail_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnv_2etail,V_24X1),V_24X2) = cCoq_2emicromega_2eEnv_2etail___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Operators.Ltl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eLtl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.I_$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('$adef_$_lam_56020_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__56020,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__56020___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkadd_mult_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkadd__mult,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2emkadd__mult___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.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.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_Coq.micromega.RingMicromega.eval_op1_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$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.micromega.EnvRing.Pphi_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eEnvRing_2ePphi___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.QArith.QArith_base.Qdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQdiv,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_prop_60316_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__60316,V_24X1),V_24X2),V_24X3) = c_24__prop__60316___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PmulC_aux_$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_2ePmulC__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eRing__polynom_2ePmulC__aux___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Ppow_pos_$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_2ePpow__pos,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_2ePpow__pos___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.QArith.QArith_base.Qeq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sumbool_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$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('$adef_list_utils.count_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(clist__utils_2ecount,V_24X1),V_24X2),V_24X3) = clist__utils_2ecount___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEeval_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Coq.setoid_ring.Field_theory.absurd_PCond_$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('$adef_Coq.setoid_ring.Ring_polynom.norm_aux_$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('$adef_$_lam_18220_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__18220,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__18220___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.setoid_ring.InitialRing.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_$_prop_60335_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__60335,V_24X1),V_24X2),V_24X3) = c_24__prop__60335___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_let_18_mkmult_pow_19025_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__19025,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__19025___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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_$_lam_55146_$a1',axiom,
! [V_24X1] : happ(c_24__lam__55146,V_24X1) = c_24__lam__55146___24a1(V_24X1) ).
fof('$adef_$_lam_37672_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__37672,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__37672___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.eval_clause_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__clause,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eeval__clause___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_55146_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__55146,V_24X1),V_24X2) = c_24__lam__55146___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkopp_pow_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkopp__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__polynom_2emkopp__pow___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mk_X_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emk__X,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emk__X___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.FinFun.Injective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eInjective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eInjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.QArith.QArith_base.Qmult_$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('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_let_18_mkmult_pow_19025_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__19025,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__19025___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$1895_$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_241895,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_241895___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Lists.List.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.EnvRing.Pphi_$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_2eEnvRing_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_pred_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon__pred,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon__pred___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.FinFun.Full_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2eFull,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2eFull___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_dev_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Psub_$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_2ePsub,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eRing__polynom_2ePsub___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
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('$adef_$_prop_28907_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__28907,V_24X1),V_24X2),V_24X3) = c_24__prop__28907___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_37680_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__37680,V_24X1),V_24X2),V_24X3) = c_24__lam__37680___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Lists.List.list_prod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2elist__prod,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2elist__prod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Lists.List.lel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2elel,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2elel___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Classes.RelationClasses.complement_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eClasses_2eRelationClasses_2ecomplement,V_24X1),V_24X2) = cCoq_2eClasses_2eRelationClasses_2ecomplement___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.Desc_$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('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Numbers.BinNums.positive$53203_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2453203,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2453203___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_let_16_mkpow_19023_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__let__16__mkpow__19023,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__19023___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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_$_lam_56026_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__56026,V_24X1),V_24X2) = c_24__lam__56026___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_28909_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__28909,V_24X1),V_24X2),V_24X3) = c_24__prop__28909___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.FinFun.Finite_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eFinFun_2eFinite,V_24X1))
<=> cCoq_2eLogic_2eFinFun_2eFinite___24a1(V_24X1) ) ).
fof('$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.Logic.FinFun.Finite\'_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eFinFun_2eFinite_27,V_24X1))
<=> cCoq_2eLogic_2eFinFun_2eFinite_27___24a1(V_24X1) ) ).
fof('$adef_Coq.Lists.List.rev_append_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2erev__append,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2erev__append___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.Tauto.eval_tt_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__tt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.micromega.ZMicromega.valid_cut_sign_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2evalid__cut__sign,V_24X1) = cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.concat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2econcat,V_24X1),V_24X2) = cCoq_2eLists_2eList_2econcat___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_38645_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38645,V_24X1),V_24X2) = c_24__prop__38645___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_$_let_16_mkpow_19023_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__19023,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__19023___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.In_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2) = cCoq_2eLists_2eList_2eIn___24a2(V_24X1,V_24X2) ).
fof('$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_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.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_$_prop_36964_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36964,V_24X1),V_24X2),V_24X3) = c_24__prop__36964___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Bool.Bool.reflect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2ereflect,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Relations_1.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons0_$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_55166_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__55166,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__55166___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RingMicromega.eval_nformula_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__nformula,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11))
<=> cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ) ).
fof('$adef_Coq.micromega.RingMicromega.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_Coq.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zcomplements.Zlength_aux_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eZArith_2eZcomplements_2eZlength__aux,V_24X1),V_24X2),V_24X3) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.gtb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2egtb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.in_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2ein__dec,V_24X1),V_24X2) = cCoq_2eLists_2eList_2ein__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zcomplements.Zlength_aux_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZcomplements_2eZlength__aux,V_24X1) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.get_sign_None_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEsub_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEsub,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.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_Coq.setoid_ring.Ring_polynom.mkPX_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkPX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eRing__polynom_2emkPX___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.eqlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.cneqb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecneqb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.map_option2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkpow_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkpow,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emkpow___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.ListDec.In_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eListDec_2eIn__dec,V_24X1),V_24X2) = cCoq_2eLists_2eListDec_2eIn__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.String.String_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.split_aux_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esplit__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eField__theory_2esplit__aux___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.micromega.RingMicromega.extract_hyps_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eextract__hyps,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eextract__hyps___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.app_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1) = cCoq_2eInit_2eDatatypes_2eapp___24a1(V_24X1) ).
fof('$adef_Coq.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.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.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_$_let_var_var_7_n_28859_28863_28872_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__var__7__n__28859__28863__28872,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__var__7__n__28859__28863__28872___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_pow_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_$_lam_63024_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__63024,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__63024___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_28838_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__28838,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__28838___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$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('$adef_$_prop_28905_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__28905,V_24X1),V_24X2),V_24X3) = c_24__prop__28905___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__right,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.BinList.jump_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2ejump,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Strings.String.string_of_list_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eString_2estring__of__list__ascii,V_24X1) = cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.nhyps_of_psatz_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.get_signZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ,V_24X1) = cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.list_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2elist__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.RingMicromega.eval_op1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Padd_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePadd,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eRing__polynom_2ePadd___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_57893_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__57893,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__57893___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.setoid_ring.Field_theory.NPEpow_$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_2eNPEpow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2eNPEpow___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_$_prop_36915_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36915,V_24X1),V_24X2),V_24X3) = c_24__prop__36915___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.rev_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLists_2eList_2erev,V_24X1) = cCoq_2eLists_2eList_2erev___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Wf_nat.ltof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2eltof,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eArith_2eWf__nat_2eltof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_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_$_case_Coq.Init.Datatypes.list$55702_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2455702,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2455702___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.FinFun.Listing_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2eListing,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2eListing___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$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('$adef_$_prop_61224_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__61224,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__61224___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.SetoidList.InA_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2) = cCoq_2eLists_2eSetoidList_2eInA___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_prop_28908_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__28908,V_24X1),V_24X2),V_24X3) = c_24__prop__28908___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.setoid_ring.Ring_polynom.Mphi_$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('$adef_$_lam_57888_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__57888,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__57888___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_38647_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38647,V_24X1),V_24X2) = c_24__prop__38647___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$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('$adef_$_prop_38646_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38646,V_24X1),V_24X2) = c_24__prop__38646___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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_$_lam_56020_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__56020,V_24X1),V_24X2) = c_24__lam__56020___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.cnf_tt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf__tt,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_37696_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__37696,V_24X1),V_24X2),V_24X3) = c_24__lam__37696___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_rec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.nth_ok_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth__ok,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth__ok___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.setoid_ring.Ring_polynom.mkX_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkX,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2emkX___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.micromega.RingMicromega.eval_Psatz_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__Psatz,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2emicromega_2eRingMicromega_2eeval__Psatz___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.micromega.ZMicromega.bdepth_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2ebdepth,V_24X1) = cCoq_2emicromega_2eZMicromega_2ebdepth___24a1(V_24X1) ).
fof('$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.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.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.Init.Datatypes.length_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1) = cCoq_2eInit_2eDatatypes_2elength___24a1(V_24X1) ).
fof('$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.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_Coq.Lists.List.Forall_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.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_$_prop_28906_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__28906,V_24X1),V_24X2),V_24X3) = c_24__prop__28906___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_1442_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1442,V_24X1),V_24X2),V_24X3) = c_24__lam__1442___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_37696_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__37696,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__37696___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PmulC_$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_2eRing__polynom_2ePmulC,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eRing__polynom_2ePmulC___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_$_lam_28964_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__28964,V_24X1),V_24X2),V_24X3) = c_24__lam__28964___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.ListDec.decidable_eq_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLists_2eListDec_2edecidable__eq,V_24X1))
<=> cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V_24X1) ) ).
fof('$adef_Coq.Lists.List.hd_error_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2ehd__error,V_24X1),V_24X2) = cCoq_2eLists_2eList_2ehd__error___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_20_lnum_27861_$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__27861,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_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__27861___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('$adef_Coq.setoid_ring.Ring_polynom.mon_of_pol_$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('$adef_$_prop_57643_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__57643,V_24X1),V_24X2) = c_24__prop__57643___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$25086_$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_2425086,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_2425086___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiN_$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('$adef_$_case_Coq.Init.Datatypes.list$1982_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_241982,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_241982___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('$adef_Coq.micromega.RingMicromega.PsatzC_$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('$adef_$_prop_38634_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38634,V_24X1),V_24X2) = c_24__prop__38634___24a2(V_24X1,V_24X2) ).
fof('$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_Coq.Lists.List.nth_default_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth__default,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth__default___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.fold_right_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_let_17_mkopp_pow_19024_$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__19024,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__19024___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.Lists.List.tl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2etl,V_24X1),V_24X2) = cCoq_2eLists_2eList_2etl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Logic.FinFun.bInjective_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2ebInjective,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2ebInjective___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2) = cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.map_option_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.NFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eNFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_55585_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__55585,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__55585___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_55166_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__55166,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__55166___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_38635_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38635,V_24X1),V_24X2) = c_24__prop__38635___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.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.Lists.List.incl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eincl,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eincl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.setoid_ring.Ring_polynom.Pol$28165_$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_2428165,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_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_2428165___24a20(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20) ).
fof('$adef_Coq.micromega.RingMicromega.eval_pol_$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_2eRingMicromega_2eeval__pol,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Lists.List.list_power_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2elist__power,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2elist__power___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_$_prop_36721_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__36721,V_24X1),V_24X2) = c_24__prop__36721___24a2(V_24X1,V_24X2) ).
fof('$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_$_fix_36598_v_CANONICAL_2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__fix__36598__v__CANONICAL__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__fix__36598__v__CANONICAL__2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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_51191',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__51191___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__51191___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_45678',axiom,
! [V_24X1,V_24Y] :
( c_24__type__45678___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__45678___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35306',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__35306___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__35306___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_24881',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__24881___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__24881___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_15860',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15860___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15860___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_410',axiom,
! [V_24X1,V_24Y] :
( c_24__type__410___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__410___24a1(V_24X1)) ) ).
fof('$tdef_$_type_535',axiom,
! [V_24Y] :
( c_24__type__535___24t(V_24Y)
<=> t(V_24Y,c_24__type__535) ) ).
fof('$tdef_$_type_422',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__422___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__422___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23264',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__23264___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__23264___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_28945',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__28945___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__28945___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_19',axiom,
! [V_24Y] :
( c_24__type__19___24t(V_24Y)
<=> t(V_24Y,c_24__type__19) ) ).
fof('$tdef_$_type_36719',axiom,
! [V_24Y] :
( c_24__type__36719___24t(V_24Y)
<=> t(V_24Y,c_24__type__36719) ) ).
fof('$tdef_$_type_30092',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__30092___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__30092___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_12424',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__12424___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__12424___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_37984',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__37984___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__37984___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_23051',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__23051___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__23051___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_468',axiom,
! [V_24Y] :
( c_24__type__468___24t(V_24Y)
<=> t(V_24Y,c_24__type__468) ) ).
fof('$tdef_$_type_29045',axiom,
! [V_24Y] :
( c_24__type__29045___24t(V_24Y)
<=> t(V_24Y,c_24__type__29045) ) ).
fof('$tdef_$_type_34314',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__34314___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__34314___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_12134',axiom,
! [V_24Y] :
( c_24__type__12134___24t(V_24Y)
<=> t(V_24Y,c_24__type__12134) ) ).
fof('$tdef_$_type_26671',axiom,
! [V_24Y] :
( c_24__type__26671___24t(V_24Y)
<=> t(V_24Y,c_24__type__26671) ) ).
fof('$tdef_$_type_25650',axiom,
! [V_24Y] :
( c_24__type__25650___24t(V_24Y)
<=> t(V_24Y,c_24__type__25650) ) ).
fof('$tdef_$_type_24681',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__24681___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__24681___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_$_type_615',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__615___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__615___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_55266',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__55266___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__55266___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_876',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__876___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__876___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_42614',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__42614___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__42614___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1449',axiom,
! [V_24Y] :
( c_24__type__1449___24t(V_24Y)
<=> t(V_24Y,c_24__type__1449) ) ).
fof('$tdef_$_type_37975',axiom,
! [V_24Y] :
( c_24__type__37975___24t(V_24Y)
<=> t(V_24Y,c_24__type__37975) ) ).
fof('$tdef_$_type_2954',axiom,
! [V_24Y] :
( c_24__type__2954___24t(V_24Y)
<=> t(V_24Y,c_24__type__2954) ) ).
fof('$tdef_$_type_4837',axiom,
! [V_24Y] :
( c_24__type__4837___24t(V_24Y)
<=> t(V_24Y,c_24__type__4837) ) ).
fof('$tdef_$_type_24506',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__24506___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__24506___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_48073',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__48073___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__48073___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_49611',axiom,
! [V_24X1,V_24Y] :
( c_24__type__49611___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__49611___24a1(V_24X1)) ) ).
fof('$tdef_$_type_26546',axiom,
! [V_24Y] :
( c_24__type__26546___24t(V_24Y)
<=> t(V_24Y,c_24__type__26546) ) ).
fof('$tdef_$_type_1309',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1309___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1309___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_56271',axiom,
! [V_24Y] :
( c_24__type__56271___24t(V_24Y)
<=> t(V_24Y,c_24__type__56271) ) ).
fof('$tdef_$_type_27299',axiom,
! [V_24Y] :
( c_24__type__27299___24t(V_24Y)
<=> t(V_24Y,c_24__type__27299) ) ).
fof('$tdef_$_type_54959',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__54959___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__54959___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2892',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2892___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2892___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28836',axiom,
! [V_24Y] :
( c_24__type__28836___24t(V_24Y)
<=> t(V_24Y,c_24__type__28836) ) ).
fof('$tdef_$_type_37906',axiom,
! [V_24Y] :
( c_24__type__37906___24t(V_24Y)
<=> t(V_24Y,c_24__type__37906) ) ).
fof('$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_$_type_193',axiom,
! [V_24X1,V_24Y] :
( c_24__type__193___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__193___24a1(V_24X1)) ) ).
fof('$tdef_$_type_61222',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__61222___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__61222___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_37898',axiom,
! [V_24Y] :
( c_24__type__37898___24t(V_24Y)
<=> t(V_24Y,c_24__type__37898) ) ).
fof('$tdef_$_type_25230',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__25230___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__25230___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_33645',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__33645___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__33645___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_86',axiom,
! [V_24Y] :
( c_24__type__86___24t(V_24Y)
<=> t(V_24Y,c_24__type__86) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_60330',axiom,
! [V_24Y] :
( c_24__type__60330___24t(V_24Y)
<=> t(V_24Y,c_24__type__60330) ) ).
fof('$tdef_$_type_13765',axiom,
! [V_24X1,V_24Y] :
( c_24__type__13765___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__13765___24a1(V_24X1)) ) ).
fof('$tdef_$_type_36624',axiom,
! [V_24X1,V_24Y] :
( c_24__type__36624___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__36624___24a1(V_24X1)) ) ).
fof('$tdef_$_type_55447',axiom,
! [V_24Y] :
( c_24__type__55447___24t(V_24Y)
<=> t(V_24Y,c_24__type__55447) ) ).
fof('$tdef_$_type_1019',axiom,
! [V_24Y] :
( c_24__type__1019___24t(V_24Y)
<=> t(V_24Y,c_24__type__1019) ) ).
fof('$tdef_$_type_38649',axiom,
! [V_24Y] :
( c_24__type__38649___24t(V_24Y)
<=> t(V_24Y,c_24__type__38649) ) ).
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_$_type_162',axiom,
! [V_24Y] :
( c_24__type__162___24t(V_24Y)
<=> t(V_24Y,c_24__type__162) ) ).
fof('$tdef_$_type_133',axiom,
! [V_24Y] :
( c_24__type__133___24t(V_24Y)
<=> t(V_24Y,c_24__type__133) ) ).
fof('$tdef_$_type_30365',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__30365___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__30365___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_17519',axiom,
! [V_24X1,V_24Y] :
( c_24__type__17519___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__17519___24a1(V_24X1)) ) ).
fof('$tdef_$_type_24098',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__24098___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__24098___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_36185',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__36185___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__36185___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_46342',axiom,
! [V_24Y] :
( c_24__type__46342___24t(V_24Y)
<=> t(V_24Y,c_24__type__46342) ) ).
fof('$tdef_$_type_42684',axiom,
! [V_24Y] :
( c_24__type__42684___24t(V_24Y)
<=> t(V_24Y,c_24__type__42684) ) ).
fof('$tdef_$_type_165',axiom,
! [V_24Y] :
( c_24__type__165___24t(V_24Y)
<=> t(V_24Y,c_24__type__165) ) ).
fof('$tdef_$_type_55752',axiom,
! [V_24Y] :
( c_24__type__55752___24t(V_24Y)
<=> t(V_24Y,c_24__type__55752) ) ).
fof('$tdef_$_type_31592',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__31592___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__31592___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_703',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__703___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__703___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_917',axiom,
! [V_24Y] :
( c_24__type__917___24t(V_24Y)
<=> t(V_24Y,c_24__type__917) ) ).
fof('$tdef_$_type_3669',axiom,
! [V_24Y] :
( c_24__type__3669___24t(V_24Y)
<=> t(V_24Y,c_24__type__3669) ) ).
fof('$tdef_$_type_27035',axiom,
! [V_24Y] :
( c_24__type__27035___24t(V_24Y)
<=> t(V_24Y,c_24__type__27035) ) ).
fof('$tdef_$_type_20365',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20365___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__20365___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_15650',axiom,
! [V_24Y] :
( c_24__type__15650___24t(V_24Y)
<=> t(V_24Y,c_24__type__15650) ) ).
fof('$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_36882',axiom,
! [V_24Y] :
( c_24__type__36882___24t(V_24Y)
<=> t(V_24Y,c_24__type__36882) ) ).
fof('$tdef_$_type_48108',axiom,
! [V_24Y] :
( c_24__type__48108___24t(V_24Y)
<=> t(V_24Y,c_24__type__48108) ) ).
fof('$tdef_$_type_44163',axiom,
! [V_24Y] :
( c_24__type__44163___24t(V_24Y)
<=> t(V_24Y,c_24__type__44163) ) ).
fof('$tdef_$_type_33',axiom,
! [V_24Y] :
( c_24__type__33___24t(V_24Y)
<=> t(V_24Y,c_24__type__33) ) ).
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_$_type_61',axiom,
! [V_24X1,V_24Y] :
( c_24__type__61___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__61___24a1(V_24X1)) ) ).
fof('$tdef_$_type_53601',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__53601___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__53601___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_17774',axiom,
! [V_24Y] :
( c_24__type__17774___24t(V_24Y)
<=> t(V_24Y,c_24__type__17774) ) ).
fof('$tdef_$_type_895',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__895___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__895___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20974',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__20974___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__20974___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_1580',axiom,
! [V_24Y] :
( c_24__type__1580___24t(V_24Y)
<=> t(V_24Y,c_24__type__1580) ) ).
fof('$tdef_$_type_25274',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__25274___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__25274___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_61209',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__61209___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__61209___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_$_type_22430',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__22430___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__22430___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_29699',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__29699___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__29699___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_147',axiom,
! [V_24X1,V_24Y] :
( c_24__type__147___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__147___24a1(V_24X1)) ) ).
fof('$tdef_$_type_30144',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30144___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30144___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Strings.Ascii.ascii',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).
fof('$tdef_$_type_17428',axiom,
! [V_24Y] :
( c_24__type__17428___24t(V_24Y)
<=> t(V_24Y,c_24__type__17428) ) ).
fof('$tdef_$_type_25678',axiom,
! [V_24Y] :
( c_24__type__25678___24t(V_24Y)
<=> t(V_24Y,c_24__type__25678) ) ).
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_$_type_10',axiom,
! [V_24Y] :
( c_24__type__10___24t(V_24Y)
<=> t(V_24Y,c_24__type__10) ) ).
fof('$tdef_$_type_55152',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__55152___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__55152___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_57638',axiom,
! [V_24Y] :
( c_24__type__57638___24t(V_24Y)
<=> t(V_24Y,c_24__type__57638) ) ).
fof('$tdef_$_type_28188',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__28188___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__28188___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_63639',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__63639___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__63639___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_52835',axiom,
! [V_24Y] :
( c_24__type__52835___24t(V_24Y)
<=> t(V_24Y,c_24__type__52835) ) ).
fof('$tdef_$_type_38673',axiom,
! [V_24Y] :
( c_24__type__38673___24t(V_24Y)
<=> t(V_24Y,c_24__type__38673) ) ).
fof('$tdef_$_type_4856',axiom,
! [V_24Y] :
( c_24__type__4856___24t(V_24Y)
<=> t(V_24Y,c_24__type__4856) ) ).
fof('$tdef_$_type_798',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__798___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__798___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_239',axiom,
! [V_24Y] :
( c_24__type__239___24t(V_24Y)
<=> t(V_24Y,c_24__type__239) ) ).
fof('$tdef_$_type_51420',axiom,
! [V_24Y] :
( c_24__type__51420___24t(V_24Y)
<=> t(V_24Y,c_24__type__51420) ) ).
fof('$tdef_$_type_25633',axiom,
! [V_24Y] :
( c_24__type__25633___24t(V_24Y)
<=> t(V_24Y,c_24__type__25633) ) ).
fof('$tdef_$_type_1394',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1394___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1394___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_36098',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__36098___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__36098___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_18793',axiom,
! [V_24Y] :
( c_24__type__18793___24t(V_24Y)
<=> t(V_24Y,c_24__type__18793) ) ).
fof('$tdef_$_type_37655',axiom,
! [V_24Y] :
( c_24__type__37655___24t(V_24Y)
<=> t(V_24Y,c_24__type__37655) ) ).
fof('$tdef_$_type_2964',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2964___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2964___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Byte.byte',axiom,
! [V_24Y] :
( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).
fof('$tdef_$_type_42498',axiom,
! [V_24Y] :
( c_24__type__42498___24t(V_24Y)
<=> t(V_24Y,c_24__type__42498) ) ).
fof('$tdef_$_type_55141',axiom,
! [V_24Y] :
( c_24__type__55141___24t(V_24Y)
<=> t(V_24Y,c_24__type__55141) ) ).
fof('$tdef_$_type_17783',axiom,
! [V_24Y] :
( c_24__type__17783___24t(V_24Y)
<=> t(V_24Y,c_24__type__17783) ) ).
fof('$tdef_$_type_36510',axiom,
! [V_24Y] :
( c_24__type__36510___24t(V_24Y)
<=> t(V_24Y,c_24__type__36510) ) ).
fof('$tdef_$_type_35911',axiom,
! [V_24Y] :
( c_24__type__35911___24t(V_24Y)
<=> t(V_24Y,c_24__type__35911) ) ).
fof('$tdef_$_type_63702',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__63702___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__63702___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_20482',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20482___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__20482___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_2856',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__2856___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__2856___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_1459',axiom,
! [V_24Y] :
( c_24__type__1459___24t(V_24Y)
<=> t(V_24Y,c_24__type__1459) ) ).
fof('$tdef_$_type_20836',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__20836___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__20836___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_26902',axiom,
! [V_24Y] :
( c_24__type__26902___24t(V_24Y)
<=> t(V_24Y,c_24__type__26902) ) ).
fof('$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_55565',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__55565___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__55565___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28524',axiom,
! [V_24Y] :
( c_24__type__28524___24t(V_24Y)
<=> t(V_24Y,c_24__type__28524) ) ).
fof('$tdef_$_type_934',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__934___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__934___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_55618',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__55618___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__55618___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_55606',axiom,
! [V_24Y] :
( c_24__type__55606___24t(V_24Y)
<=> t(V_24Y,c_24__type__55606) ) ).
fof('$tdef_$_type_53234',axiom,
! [V_24Y] :
( c_24__type__53234___24t(V_24Y)
<=> t(V_24Y,c_24__type__53234) ) ).
fof('$tdef_$_type_28919',axiom,
! [V_24Y] :
( c_24__type__28919___24t(V_24Y)
<=> t(V_24Y,c_24__type__28919) ) ).
fof('$tdef_$_type_608',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__608___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__608___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_20302',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20302___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__20302___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_446',axiom,
! [V_24Y] :
( c_24__type__446___24t(V_24Y)
<=> t(V_24Y,c_24__type__446) ) ).
fof('$tdef_$_type_30311',axiom,
! [V_24Y] :
( c_24__type__30311___24t(V_24Y)
<=> t(V_24Y,c_24__type__30311) ) ).
fof('$tdef_$_type_18352',axiom,
! [V_24Y] :
( c_24__type__18352___24t(V_24Y)
<=> t(V_24Y,c_24__type__18352) ) ).
fof('$tdef_$_type_56306',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__56306___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__56306___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_12867',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__12867___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__12867___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_1288',axiom,
! [V_24Y] :
( c_24__type__1288___24t(V_24Y)
<=> t(V_24Y,c_24__type__1288) ) ).
fof('$tdef_$_type_25402',axiom,
! [V_24Y] :
( c_24__type__25402___24t(V_24Y)
<=> t(V_24Y,c_24__type__25402) ) ).
fof('$tdef_$_type_18133',axiom,
! [V_24Y] :
( c_24__type__18133___24t(V_24Y)
<=> t(V_24Y,c_24__type__18133) ) ).
fof('$tdef_$_type_177',axiom,
! [V_24Y] :
( c_24__type__177___24t(V_24Y)
<=> t(V_24Y,c_24__type__177) ) ).
fof('$tdef_$_type_382',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__382___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__382___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_25366',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__25366___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__25366___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1293',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1293___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1293___24a1(V_24X1)) ) ).
fof('$tdef_$_type_36534',axiom,
! [V_24Y] :
( c_24__type__36534___24t(V_24Y)
<=> t(V_24Y,c_24__type__36534) ) ).
fof('$tdef_$_type_23903',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__23903___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__23903___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_1524',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1524___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1524___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_57906',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__57906___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__57906___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_37556',axiom,
! [V_24Y] :
( c_24__type__37556___24t(V_24Y)
<=> t(V_24Y,c_24__type__37556) ) ).
fof('$tdef_$_type_4843',axiom,
! [V_24Y] :
( c_24__type__4843___24t(V_24Y)
<=> t(V_24Y,c_24__type__4843) ) ).
fof('$tdef_$_type_35916',axiom,
! [V_24Y] :
( c_24__type__35916___24t(V_24Y)
<=> t(V_24Y,c_24__type__35916) ) ).
fof('$tdef_$_type_696',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__696___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__696___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_25673',axiom,
! [V_24Y] :
( c_24__type__25673___24t(V_24Y)
<=> t(V_24Y,c_24__type__25673) ) ).
fof('$tdef_$_type_45775',axiom,
! [V_24Y] :
( c_24__type__45775___24t(V_24Y)
<=> t(V_24Y,c_24__type__45775) ) ).
fof('$tdef_$_type_28725',axiom,
! [V_24Y] :
( c_24__type__28725___24t(V_24Y)
<=> t(V_24Y,c_24__type__28725) ) ).
fof('$tdef_$_type_56178',axiom,
! [V_24Y] :
( c_24__type__56178___24t(V_24Y)
<=> t(V_24Y,c_24__type__56178) ) ).
fof('$tdef_$_type_27055',axiom,
! [V_24Y] :
( c_24__type__27055___24t(V_24Y)
<=> t(V_24Y,c_24__type__27055) ) ).
fof('$tdef_$_type_35652',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__35652___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__35652___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_26414',axiom,
! [V_24Y] :
( c_24__type__26414___24t(V_24Y)
<=> t(V_24Y,c_24__type__26414) ) ).
fof('$tdef_$_type_25591',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__25591___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__25591___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_601',axiom,
! [V_24Y] :
( c_24__type__601___24t(V_24Y)
<=> t(V_24Y,c_24__type__601) ) ).
fof('$tdef_$_type_37888',axiom,
! [V_24Y] :
( c_24__type__37888___24t(V_24Y)
<=> t(V_24Y,c_24__type__37888) ) ).
fof('$tdef_$_type_36734',axiom,
! [V_24Y] :
( c_24__type__36734___24t(V_24Y)
<=> t(V_24Y,c_24__type__36734) ) ).
fof('$tdef_$_type_157',axiom,
! [V_24Y] :
( c_24__type__157___24t(V_24Y)
<=> t(V_24Y,c_24__type__157) ) ).
fof('$tdef_$_type_17417',axiom,
! [V_24Y] :
( c_24__type__17417___24t(V_24Y)
<=> t(V_24Y,c_24__type__17417) ) ).
fof('$tdef_$_type_42621',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__42621___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__42621___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_3211',axiom,
! [V_24Y] :
( c_24__type__3211___24t(V_24Y)
<=> t(V_24Y,c_24__type__3211) ) ).
fof('$tdef_$_type_38632',axiom,
! [V_24Y] :
( c_24__type__38632___24t(V_24Y)
<=> t(V_24Y,c_24__type__38632) ) ).
fof('$tdef_Coq.Numbers.BinNums.Z',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eZ) ) ).
fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_35720',axiom,
! [V_24Y] :
( c_24__type__35720___24t(V_24Y)
<=> t(V_24Y,c_24__type__35720) ) ).
fof('$tdef_$_type_28741',axiom,
! [V_24Y] :
( c_24__type__28741___24t(V_24Y)
<=> t(V_24Y,c_24__type__28741) ) ).
fof('$tdef_$_type_25752',axiom,
! [V_24Y] :
( c_24__type__25752___24t(V_24Y)
<=> t(V_24Y,c_24__type__25752) ) ).
fof('$tdef_$_type_41446',axiom,
! [V_24Y] :
( c_24__type__41446___24t(V_24Y)
<=> t(V_24Y,c_24__type__41446) ) ).
fof('$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_29497',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__29497___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__29497___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_12331',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__12331___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__12331___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Formula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_49479',axiom,
! [V_24Y] :
( c_24__type__49479___24t(V_24Y)
<=> t(V_24Y,c_24__type__49479) ) ).
fof('$tdef_$_type_1314',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1314___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1314___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Init.Datatypes.ID',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).
fof('$tdef_$_type_28796',axiom,
! [V_24Y] :
( c_24__type__28796___24t(V_24Y)
<=> t(V_24Y,c_24__type__28796) ) ).
fof('$tdef_$_type_26992',axiom,
! [V_24Y] :
( c_24__type__26992___24t(V_24Y)
<=> t(V_24Y,c_24__type__26992) ) ).
fof('$tdef_$_type_15729',axiom,
! [V_24Y] :
( c_24__type__15729___24t(V_24Y)
<=> t(V_24Y,c_24__type__15729) ) ).
fof('$tdef_$_type_20752',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__20752___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__20752___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_938',axiom,
! [V_24Y] :
( c_24__type__938___24t(V_24Y)
<=> t(V_24Y,c_24__type__938) ) ).
fof('$tdef_$_type_35716',axiom,
! [V_24Y] :
( c_24__type__35716___24t(V_24Y)
<=> t(V_24Y,c_24__type__35716) ) ).
fof('$tdef_$_type_20428',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20428___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__20428___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_55574',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__55574___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__55574___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31',axiom,
! [V_24Y] :
( c_24__type__31___24t(V_24Y)
<=> t(V_24Y,c_24__type__31) ) ).
fof('$tdef_$_type_24667',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__24667___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__24667___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_29037',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__29037___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__29037___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_4752',axiom,
! [V_24Y] :
( c_24__type__4752___24t(V_24Y)
<=> t(V_24Y,c_24__type__4752) ) ).
fof('$tdef_$_type_55458',axiom,
! [V_24Y] :
( c_24__type__55458___24t(V_24Y)
<=> t(V_24Y,c_24__type__55458) ) ).
fof('$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_14369',axiom,
! [V_24Y] :
( c_24__type__14369___24t(V_24Y)
<=> t(V_24Y,c_24__type__14369) ) ).
fof('$tdef_$_type_30292',axiom,
! [V_24Y] :
( c_24__type__30292___24t(V_24Y)
<=> t(V_24Y,c_24__type__30292) ) ).
fof('$tdef_$_type_26905',axiom,
! [V_24Y] :
( c_24__type__26905___24t(V_24Y)
<=> t(V_24Y,c_24__type__26905) ) ).
fof('$tdef_$_type_17818',axiom,
! [V_24Y] :
( c_24__type__17818___24t(V_24Y)
<=> t(V_24Y,c_24__type__17818) ) ).
fof('$tdef_$_type_36144',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__36144___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__36144___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_63576',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__63576___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__63576___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_15754',axiom,
! [V_24Y] :
( c_24__type__15754___24t(V_24Y)
<=> t(V_24Y,c_24__type__15754) ) ).
fof('$tdef_$_type_36167',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__36167___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__36167___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_41469',axiom,
! [V_24Y] :
( c_24__type__41469___24t(V_24Y)
<=> t(V_24Y,c_24__type__41469) ) ).
fof('$tdef_$_type_25107',axiom,
! [V_24Y] :
( c_24__type__25107___24t(V_24Y)
<=> t(V_24Y,c_24__type__25107) ) ).
fof('$tdef_$_type_8',axiom,
! [V_24Y] :
( c_24__type__8___24t(V_24Y)
<=> t(V_24Y,c_24__type__8) ) ).
fof('$tdef_$_type_42759',axiom,
! [V_24Y] :
( c_24__type__42759___24t(V_24Y)
<=> t(V_24Y,c_24__type__42759) ) ).
fof('$tdef_$_type_36496',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__36496___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__36496___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27030',axiom,
! [V_24Y] :
( c_24__type__27030___24t(V_24Y)
<=> t(V_24Y,c_24__type__27030) ) ).
fof('$tdef_$_type_27291',axiom,
! [V_24Y] :
( c_24__type__27291___24t(V_24Y)
<=> t(V_24Y,c_24__type__27291) ) ).
fof('$tdef_$_type_335',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__335___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__335___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_27317',axiom,
! [V_24Y] :
( c_24__type__27317___24t(V_24Y)
<=> t(V_24Y,c_24__type__27317) ) ).
fof('$tdef_$_type_25597',axiom,
! [V_24Y] :
( c_24__type__25597___24t(V_24Y)
<=> t(V_24Y,c_24__type__25597) ) ).
fof('$tdef_$_type_24648',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__24648___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__24648___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_27294',axiom,
! [V_24Y] :
( c_24__type__27294___24t(V_24Y)
<=> t(V_24Y,c_24__type__27294) ) ).
fof('$tdef_$_type_56050',axiom,
! [V_24Y] :
( c_24__type__56050___24t(V_24Y)
<=> t(V_24Y,c_24__type__56050) ) ).
fof('$tdef_$_type_36693',axiom,
! [V_24Y] :
( c_24__type__36693___24t(V_24Y)
<=> t(V_24Y,c_24__type__36693) ) ).
fof('$tdef_$_type_17777',axiom,
! [V_24Y] :
( c_24__type__17777___24t(V_24Y)
<=> t(V_24Y,c_24__type__17777) ) ).
fof('$tdef_$_type_37344',axiom,
! [V_24Y] :
( c_24__type__37344___24t(V_24Y)
<=> t(V_24Y,c_24__type__37344) ) ).
fof('$tdef_$_type_25023',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__25023___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__25023___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_2813',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2813___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2813___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_17473',axiom,
! [V_24Y] :
( c_24__type__17473___24t(V_24Y)
<=> t(V_24Y,c_24__type__17473) ) ).
fof('$tdef_$_type_22643',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__22643___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__22643___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('$tdef_Coq.micromega.Env.Env',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_$_type_26423',axiom,
! [V_24Y] :
( c_24__type__26423___24t(V_24Y)
<=> t(V_24Y,c_24__type__26423) ) ).
fof('$tdef_$_type_55583',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__55583___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__55583___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28779',axiom,
! [V_24Y] :
( c_24__type__28779___24t(V_24Y)
<=> t(V_24Y,c_24__type__28779) ) ).
fof('$tdef_$_type_15058',axiom,
! [V_24Y] :
( c_24__type__15058___24t(V_24Y)
<=> t(V_24Y,c_24__type__15058) ) ).
fof('$tdef_$_type_1302',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1302___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1302___24a1(V_24X1)) ) ).
fof('$tdef_$_type_27002',axiom,
! [V_24Y] :
( c_24__type__27002___24t(V_24Y)
<=> t(V_24Y,c_24__type__27002) ) ).
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_$_type_55683',axiom,
! [V_24Y] :
( c_24__type__55683___24t(V_24Y)
<=> t(V_24Y,c_24__type__55683) ) ).
fof('$tdef_$_type_862',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__862___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__862___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27058',axiom,
! [V_24X1,V_24Y] :
( c_24__type__27058___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__27058___24a1(V_24X1)) ) ).
fof('$tdef_$_type_64181',axiom,
! [V_24Y] :
( c_24__type__64181___24t(V_24Y)
<=> t(V_24Y,c_24__type__64181) ) ).
fof('$tdef_$_type_36983',axiom,
! [V_24Y] :
( c_24__type__36983___24t(V_24Y)
<=> t(V_24Y,c_24__type__36983) ) ).
fof('$tdef_$_type_45802',axiom,
! [V_24Y] :
( c_24__type__45802___24t(V_24Y)
<=> t(V_24Y,c_24__type__45802) ) ).
fof('$tdef_$_type_49599',axiom,
! [V_24Y] :
( c_24__type__49599___24t(V_24Y)
<=> t(V_24Y,c_24__type__49599) ) ).
fof('$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_28902',axiom,
! [V_24X1,V_24Y] :
( c_24__type__28902___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__28902___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20866',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__20866___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__20866___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_12122',axiom,
! [V_24Y] :
( c_24__type__12122___24t(V_24Y)
<=> t(V_24Y,c_24__type__12122) ) ).
fof('$tdef_Coq.micromega.QMicromega.QWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eQMicromega_2eQWitness) ) ).
fof('$tdef_$_type_259',axiom,
! [V_24X1,V_24Y] :
( c_24__type__259___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__259___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1554',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1554___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1554___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20782',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__20782___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__20782___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_27821',axiom,
! [V_24Y] :
( c_24__type__27821___24t(V_24Y)
<=> t(V_24Y,c_24__type__27821) ) ).
fof('$tdef_$_type_15811',axiom,
! [V_24Y] :
( c_24__type__15811___24t(V_24Y)
<=> t(V_24Y,c_24__type__15811) ) ).
fof('$tdef_$_type_25354',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__25354___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__25354___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_35786',axiom,
! [V_24Y] :
( c_24__type__35786___24t(V_24Y)
<=> t(V_24Y,c_24__type__35786) ) ).
fof('$tdef_$_type_55289',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__55289___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__55289___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_809',axiom,
! [V_24Y] :
( c_24__type__809___24t(V_24Y)
<=> t(V_24Y,c_24__type__809) ) ).
fof('$tdef_$_type_53',axiom,
! [V_24Y] :
( c_24__type__53___24t(V_24Y)
<=> t(V_24Y,c_24__type__53) ) ).
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_$_type_634',axiom,
! [V_24X1,V_24Y] :
( c_24__type__634___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__634___24a1(V_24X1)) ) ).
fof('$tdef_$_type_55767',axiom,
! [V_24Y] :
( c_24__type__55767___24t(V_24Y)
<=> t(V_24Y,c_24__type__55767) ) ).
fof('$tdef_$_type_222',axiom,
! [V_24Y] :
( c_24__type__222___24t(V_24Y)
<=> t(V_24Y,c_24__type__222) ) ).
fof('$tdef_$_type_565',axiom,
! [V_24Y] :
( c_24__type__565___24t(V_24Y)
<=> t(V_24Y,c_24__type__565) ) ).
fof('$tdef_$_type_41967',axiom,
! [V_24Y] :
( c_24__type__41967___24t(V_24Y)
<=> t(V_24Y,c_24__type__41967) ) ).
fof('$tdef_$_type_28954',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__28954___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__28954___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_25522',axiom,
! [V_24Y] :
( c_24__type__25522___24t(V_24Y)
<=> t(V_24Y,c_24__type__25522) ) ).
fof('$tdef_$_type_12774',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__12774___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__12774___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_60314',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__60314___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__60314___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28735',axiom,
! [V_24Y] :
( c_24__type__28735___24t(V_24Y)
<=> t(V_24Y,c_24__type__28735) ) ).
fof('$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_63819',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__63819___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__63819___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_2314',axiom,
! [V_24Y] :
( c_24__type__2314___24t(V_24Y)
<=> t(V_24Y,c_24__type__2314) ) ).
fof('$tdef_$_type_518',axiom,
! [V_24Y] :
( c_24__type__518___24t(V_24Y)
<=> t(V_24Y,c_24__type__518) ) ).
fof('$tdef_$_type_13839',axiom,
! [V_24Y] :
( c_24__type__13839___24t(V_24Y)
<=> t(V_24Y,c_24__type__13839) ) ).
fof('$tdef_$_type_37885',axiom,
! [V_24Y] :
( c_24__type__37885___24t(V_24Y)
<=> t(V_24Y,c_24__type__37885) ) ).
fof('$tdef_$_type_539',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__539___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__539___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23690',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__23690___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__23690___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_36690',axiom,
! [V_24Y] :
( c_24__type__36690___24t(V_24Y)
<=> t(V_24Y,c_24__type__36690) ) ).
fof('$tdef_$_type_37941',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__37941___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__37941___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1546',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1546___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1546___24a1(V_24X1)) ) ).
fof('$tdef_$_type_37865',axiom,
! [V_24Y] :
( c_24__type__37865___24t(V_24Y)
<=> t(V_24Y,c_24__type__37865) ) ).
fof('$tdef_$_type_25777',axiom,
! [V_24Y] :
( c_24__type__25777___24t(V_24Y)
<=> t(V_24Y,c_24__type__25777) ) ).
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_$_type_63756',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__63756___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__63756___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_18031',axiom,
! [V_24Y] :
( c_24__type__18031___24t(V_24Y)
<=> t(V_24Y,c_24__type__18031) ) ).
fof('$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_25099',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__25099___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__25099___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_190',axiom,
! [V_24Y] :
( c_24__type__190___24t(V_24Y)
<=> t(V_24Y,c_24__type__190) ) ).
fof('$tdef_$_type_26065',axiom,
! [V_24Y] :
( c_24__type__26065___24t(V_24Y)
<=> t(V_24Y,c_24__type__26065) ) ).
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_$_type_56213',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__56213___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__56213___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_55247',axiom,
! [V_24Y] :
( c_24__type__55247___24t(V_24Y)
<=> t(V_24Y,c_24__type__55247) ) ).
fof('$tdef_$_type_24311',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__24311___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__24311___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_36211',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__36211___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__36211___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_29598',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__29598___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__29598___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_26871',axiom,
! [V_24Y] :
( c_24__type__26871___24t(V_24Y)
<=> t(V_24Y,c_24__type__26871) ) ).
fof('$tdef_$_type_36925',axiom,
! [V_24Y] :
( c_24__type__36925___24t(V_24Y)
<=> t(V_24Y,c_24__type__36925) ) ).
fof('$tdef_$_type_18130',axiom,
! [V_24Y] :
( c_24__type__18130___24t(V_24Y)
<=> t(V_24Y,c_24__type__18130) ) ).
fof('$tdef_$_type_16422',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__16422___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__16422___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_29789',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__29789___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__29789___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.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_19759',axiom,
! [V_24Y] :
( c_24__type__19759___24t(V_24Y)
<=> t(V_24Y,c_24__type__19759) ) ).
fof('$tdef_$_type_32953',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__32953___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__32953___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_37937',axiom,
! [V_24Y] :
( c_24__type__37937___24t(V_24Y)
<=> t(V_24Y,c_24__type__37937) ) ).
fof('$tdef_$_type_31246',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__31246___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__31246___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_53596',axiom,
! [V_24Y] :
( c_24__type__53596___24t(V_24Y)
<=> t(V_24Y,c_24__type__53596) ) ).
fof('$tdef_$_type_899',axiom,
! [V_24Y] :
( c_24__type__899___24t(V_24Y)
<=> t(V_24Y,c_24__type__899) ) ).
fof('$tdef_$_type_51175',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__51175___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__51175___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).
fof('$tdef_$_type_36121',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__36121___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__36121___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_74',axiom,
! [V_24Y] :
( c_24__type__74___24t(V_24Y)
<=> t(V_24Y,c_24__type__74) ) ).
fof('$tdef_$_type_1323',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1323___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1323___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_36492',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36492___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36492___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_15709',axiom,
! [V_24Y] :
( c_24__type__15709___24t(V_24Y)
<=> t(V_24Y,c_24__type__15709) ) ).
fof('$tdef_$_type_138',axiom,
! [V_24Y] :
( c_24__type__138___24t(V_24Y)
<=> t(V_24Y,c_24__type__138) ) ).
fof('$tdef_$_type_26852',axiom,
! [V_24Y] :
( c_24__type__26852___24t(V_24Y)
<=> t(V_24Y,c_24__type__26852) ) ).
fof('$tdef_$_type_1697',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1697___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1697___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_36725',axiom,
! [V_24Y] :
( c_24__type__36725___24t(V_24Y)
<=> t(V_24Y,c_24__type__36725) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_35703',axiom,
! [V_24Y] :
( c_24__type__35703___24t(V_24Y)
<=> t(V_24Y,c_24__type__35703) ) ).
fof('$tdef_$_type_18608',axiom,
! [V_24Y] :
( c_24__type__18608___24t(V_24Y)
<=> t(V_24Y,c_24__type__18608) ) ).
fof('$tdef_$_type_18138',axiom,
! [V_24Y] :
( c_24__type__18138___24t(V_24Y)
<=> t(V_24Y,c_24__type__18138) ) ).
fof('$tdef_$_type_37904',axiom,
! [V_24Y] :
( c_24__type__37904___24t(V_24Y)
<=> t(V_24Y,c_24__type__37904) ) ).
fof('$tdef_$_type_1483',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1483___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1483___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_15841',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15841___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15841___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_26430',axiom,
! [V_24Y] :
( c_24__type__26430___24t(V_24Y)
<=> t(V_24Y,c_24__type__26430) ) ).
fof('$tdef_$_type_28737',axiom,
! [V_24Y] :
( c_24__type__28737___24t(V_24Y)
<=> t(V_24Y,c_24__type__28737) ) ).
fof('$tdef_$_type_271',axiom,
! [V_24X1,V_24Y] :
( c_24__type__271___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__271___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35955',axiom,
! [V_24Y] :
( c_24__type__35955___24t(V_24Y)
<=> t(V_24Y,c_24__type__35955) ) ).
fof('$tdef_$_type_22856',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__22856___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__22856___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_26981',axiom,
! [V_24Y] :
( c_24__type__26981___24t(V_24Y)
<=> t(V_24Y,c_24__type__26981) ) ).
fof('$tdef_$_type_25769',axiom,
! [V_24Y] :
( c_24__type__25769___24t(V_24Y)
<=> t(V_24Y,c_24__type__25769) ) ).
fof('$tdef_$_type_17812',axiom,
! [V_24Y] :
( c_24__type__17812___24t(V_24Y)
<=> t(V_24Y,c_24__type__17812) ) ).
fof('$tdef_$_type_24973',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__24973___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__24973___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_31915',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__31915___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__31915___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_1454',axiom,
! [V_24Y] :
( c_24__type__1454___24t(V_24Y)
<=> t(V_24Y,c_24__type__1454) ) ).
fof('$tdef_$_type_33968',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__33968___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__33968___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_17809',axiom,
! [V_24Y] :
( c_24__type__17809___24t(V_24Y)
<=> t(V_24Y,c_24__type__17809) ) ).
fof('$tdef_$_type_19303',axiom,
! [V_24Y] :
( c_24__type__19303___24t(V_24Y)
<=> t(V_24Y,c_24__type__19303) ) ).
fof('$tdef_$_type_18117',axiom,
! [V_24Y] :
( c_24__type__18117___24t(V_24Y)
<=> t(V_24Y,c_24__type__18117) ) ).
fof('$tdef_$_type_20806',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__20806___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__20806___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_28702',axiom,
! [V_24Y] :
( c_24__type__28702___24t(V_24Y)
<=> t(V_24Y,c_24__type__28702) ) ).
fof('$tdef_$_type_20947',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__20947___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__20947___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2744',axiom,
! [V_24Y] :
( c_24__type__2744___24t(V_24Y)
<=> t(V_24Y,c_24__type__2744) ) ).
fof('$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_26972',axiom,
! [V_24Y] :
( c_24__type__26972___24t(V_24Y)
<=> t(V_24Y,c_24__type__26972) ) ).
fof('$tdef_$_type_12517',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__12517___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__12517___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_58564',axiom,
! [V_24Y] :
( c_24__type__58564___24t(V_24Y)
<=> t(V_24Y,c_24__type__58564) ) ).
fof('$tdef_$_type_20545',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20545___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__20545___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_844',axiom,
! [V_24Y] :
( c_24__type__844___24t(V_24Y)
<=> t(V_24Y,c_24__type__844) ) ).
fof('$tdef_$_type_20923',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__20923___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__20923___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_42610',axiom,
! [V_24Y] :
( c_24__type__42610___24t(V_24Y)
<=> t(V_24Y,c_24__type__42610) ) ).
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_$_type_25638',axiom,
! [V_24Y] :
( c_24__type__25638___24t(V_24Y)
<=> t(V_24Y,c_24__type__25638) ) ).
fof('$tdef_$_type_15698',axiom,
! [V_24Y] :
( c_24__type__15698___24t(V_24Y)
<=> t(V_24Y,c_24__type__15698) ) ).
fof('$tdef_$_type_42660',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__42660___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__42660___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_55116',axiom,
! [V_24Y] :
( c_24__type__55116___24t(V_24Y)
<=> t(V_24Y,c_24__type__55116) ) ).
fof('$tdef_$_type_572',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__572___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__572___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1069',axiom,
! [V_24Y] :
( c_24__type__1069___24t(V_24Y)
<=> t(V_24Y,c_24__type__1069) ) ).
fof('$tdef_$_type_54876',axiom,
! [V_24Y] :
( c_24__type__54876___24t(V_24Y)
<=> t(V_24Y,c_24__type__54876) ) ).
fof('$tdef_$_type_12692',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__12692___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__12692___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_58',axiom,
! [V_24Y] :
( c_24__type__58___24t(V_24Y)
<=> t(V_24Y,c_24__type__58) ) ).
fof('$tdef_$_type_55455',axiom,
! [V_24X1,V_24Y] :
( c_24__type__55455___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__55455___24a1(V_24X1)) ) ).
fof('$tdef_$_type_37893',axiom,
! [V_24Y] :
( c_24__type__37893___24t(V_24Y)
<=> t(V_24Y,c_24__type__37893) ) ).
fof('$tdef_$_type_28982',axiom,
! [V_24Y] :
( c_24__type__28982___24t(V_24Y)
<=> t(V_24Y,c_24__type__28982) ) ).
fof('$tdef_$_type_55749',axiom,
! [V_24Y] :
( c_24__type__55749___24t(V_24Y)
<=> t(V_24Y,c_24__type__55749) ) ).
fof('$tdef_$_type_1390',axiom,
! [V_24Y] :
( c_24__type__1390___24t(V_24Y)
<=> t(V_24Y,c_24__type__1390) ) ).
fof('$tdef_$_type_37054',axiom,
! [V_24Y] :
( c_24__type__37054___24t(V_24Y)
<=> t(V_24Y,c_24__type__37054) ) ).
fof('$tdef_$_type_36229',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__36229___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__36229___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_28828',axiom,
! [V_24Y] :
( c_24__type__28828___24t(V_24Y)
<=> t(V_24Y,c_24__type__28828) ) ).
fof('$tdef_$_type_13247',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__13247___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__13247___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_29890',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__29890___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__29890___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_1426',axiom,
! [V_24Y] :
( c_24__type__1426___24t(V_24Y)
<=> t(V_24Y,c_24__type__1426) ) ).
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_$_type_35934',axiom,
! [V_24Y] :
( c_24__type__35934___24t(V_24Y)
<=> t(V_24Y,c_24__type__35934) ) ).
fof('$tdef_$_type_111',axiom,
! [V_24Y] :
( c_24__type__111___24t(V_24Y)
<=> t(V_24Y,c_24__type__111) ) ).
fof('$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_29055',axiom,
! [V_24Y] :
( c_24__type__29055___24t(V_24Y)
<=> t(V_24Y,c_24__type__29055) ) ).
fof('$tdef_$_type_19645',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__19645___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__19645___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_48077',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__48077___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__48077___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_33299',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__33299___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__33299___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_370',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__370___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__370___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_55007',axiom,
! [V_24Y] :
( c_24__type__55007___24t(V_24Y)
<=> t(V_24Y,c_24__type__55007) ) ).
fof('$tdef_$_type_24831',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__24831___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__24831___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_35708',axiom,
! [V_24Y] :
( c_24__type__35708___24t(V_24Y)
<=> t(V_24Y,c_24__type__35708) ) ).
fof('$tdef_$_type_51382',axiom,
! [V_24Y] :
( c_24__type__51382___24t(V_24Y)
<=> t(V_24Y,c_24__type__51382) ) ).
fof('$tdef_$_type_25310',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__25310___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__25310___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_34983',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__34983___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__34983___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_941',axiom,
! [V_24X1,V_24Y] :
( c_24__type__941___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__941___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34660',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__34660___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__34660___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_23477',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__23477___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__23477___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$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_46291',axiom,
! [V_24Y] :
( c_24__type__46291___24t(V_24Y)
<=> t(V_24Y,c_24__type__46291) ) ).
fof('$tdef_$_type_36612',axiom,
! [V_24Y] :
( c_24__type__36612___24t(V_24Y)
<=> t(V_24Y,c_24__type__36612) ) ).
fof('$tdef_$_type_27308',axiom,
! [V_24Y] :
( c_24__type__27308___24t(V_24Y)
<=> t(V_24Y,c_24__type__27308) ) ).
fof('$tdef_$_type_57900',axiom,
! [V_24Y] :
( c_24__type__57900___24t(V_24Y)
<=> t(V_24Y,c_24__type__57900) ) ).
fof('$tdef_$_type_25610',axiom,
! [V_24Y] :
( c_24__type__25610___24t(V_24Y)
<=> t(V_24Y,c_24__type__25610) ) ).
fof('$tdef_$_type_17444',axiom,
! [V_24Y] :
( c_24__type__17444___24t(V_24Y)
<=> t(V_24Y,c_24__type__17444) ) ).
fof('$tdef_$_type_55405',axiom,
! [V_24Y] :
( c_24__type__55405___24t(V_24Y)
<=> t(V_24Y,c_24__type__55405) ) ).
fof('$tdef_$_type_32261',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__32261___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__32261___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.RMicromega.RWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRWitness) ) ).
fof('$tdef_$_type_20890',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__20890___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__20890___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_28580',axiom,
! [V_24X1,V_24Y] :
( c_24__type__28580___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__28580___24a1(V_24X1)) ) ).
fof('$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_17446',axiom,
! [V_24Y] :
( c_24__type__17446___24t(V_24Y)
<=> t(V_24Y,c_24__type__17446) ) ).
fof('$tdef_$_type_18127',axiom,
! [V_24Y] :
( c_24__type__18127___24t(V_24Y)
<=> t(V_24Y,c_24__type__18127) ) ).
fof('$tdef_$_type_18370',axiom,
! [V_24X1,V_24Y] :
( c_24__type__18370___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__18370___24a1(V_24X1)) ) ).
fof('$tdef_$_type_42628',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__42628___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__42628___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_X',axiom,
! [V_24Y] :
( cX___24t(V_24Y)
<=> t(V_24Y,cX) ) ).
fof('$tdef_$_type_4822',axiom,
! [V_24Y] :
( c_24__type__4822___24t(V_24Y)
<=> t(V_24Y,c_24__type__4822) ) ).
fof('$tdef_$_type_407',axiom,
! [V_24Y] :
( c_24__type__407___24t(V_24Y)
<=> t(V_24Y,c_24__type__407) ) ).
fof('$tdef_$_type_36621',axiom,
! [V_24Y] :
( c_24__type__36621___24t(V_24Y)
<=> t(V_24Y,c_24__type__36621) ) ).
fof('$tdef_$_type_17671',axiom,
! [V_24Y] :
( c_24__type__17671___24t(V_24Y)
<=> t(V_24Y,c_24__type__17671) ) ).
fof('$tdef_$_type_30900',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__30900___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__30900___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_28575',axiom,
! [V_24Y] :
( c_24__type__28575___24t(V_24Y)
<=> t(V_24Y,c_24__type__28575) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_26867',axiom,
! [V_24Y] :
( c_24__type__26867___24t(V_24Y)
<=> t(V_24Y,c_24__type__26867) ) ).
fof('$tdef_$_type_24931',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__24931___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__24931___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_13163',axiom,
! [V_24Y] :
( c_24__type__13163___24t(V_24Y)
<=> t(V_24Y,c_24__type__13163) ) ).
fof('$tdef_$_type_61576',axiom,
! [V_24Y] :
( c_24__type__61576___24t(V_24Y)
<=> t(V_24Y,c_24__type__61576) ) ).
fof('$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_44132',axiom,
! [V_24Y] :
( c_24__type__44132___24t(V_24Y)
<=> t(V_24Y,c_24__type__44132) ) ).
fof('$tdef_$_type_4835',axiom,
! [V_24Y] :
( c_24__type__4835___24t(V_24Y)
<=> t(V_24Y,c_24__type__4835) ) ).
fof('$tdef_$_type_28849',axiom,
! [V_24Y] :
( c_24__type__28849___24t(V_24Y)
<=> t(V_24Y,c_24__type__28849) ) ).
fof('$tdef_$_type_13252',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__13252___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__13252___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_37739',axiom,
! [V_24Y] :
( c_24__type__37739___24t(V_24Y)
<=> t(V_24Y,c_24__type__37739) ) ).
fof('$tdef_$_type_958',axiom,
! [V_24Y] :
( c_24__type__958___24t(V_24Y)
<=> t(V_24Y,c_24__type__958) ) ).
fof('$tdef_$_type_977',axiom,
! [V_24Y] :
( c_24__type__977___24t(V_24Y)
<=> t(V_24Y,c_24__type__977) ) ).
fof('$tdef_$_type_25731',axiom,
! [V_24Y] :
( c_24__type__25731___24t(V_24Y)
<=> t(V_24Y,c_24__type__25731) ) ).
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_$_type_1549',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1549___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1549___24a1(V_24X1)) ) ).
fof('$tdef_$_type_36457',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36457___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36457___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_29991',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__29991___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__29991___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_32607',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__32607___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__32607___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_12599',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__12599___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__12599___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('_HAMMER_GOAL',conjecture,
( p(cCoq_2eLists_2eList_2eIn___24a3(cX,cx,cs))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(cX),cs,cl))
=> p(cCoq_2eLists_2eList_2eIn___24a3(cX,cx,clist__utils_2econcat___24a2(cX,cl))) ) ) ).
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