TPTP Problem File: SEV626+1.p
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%------------------------------------------------------------------------------
% File : SEV626+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - HahnRelationsBasic functional seq
% 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 : HahnRelationsBasic.functional.seq.p [Kal26]
% Status : Theorem
% Rating : 0.96 v9.3.0
% Syntax : Number of formulae : 2839 (1130 unt; 0 def)
% Number of atoms : 9700 (2239 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 6955 ( 94 ~; 672 |;1485 &)
% (1133 <=>;3571 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 6 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 611 ( 610 usr; 0 prp; 1-23 aty)
% Number of functors : 1589 (1589 usr;1070 con; 0-22 aty)
% Number of variables : 9451 (8861 !; 590 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.list$22354',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2422441___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2422354___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__22358] :
( t(Vvar__1___24Anonymous__22358,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__22359] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__22359)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2422441___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__22358,Vvar__2___24Anonymous__22359)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2422354___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__22358,c_24__fix__22486__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__22359,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$22441',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2422441___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__22445] :
( t(Vvar__1___24Anonymous__22445,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__22446] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__22446)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__22445,Vvar__2___24Anonymous__22446)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2422441___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__22445,c_24__fix__22486__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__22446,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$22605',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2422605___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__22606] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22606)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22606)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2422605___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__22606)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$22627',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2422627___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__22628] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22628)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22628)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2422627___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__22628)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$29797',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__29810___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__29802] :
( t(Vvar__2___24Anonymous__29802,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__29803] :
( t(Vvar__3___24Anonymous__29803,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__29802,Vvar__3___24Anonymous__29803)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2429797___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__29802)),Vvar__3___24Anonymous__29803)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.N$456',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__type__459___24t(Vv__CANONICAL__0,Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
& c_24__case__Coq_2eNumbers_2eBinNums_2eN_24456___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 )
| ? [Vvar__0___24Anonymous__457] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__457)
& Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__457)
& c_24__case__Coq_2eNumbers_2eBinNums_2eN_24456___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect___24a4(c_24__let__4__P_27__442___24a1(Vv__CANONICAL__0),happ(happ(Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0),Vv__CANONICAL__1),c_24__let__5__f_27__443___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vvar__0___24Anonymous__457) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$22622',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2422627___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2422622___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__22623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22623)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2422627___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22623)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2422622___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22623) )
| ? [Vvar__0___24Anonymous__22624] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22624)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2422627___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22624)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2422622___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22624) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.positive$30828',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__30829] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30829)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30829)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2430828___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__30844__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__30829)) )
| ? [Vvar__0___24Anonymous__30836] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30836)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30836)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2430828___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30836) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2430828___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_$_let_4_P\'_442',axiom,
! [V0__P,V4__p] : c_24__let__4__P_27__442___24a2(V0__P,V4__p) = happ(V0__P,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V4__p)) ).
fof('$_def_$_let_5_f\'_443',axiom,
! [V0__P,V2__f,V5__p] : c_24__let__5__f_27__443___24a3(V0__P,V2__f,V5__p) = happ(V2__f,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V5__p)) ).
fof('$_def_$_let_var_6_p_1275_1278',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1274] : c_24__let__var__6__p__1275__1278___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1274) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1274) ).
fof('$_def_$_let_var_6_p_1277_1279',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1276] : c_24__let__var__6__p__1277__1279___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1276) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1276) ).
fof('$_def_Coq.Arith.EqNat.eq_nat',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__18717] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18717)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18717)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__18718] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18718)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18718)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__18721] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18721)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18721)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__18718,Vvar__0___24Anonymous__18721) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eq',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.le',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2ele = cCoq_2eInit_2ePeano_2ele ).
fof('$_def_Coq.Arith.PeanoNat.Nat.lt',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2elt = cCoq_2eInit_2ePeano_2elt ).
fof('$_def_Coq.Arith.PeanoNat.Nat.recursion',axiom,
! [V0__A] : cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(c_24__lam__194___24a1(V0__A)) ).
fof('$_def_Coq.Arith.Plus.tail_plus',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__21485] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21485)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__21485)
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__21485,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
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.Bool.Bool.Is_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24True) ) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24False) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.eqb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.ifb',axiom,
! [V0__b1,V1__b2,V2__b3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eifb___24a3(V0__b1,V1__b2,V2__b3) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eifb___24a3(V0__b1,V1__b2,V2__b3) = V2__b3 ) ) ) ).
fof('$_def_Coq.Bool.Bvector.Bvector',axiom,
cCoq_2eBool_2eBvector_2eBvector = cCoq_2eVectors_2eVectorDef_2et___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__16367] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__16367)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__16367) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__16381] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__16381)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__16381) ) ).
fof('$_def_Coq.Init.Byte.byte_of_byte',axiom,
! [V0__b] : cCoq_2eInit_2eByte_2ebyte__of__byte___24a1(V0__b) = V0__b ).
fof('$_def_Coq.Init.Datatypes.CompOpp',axiom,
! [V0__r] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__r)
=> ( ( V0__r = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eEq )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eGt )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ).
fof('$_def_Coq.Init.Datatypes.ID',axiom,
! [Vvar__18656] :
( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__18656)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> t(happ(happ(Vvar__18656,V0__A),V1___24Anonymous),V0__A) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.IDProp',axiom,
( p(cCoq_2eInit_2eDatatypes_2eIDProp)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> p(V0__A) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.andb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__5857] :
( t(Vvar__1___24Anonymous__5857,V0__A)
& ? [Vvar__2___24Anonymous__5858] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__5858)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5857,Vvar__2___24Anonymous__5858)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5857,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__5858,V3__m)) ) ) ) ) ) ).
fof('$_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__18557] :
( t(Vvar__2___24Anonymous__18557,V0__A)
& ? [Vvar__3___24Anonymous__18558] :
( t(Vvar__3___24Anonymous__18558,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__18557,Vvar__3___24Anonymous__18558)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__18557 ) ) ) ) ) ).
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.implb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eimplb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eimplb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__5847] :
( t(Vvar__1___24Anonymous__5847,V0__A)
& ? [Vvar__2___24Anonymous__5848] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__5848)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5847,Vvar__2___24Anonymous__5848)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__5848)) ) ) ) ) ) ).
fof('$_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__18569] :
( t(Vvar__2___24Anonymous__18569,V0__A)
& ? [Vvar__3___24Anonymous__18570] :
( t(Vvar__3___24Anonymous__18570,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__18569,Vvar__3___24Anonymous__18570)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__18570 ) ) ) ) ) ).
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.Decimal.nzhead',axiom,
! [V1__d] :
( cCoq_2eInit_2eDecimal_2euint___24t(V1__d)
=> ( ( V1__d = cCoq_2eInit_2eDecimal_2eNil
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__18693] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__18693)
& V1__d = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__18693)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = cCoq_2eInit_2eDecimal_2enzhead___24a1(Vvar__0___24Anonymous__18693) )
| ? [Vvar__0___24Anonymous__18694] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__18694)
& V1__d = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__18694)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__18695] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__18695)
& V1__d = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__18695)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__18696] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__18696)
& V1__d = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__18696)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__18697] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__18697)
& V1__d = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__18697)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__18698] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__18698)
& V1__d = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__18698)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__18699] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__18699)
& V1__d = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__18699)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__18700] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__18700)
& V1__d = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__18700)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__18701] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__18701)
& V1__d = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__18701)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__18702] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__18702)
& V1__d = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__18702)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d ) ) ) ).
fof('$_def_Coq.Init.Decimal.uint_of_uint',axiom,
! [V0__i] : cCoq_2eInit_2eDecimal_2euint__of__uint___24a1(V0__i) = V0__i ).
fof('$_def_Coq.Init.Logic_Type.notT',axiom,
! [V0__A] :
( cCoq_2eInit_2eLogic__Type_2enotT___24a1(V0__A)
<=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> p(c_24False) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__8810] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8810)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8810)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__8810,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.compare',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_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__8828] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8828)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8828)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__8829] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8829)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8829)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__8832] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8832)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8832)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__8829,Vvar__0___24Anonymous__8832) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.div2',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__8863] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8863)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8863)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8863)
& ( ( Vvar__0___24Anonymous__8863 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__8866] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8866)
& Vvar__0___24Anonymous__8863 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8866)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__8866)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.double',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2edouble___24a1(V0__n) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V0__n) ).
fof('$_def_Coq.Init.Nat.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__20773] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20773)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20773)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__20774] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20774)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20774)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__20777] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20777)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20777)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__20774,Vvar__0___24Anonymous__20777) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.even',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__20786] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20786)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20786)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20786)
& ( ( Vvar__0___24Anonymous__20786 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__20789] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20789)
& Vvar__0___24Anonymous__20786 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20789)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__20789) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.leb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__8822] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8822)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8822)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__8825] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8825)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8825)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__8822,Vvar__0___24Anonymous__8825) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.log2_iter',axiom,
! [V1__k,V2__p,V3__q,V4__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( ( V1__k = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
| ? [Vvar__0___24Anonymous__8850] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8850)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8850)
& ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__8850,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V3__q) )
| ? [Vvar__0___24Anonymous__8853] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8853)
& V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8853)
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__8850,V2__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),Vvar__0___24Anonymous__8853) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__8837] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8837)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8837)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__8840] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8840)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8840)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__8837,Vvar__0___24Anonymous__8840)) ) ) ) ) ) ) ) ).
fof('$_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__20780] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20780)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20780)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__20783] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20783)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20783)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__20780,Vvar__0___24Anonymous__20783)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__8813] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8813)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8813)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__8813,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pow',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__8843] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8843)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8843)
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__n,cCoq_2eInit_2eNat_2epow___24a2(V1__n,Vvar__0___24Anonymous__8843)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__8808] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8808)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8808)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__8808 ) ) ) ).
fof('$_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__8816] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8816)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8816)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__8819] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8819)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8819)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__8816,Vvar__0___24Anonymous__8819) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.succ',axiom,
cCoq_2eInit_2eNat_2esucc = cCoq_2eInit_2eDatatypes_2eS ).
fof('$_def_Coq.Init.Nat.t',axiom,
! [Vvar__20771] :
( cCoq_2eInit_2eNat_2et___24t(Vvar__20771)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__20771) ) ).
fof('$_def_Coq.Init.Nat.tail_add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__20791] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20791)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20791)
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__20791,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.zero',axiom,
cCoq_2eInit_2eNat_2ezero = cCoq_2eInit_2eDatatypes_2eO ).
fof('$_def_Coq.Init.Peano.IsSucc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__21462] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21462)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__21462)
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ).
fof('$_def_Coq.Init.Specif.Exc',axiom,
! [V0__A] : cCoq_2eInit_2eSpecif_2eExc___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V0__A) ).
fof('$_def_Coq.Init.Specif.except',axiom,
cCoq_2eInit_2eSpecif_2eexcept = cCoq_2eInit_2eLogic_2eFalse__rec ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__14058___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__14052] :
( t(Vvar__2__x__14052,V0__A)
& p(happ(V1__P,Vvar__2__x__14052))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__14052)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__14052 ) ) ) ) ).
fof('$_def_Coq.Init.Wf.well_founded',axiom,
! [V0__A,V1__R] :
( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__a) ) ) ).
fof('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__825] :
( t(Vvar__1___24Anonymous__825,V0__A)
& ? [Vvar__2___24Anonymous__826] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__826)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__825,Vvar__2___24Anonymous__826)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__825 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__826) ) ) ) ) ) ) ) ).
fof('$_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__20619] :
( t(Vvar__1___24Anonymous__20619,V1__B)
& ? [Vvar__2___24Anonymous__20620] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__20620)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__20619,Vvar__2___24Anonymous__20620)
& 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__20620,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__20619)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_right',axiom,
! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
| ? [Vvar__1___24Anonymous__20648] :
( t(Vvar__1___24Anonymous__20648,V1__B)
& ? [Vvar__2___24Anonymous__20649] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__20649)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__20648,Vvar__2___24Anonymous__20649)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__20648),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__20649)) ) ) ) ) ) ) ).
fof('$_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__804] :
( t(Vvar__1___24Anonymous__804,V0__A)
& ? [Vvar__2___24Anonymous__805] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__805)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__804,Vvar__2___24Anonymous__805)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__804 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__20595] :
( t(Vvar__1___24Anonymous__20595,V0__A)
& ? [Vvar__2___24Anonymous__20596] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__20596)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__20596)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__20595,Vvar__2___24Anonymous__20596)
& ( ( Vvar__2___24Anonymous__20596 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__20595 )
| ? [Vvar__1___24Anonymous__20607] :
( t(Vvar__1___24Anonymous__20607,V0__A)
& ? [Vvar__2___24Anonymous__20608] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__20608)
& Vvar__2___24Anonymous__20596 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__20607,Vvar__2___24Anonymous__20608)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__20596,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__20570] :
( t(Vvar__1___24Anonymous__20570,V0__A)
& ? [Vvar__2___24Anonymous__20571] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__20571)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__20570,Vvar__2___24Anonymous__20571)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__20570 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__20573] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20573)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20573)
& ( ( 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__20580] :
( t(Vvar__1___24Anonymous__20580,V0__A)
& ? [Vvar__2___24Anonymous__20581] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__20581)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__20580,Vvar__2___24Anonymous__20581)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__20573,Vvar__2___24Anonymous__20581,V4__default) ) ) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.Logic.ChoiceFacts.ConstructiveIndefiniteDescription_on',axiom,
! [V0__A] : cCoq_2eLogic_2eChoiceFacts_2eConstructiveIndefiniteDescription__on___24a1(V0__A) = c_24__type__18423___24a1(V0__A) ).
fof('$_def_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__18328___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,happ(V1__B,V3__x))
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__18335___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.ExcludedMiddle',axiom,
( p(cCoq_2eLogic_2eChoiceFacts_2eExcludedMiddle)
<=> ! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__5680___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,V1__B)
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__268___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalChoice_on_rel',axiom,
! [V0__A,V1__B,V2__R] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel___24a3(V0__A,V1__B,V2__R)
<=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,V1__B)
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__268___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on',axiom,
! [V0__A] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on___24a1(V0__A)
<=> ! [V1__R] :
( c_24__type__18345___24t(V0__A,V1__R)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ? [V3__y] :
( t(V3__y,V0__A)
& p(happ(happ(V1__R,V2__n),V3__y)) ) )
=> ? [V3__f] :
( c_24__type__244___24t(V0__A,V3__f)
& ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(happ(happ(V1__R,V4__n),happ(V3__f,V4__n))) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.GeneralizedSetoidFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eGeneralizedSetoidFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__15___24t(V0__A,V2__R)
=> ! [V3__S] :
( c_24__type__18380___24t(V0__A,V1__B,V3__S)
=> ! [V4__T] :
( c_24__type__5680___24t(V0__A,V1__B,V4__T)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V2__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V1__B,V3__S)
=> ( ! [V7__x] :
( t(V7__x,V0__A)
=> ! [V8__x_27] :
( t(V8__x_27,V0__A)
=> ! [V9__y] :
( t(V9__y,V1__B)
=> ! [V10__y_27] :
( t(V10__y_27,V1__B)
=> ( p(happ(happ(V2__R,V7__x),V8__x_27))
=> ( p(happ(happ(V3__S,V9__y),V10__y_27))
=> ( p(happ(happ(V4__T,V7__x),V9__y))
=> p(happ(happ(V4__T,V8__x_27),V10__y_27)) ) ) ) ) ) ) )
=> ( ! [V8__x] :
( t(V8__x,V0__A)
=> ? [V9__y] :
( t(V9__y,V1__B)
& p(happ(happ(V4__T,V8__x),V9__y)) ) )
=> ? [V9__f] :
( c_24__type__268___24t(V0__A,V1__B,V9__f)
& ! [V10__x] :
( t(V10__x,V0__A)
=> ( p(happ(happ(V4__T,V10__x),happ(V9__f,V10__x)))
& ! [V11__x_27] :
( t(V11__x_27,V0__A)
=> ( p(happ(happ(V2__R,V10__x),V11__x_27))
=> p(happ(happ(V3__S,happ(V9__f,V10__x)),happ(V9__f,V11__x_27))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.ProofIrrelevance',axiom,
( p(cCoq_2eLogic_2eChoiceFacts_2eProofIrrelevance)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> ( p(V0__A)
=> c_24Proof = c_24Proof ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.RepresentativeFunctionalChoice_on',axiom,
! [V0__A] :
( cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on___24a1(V0__A)
<=> ! [V1__R] :
( c_24__type__15___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__R)
=> ? [V3__f] :
( c_24__type__247___24t(V0__A,V3__f)
& ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(happ(happ(V1__R,V4__x),happ(V3__f,V4__x)))
& ! [V5__x_27] :
( t(V5__x_27,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__x_27))
=> happ(V3__f,V4__x) = happ(V3__f,V5__x_27) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.SetoidFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eSetoidFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__15___24t(V0__A,V2__R)
=> ! [V3__T] :
( c_24__type__5680___24t(V0__A,V1__B,V3__T)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V2__R)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__x_27] :
( t(V6__x_27,V0__A)
=> ! [V7__y] :
( t(V7__y,V1__B)
=> ( p(happ(happ(V2__R,V5__x),V6__x_27))
=> ( p(happ(happ(V3__T,V5__x),V7__y))
=> p(happ(happ(V3__T,V6__x_27),V7__y)) ) ) ) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__A)
=> ? [V7__y] :
( t(V7__y,V1__B)
& p(happ(happ(V3__T,V6__x),V7__y)) ) )
=> ? [V7__f] :
( c_24__type__268___24t(V0__A,V1__B,V7__f)
& ! [V8__x] :
( t(V8__x,V0__A)
=> ( p(happ(happ(V3__T,V8__x),happ(V7__f,V8__x)))
& ! [V9__x_27] :
( t(V9__x_27,V0__A)
=> ( p(happ(happ(V2__R,V8__x),V9__x_27))
=> happ(V7__f,V8__x) = happ(V7__f,V9__x_27) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__15___24t(V0__A,V2__R)
=> ! [V3__T] :
( c_24__type__5680___24t(V0__A,V1__B,V3__T)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V2__R)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ? [V6__y] :
( t(V6__y,V1__B)
& ! [V7__x_27] :
( t(V7__x_27,V0__A)
=> ( p(happ(happ(V2__R,V5__x),V7__x_27))
=> p(happ(happ(V3__T,V7__x_27),V6__y)) ) ) ) )
=> ? [V6__f] :
( c_24__type__268___24t(V0__A,V1__B,V6__f)
& ! [V7__x] :
( t(V7__x,V0__A)
=> ( p(happ(happ(V3__T,V7__x),happ(V6__f,V7__x)))
& ! [V8__x_27] :
( t(V8__x_27,V0__A)
=> ( p(happ(happ(V2__R,V7__x),V8__x_27))
=> happ(V6__f,V7__x) = happ(V6__f,V8__x_27) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.BoolP',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eBoolP)
<=> ! [V0__C] :
( cProp___24t(V0__C)
=> ( p(V0__C)
=> ( p(V0__C)
=> p(V0__C) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.DrinkerParadox',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eDrinkerParadox)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__161___24t(V0__A,V1__P)
=> ! [V2___24Anonymous] :
( t(V2___24Anonymous,V0__A)
=> ? [V3__x] :
( t(V3__x,V0__A)
& ( ? [V4__x] :
( t(V4__x,V0__A)
& p(happ(V1__P,V4__x)) )
=> p(happ(V1__P,V3__x)) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.GodelDummett',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eGodelDummett)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
=> p(V1__B) )
| ( p(V1__B)
=> p(V0__A) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.IndependenceOfGeneralPremises',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eIndependenceOfGeneralPremises)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__161___24t(V0__A,V1__P)
=> ! [V2__Q] :
( cProp___24t(V2__Q)
=> ! [V3___24Anonymous] :
( t(V3___24Anonymous,V0__A)
=> ( ( p(V2__Q)
=> ? [V5__x] :
( t(V5__x,V0__A)
& p(happ(V1__P,V5__x)) ) )
=> ? [V5__x] :
( t(V5__x,V0__A)
& ( p(V2__Q)
=> p(happ(V1__P,V5__x)) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.Minimal',axiom,
! [V0__P,V1__n] :
( cCoq_2eLogic_2eClassicalFacts_2eMinimal___24a2(V0__P,V1__n)
<=> ( p(happ(V0__P,V1__n))
& ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ( p(happ(V0__P,V2__k))
=> cCoq_2eInit_2ePeano_2ele___24a2(V1__n,V2__k) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.RightDistributivityImplicationOverDisjunction',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eRightDistributivityImplicationOverDisjunction)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__C] :
( cProp___24t(V2__C)
=> ( ( p(V2__C)
=> ( p(V0__A)
| p(V1__B) ) )
=> ( ( p(V2__C)
=> p(V0__A) )
| ( p(V2__C)
=> p(V1__B) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eexcluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
| ~ p(V0__A) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.generalized_excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2egeneralized__excluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( p(V0__A)
| ( p(V0__A)
=> p(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.proof_irrelevance',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eproof__irrelevance)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> ( p(V0__A)
=> c_24Proof = c_24Proof ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.prop_extensionality',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
<=> p(V1__B) )
=> V0__A = V1__B ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.weak_generalized_excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eweak__generalized__excluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
=> p(V1__B) )
=> p(V1__B) )
| ( p(V0__A)
=> p(V1__B) ) ) ) ) ) ).
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.Bijective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eBijective___24a3(V0__A,V1__B,V2__f)
<=> ? [V3__g] :
( c_24__type__1180___24t(V0__A,V1__B,V3__g)
& ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V3__g,happ(V2__f,V4__x)) = V4__x )
& ! [V4__y] :
( t(V4__y,V1__B)
=> happ(V2__f,happ(V3__g,V4__y)) = V4__y ) ) ) ).
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.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('$_def_Coq.NArith.BinNat.N.eq',axiom,
cCoq_2eNArith_2eBinNat_2eN_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.NArith.BinNat.N.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNat.N.peano_rect',axiom,
! [V0__P,V1__f0,V2__f,V3__n] : cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V0__P,V1__f0,V2__f,V3__n) = c_24__case__Coq_2eNumbers_2eBinNums_2eN_24456___24a4(V0__P,V1__f0,V2__f,V3__n) ).
fof('$_def_Coq.NArith.BinNat.N.recursion',axiom,
! [V0__A] : cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(c_24__lam__491___24a1(V0__A)) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__16077] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16077)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__16077)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__16080] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16080)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__16080)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__16077,Vvar__0___24Anonymous__16080)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__16104] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16104)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16104)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__16104)
& ( ? [Vvar__0___24Anonymous__16108] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16108)
& Vvar__0___24Anonymous__16104 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16108)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__16108) )
| ? [Vvar__0___24Anonymous__16109] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16109)
& Vvar__0___24Anonymous__16104 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16109)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__16109) )
| ( Vvar__0___24Anonymous__16104 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__30726] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30726)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30726)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30726)
& ( ? [Vvar__0___24Anonymous__30730] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30730)
& Vvar__0___24Anonymous__30726 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30730)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__30731] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30731)
& Vvar__0___24Anonymous__30726 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30731)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__30726 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.max',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V0__n ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.min',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V1__n_27 ) ) ) ) ).
fof('$_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__16082] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16082)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__16082)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__16085] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16085)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__16085)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__16082,Vvar__0___24Anonymous__16085)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__30724] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30724)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30724)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__30724) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__419] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__419)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__419)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__419)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
! [Vvar__30723] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__30723)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__30723) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__30732] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30732)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30732)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__30732,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__16189] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16189)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__16189)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__16189) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.zero',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2ezero = cCoq_2eNumbers_2eBinNums_2eN0 ).
fof('$_def_Coq.NArith.Ndigits.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eNdigits_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.eq',axiom,
cCoq_2ePArith_2eBinPos_2ePos_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.compare',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.div2',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__30750] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30750)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30750)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__30750 )
| ? [Vvar__0___24Anonymous__30751] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30751)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30751)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__30751 )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.eqb',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__30753] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30753)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30753)
& ( ? [Vvar__0___24Anonymous__30757] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30757)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30757)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__30753,Vvar__0___24Anonymous__30757) )
| ? [Vvar__0___24Anonymous__30758] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30758)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30758)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__30759] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30759)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30759)
& ( ? [Vvar__0___24Anonymous__30763] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30763)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30763)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__30764] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30764)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30764)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__30759,Vvar__0___24Anonymous__30764) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__30765] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30765)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30765)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__30766] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30766)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30766)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__16272] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16272)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16272)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__16272),Vvar__0___24Anonymous__16272)) )
| ? [Vvar__0___24Anonymous__16273] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16273)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16273)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__16273),Vvar__0___24Anonymous__16273) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
! [V0__A,V1__op,V3__p,V4__a] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__30769] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30769)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30769)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__30769,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__30770] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30770)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30770)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__30770,happ(happ(V1__op,V4__a),V4__a)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.max',axiom,
! [V0__p,V1__p_27] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V0__p ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.min',axiom,
! [V0__p,V1__p_27] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V1__p_27 ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__16222] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16222)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16222)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__16222)) )
| ? [Vvar__0___24Anonymous__16223] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16223)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16223)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16223) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.t',axiom,
! [Vvar__30749] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__30749)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__30749) ) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__21495] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__21495)
& ? [Vvar__1__Qden__21496] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__21496)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__21495,Vvar__1__Qden__21496)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__21496 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__21490] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__21490)
& ? [Vvar__1__Qden__21491] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__21491)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__21490,Vvar__1__Qden__21491)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__21490 ) ) ) ).
fof('$_def_Coq.Reals.RIneq.Rsqr',axiom,
! [V0__r] : cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V0__r) ).
fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V2__x))
=> V2__x = V3__y ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.commut',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2ecommut___24a3(V0__A,V1__R1,V2__R2)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R1,V4__y),V3__x))
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V2__R2,V6__z),V4__y))
=> cCoq_2eInit_2eLogic_2eex2___24a3(V0__A,c_24__lam__569___24a3(V0__A,V2__R2,V3__x),c_24__lam__573___24a3(V0__A,V1__R1,V6__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.equiv',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2(V0__A,V1__R)
<=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.inclusion',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__R1,V2__R2)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R1,V3__x),V4__y))
=> p(happ(happ(V2__R2,V3__x),V4__y)) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.reflexive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__15___24a1(V0__A) ).
fof('$_def_Coq.Relations.Relation_Definitions.same_relation',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__R1,V2__R2)
<=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__R1,V2__R2)
& cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__R2,V1__R1) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.symmetric',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> p(happ(happ(V1__R,V3__y),V2__x)) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.transitive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Operators.transp',axiom,
! [V0__A,V1__R,V2__x,V3__y] :
( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4(V0__A,V1__R,V2__x,V3__y)
<=> p(happ(happ(V1__R,V3__y),V2__x)) ) ).
fof('$_def_Coq.Relations.Relation_Operators.union',axiom,
! [V0__A,V1__R1,V2__R2,V3__x,V4__y] :
( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5(V0__A,V1__R1,V2__R2,V3__x,V4__y)
<=> ( p(happ(happ(V1__R1,V3__x),V4__y))
| p(happ(happ(V2__R2,V3__x),V4__y)) ) ) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__15___24a1(V0__U) ).
fof('$_def_Coq.Structures.GenericMinMax.gmax',axiom,
! [V0__A,V1__cmp,V2__x,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__20348___24t(V0__A,V1__cmp)
=> ( t(V2__x,V0__A)
=> ( t(V3__y,V0__A)
=> ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.GenericMinMax.gmin',axiom,
! [V0__A,V1__cmp,V2__x,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__20348___24t(V0__A,V1__cmp)
=> ( t(V2__x,V0__A)
=> ( t(V3__y,V0__A)
=> ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt = cCoq_2eNArith_2eBinNat_2eN_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [Vvar__30739] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__30739)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__30739) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt = cCoq_2eInit_2ePeano_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__30746] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__30746)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__30746) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__30630] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30630)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30630)
& ( ? [Vvar__0___24Anonymous__30634] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30634)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30634)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__30630,Vvar__0___24Anonymous__30634) ) )
| ? [Vvar__0___24Anonymous__30635] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30635)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30635)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__30636] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30636)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30636)
& ( ? [Vvar__0___24Anonymous__30640] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30640)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30640)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__30641] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30641)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30641)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__30636,Vvar__0___24Anonymous__30641) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__30642] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30642)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30642)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__30643] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30643)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30643)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt = cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__30628] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__30628)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__30628) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt = cCoq_2ePArith_2eBinPos_2ePos_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__30873] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__30873)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__30873) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__30878] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__30878)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__30878) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__30889] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__30889)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__30889) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv = cCoq_2eZArith_2eBinIntDef_2eZ_2equot ).
fof('$_def_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo = cCoq_2eZArith_2eBinIntDef_2eZ_2erem ).
fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
& V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eq',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__30880] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30880)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30880)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30880) )
| ? [Vvar__0___24Anonymous__30881] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30881)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30881)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30881) ) ) ) ).
fof('$_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__4828] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4828)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4828)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__4832] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4832)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4832)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__4828,Vvar__0___24Anonymous__4832)) )
| ? [Vvar__0___24Anonymous__4833] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4833)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4833)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__4828,Vvar__0___24Anonymous__4833) ) ) ) ) )
| ? [Vvar__0___24Anonymous__4834] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4834)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4834)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__4838] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4838)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4838)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__4838,Vvar__0___24Anonymous__4834) )
| ? [Vvar__0___24Anonymous__4839] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4839)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4839)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__4834,Vvar__0___24Anonymous__4839)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__16949] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__16949)
& ? [Vvar__3___24Anonymous__16950] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__16950)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__16949,Vvar__3___24Anonymous__16950)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__16949 ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.even',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__17027] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17027)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17027)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17027)
& ( ? [Vvar__0___24Anonymous__17031] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17031)
& Vvar__0___24Anonymous__17027 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17031)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__17032] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17032)
& Vvar__0___24Anonymous__17027 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17032)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__17027 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__17033] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17033)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17033)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17033)
& ( ? [Vvar__0___24Anonymous__17037] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17037)
& Vvar__0___24Anonymous__17033 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17037)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__17038] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17038)
& Vvar__0___24Anonymous__17033 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17038)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__17033 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.min',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__16957] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__16957)
& ? [Vvar__3___24Anonymous__16958] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__16958)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__16957,Vvar__3___24Anonymous__16958)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__16958 ) ) ) ) ).
fof('$_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__16809] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16809)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__16809)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__16813] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16813)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__16813)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__16809,Vvar__0___24Anonymous__16813)) )
| ? [Vvar__0___24Anonymous__16814] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16814)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16814)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__16809,Vvar__0___24Anonymous__16814)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__16815] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16815)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16815)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__16819] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16819)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__16819)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__16815,Vvar__0___24Anonymous__16819)) )
| ? [Vvar__0___24Anonymous__16820] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16820)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16820)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__16815,Vvar__0___24Anonymous__16820)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.odd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__17041] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17041)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17041)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17041)
& ( ? [Vvar__0___24Anonymous__17045] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17045)
& Vvar__0___24Anonymous__17041 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17045)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__17046] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17046)
& Vvar__0___24Anonymous__17041 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17046)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__17041 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__17047] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17047)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17047)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17047)
& ( ? [Vvar__0___24Anonymous__17051] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17051)
& Vvar__0___24Anonymous__17047 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17051)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__17052] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17052)
& Vvar__0___24Anonymous__17047 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17052)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__17047 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__4846] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4846)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4846)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4846) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__16804] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16804)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__16804)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16804) )
| ? [Vvar__0___24Anonymous__16805] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16805)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16805)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__16805) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.t',axiom,
! [Vvar__30879] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__30879)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__30879) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__16855] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16855)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__16855)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__16855) )
| ? [Vvar__0___24Anonymous__16856] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16856)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16856)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__16859] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16859)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__16859)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__16859 )
| ? [Vvar__0___24Anonymous__16860] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16860)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16860)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.zero',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2ezero = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('$_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.Zeven.Zeven',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__30578] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30578)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30578)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30578)
& ( ? [Vvar__0___24Anonymous__30582] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30582)
& Vvar__0___24Anonymous__30578 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30582)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__30583] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30583)
& Vvar__0___24Anonymous__30578 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30583)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__30578 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__30584] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30584)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30584)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30584)
& ( ? [Vvar__0___24Anonymous__30588] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30588)
& Vvar__0___24Anonymous__30584 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30588)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__30589] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30589)
& Vvar__0___24Anonymous__30584 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30589)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__30584 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zodd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__15746] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15746)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15746)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__15746)
& ( ? [Vvar__0___24Anonymous__15750] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15750)
& Vvar__0___24Anonymous__15746 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15750)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__15751] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15751)
& Vvar__0___24Anonymous__15746 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15751)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__15746 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__15752] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15752)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15752)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__15752)
& ( ? [Vvar__0___24Anonymous__15756] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15756)
& Vvar__0___24Anonymous__15752 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15756)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__15757] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15757)
& Vvar__0___24Anonymous__15752 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15757)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__15752 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zlogarithm.Is_power',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__30591] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30591)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30591)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__30592] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30592)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30592)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__30592) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__5886___24a1(V0__D) ).
fof('$_def_Coq.micromega.Refl.make_conj',axiom,
! [V1__A,V2__eval,V3__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__10152] :
( t(Vvar__1___24Anonymous__10152,V1__A)
& ? [Vvar__2___24Anonymous__10153] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__10153)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__10153)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__10152,Vvar__2___24Anonymous__10153)
& ( ( Vvar__2___24Anonymous__10153 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(happ(V2__eval,Vvar__1___24Anonymous__10152)) ) )
| ? [Vvar__1___24Anonymous__10164] :
( t(Vvar__1___24Anonymous__10164,V1__A)
& ? [Vvar__2___24Anonymous__10165] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__10165)
& Vvar__2___24Anonymous__10153 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__10164,Vvar__2___24Anonymous__10165)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__10152))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__10153) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__21707] :
( t(Vvar__1___24Anonymous__21707,V1__A)
& ? [Vvar__2___24Anonymous__21708] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__21708)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__21707,Vvar__2___24Anonymous__21708)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__21707))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__21708,V4__goal) ) ) ) ) ) ) ) ).
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('$_def_Coq.micromega.ZMicromega.coneMember',axiom,
! [Vvar__30576] :
( cCoq_2emicromega_2eZMicromega_2econeMember___24t(Vvar__30576)
<=> cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__30576) ) ).
fof('$_def_Coq.omega.PreOmega.Z_of_N\'',axiom,
cCoq_2eomega_2ePreOmega_2eZ__of__N_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N ).
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.omega.PreOmega.Zneg\'',axiom,
cCoq_2eomega_2ePreOmega_2eZneg_27 = cCoq_2eNumbers_2eBinNums_2eZneg ).
fof('$_def_Coq.omega.PreOmega.Zpos\'',axiom,
cCoq_2eomega_2ePreOmega_2eZpos_27 = cCoq_2eNumbers_2eBinNums_2eZpos ).
fof('$_def_Coq.setoid_ring.InitialRing.NotConstant',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNotConstant = cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
! [Vvar__20555] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__20555)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__20555) ) ).
fof('$_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__20521] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20521)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20521)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20521)
& ( ? [Vvar__0___24Anonymous__20525] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20525)
& Vvar__0___24Anonymous__20521 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20525)
& 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__20521))) )
| ? [Vvar__0___24Anonymous__20526] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20526)
& Vvar__0___24Anonymous__20521 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20526)
& 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__20521))) )
| ( Vvar__0___24Anonymous__20521 = 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__20527] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20527)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20527)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20527)
& ( ? [Vvar__0___24Anonymous__20531] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20531)
& Vvar__0___24Anonymous__20527 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20531)
& 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__20527)) )
| ? [Vvar__0___24Anonymous__20532] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20532)
& Vvar__0___24Anonymous__20527 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20532)
& 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__20527)) )
| ( Vvar__0___24Anonymous__20527 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),V1__rI) ) ) ) ) ) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__20488] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20488)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20488)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__20488))) )
| ? [Vvar__0___24Anonymous__20489] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20489)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20489)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__20489)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.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__28123] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28123)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28123)
& 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__28123),V4__x,Vvar__0___24Anonymous__28123) )
| ? [Vvar__0___24Anonymous__28124] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28124)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28124)
& 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__28124),V4__x,Vvar__0___24Anonymous__28124) )
| ( 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('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_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.id_phi_N',axiom,
! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__12682] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12682)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12682)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__12682) ) ) ) ) ).
fof('$_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__1274] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1274)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1274)
& 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__1275__1278___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1274)),c_24__let__var__6__p__1275__1278___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1274))) )
| ? [Vvar__0___24Anonymous__1276] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1276)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1276)
& 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__1277__1279___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1276)),c_24__let__var__6__p__1277__1279___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1276)) )
| ( 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('$_def_HahnRelationsBasic.acyclic',axiom,
! [V0__A,V1__r] :
( cHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
<=> cHahnRelationsBasic_2eirreflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ).
fof('$_def_HahnRelationsBasic.bunion',axiom,
! [V0__A,V1__B,V2__P,V3__r,V4__x,V5__y] :
( cHahnRelationsBasic_2ebunion___24a6(V0__A,V1__B,V2__P,V3__r,V4__x,V5__y)
<=> ? [V6__a] :
( t(V6__a,V0__A)
& p(happ(V2__P,V6__a))
& p(happ(happ(happ(V3__r,V6__a),V4__x),V5__y)) ) ) ).
fof('$_def_HahnRelationsBasic.clos_refl',axiom,
! [V0__A,V1__r,V2__x,V3__y] :
( cHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ( V2__x = V3__y
| p(happ(happ(V1__r,V2__x),V3__y)) ) ) ).
fof('$_def_HahnRelationsBasic.codom_rel',axiom,
! [V0__A,V1__r,V2__y] :
( cHahnRelationsBasic_2ecodom__rel___24a3(V0__A,V1__r,V2__y)
<=> ? [V3__x] :
( t(V3__x,V0__A)
& p(happ(happ(V1__r,V3__x),V2__y)) ) ) ).
fof('$_def_HahnRelationsBasic.collect_rel',axiom,
! [V0__A,V1__B,V2__f,V3__r,V4__x,V5__y] :
( cHahnRelationsBasic_2ecollect__rel___24a6(V0__A,V1__B,V2__f,V3__r,V4__x,V5__y)
<=> ? [V6__x_27] :
( t(V6__x_27,V0__A)
& ? [V7__y_27] :
( t(V7__y_27,V0__A)
& p(happ(happ(V3__r,V6__x_27),V7__y_27))
& happ(V2__f,V6__x_27) = V4__x
& happ(V2__f,V7__y_27) = V5__y ) ) ) ).
fof('$_def_HahnRelationsBasic.cross_rel',axiom,
! [V0__A,V1__r,V2__r_27,V3__a,V4__b] :
( cHahnRelationsBasic_2ecross__rel___24a5(V0__A,V1__r,V2__r_27,V3__a,V4__b)
<=> ( p(happ(V1__r,V3__a))
& p(happ(V2__r_27,V4__b)) ) ) ).
fof('$_def_HahnRelationsBasic.dom_rel',axiom,
! [V0__A,V1__r,V2__x] :
( cHahnRelationsBasic_2edom__rel___24a3(V0__A,V1__r,V2__x)
<=> ? [V3__y] :
( t(V3__y,V0__A)
& p(happ(happ(V1__r,V2__x),V3__y)) ) ) ).
fof('$_def_HahnRelationsBasic.eq_rel',axiom,
! [V0__A,V1__B,V2__f,V3__x,V4__y] :
( cHahnRelationsBasic_2eeq__rel___24a5(V0__A,V1__B,V2__f,V3__x,V4__y)
<=> happ(V2__f,V3__x) = happ(V2__f,V4__y) ) ).
fof('$_def_HahnRelationsBasic.eqv_dom_rel',axiom,
! [V0__A,V1__dom,V2__x,V3__y] :
( cHahnRelationsBasic_2eeqv__dom__rel___24a4(V0__A,V1__dom,V2__x,V3__y)
<=> ( V2__x = V3__y
& cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V1__dom) ) ) ).
fof('$_def_HahnRelationsBasic.eqv_rel',axiom,
! [V0__A,V1__cond,V2__x,V3__y] :
( cHahnRelationsBasic_2eeqv__rel___24a4(V0__A,V1__cond,V2__x,V3__y)
<=> ( V2__x = V3__y
& p(happ(V1__cond,V2__x)) ) ) ).
fof('$_def_HahnRelationsBasic.functional',axiom,
! [V0__A,V1__r] :
( cHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V3__y))
=> ( p(happ(happ(V1__r,V2__x),V4__z))
=> V3__y = V4__z ) ) ) ) ) ) ).
fof('$_def_HahnRelationsBasic.immediate',axiom,
! [V0__A,V1__r,V2__a,V3__b] :
( cHahnRelationsBasic_2eimmediate___24a4(V0__A,V1__r,V2__a,V3__b)
<=> ( p(happ(happ(V1__r,V2__a),V3__b))
& ! [V4__c] :
( t(V4__c,V0__A)
=> ( p(happ(happ(V1__r,V2__a),V4__c))
=> ( p(happ(happ(V1__r,V4__c),V3__b))
=> p(c_24False) ) ) ) ) ) ).
fof('$_def_HahnRelationsBasic.inter_rel',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( cHahnRelationsBasic_2einter__rel___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ( p(happ(happ(V1__r,V3__x),V4__y))
& p(happ(happ(V2__r_27,V3__x),V4__y)) ) ) ).
fof('$_def_HahnRelationsBasic.irreflexive',axiom,
! [V0__A,V1__r] :
( cHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V2__x))
=> p(c_24False) ) ) ) ).
fof('$_def_HahnRelationsBasic.is_total',axiom,
! [V0__A,V1__cond,V2__r] :
( cHahnRelationsBasic_2eis__total___24a3(V0__A,V1__cond,V2__r)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(happ(V1__cond,V3__a))
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(V1__cond,V5__b))
=> ( V3__a != V5__b
=> ( p(happ(happ(V2__r,V3__a),V5__b))
| p(happ(happ(V2__r,V5__b),V3__a)) ) ) ) ) ) ) ) ).
fof('$_def_HahnRelationsBasic.map_rel',axiom,
! [V0__A,V1__B,V2__f,V3__r_27_27,V4__x,V5__y] :
( cHahnRelationsBasic_2emap__rel___24a6(V0__A,V1__B,V2__f,V3__r_27_27,V4__x,V5__y)
<=> p(happ(happ(V3__r_27_27,happ(V2__f,V4__x)),happ(V2__f,V5__y))) ) ).
fof('$_def_HahnRelationsBasic.minus_rel',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( cHahnRelationsBasic_2eminus__rel___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ( p(happ(happ(V1__r,V3__x),V4__y))
& ~ p(happ(happ(V2__r_27,V3__x),V4__y)) ) ) ).
fof('$_def_HahnRelationsBasic.pow_rel',axiom,
! [V1__A,V2__r,V3__n] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& cHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V3__n) = cHahnRelationsBasic_2eeqv__rel___24a2(V1__A,c_24__lam__701___24a1(V1__A)) )
| ? [Vvar__0___24Anonymous__699] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__699)
& V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__699)
& cHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V3__n) = cHahnRelationsBasic_2eseq___24a3(V1__A,cHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,Vvar__0___24Anonymous__699),V2__r) ) ) ) ) ).
fof('$_def_HahnRelationsBasic.restr_eq_rel',axiom,
! [V0__A,V1__B,V2__f,V3__r,V4__x,V5__y] :
( cHahnRelationsBasic_2erestr__eq__rel___24a6(V0__A,V1__B,V2__f,V3__r,V4__x,V5__y)
<=> ( p(happ(happ(V3__r,V4__x),V5__y))
& happ(V2__f,V4__x) = happ(V2__f,V5__y) ) ) ).
fof('$_def_HahnRelationsBasic.restr_rel',axiom,
! [V0__A,V1__cond,V2__r,V3__x,V4__y] :
( cHahnRelationsBasic_2erestr__rel___24a5(V0__A,V1__cond,V2__r,V3__x,V4__y)
<=> ( p(happ(happ(V2__r,V3__x),V4__y))
& p(happ(V1__cond,V3__x))
& p(happ(V1__cond,V4__y)) ) ) ).
fof('$_def_HahnRelationsBasic.restr_subset',axiom,
! [V0__A,V1__cond,V2__r,V3__r_27] :
( cHahnRelationsBasic_2erestr__subset___24a4(V0__A,V1__cond,V2__r,V3__r_27)
<=> ! [V4__a] :
( t(V4__a,V0__A)
=> ( p(happ(V1__cond,V4__a))
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ( p(happ(V1__cond,V6__b))
=> ( p(happ(happ(V2__r,V4__a),V6__b))
=> p(happ(happ(V3__r_27,V4__a),V6__b)) ) ) ) ) ) ) ).
fof('$_def_HahnRelationsBasic.seq',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( cHahnRelationsBasic_2eseq___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ? [V5__z] :
( t(V5__z,V0__A)
& p(happ(happ(V1__r,V3__x),V5__z))
& p(happ(happ(V2__r_27,V5__z),V4__y)) ) ) ).
fof('$_def_HahnRelationsBasic.strict_partial_order',axiom,
! [V0__A,V1__r] :
( cHahnRelationsBasic_2estrict__partial__order___24a2(V0__A,V1__r)
<=> ( cHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r) ) ) ).
fof('$_def_HahnRelationsBasic.strict_total_order',axiom,
! [V0__A,V1__cond,V2__r] :
( cHahnRelationsBasic_2estrict__total__order___24a3(V0__A,V1__cond,V2__r)
<=> ( cHahnRelationsBasic_2estrict__partial__order___24a2(V0__A,V2__r)
& cHahnRelationsBasic_2eis__total___24a3(V0__A,V1__cond,V2__r) ) ) ).
fof('$_def_HahnRelationsBasic.upward_closed',axiom,
! [V0__A,V1__r,V2__P] :
( cHahnRelationsBasic_2eupward__closed___24a3(V0__A,V1__r,V2__P)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__r,V3__x),V4__y))
=> ( p(happ(V2__P,V4__y))
=> p(happ(V2__P,V3__x)) ) ) ) ) ) ).
fof('$_def_Hammer.Tactics.Reconstr.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eReconstr_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_Hammer.Tactics.Tactics.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eTactics_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_hahn.HahnSets.set_bunion',axiom,
! [V0__A,V1__B,V2__s,V3__ss,V4__x] :
( chahn_2eHahnSets_2eset__bunion___24a5(V0__A,V1__B,V2__s,V3__ss,V4__x)
<=> ? [V5__y] :
( t(V5__y,V0__A)
& p(happ(V2__s,V5__y))
& p(happ(happ(V3__ss,V5__y),V4__x)) ) ) ).
fof('$_def_hahn.HahnSets.set_collect',axiom,
! [V0__A,V1__B,V2__f,V3__s,V4__x] :
( chahn_2eHahnSets_2eset__collect___24a5(V0__A,V1__B,V2__f,V3__s,V4__x)
<=> ? [V5__y] :
( t(V5__y,V0__A)
& p(happ(V3__s,V5__y))
& happ(V2__f,V5__y) = V4__x ) ) ).
fof('$_def_hahn.HahnSets.set_compl',axiom,
! [V0__A,V1__s,V2__x] :
( chahn_2eHahnSets_2eset__compl___24a3(V0__A,V1__s,V2__x)
<=> ~ p(happ(V1__s,V2__x)) ) ).
fof('$_def_hahn.HahnSets.set_disjoint',axiom,
! [V0__A,V1__s,V2__s_27] :
( chahn_2eHahnSets_2eset__disjoint___24a3(V0__A,V1__s,V2__s_27)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__s,V3__x))
=> ( p(happ(V2__s_27,V3__x))
=> p(c_24False) ) ) ) ) ).
fof('$_def_hahn.HahnSets.set_empty',axiom,
! [V0__A,V1__x] :
( chahn_2eHahnSets_2eset__empty___24a2(V0__A,V1__x)
<=> p(c_24False) ) ).
fof('$_def_hahn.HahnSets.set_equiv',axiom,
! [V0__A,V1__s,V2__s_27] :
( chahn_2eHahnSets_2eset__equiv___24a3(V0__A,V1__s,V2__s_27)
<=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,V1__s,V2__s_27)
& chahn_2eHahnSets_2eset__subset___24a3(V0__A,V2__s_27,V1__s) ) ) ).
fof('$_def_hahn.HahnSets.set_full',axiom,
! [V0__A,V1__x] :
( chahn_2eHahnSets_2eset__full___24a2(V0__A,V1__x)
<=> p(c_24True) ) ).
fof('$_def_hahn.HahnSets.set_inter',axiom,
! [V0__A,V1__s,V2__s_27,V3__x] :
( chahn_2eHahnSets_2eset__inter___24a4(V0__A,V1__s,V2__s_27,V3__x)
<=> ( p(happ(V1__s,V3__x))
& p(happ(V2__s_27,V3__x)) ) ) ).
fof('$_def_hahn.HahnSets.set_map',axiom,
! [V0__A,V1__B,V2__f,V3__d,V4__x] :
( chahn_2eHahnSets_2eset__map___24a5(V0__A,V1__B,V2__f,V3__d,V4__x)
<=> p(happ(V3__d,happ(V2__f,V4__x))) ) ).
fof('$_def_hahn.HahnSets.set_minus',axiom,
! [V0__A,V1__s,V2__s_27,V3__x] :
( chahn_2eHahnSets_2eset__minus___24a4(V0__A,V1__s,V2__s_27,V3__x)
<=> ( p(happ(V1__s,V3__x))
& ~ p(happ(V2__s_27,V3__x)) ) ) ).
fof('$_def_hahn.HahnSets.set_subset',axiom,
! [V0__A,V1__s,V2__s_27] :
( chahn_2eHahnSets_2eset__subset___24a3(V0__A,V1__s,V2__s_27)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__s,V3__x))
=> p(happ(V2__s_27,V3__x)) ) ) ) ).
fof('$_def_hahn.HahnSets.set_union',axiom,
! [V0__A,V1__s,V2__s_27,V3__x] :
( chahn_2eHahnSets_2eset__union___24a4(V0__A,V1__s,V2__s_27,V3__x)
<=> ( p(happ(V1__s,V3__x))
| p(happ(V2__s_27,V3__x)) ) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__5007,Vvar__1___24Anonymous__5008,Vvar__0__P__5009,Vvar__1___24Anonymous__5010] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5007) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5009) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__16372,Vvar__1___24Anonymous__16373,Vvar__2___24Anonymous__16374] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__16372,Vvar__1___24Anonymous__16373,Vvar__2___24Anonymous__16374) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__18618,Vvar__1__Plt__18619,Vvar__2__Pgt__18620,Vvar__3___24Anonymous__18621,Vvar__0__Peq__18622,Vvar__1__Plt__18623,Vvar__2__Pgt__18624,Vvar__3___24Anonymous__18625] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__18618,Vvar__1__Plt__18619,Vvar__2__Pgt__18620) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__18622,Vvar__1__Plt__18623,Vvar__2__Pgt__18624) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__3] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__5750,Vvar__1___24Anonymous__5751,Vvar__0__A__5752] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__5750,Vvar__1___24Anonymous__5751) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__5752) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__18525,Vvar__1__B__18526,Vvar__2___24Anonymous__18527,Vvar__0__A__18528,Vvar__1__B__18529,Vvar__2___24Anonymous__18530] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__18525,Vvar__1__B__18526,Vvar__2___24Anonymous__18527) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__18528,Vvar__1__B__18529,Vvar__2___24Anonymous__18530) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__789,Vvar__0__A__790,Vvar__1___24Anonymous__791,Vvar__2___24Anonymous__792] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__789) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__790,Vvar__1___24Anonymous__791,Vvar__2___24Anonymous__792) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Decimal.Decimal$Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__18677,Vvar__1__f__18678,Vvar__0__i__18679,Vvar__1__f__18680,Vvar__2__e__18681] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__18677,Vvar__1__f__18678) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__18679,Vvar__1__f__18680,Vvar__2__e__18681) ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__17722] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__17722) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__18665,Vvar__0__d__18666] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__18665) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__18666) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__18139,Vvar__1__B__18140,Vvar__2___24Anonymous__18141,Vvar__0__A__18142,Vvar__1__B__18143,Vvar__2___24Anonymous__18144] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__18139,Vvar__1__B__18140,Vvar__2___24Anonymous__18141) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__18142,Vvar__1__B__18143) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__14139,Vvar__1__B__14140,Vvar__2___24Anonymous__14141,Vvar__0__A__14142,Vvar__1__B__14143,Vvar__2___24Anonymous__14144] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__14139,Vvar__1__B__14140) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__14142,Vvar__1__B__14143) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__272] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__272) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__771] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__771) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__759,Vvar__0___24Anonymous__760] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__759) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__760) ).
fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__30847,Vvar__1___24Anonymous__30848] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__30847,Vvar__1___24Anonymous__30848) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__16257] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__16257) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__22647,Vvar__1___24Anonymous__22648,Vvar__0__x__22649,Vvar__1__n__22650,Vvar__2___24Anonymous__22651] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__22647) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__22649,Vvar__1__n__22650) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__14176,Vvar__1___24Anonymous__14177] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__14176,Vvar__1___24Anonymous__14177) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__21414,Vvar__1__lt__21415,Vvar__2__eq__21416,Vvar__3__x__21417,Vvar__4__y__21418,Vvar__5___24Anonymous__21419,Vvar__0__X__21420,Vvar__1__lt__21421,Vvar__2__eq__21422,Vvar__3__x__21423,Vvar__4__y__21424,Vvar__5___24Anonymous__21425] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__21414,Vvar__1__lt__21415,Vvar__2__eq__21416,Vvar__3__x__21417,Vvar__4__y__21418) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__21420,Vvar__1__lt__21421,Vvar__2__eq__21422,Vvar__3__x__21423,Vvar__4__y__21424) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__20258,Vvar__0__n__20259,Vvar__1___24Anonymous__20260] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__20258) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__20259,Vvar__1___24Anonymous__20260) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__14862,Vvar__0__A__14863,Vvar__1__h__14864,Vvar__2__n__14865,Vvar__3___24Anonymous__14866] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__14862) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__14863,Vvar__1__h__14864,Vvar__2__n__14865,Vvar__3___24Anonymous__14866) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__6033,Vvar__1___24Anonymous__6034,Vvar__0__C__6035,Vvar__1___24Anonymous__6036] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__6033,Vvar__1___24Anonymous__6034) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__6035,Vvar__1___24Anonymous__6036) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__6097,Vvar__1___24Anonymous__6098,Vvar__0__C__6099,Vvar__1___24Anonymous__6100,Vvar__2___24Anonymous__6101] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__6097,Vvar__1___24Anonymous__6098) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__6099,Vvar__1___24Anonymous__6100,Vvar__2___24Anonymous__6101) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__17754,Vvar__1___24Anonymous__17755] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__17754,Vvar__1___24Anonymous__17755) ).
fof('$_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$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__28072,Vvar__1___24Anonymous__28073,Vvar__0__C__28074,Vvar__1___24Anonymous__28075] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__28072,Vvar__1___24Anonymous__28073) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__28074,Vvar__1___24Anonymous__28075) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__14588,Vvar__1__TX__14589,Vvar__2__AA__14590,Vvar__3__AF__14591,Vvar__0__TA__14592,Vvar__1__TX__14593,Vvar__2__AA__14594,Vvar__3__AF__14595] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__14588,Vvar__1__TX__14589,Vvar__2__AA__14590,Vvar__3__AF__14591) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__14592,Vvar__1__TX__14593,Vvar__2__AA__14594,Vvar__3__AF__14595) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__30466,Vvar__0__A__30467,Vvar__1___24Anonymous__30468] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__30466) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__30467,Vvar__1___24Anonymous__30468) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__30560,Vvar__1___24Anonymous__30561] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__30560,Vvar__1___24Anonymous__30561) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__19034,Vvar__0__C__19035] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__19034) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__19035) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__10692,Vvar__0__C__10693] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10692) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10693) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__941,Vvar__1___24Anonymous__942,Vvar__0__C__943,Vvar__1___24Anonymous__944,Vvar__2___24Anonymous__945] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__941,Vvar__1___24Anonymous__942) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__943,Vvar__1___24Anonymous__944,Vvar__2___24Anonymous__945) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__10490,Vvar__1___24Anonymous__10491] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__10490,Vvar__1___24Anonymous__10491) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__29996,Vvar__1__req__29997,Vvar__2__reqb__29998,Vvar__3___24Anonymous__29999] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__29996,Vvar__1__req__29997,Vvar__2__reqb__29998) ).
fof('$_discrim_Hammer.Tactics.Reconstr.Empty$Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eEmpty != cHammer_2eTactics_2eReconstr_2eAllHyps ).
fof('$_fix_22486_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__22486__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__22490] :
( t(Vvar__1___24Anonymous__22490,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__22491] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__22491)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__22490,Vvar__2___24Anonymous__22491)
& c_24__fix__22486__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__22490,c_24__fix__22486__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__22491,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_30844_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__30845] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30845)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30845)
& c_24__fix__30844__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__30844__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__30845)) )
| ? [Vvar__0___24Anonymous__30846] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30846)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30846)
& c_24__fix__30844__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30846) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__30844__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__5015,Vvar__0__P__5016,Vvar__1___24Anonymous__5017,Vvar__1___24Anonymous__5018] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5015) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5016)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__5015 = Vvar__0__P__5016 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__5011,Vvar__0__P__5012,Vvar__1___24Anonymous__5013,Vvar__1___24Anonymous__5014] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5011) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5012)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__5011 = Vvar__0__P__5012 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__16375,Vvar__0___24Anonymous__16376,Vvar__1___24Anonymous__16377,Vvar__1___24Anonymous__16378,Vvar__2___24Anonymous__16379,Vvar__2___24Anonymous__16380] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__16375,Vvar__1___24Anonymous__16377,Vvar__2___24Anonymous__16379) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__16376,Vvar__1___24Anonymous__16378,Vvar__2___24Anonymous__16380)
=> ( Vvar__2___24Anonymous__16379 = Vvar__2___24Anonymous__16380
& Vvar__1___24Anonymous__16377 = Vvar__1___24Anonymous__16378
& Vvar__0___24Anonymous__16375 = Vvar__0___24Anonymous__16376 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__18626,Vvar__0__Peq__18627,Vvar__1__Plt__18628,Vvar__1__Plt__18629,Vvar__2__Pgt__18630,Vvar__2__Pgt__18631,Vvar__3___24Anonymous__18632,Vvar__3___24Anonymous__18633] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__18626,Vvar__1__Plt__18628,Vvar__2__Pgt__18630) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__18627,Vvar__1__Plt__18629,Vvar__2__Pgt__18631)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__18630 = Vvar__2__Pgt__18631
& Vvar__1__Plt__18628 = Vvar__1__Plt__18629
& Vvar__0__Peq__18626 = Vvar__0__Peq__18627 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__18642,Vvar__0__Peq__18643,Vvar__1__Plt__18644,Vvar__1__Plt__18645,Vvar__2__Pgt__18646,Vvar__2__Pgt__18647,Vvar__3___24Anonymous__18648,Vvar__3___24Anonymous__18649] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__18642,Vvar__1__Plt__18644,Vvar__2__Pgt__18646) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__18643,Vvar__1__Plt__18645,Vvar__2__Pgt__18647)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__18646 = Vvar__2__Pgt__18647
& Vvar__1__Plt__18644 = Vvar__1__Plt__18645
& Vvar__0__Peq__18642 = Vvar__0__Peq__18643 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__18634,Vvar__0__Peq__18635,Vvar__1__Plt__18636,Vvar__1__Plt__18637,Vvar__2__Pgt__18638,Vvar__2__Pgt__18639,Vvar__3___24Anonymous__18640,Vvar__3___24Anonymous__18641] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__18634,Vvar__1__Plt__18636,Vvar__2__Pgt__18638) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__18635,Vvar__1__Plt__18637,Vvar__2__Pgt__18639)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__18638 = Vvar__2__Pgt__18639
& Vvar__1__Plt__18636 = Vvar__1__Plt__18637
& Vvar__0__Peq__18634 = Vvar__0__Peq__18635 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__5757,Vvar__0__A__5758] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__5757) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__5758)
=> Vvar__0__A__5757 = Vvar__0__A__5758 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__4,Vvar__0___24Anonymous__5] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5)
=> Vvar__0___24Anonymous__4 = Vvar__0___24Anonymous__5 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__5753,Vvar__0__A__5754,Vvar__1___24Anonymous__5755,Vvar__1___24Anonymous__5756] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__5753,Vvar__1___24Anonymous__5755) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__5754,Vvar__1___24Anonymous__5756)
=> ( Vvar__1___24Anonymous__5755 = Vvar__1___24Anonymous__5756
& Vvar__0__A__5753 = Vvar__0__A__5754 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__795,Vvar__0__A__796,Vvar__1___24Anonymous__797,Vvar__1___24Anonymous__798,Vvar__2___24Anonymous__799,Vvar__2___24Anonymous__800] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__795,Vvar__1___24Anonymous__797,Vvar__2___24Anonymous__799) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__796,Vvar__1___24Anonymous__798,Vvar__2___24Anonymous__800)
=> ( Vvar__2___24Anonymous__799 = Vvar__2___24Anonymous__800
& Vvar__1___24Anonymous__797 = Vvar__1___24Anonymous__798
& Vvar__0__A__795 = Vvar__0__A__796 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__18531,Vvar__0__A__18532,Vvar__1__B__18533,Vvar__1__B__18534,Vvar__2___24Anonymous__18535,Vvar__2___24Anonymous__18536] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__18531,Vvar__1__B__18533,Vvar__2___24Anonymous__18535) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__18532,Vvar__1__B__18534,Vvar__2___24Anonymous__18536)
=> ( Vvar__2___24Anonymous__18535 = Vvar__2___24Anonymous__18536
& Vvar__1__B__18533 = Vvar__1__B__18534
& Vvar__0__A__18531 = Vvar__0__A__18532 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__18537,Vvar__0__A__18538,Vvar__1__B__18539,Vvar__1__B__18540,Vvar__2___24Anonymous__18541,Vvar__2___24Anonymous__18542] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__18537,Vvar__1__B__18539,Vvar__2___24Anonymous__18541) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__18538,Vvar__1__B__18540,Vvar__2___24Anonymous__18542)
=> ( Vvar__2___24Anonymous__18541 = Vvar__2___24Anonymous__18542
& Vvar__1__B__18539 = Vvar__1__B__18540
& Vvar__0__A__18537 = Vvar__0__A__18538 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__793,Vvar__0__A__794] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__793) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__794)
=> Vvar__0__A__793 = Vvar__0__A__794 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__5774,Vvar__0__A__5775,Vvar__1__B__5776,Vvar__1__B__5777,Vvar__2___24Anonymous__5778,Vvar__2___24Anonymous__5779,Vvar__3___24Anonymous__5780,Vvar__3___24Anonymous__5781] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__5774,Vvar__1__B__5776,Vvar__2___24Anonymous__5778,Vvar__3___24Anonymous__5780) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__5775,Vvar__1__B__5777,Vvar__2___24Anonymous__5779,Vvar__3___24Anonymous__5781)
=> ( Vvar__3___24Anonymous__5780 = Vvar__3___24Anonymous__5781
& Vvar__2___24Anonymous__5778 = Vvar__2___24Anonymous__5779
& Vvar__1__B__5776 = Vvar__1__B__5777
& Vvar__0__A__5774 = Vvar__0__A__5775 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__17723,Vvar__0___24Anonymous__17724] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__17723) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__17724)
=> Vvar__0___24Anonymous__17723 = Vvar__0___24Anonymous__17724 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__17725,Vvar__0___24Anonymous__17726] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__17725) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__17726)
=> Vvar__0___24Anonymous__17725 = Vvar__0___24Anonymous__17726 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__17727,Vvar__0___24Anonymous__17728] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__17727) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__17728)
=> Vvar__0___24Anonymous__17727 = Vvar__0___24Anonymous__17728 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__17729,Vvar__0___24Anonymous__17730] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__17729) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__17730)
=> Vvar__0___24Anonymous__17729 = Vvar__0___24Anonymous__17730 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__17731,Vvar__0___24Anonymous__17732] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__17731) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__17732)
=> Vvar__0___24Anonymous__17731 = Vvar__0___24Anonymous__17732 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__17733,Vvar__0___24Anonymous__17734] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__17733) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__17734)
=> Vvar__0___24Anonymous__17733 = Vvar__0___24Anonymous__17734 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__17735,Vvar__0___24Anonymous__17736] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__17735) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__17736)
=> Vvar__0___24Anonymous__17735 = Vvar__0___24Anonymous__17736 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__17737,Vvar__0___24Anonymous__17738] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__17737) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__17738)
=> Vvar__0___24Anonymous__17737 = Vvar__0___24Anonymous__17738 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__17739,Vvar__0___24Anonymous__17740] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__17739) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__17740)
=> Vvar__0___24Anonymous__17739 = Vvar__0___24Anonymous__17740 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__17741,Vvar__0___24Anonymous__17742] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__17741) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__17742)
=> Vvar__0___24Anonymous__17741 = Vvar__0___24Anonymous__17742 ) ).
fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
! [Vvar__0__i__18682,Vvar__0__i__18683,Vvar__1__f__18684,Vvar__1__f__18685] :
( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__18682,Vvar__1__f__18684) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__18683,Vvar__1__f__18685)
=> ( Vvar__1__f__18684 = Vvar__1__f__18685
& Vvar__0__i__18682 = Vvar__0__i__18683 ) ) ).
fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__18686,Vvar__0__i__18687,Vvar__1__f__18688,Vvar__1__f__18689,Vvar__2__e__18690,Vvar__2__e__18691] :
( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__18686,Vvar__1__f__18688,Vvar__2__e__18690) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__18687,Vvar__1__f__18689,Vvar__2__e__18691)
=> ( Vvar__2__e__18690 = Vvar__2__e__18691
& Vvar__1__f__18688 = Vvar__1__f__18689
& Vvar__0__i__18686 = Vvar__0__i__18687 ) ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__18669,Vvar__0__d__18670] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__18669) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__18670)
=> Vvar__0__d__18669 = Vvar__0__d__18670 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__18667,Vvar__0__d__18668] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__18667) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__18668)
=> Vvar__0__d__18667 = Vvar__0__d__18668 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__14018,Vvar__0__A__14019,Vvar__1__P__14020,Vvar__1__P__14021,Vvar__2__x__14022,Vvar__2__x__14023,Vvar__3___24Anonymous__14024,Vvar__3___24Anonymous__14025] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__14018,Vvar__1__P__14020,Vvar__2__x__14022) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__14019,Vvar__1__P__14021,Vvar__2__x__14023)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__14022 = Vvar__2__x__14023
& Vvar__1__P__14020 = Vvar__1__P__14021
& Vvar__0__A__14018 = Vvar__0__A__14019 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__30364,Vvar__0__A__30365,Vvar__1__P__30366,Vvar__1__P__30367,Vvar__2__Q__30368,Vvar__2__Q__30369,Vvar__3__x__30370,Vvar__3__x__30371,Vvar__4___24Anonymous__30372,Vvar__4___24Anonymous__30373,Vvar__5___24Anonymous__30374,Vvar__5___24Anonymous__30375] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__30364,Vvar__1__P__30366,Vvar__2__Q__30368,Vvar__3__x__30370) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__30365,Vvar__1__P__30367,Vvar__2__Q__30369,Vvar__3__x__30371)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__30370 = Vvar__3__x__30371
& Vvar__2__Q__30368 = Vvar__2__Q__30369
& Vvar__1__P__30366 = Vvar__1__P__30367
& Vvar__0__A__30364 = Vvar__0__A__30365 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__18119,Vvar__0__A__18120,Vvar__1__P__18121,Vvar__1__P__18122,Vvar__2__x__18123,Vvar__2__x__18124,Vvar__3___24Anonymous__18125,Vvar__3___24Anonymous__18126] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__18119,Vvar__1__P__18121,Vvar__2__x__18123,Vvar__3___24Anonymous__18125) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__18120,Vvar__1__P__18122,Vvar__2__x__18124,Vvar__3___24Anonymous__18126)
=> ( Vvar__3___24Anonymous__18125 = Vvar__3___24Anonymous__18126
& Vvar__2__x__18123 = Vvar__2__x__18124
& Vvar__1__P__18121 = Vvar__1__P__18122
& Vvar__0__A__18119 = Vvar__0__A__18120 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__30430,Vvar__0__A__30431,Vvar__1__P__30432,Vvar__1__P__30433,Vvar__2__Q__30434,Vvar__2__Q__30435,Vvar__3__x__30436,Vvar__3__x__30437,Vvar__4___24Anonymous__30438,Vvar__4___24Anonymous__30439,Vvar__5___24Anonymous__30440,Vvar__5___24Anonymous__30441] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__30430,Vvar__1__P__30432,Vvar__2__Q__30434,Vvar__3__x__30436,Vvar__4___24Anonymous__30438,Vvar__5___24Anonymous__30440) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__30431,Vvar__1__P__30433,Vvar__2__Q__30435,Vvar__3__x__30437,Vvar__4___24Anonymous__30439,Vvar__5___24Anonymous__30441)
=> ( Vvar__5___24Anonymous__30440 = Vvar__5___24Anonymous__30441
& Vvar__4___24Anonymous__30438 = Vvar__4___24Anonymous__30439
& Vvar__3__x__30436 = Vvar__3__x__30437
& Vvar__2__Q__30434 = Vvar__2__Q__30435
& Vvar__1__P__30432 = Vvar__1__P__30433
& Vvar__0__A__30430 = Vvar__0__A__30431 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__18145,Vvar__0__A__18146,Vvar__1__B__18147,Vvar__1__B__18148,Vvar__2___24Anonymous__18149,Vvar__2___24Anonymous__18150] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__18145,Vvar__1__B__18147,Vvar__2___24Anonymous__18149) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__18146,Vvar__1__B__18148,Vvar__2___24Anonymous__18150)
=> ( Vvar__2___24Anonymous__18149 = Vvar__2___24Anonymous__18150
& Vvar__1__B__18147 = Vvar__1__B__18148
& Vvar__0__A__18145 = Vvar__0__A__18146 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__18151,Vvar__0__A__18152,Vvar__1__B__18153,Vvar__1__B__18154,Vvar__2___24Anonymous__18155,Vvar__2___24Anonymous__18156] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__18151,Vvar__1__B__18153) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__18152,Vvar__1__B__18154)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__18153 = Vvar__1__B__18154
& Vvar__0__A__18151 = Vvar__0__A__18152 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__14145,Vvar__0__A__14146,Vvar__1__B__14147,Vvar__1__B__14148,Vvar__2___24Anonymous__14149,Vvar__2___24Anonymous__14150] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__14145,Vvar__1__B__14147) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__14146,Vvar__1__B__14148)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__14147 = Vvar__1__B__14148
& Vvar__0__A__14145 = Vvar__0__A__14146 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__14151,Vvar__0__A__14152,Vvar__1__B__14153,Vvar__1__B__14154,Vvar__2___24Anonymous__14155,Vvar__2___24Anonymous__14156] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__14151,Vvar__1__B__14153) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__14152,Vvar__1__B__14154)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__14153 = Vvar__1__B__14154
& Vvar__0__A__14151 = Vvar__0__A__14152 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__273,Vvar__0___24Anonymous__274] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__273) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__274)
=> Vvar__0___24Anonymous__273 = Vvar__0___24Anonymous__274 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__774,Vvar__0___24Anonymous__775] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__774) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__775)
=> Vvar__0___24Anonymous__774 = Vvar__0___24Anonymous__775 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__772,Vvar__0___24Anonymous__773] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__772) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__773)
=> Vvar__0___24Anonymous__772 = Vvar__0___24Anonymous__773 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__761,Vvar__0___24Anonymous__762] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__761) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__762)
=> Vvar__0___24Anonymous__761 = Vvar__0___24Anonymous__762 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__763,Vvar__0___24Anonymous__764] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__763) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__764)
=> Vvar__0___24Anonymous__763 = Vvar__0___24Anonymous__764 ) ).
fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__30849,Vvar__0__p__30850,Vvar__1___24Anonymous__30851,Vvar__1___24Anonymous__30852] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__30849,Vvar__1___24Anonymous__30851) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__30850,Vvar__1___24Anonymous__30852)
=> ( Vvar__1___24Anonymous__30851 = Vvar__1___24Anonymous__30852
& Vvar__0__p__30849 = Vvar__0__p__30850 ) ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__16258,Vvar__0___24Anonymous__16259] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__16258) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__16259)
=> Vvar__0___24Anonymous__16258 = Vvar__0___24Anonymous__16259 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__17823,Vvar__0__Qnum__17824,Vvar__1__Qden__17825,Vvar__1__Qden__17826] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__17823,Vvar__1__Qden__17825) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__17824,Vvar__1__Qden__17826)
=> ( Vvar__1__Qden__17825 = Vvar__1__Qden__17826
& Vvar__0__Qnum__17823 = Vvar__0__Qnum__17824 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
! [Vvar__0__neg__21526,Vvar__0__neg__21527,Vvar__1__cond__neg__21528,Vvar__1__cond__neg__21529] :
( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__21526) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__21527)
=> ( c_24Proof = c_24Proof
& Vvar__0__neg__21526 = Vvar__0__neg__21527 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__21505,Vvar__0__nonneg__21506,Vvar__1__cond__nonneg__21507,Vvar__1__cond__nonneg__21508] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__21505) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__21506)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__21505 = Vvar__0__nonneg__21506 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
! [Vvar__0__nonpos__21519,Vvar__0__nonpos__21520,Vvar__1__cond__nonpos__21521,Vvar__1__cond__nonpos__21522] :
( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__21519) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__21520)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonpos__21519 = Vvar__0__nonpos__21520 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__21533,Vvar__0__nonzero__21534,Vvar__1__cond__nonzero__21535,Vvar__1__cond__nonzero__21536] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__21533) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__21534)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__21533 = Vvar__0__nonzero__21534 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__21512,Vvar__0__pos__21513,Vvar__1__cond__pos__21514,Vvar__1__cond__pos__21515] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__21512) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__21513)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__21512 = Vvar__0__pos__21513 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__22662,Vvar__0__x__22663,Vvar__1__n__22664,Vvar__1__n__22665,Vvar__2___24Anonymous__22666,Vvar__2___24Anonymous__22667] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__22662,Vvar__1__n__22664) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__22663,Vvar__1__n__22665)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__22664 = Vvar__1__n__22665
& Vvar__0__x__22662 = Vvar__0__x__22663 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__22652,Vvar__0__x__22653,Vvar__1___24Anonymous__22654,Vvar__1___24Anonymous__22655] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__22652) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__22653)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__22652 = Vvar__0__x__22653 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__22656,Vvar__0__x__22657,Vvar__1__n__22658,Vvar__1__n__22659,Vvar__2___24Anonymous__22660,Vvar__2___24Anonymous__22661] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__22656,Vvar__1__n__22658) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__22657,Vvar__1__n__22659)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__22658 = Vvar__1__n__22659
& Vvar__0__x__22656 = Vvar__0__x__22657 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__4920,Vvar__0___24Anonymous__4921,Vvar__1___24Anonymous__4922,Vvar__1___24Anonymous__4923,Vvar__2___24Anonymous__4924,Vvar__2___24Anonymous__4925,Vvar__3___24Anonymous__4926,Vvar__3___24Anonymous__4927,Vvar__4___24Anonymous__4928,Vvar__4___24Anonymous__4929,Vvar__5___24Anonymous__4930,Vvar__5___24Anonymous__4931,Vvar__6___24Anonymous__4932,Vvar__6___24Anonymous__4933,Vvar__7___24Anonymous__4934,Vvar__7___24Anonymous__4935] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4920,Vvar__1___24Anonymous__4922,Vvar__2___24Anonymous__4924,Vvar__3___24Anonymous__4926,Vvar__4___24Anonymous__4928,Vvar__5___24Anonymous__4930,Vvar__6___24Anonymous__4932,Vvar__7___24Anonymous__4934) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4921,Vvar__1___24Anonymous__4923,Vvar__2___24Anonymous__4925,Vvar__3___24Anonymous__4927,Vvar__4___24Anonymous__4929,Vvar__5___24Anonymous__4931,Vvar__6___24Anonymous__4933,Vvar__7___24Anonymous__4935)
=> ( Vvar__7___24Anonymous__4934 = Vvar__7___24Anonymous__4935
& Vvar__6___24Anonymous__4932 = Vvar__6___24Anonymous__4933
& Vvar__5___24Anonymous__4930 = Vvar__5___24Anonymous__4931
& Vvar__4___24Anonymous__4928 = Vvar__4___24Anonymous__4929
& Vvar__3___24Anonymous__4926 = Vvar__3___24Anonymous__4927
& Vvar__2___24Anonymous__4924 = Vvar__2___24Anonymous__4925
& Vvar__1___24Anonymous__4922 = Vvar__1___24Anonymous__4923
& Vvar__0___24Anonymous__4920 = Vvar__0___24Anonymous__4921 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__14178,Vvar__0___24Anonymous__14179,Vvar__1___24Anonymous__14180,Vvar__1___24Anonymous__14181] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__14178,Vvar__1___24Anonymous__14180) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__14179,Vvar__1___24Anonymous__14181)
=> ( Vvar__1___24Anonymous__14180 = Vvar__1___24Anonymous__14181
& Vvar__0___24Anonymous__14178 = Vvar__0___24Anonymous__14179 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__21438,Vvar__0__X__21439,Vvar__1__lt__21440,Vvar__1__lt__21441,Vvar__2__eq__21442,Vvar__2__eq__21443,Vvar__3__x__21444,Vvar__3__x__21445,Vvar__4__y__21446,Vvar__4__y__21447,Vvar__5___24Anonymous__21448,Vvar__5___24Anonymous__21449] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__21438,Vvar__1__lt__21440,Vvar__2__eq__21442,Vvar__3__x__21444,Vvar__4__y__21446) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__21439,Vvar__1__lt__21441,Vvar__2__eq__21443,Vvar__3__x__21445,Vvar__4__y__21447)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__21446 = Vvar__4__y__21447
& Vvar__3__x__21444 = Vvar__3__x__21445
& Vvar__2__eq__21442 = Vvar__2__eq__21443
& Vvar__1__lt__21440 = Vvar__1__lt__21441
& Vvar__0__X__21438 = Vvar__0__X__21439 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__21450,Vvar__0__X__21451,Vvar__1__lt__21452,Vvar__1__lt__21453,Vvar__2__eq__21454,Vvar__2__eq__21455,Vvar__3__x__21456,Vvar__3__x__21457,Vvar__4__y__21458,Vvar__4__y__21459,Vvar__5___24Anonymous__21460,Vvar__5___24Anonymous__21461] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__21450,Vvar__1__lt__21452,Vvar__2__eq__21454,Vvar__3__x__21456,Vvar__4__y__21458) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__21451,Vvar__1__lt__21453,Vvar__2__eq__21455,Vvar__3__x__21457,Vvar__4__y__21459)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__21458 = Vvar__4__y__21459
& Vvar__3__x__21456 = Vvar__3__x__21457
& Vvar__2__eq__21454 = Vvar__2__eq__21455
& Vvar__1__lt__21452 = Vvar__1__lt__21453
& Vvar__0__X__21450 = Vvar__0__X__21451 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__21426,Vvar__0__X__21427,Vvar__1__lt__21428,Vvar__1__lt__21429,Vvar__2__eq__21430,Vvar__2__eq__21431,Vvar__3__x__21432,Vvar__3__x__21433,Vvar__4__y__21434,Vvar__4__y__21435,Vvar__5___24Anonymous__21436,Vvar__5___24Anonymous__21437] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__21426,Vvar__1__lt__21428,Vvar__2__eq__21430,Vvar__3__x__21432,Vvar__4__y__21434) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__21427,Vvar__1__lt__21429,Vvar__2__eq__21431,Vvar__3__x__21433,Vvar__4__y__21435)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__21434 = Vvar__4__y__21435
& Vvar__3__x__21432 = Vvar__3__x__21433
& Vvar__2__eq__21430 = Vvar__2__eq__21431
& Vvar__1__lt__21428 = Vvar__1__lt__21429
& Vvar__0__X__21426 = Vvar__0__X__21427 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__20261,Vvar__0__n__20262] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__20261) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__20262)
=> Vvar__0__n__20261 = Vvar__0__n__20262 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__20263,Vvar__0__n__20264,Vvar__1___24Anonymous__20265,Vvar__1___24Anonymous__20266] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__20263,Vvar__1___24Anonymous__20265) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__20264,Vvar__1___24Anonymous__20266)
=> ( Vvar__1___24Anonymous__20265 = Vvar__1___24Anonymous__20266
& Vvar__0__n__20263 = Vvar__0__n__20264 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__14869,Vvar__0__A__14870,Vvar__1__h__14871,Vvar__1__h__14872,Vvar__2__n__14873,Vvar__2__n__14874,Vvar__3___24Anonymous__14875,Vvar__3___24Anonymous__14876] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__14869,Vvar__1__h__14871,Vvar__2__n__14873,Vvar__3___24Anonymous__14875) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__14870,Vvar__1__h__14872,Vvar__2__n__14874,Vvar__3___24Anonymous__14876)
=> ( Vvar__3___24Anonymous__14875 = Vvar__3___24Anonymous__14876
& Vvar__2__n__14873 = Vvar__2__n__14874
& Vvar__1__h__14871 = Vvar__1__h__14872
& Vvar__0__A__14869 = Vvar__0__A__14870 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__14867,Vvar__0__A__14868] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__14867) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__14868)
=> Vvar__0__A__14867 = Vvar__0__A__14868 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__30604,Vvar__0__a__30605,Vvar__1__b__30606,Vvar__1__b__30607,Vvar__2__u__30608,Vvar__2__u__30609,Vvar__3__v__30610,Vvar__3__v__30611,Vvar__4__d__30612,Vvar__4__d__30613,Vvar__5___24Anonymous__30614,Vvar__5___24Anonymous__30615,Vvar__6___24Anonymous__30616,Vvar__6___24Anonymous__30617] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__30604,Vvar__1__b__30606,Vvar__2__u__30608,Vvar__3__v__30610,Vvar__4__d__30612) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__30605,Vvar__1__b__30607,Vvar__2__u__30609,Vvar__3__v__30611,Vvar__4__d__30613)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__30612 = Vvar__4__d__30613
& Vvar__3__v__30610 = Vvar__3__v__30611
& Vvar__2__u__30608 = Vvar__2__u__30609
& Vvar__1__b__30606 = Vvar__1__b__30607
& Vvar__0__a__30604 = Vvar__0__a__30605 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__16032,Vvar__0__x__16033,Vvar__1__p__16034,Vvar__1__p__16035,Vvar__2__q__16036,Vvar__2__q__16037,Vvar__3__r__16038,Vvar__3__r__16039,Vvar__4___24Anonymous__16040,Vvar__4___24Anonymous__16041,Vvar__5___24Anonymous__16042,Vvar__5___24Anonymous__16043,Vvar__6___24Anonymous__16044,Vvar__6___24Anonymous__16045] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__16032,Vvar__1__p__16034,Vvar__2__q__16036,Vvar__3__r__16038) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__16033,Vvar__1__p__16035,Vvar__2__q__16037,Vvar__3__r__16039)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__16038 = Vvar__3__r__16039
& Vvar__2__q__16036 = Vvar__2__q__16037
& Vvar__1__p__16034 = Vvar__1__p__16035
& Vvar__0__x__16032 = Vvar__0__x__16033 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__6041,Vvar__0__C__6042,Vvar__1___24Anonymous__6043,Vvar__1___24Anonymous__6044] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__6041,Vvar__1___24Anonymous__6043) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__6042,Vvar__1___24Anonymous__6044)
=> ( Vvar__1___24Anonymous__6043 = Vvar__1___24Anonymous__6044
& Vvar__0__C__6041 = Vvar__0__C__6042 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__6045,Vvar__0__C__6046,Vvar__1___24Anonymous__6047,Vvar__1___24Anonymous__6048,Vvar__2___24Anonymous__6049,Vvar__2___24Anonymous__6050] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__6045,Vvar__1___24Anonymous__6047,Vvar__2___24Anonymous__6049) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__6046,Vvar__1___24Anonymous__6048,Vvar__2___24Anonymous__6050)
=> ( Vvar__2___24Anonymous__6049 = Vvar__2___24Anonymous__6050
& Vvar__1___24Anonymous__6047 = Vvar__1___24Anonymous__6048
& Vvar__0__C__6045 = Vvar__0__C__6046 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__6037,Vvar__0__C__6038,Vvar__1___24Anonymous__6039,Vvar__1___24Anonymous__6040] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__6037,Vvar__1___24Anonymous__6039) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__6038,Vvar__1___24Anonymous__6040)
=> ( Vvar__1___24Anonymous__6039 = Vvar__1___24Anonymous__6040
& Vvar__0__C__6037 = Vvar__0__C__6038 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__6057,Vvar__0__C__6058,Vvar__1___24Anonymous__6059,Vvar__1___24Anonymous__6060,Vvar__2___24Anonymous__6061,Vvar__2___24Anonymous__6062] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__6057,Vvar__1___24Anonymous__6059,Vvar__2___24Anonymous__6061) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__6058,Vvar__1___24Anonymous__6060,Vvar__2___24Anonymous__6062)
=> ( Vvar__2___24Anonymous__6061 = Vvar__2___24Anonymous__6062
& Vvar__1___24Anonymous__6059 = Vvar__1___24Anonymous__6060
& Vvar__0__C__6057 = Vvar__0__C__6058 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__6063,Vvar__0__C__6064,Vvar__1___24Anonymous__6065,Vvar__1___24Anonymous__6066] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__6063,Vvar__1___24Anonymous__6065) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__6064,Vvar__1___24Anonymous__6066)
=> ( Vvar__1___24Anonymous__6065 = Vvar__1___24Anonymous__6066
& Vvar__0__C__6063 = Vvar__0__C__6064 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__6067,Vvar__0__C__6068,Vvar__1___24Anonymous__6069,Vvar__1___24Anonymous__6070,Vvar__2___24Anonymous__6071,Vvar__2___24Anonymous__6072] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__6067,Vvar__1___24Anonymous__6069,Vvar__2___24Anonymous__6071) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__6068,Vvar__1___24Anonymous__6070,Vvar__2___24Anonymous__6072)
=> ( Vvar__2___24Anonymous__6071 = Vvar__2___24Anonymous__6072
& Vvar__1___24Anonymous__6069 = Vvar__1___24Anonymous__6070
& Vvar__0__C__6067 = Vvar__0__C__6068 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__6051,Vvar__0__C__6052,Vvar__1___24Anonymous__6053,Vvar__1___24Anonymous__6054,Vvar__2___24Anonymous__6055,Vvar__2___24Anonymous__6056] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__6051,Vvar__1___24Anonymous__6053,Vvar__2___24Anonymous__6055) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__6052,Vvar__1___24Anonymous__6054,Vvar__2___24Anonymous__6056)
=> ( Vvar__2___24Anonymous__6055 = Vvar__2___24Anonymous__6056
& Vvar__1___24Anonymous__6053 = Vvar__1___24Anonymous__6054
& Vvar__0__C__6051 = Vvar__0__C__6052 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__6112,Vvar__0__C__6113,Vvar__1___24Anonymous__6114,Vvar__1___24Anonymous__6115,Vvar__2___24Anonymous__6116,Vvar__2___24Anonymous__6117,Vvar__3___24Anonymous__6118,Vvar__3___24Anonymous__6119] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__6112,Vvar__1___24Anonymous__6114,Vvar__2___24Anonymous__6116,Vvar__3___24Anonymous__6118) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__6113,Vvar__1___24Anonymous__6115,Vvar__2___24Anonymous__6117,Vvar__3___24Anonymous__6119)
=> ( Vvar__3___24Anonymous__6118 = Vvar__3___24Anonymous__6119
& Vvar__2___24Anonymous__6116 = Vvar__2___24Anonymous__6117
& Vvar__1___24Anonymous__6114 = Vvar__1___24Anonymous__6115
& Vvar__0__C__6112 = Vvar__0__C__6113 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__6102,Vvar__0__C__6103,Vvar__1___24Anonymous__6104,Vvar__1___24Anonymous__6105] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__6102,Vvar__1___24Anonymous__6104) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__6103,Vvar__1___24Anonymous__6105)
=> ( Vvar__1___24Anonymous__6104 = Vvar__1___24Anonymous__6105
& Vvar__0__C__6102 = Vvar__0__C__6103 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__6106,Vvar__0__C__6107,Vvar__1___24Anonymous__6108,Vvar__1___24Anonymous__6109,Vvar__2___24Anonymous__6110,Vvar__2___24Anonymous__6111] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__6106,Vvar__1___24Anonymous__6108,Vvar__2___24Anonymous__6110) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__6107,Vvar__1___24Anonymous__6109,Vvar__2___24Anonymous__6111)
=> ( Vvar__2___24Anonymous__6110 = Vvar__2___24Anonymous__6111
& Vvar__1___24Anonymous__6108 = Vvar__1___24Anonymous__6109
& Vvar__0__C__6106 = Vvar__0__C__6107 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__17760,Vvar__0___24Anonymous__17761,Vvar__1___24Anonymous__17762,Vvar__1___24Anonymous__17763] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__17760,Vvar__1___24Anonymous__17762) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__17761,Vvar__1___24Anonymous__17763)
=> ( Vvar__1___24Anonymous__17762 = Vvar__1___24Anonymous__17763
& Vvar__0___24Anonymous__17760 = Vvar__0___24Anonymous__17761 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__17756,Vvar__0___24Anonymous__17757,Vvar__1___24Anonymous__17758,Vvar__1___24Anonymous__17759] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__17756,Vvar__1___24Anonymous__17758) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__17757,Vvar__1___24Anonymous__17759)
=> ( Vvar__1___24Anonymous__17758 = Vvar__1___24Anonymous__17759
& Vvar__0___24Anonymous__17756 = Vvar__0___24Anonymous__17757 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__21678,Vvar__0__r__21679] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__21678) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__21679)
=> Vvar__0__r__21678 = Vvar__0__r__21679 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__21666,Vvar__0__r1__21667,Vvar__1__r2__21668,Vvar__1__r2__21669] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__21666,Vvar__1__r2__21668) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__21667,Vvar__1__r2__21669)
=> ( Vvar__1__r2__21668 = Vvar__1__r2__21669
& Vvar__0__r1__21666 = Vvar__0__r1__21667 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__21670,Vvar__0__r1__21671,Vvar__1__r2__21672,Vvar__1__r2__21673] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__21670,Vvar__1__r2__21672) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__21671,Vvar__1__r2__21673)
=> ( Vvar__1__r2__21672 = Vvar__1__r2__21673
& Vvar__0__r1__21670 = Vvar__0__r1__21671 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__21680,Vvar__0__r__21681] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__21680) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__21681)
=> Vvar__0__r__21680 = Vvar__0__r__21681 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__21662,Vvar__0__r1__21663,Vvar__1__r2__21664,Vvar__1__r2__21665] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__21662,Vvar__1__r2__21664) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__21663,Vvar__1__r2__21665)
=> ( Vvar__1__r2__21664 = Vvar__1__r2__21665
& Vvar__0__r1__21662 = Vvar__0__r1__21663 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__21674,Vvar__0__r1__21675,Vvar__1__z__21676,Vvar__1__z__21677] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__21674,Vvar__1__z__21676) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__21675,Vvar__1__z__21677)
=> ( Vvar__1__z__21676 = Vvar__1__z__21677
& Vvar__0__r1__21674 = Vvar__0__r1__21675 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__21658,Vvar__0__r__21659] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__21658) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__21659)
=> Vvar__0__r__21658 = Vvar__0__r__21659 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__21660,Vvar__0__r__21661] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__21660) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__21661)
=> Vvar__0__r__21660 = Vvar__0__r__21661 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__28114,Vvar__0__T__28115,Vvar__1__Flhs__28116,Vvar__1__Flhs__28117,Vvar__2__Fop__28118,Vvar__2__Fop__28119,Vvar__3__Frhs__28120,Vvar__3__Frhs__28121] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__28114,Vvar__1__Flhs__28116,Vvar__2__Fop__28118,Vvar__3__Frhs__28120) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__28115,Vvar__1__Flhs__28117,Vvar__2__Fop__28119,Vvar__3__Frhs__28121)
=> ( Vvar__3__Frhs__28120 = Vvar__3__Frhs__28121
& Vvar__2__Fop__28118 = Vvar__2__Fop__28119
& Vvar__1__Flhs__28116 = Vvar__1__Flhs__28117
& Vvar__0__T__28114 = Vvar__0__T__28115 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__28096,Vvar__0__C__28097,Vvar__1___24Anonymous__28098,Vvar__1___24Anonymous__28099,Vvar__2___24Anonymous__28100,Vvar__2___24Anonymous__28101] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__28096,Vvar__1___24Anonymous__28098,Vvar__2___24Anonymous__28100) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__28097,Vvar__1___24Anonymous__28099,Vvar__2___24Anonymous__28101)
=> ( Vvar__2___24Anonymous__28100 = Vvar__2___24Anonymous__28101
& Vvar__1___24Anonymous__28098 = Vvar__1___24Anonymous__28099
& Vvar__0__C__28096 = Vvar__0__C__28097 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__28102,Vvar__0__C__28103,Vvar__1___24Anonymous__28104,Vvar__1___24Anonymous__28105] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__28102,Vvar__1___24Anonymous__28104) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__28103,Vvar__1___24Anonymous__28105)
=> ( Vvar__1___24Anonymous__28104 = Vvar__1___24Anonymous__28105
& Vvar__0__C__28102 = Vvar__0__C__28103 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__28076,Vvar__0__C__28077,Vvar__1___24Anonymous__28078,Vvar__1___24Anonymous__28079] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__28076,Vvar__1___24Anonymous__28078) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__28077,Vvar__1___24Anonymous__28079)
=> ( Vvar__1___24Anonymous__28078 = Vvar__1___24Anonymous__28079
& Vvar__0__C__28076 = Vvar__0__C__28077 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__28084,Vvar__0__C__28085,Vvar__1___24Anonymous__28086,Vvar__1___24Anonymous__28087,Vvar__2___24Anonymous__28088,Vvar__2___24Anonymous__28089] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__28084,Vvar__1___24Anonymous__28086,Vvar__2___24Anonymous__28088) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__28085,Vvar__1___24Anonymous__28087,Vvar__2___24Anonymous__28089)
=> ( Vvar__2___24Anonymous__28088 = Vvar__2___24Anonymous__28089
& Vvar__1___24Anonymous__28086 = Vvar__1___24Anonymous__28087
& Vvar__0__C__28084 = Vvar__0__C__28085 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__28090,Vvar__0__C__28091,Vvar__1___24Anonymous__28092,Vvar__1___24Anonymous__28093,Vvar__2___24Anonymous__28094,Vvar__2___24Anonymous__28095] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__28090,Vvar__1___24Anonymous__28092,Vvar__2___24Anonymous__28094) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__28091,Vvar__1___24Anonymous__28093,Vvar__2___24Anonymous__28095)
=> ( Vvar__2___24Anonymous__28094 = Vvar__2___24Anonymous__28095
& Vvar__1___24Anonymous__28092 = Vvar__1___24Anonymous__28093
& Vvar__0__C__28090 = Vvar__0__C__28091 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__28080,Vvar__0__C__28081,Vvar__1___24Anonymous__28082,Vvar__1___24Anonymous__28083] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__28080,Vvar__1___24Anonymous__28082) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__28081,Vvar__1___24Anonymous__28083)
=> ( Vvar__1___24Anonymous__28082 = Vvar__1___24Anonymous__28083
& Vvar__0__C__28080 = Vvar__0__C__28081 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__28106,Vvar__0__C__28107] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__28106) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__28107)
=> Vvar__0__C__28106 = Vvar__0__C__28107 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__14622,Vvar__0__TA__14623,Vvar__1__TX__14624,Vvar__1__TX__14625,Vvar__2__AA__14626,Vvar__2__AA__14627,Vvar__3__AF__14628,Vvar__3__AF__14629,Vvar__4___24Anonymous__14630,Vvar__4___24Anonymous__14631,Vvar__5___24Anonymous__14632,Vvar__5___24Anonymous__14633] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__14622,Vvar__1__TX__14624,Vvar__2__AA__14626,Vvar__3__AF__14628,Vvar__4___24Anonymous__14630,Vvar__5___24Anonymous__14632) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__14623,Vvar__1__TX__14625,Vvar__2__AA__14627,Vvar__3__AF__14629,Vvar__4___24Anonymous__14631,Vvar__5___24Anonymous__14633)
=> ( Vvar__5___24Anonymous__14632 = Vvar__5___24Anonymous__14633
& Vvar__4___24Anonymous__14630 = Vvar__4___24Anonymous__14631
& Vvar__3__AF__14628 = Vvar__3__AF__14629
& Vvar__2__AA__14626 = Vvar__2__AA__14627
& Vvar__1__TX__14624 = Vvar__1__TX__14625
& Vvar__0__TA__14622 = Vvar__0__TA__14623 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__14634,Vvar__0__TA__14635,Vvar__1__TX__14636,Vvar__1__TX__14637,Vvar__2__AA__14638,Vvar__2__AA__14639,Vvar__3__AF__14640,Vvar__3__AF__14641,Vvar__4___24Anonymous__14642,Vvar__4___24Anonymous__14643,Vvar__5___24Anonymous__14644,Vvar__5___24Anonymous__14645] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__14634,Vvar__1__TX__14636,Vvar__2__AA__14638,Vvar__3__AF__14640,Vvar__4___24Anonymous__14642,Vvar__5___24Anonymous__14644) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__14635,Vvar__1__TX__14637,Vvar__2__AA__14639,Vvar__3__AF__14641,Vvar__4___24Anonymous__14643,Vvar__5___24Anonymous__14645)
=> ( Vvar__5___24Anonymous__14644 = Vvar__5___24Anonymous__14645
& Vvar__4___24Anonymous__14642 = Vvar__4___24Anonymous__14643
& Vvar__3__AF__14640 = Vvar__3__AF__14641
& Vvar__2__AA__14638 = Vvar__2__AA__14639
& Vvar__1__TX__14636 = Vvar__1__TX__14637
& Vvar__0__TA__14634 = Vvar__0__TA__14635 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__14646,Vvar__0__TA__14647,Vvar__1__TX__14648,Vvar__1__TX__14649,Vvar__2__AA__14650,Vvar__2__AA__14651,Vvar__3__AF__14652,Vvar__3__AF__14653,Vvar__4___24Anonymous__14654,Vvar__4___24Anonymous__14655,Vvar__5___24Anonymous__14656,Vvar__5___24Anonymous__14657] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__14646,Vvar__1__TX__14648,Vvar__2__AA__14650,Vvar__3__AF__14652,Vvar__4___24Anonymous__14654,Vvar__5___24Anonymous__14656) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__14647,Vvar__1__TX__14649,Vvar__2__AA__14651,Vvar__3__AF__14653,Vvar__4___24Anonymous__14655,Vvar__5___24Anonymous__14657)
=> ( Vvar__5___24Anonymous__14656 = Vvar__5___24Anonymous__14657
& Vvar__4___24Anonymous__14654 = Vvar__4___24Anonymous__14655
& Vvar__3__AF__14652 = Vvar__3__AF__14653
& Vvar__2__AA__14650 = Vvar__2__AA__14651
& Vvar__1__TX__14648 = Vvar__1__TX__14649
& Vvar__0__TA__14646 = Vvar__0__TA__14647 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__14604,Vvar__0__TA__14605,Vvar__1__TX__14606,Vvar__1__TX__14607,Vvar__2__AA__14608,Vvar__2__AA__14609,Vvar__3__AF__14610,Vvar__3__AF__14611] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__14604,Vvar__1__TX__14606,Vvar__2__AA__14608,Vvar__3__AF__14610) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__14605,Vvar__1__TX__14607,Vvar__2__AA__14609,Vvar__3__AF__14611)
=> ( Vvar__3__AF__14610 = Vvar__3__AF__14611
& Vvar__2__AA__14608 = Vvar__2__AA__14609
& Vvar__1__TX__14606 = Vvar__1__TX__14607
& Vvar__0__TA__14604 = Vvar__0__TA__14605 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__14668,Vvar__0__TA__14669,Vvar__1__TX__14670,Vvar__1__TX__14671,Vvar__2__AA__14672,Vvar__2__AA__14673,Vvar__3__AF__14674,Vvar__3__AF__14675,Vvar__4___24Anonymous__14676,Vvar__4___24Anonymous__14677,Vvar__5___24Anonymous__14678,Vvar__5___24Anonymous__14679,Vvar__6___24Anonymous__14680,Vvar__6___24Anonymous__14681] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__14668,Vvar__1__TX__14670,Vvar__2__AA__14672,Vvar__3__AF__14674,Vvar__4___24Anonymous__14676,Vvar__5___24Anonymous__14678,Vvar__6___24Anonymous__14680) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__14669,Vvar__1__TX__14671,Vvar__2__AA__14673,Vvar__3__AF__14675,Vvar__4___24Anonymous__14677,Vvar__5___24Anonymous__14679,Vvar__6___24Anonymous__14681)
=> ( Vvar__6___24Anonymous__14680 = Vvar__6___24Anonymous__14681
& Vvar__5___24Anonymous__14678 = Vvar__5___24Anonymous__14679
& Vvar__4___24Anonymous__14676 = Vvar__4___24Anonymous__14677
& Vvar__3__AF__14674 = Vvar__3__AF__14675
& Vvar__2__AA__14672 = Vvar__2__AA__14673
& Vvar__1__TX__14670 = Vvar__1__TX__14671
& Vvar__0__TA__14668 = Vvar__0__TA__14669 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__14658,Vvar__0__TA__14659,Vvar__1__TX__14660,Vvar__1__TX__14661,Vvar__2__AA__14662,Vvar__2__AA__14663,Vvar__3__AF__14664,Vvar__3__AF__14665,Vvar__4___24Anonymous__14666,Vvar__4___24Anonymous__14667] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__14658,Vvar__1__TX__14660,Vvar__2__AA__14662,Vvar__3__AF__14664,Vvar__4___24Anonymous__14666) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__14659,Vvar__1__TX__14661,Vvar__2__AA__14663,Vvar__3__AF__14665,Vvar__4___24Anonymous__14667)
=> ( Vvar__4___24Anonymous__14666 = Vvar__4___24Anonymous__14667
& Vvar__3__AF__14664 = Vvar__3__AF__14665
& Vvar__2__AA__14662 = Vvar__2__AA__14663
& Vvar__1__TX__14660 = Vvar__1__TX__14661
& Vvar__0__TA__14658 = Vvar__0__TA__14659 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__14596,Vvar__0__TA__14597,Vvar__1__TX__14598,Vvar__1__TX__14599,Vvar__2__AA__14600,Vvar__2__AA__14601,Vvar__3__AF__14602,Vvar__3__AF__14603] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__14596,Vvar__1__TX__14598,Vvar__2__AA__14600,Vvar__3__AF__14602) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__14597,Vvar__1__TX__14599,Vvar__2__AA__14601,Vvar__3__AF__14603)
=> ( Vvar__3__AF__14602 = Vvar__3__AF__14603
& Vvar__2__AA__14600 = Vvar__2__AA__14601
& Vvar__1__TX__14598 = Vvar__1__TX__14599
& Vvar__0__TA__14596 = Vvar__0__TA__14597 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__14612,Vvar__0__TA__14613,Vvar__1__TX__14614,Vvar__1__TX__14615,Vvar__2__AA__14616,Vvar__2__AA__14617,Vvar__3__AF__14618,Vvar__3__AF__14619,Vvar__4___24Anonymous__14620,Vvar__4___24Anonymous__14621] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__14612,Vvar__1__TX__14614,Vvar__2__AA__14616,Vvar__3__AF__14618,Vvar__4___24Anonymous__14620) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__14613,Vvar__1__TX__14615,Vvar__2__AA__14617,Vvar__3__AF__14619,Vvar__4___24Anonymous__14621)
=> ( Vvar__4___24Anonymous__14620 = Vvar__4___24Anonymous__14621
& Vvar__3__AF__14618 = Vvar__3__AF__14619
& Vvar__2__AA__14616 = Vvar__2__AA__14617
& Vvar__1__TX__14614 = Vvar__1__TX__14615
& Vvar__0__TA__14612 = Vvar__0__TA__14613 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__30475,Vvar__0__A__30476,Vvar__1___24Anonymous__30477,Vvar__1___24Anonymous__30478,Vvar__2___24Anonymous__30479,Vvar__2___24Anonymous__30480,Vvar__3___24Anonymous__30481,Vvar__3___24Anonymous__30482] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__30475,Vvar__1___24Anonymous__30477,Vvar__2___24Anonymous__30479,Vvar__3___24Anonymous__30481) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__30476,Vvar__1___24Anonymous__30478,Vvar__2___24Anonymous__30480,Vvar__3___24Anonymous__30482)
=> ( Vvar__3___24Anonymous__30481 = Vvar__3___24Anonymous__30482
& Vvar__2___24Anonymous__30479 = Vvar__2___24Anonymous__30480
& Vvar__1___24Anonymous__30477 = Vvar__1___24Anonymous__30478
& Vvar__0__A__30475 = Vvar__0__A__30476 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__30471,Vvar__0__A__30472,Vvar__1___24Anonymous__30473,Vvar__1___24Anonymous__30474] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__30471,Vvar__1___24Anonymous__30473) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__30472,Vvar__1___24Anonymous__30474)
=> ( Vvar__1___24Anonymous__30473 = Vvar__1___24Anonymous__30474
& Vvar__0__A__30471 = Vvar__0__A__30472 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__30469,Vvar__0__A__30470] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__30469) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__30470)
=> Vvar__0__A__30469 = Vvar__0__A__30470 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__30566,Vvar__0___24Anonymous__30567,Vvar__1___24Anonymous__30568,Vvar__1___24Anonymous__30569] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__30566,Vvar__1___24Anonymous__30568) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__30567,Vvar__1___24Anonymous__30569)
=> ( Vvar__1___24Anonymous__30568 = Vvar__1___24Anonymous__30569
& Vvar__0___24Anonymous__30566 = Vvar__0___24Anonymous__30567 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__30570,Vvar__0___24Anonymous__30571,Vvar__1___24Anonymous__30572,Vvar__1___24Anonymous__30573,Vvar__2___24Anonymous__30574,Vvar__2___24Anonymous__30575] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__30570,Vvar__1___24Anonymous__30572,Vvar__2___24Anonymous__30574) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__30571,Vvar__1___24Anonymous__30573,Vvar__2___24Anonymous__30575)
=> ( Vvar__2___24Anonymous__30574 = Vvar__2___24Anonymous__30575
& Vvar__1___24Anonymous__30572 = Vvar__1___24Anonymous__30573
& Vvar__0___24Anonymous__30570 = Vvar__0___24Anonymous__30571 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__30562,Vvar__0___24Anonymous__30563,Vvar__1___24Anonymous__30564,Vvar__1___24Anonymous__30565] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__30562,Vvar__1___24Anonymous__30564) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__30563,Vvar__1___24Anonymous__30565)
=> ( Vvar__1___24Anonymous__30564 = Vvar__1___24Anonymous__30565
& Vvar__0___24Anonymous__30562 = Vvar__0___24Anonymous__30563 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__19038,Vvar__0__C__19039] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__19038) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__19039)
=> Vvar__0__C__19038 = Vvar__0__C__19039 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__19036,Vvar__0__C__19037] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__19036) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__19037)
=> Vvar__0__C__19036 = Vvar__0__C__19037 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__19044,Vvar__0__C__19045,Vvar__1___24Anonymous__19046,Vvar__1___24Anonymous__19047] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__19044,Vvar__1___24Anonymous__19046) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__19045,Vvar__1___24Anonymous__19047)
=> ( Vvar__1___24Anonymous__19046 = Vvar__1___24Anonymous__19047
& Vvar__0__C__19044 = Vvar__0__C__19045 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__19048,Vvar__0__C__19049,Vvar__1___24Anonymous__19050,Vvar__1___24Anonymous__19051,Vvar__2___24Anonymous__19052,Vvar__2___24Anonymous__19053] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__19048,Vvar__1___24Anonymous__19050,Vvar__2___24Anonymous__19052) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__19049,Vvar__1___24Anonymous__19051,Vvar__2___24Anonymous__19053)
=> ( Vvar__2___24Anonymous__19052 = Vvar__2___24Anonymous__19053
& Vvar__1___24Anonymous__19050 = Vvar__1___24Anonymous__19051
& Vvar__0__C__19048 = Vvar__0__C__19049 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__19040,Vvar__0__C__19041,Vvar__1___24Anonymous__19042,Vvar__1___24Anonymous__19043] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__19040,Vvar__1___24Anonymous__19042) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__19041,Vvar__1___24Anonymous__19043)
=> ( Vvar__1___24Anonymous__19042 = Vvar__1___24Anonymous__19043
& Vvar__0__C__19040 = Vvar__0__C__19041 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__19074,Vvar__0__C__19075,Vvar__1___24Anonymous__19076,Vvar__1___24Anonymous__19077,Vvar__2___24Anonymous__19078,Vvar__2___24Anonymous__19079] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__19074,Vvar__1___24Anonymous__19076,Vvar__2___24Anonymous__19078) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__19075,Vvar__1___24Anonymous__19077,Vvar__2___24Anonymous__19079)
=> ( Vvar__2___24Anonymous__19078 = Vvar__2___24Anonymous__19079
& Vvar__1___24Anonymous__19076 = Vvar__1___24Anonymous__19077
& Vvar__0__C__19074 = Vvar__0__C__19075 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__19070,Vvar__0__C__19071,Vvar__1___24Anonymous__19072,Vvar__1___24Anonymous__19073] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__19070,Vvar__1___24Anonymous__19072) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__19071,Vvar__1___24Anonymous__19073)
=> ( Vvar__1___24Anonymous__19072 = Vvar__1___24Anonymous__19073
& Vvar__0__C__19070 = Vvar__0__C__19071 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__19060,Vvar__0__C__19061,Vvar__1___24Anonymous__19062,Vvar__1___24Anonymous__19063,Vvar__2___24Anonymous__19064,Vvar__2___24Anonymous__19065] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__19060,Vvar__1___24Anonymous__19062,Vvar__2___24Anonymous__19064) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__19061,Vvar__1___24Anonymous__19063,Vvar__2___24Anonymous__19065)
=> ( Vvar__2___24Anonymous__19064 = Vvar__2___24Anonymous__19065
& Vvar__1___24Anonymous__19062 = Vvar__1___24Anonymous__19063
& Vvar__0__C__19060 = Vvar__0__C__19061 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__19066,Vvar__0__C__19067,Vvar__1___24Anonymous__19068,Vvar__1___24Anonymous__19069] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__19066,Vvar__1___24Anonymous__19068) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__19067,Vvar__1___24Anonymous__19069)
=> ( Vvar__1___24Anonymous__19068 = Vvar__1___24Anonymous__19069
& Vvar__0__C__19066 = Vvar__0__C__19067 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__19080,Vvar__0__C__19081,Vvar__1___24Anonymous__19082,Vvar__1___24Anonymous__19083,Vvar__2___24Anonymous__19084,Vvar__2___24Anonymous__19085] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__19080,Vvar__1___24Anonymous__19082,Vvar__2___24Anonymous__19084) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__19081,Vvar__1___24Anonymous__19083,Vvar__2___24Anonymous__19085)
=> ( Vvar__2___24Anonymous__19084 = Vvar__2___24Anonymous__19085
& Vvar__1___24Anonymous__19082 = Vvar__1___24Anonymous__19083
& Vvar__0__C__19080 = Vvar__0__C__19081 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__19054,Vvar__0__C__19055,Vvar__1___24Anonymous__19056,Vvar__1___24Anonymous__19057,Vvar__2___24Anonymous__19058,Vvar__2___24Anonymous__19059] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__19054,Vvar__1___24Anonymous__19056,Vvar__2___24Anonymous__19058) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__19055,Vvar__1___24Anonymous__19057,Vvar__2___24Anonymous__19059)
=> ( Vvar__2___24Anonymous__19058 = Vvar__2___24Anonymous__19059
& Vvar__1___24Anonymous__19056 = Vvar__1___24Anonymous__19057
& Vvar__0__C__19054 = Vvar__0__C__19055 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__19098,Vvar__0__C__19099,Vvar__1__num__19100,Vvar__1__num__19101,Vvar__2__denum__19102,Vvar__2__denum__19103,Vvar__3__condition__19104,Vvar__3__condition__19105] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__19098,Vvar__1__num__19100,Vvar__2__denum__19102,Vvar__3__condition__19104) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__19099,Vvar__1__num__19101,Vvar__2__denum__19103,Vvar__3__condition__19105)
=> ( Vvar__3__condition__19104 = Vvar__3__condition__19105
& Vvar__2__denum__19102 = Vvar__2__denum__19103
& Vvar__1__num__19100 = Vvar__1__num__19101
& Vvar__0__C__19098 = Vvar__0__C__19099 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__19112,Vvar__0__C__19113,Vvar__1__rsplit__left__19114,Vvar__1__rsplit__left__19115,Vvar__2__rsplit__common__19116,Vvar__2__rsplit__common__19117,Vvar__3__rsplit__right__19118,Vvar__3__rsplit__right__19119] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__19112,Vvar__1__rsplit__left__19114,Vvar__2__rsplit__common__19116,Vvar__3__rsplit__right__19118) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__19113,Vvar__1__rsplit__left__19115,Vvar__2__rsplit__common__19117,Vvar__3__rsplit__right__19119)
=> ( Vvar__3__rsplit__right__19118 = Vvar__3__rsplit__right__19119
& Vvar__2__rsplit__common__19116 = Vvar__2__rsplit__common__19117
& Vvar__1__rsplit__left__19114 = Vvar__1__rsplit__left__19115
& Vvar__0__C__19112 = Vvar__0__C__19113 ) ) ).
fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
! [Vvar__0__hypo__type__20559,Vvar__0__hypo__type__20560,Vvar__1__hypo__proof__20561,Vvar__1__hypo__proof__20562] :
( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__20559,Vvar__1__hypo__proof__20561) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__20560,Vvar__1__hypo__proof__20562)
=> ( Vvar__1__hypo__proof__20561 = Vvar__1__hypo__proof__20562
& Vvar__0__hypo__type__20559 = Vvar__0__hypo__type__20560 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__10696,Vvar__0__C__10697] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10696) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10697)
=> Vvar__0__C__10696 = Vvar__0__C__10697 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__10694,Vvar__0__C__10695] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10694) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10695)
=> Vvar__0__C__10694 = Vvar__0__C__10695 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__10702,Vvar__0__C__10703,Vvar__1___24Anonymous__10704,Vvar__1___24Anonymous__10705] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__10702,Vvar__1___24Anonymous__10704) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__10703,Vvar__1___24Anonymous__10705)
=> ( Vvar__1___24Anonymous__10704 = Vvar__1___24Anonymous__10705
& Vvar__0__C__10702 = Vvar__0__C__10703 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__10706,Vvar__0__C__10707,Vvar__1___24Anonymous__10708,Vvar__1___24Anonymous__10709,Vvar__2___24Anonymous__10710,Vvar__2___24Anonymous__10711] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__10706,Vvar__1___24Anonymous__10708,Vvar__2___24Anonymous__10710) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__10707,Vvar__1___24Anonymous__10709,Vvar__2___24Anonymous__10711)
=> ( Vvar__2___24Anonymous__10710 = Vvar__2___24Anonymous__10711
& Vvar__1___24Anonymous__10708 = Vvar__1___24Anonymous__10709
& Vvar__0__C__10706 = Vvar__0__C__10707 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__10698,Vvar__0__C__10699,Vvar__1___24Anonymous__10700,Vvar__1___24Anonymous__10701] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__10698,Vvar__1___24Anonymous__10700) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__10699,Vvar__1___24Anonymous__10701)
=> ( Vvar__1___24Anonymous__10700 = Vvar__1___24Anonymous__10701
& Vvar__0__C__10698 = Vvar__0__C__10699 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__10718,Vvar__0__C__10719,Vvar__1___24Anonymous__10720,Vvar__1___24Anonymous__10721,Vvar__2___24Anonymous__10722,Vvar__2___24Anonymous__10723] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__10718,Vvar__1___24Anonymous__10720,Vvar__2___24Anonymous__10722) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__10719,Vvar__1___24Anonymous__10721,Vvar__2___24Anonymous__10723)
=> ( Vvar__2___24Anonymous__10722 = Vvar__2___24Anonymous__10723
& Vvar__1___24Anonymous__10720 = Vvar__1___24Anonymous__10721
& Vvar__0__C__10718 = Vvar__0__C__10719 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__10724,Vvar__0__C__10725,Vvar__1___24Anonymous__10726,Vvar__1___24Anonymous__10727] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__10724,Vvar__1___24Anonymous__10726) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__10725,Vvar__1___24Anonymous__10727)
=> ( Vvar__1___24Anonymous__10726 = Vvar__1___24Anonymous__10727
& Vvar__0__C__10724 = Vvar__0__C__10725 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__10728,Vvar__0__C__10729,Vvar__1___24Anonymous__10730,Vvar__1___24Anonymous__10731,Vvar__2___24Anonymous__10732,Vvar__2___24Anonymous__10733] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__10728,Vvar__1___24Anonymous__10730,Vvar__2___24Anonymous__10732) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__10729,Vvar__1___24Anonymous__10731,Vvar__2___24Anonymous__10733)
=> ( Vvar__2___24Anonymous__10732 = Vvar__2___24Anonymous__10733
& Vvar__1___24Anonymous__10730 = Vvar__1___24Anonymous__10731
& Vvar__0__C__10728 = Vvar__0__C__10729 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__10712,Vvar__0__C__10713,Vvar__1___24Anonymous__10714,Vvar__1___24Anonymous__10715,Vvar__2___24Anonymous__10716,Vvar__2___24Anonymous__10717] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__10712,Vvar__1___24Anonymous__10714,Vvar__2___24Anonymous__10716) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__10713,Vvar__1___24Anonymous__10715,Vvar__2___24Anonymous__10717)
=> ( Vvar__2___24Anonymous__10716 = Vvar__2___24Anonymous__10717
& Vvar__1___24Anonymous__10714 = Vvar__1___24Anonymous__10715
& Vvar__0__C__10712 = Vvar__0__C__10713 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__956,Vvar__0__C__957,Vvar__1___24Anonymous__958,Vvar__1___24Anonymous__959,Vvar__2___24Anonymous__960,Vvar__2___24Anonymous__961,Vvar__3___24Anonymous__962,Vvar__3___24Anonymous__963] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__956,Vvar__1___24Anonymous__958,Vvar__2___24Anonymous__960,Vvar__3___24Anonymous__962) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__957,Vvar__1___24Anonymous__959,Vvar__2___24Anonymous__961,Vvar__3___24Anonymous__963)
=> ( Vvar__3___24Anonymous__962 = Vvar__3___24Anonymous__963
& Vvar__2___24Anonymous__960 = Vvar__2___24Anonymous__961
& Vvar__1___24Anonymous__958 = Vvar__1___24Anonymous__959
& Vvar__0__C__956 = Vvar__0__C__957 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__946,Vvar__0__C__947,Vvar__1___24Anonymous__948,Vvar__1___24Anonymous__949] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__946,Vvar__1___24Anonymous__948) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__947,Vvar__1___24Anonymous__949)
=> ( Vvar__1___24Anonymous__948 = Vvar__1___24Anonymous__949
& Vvar__0__C__946 = Vvar__0__C__947 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__950,Vvar__0__C__951,Vvar__1___24Anonymous__952,Vvar__1___24Anonymous__953,Vvar__2___24Anonymous__954,Vvar__2___24Anonymous__955] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__950,Vvar__1___24Anonymous__952,Vvar__2___24Anonymous__954) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__951,Vvar__1___24Anonymous__953,Vvar__2___24Anonymous__955)
=> ( Vvar__2___24Anonymous__954 = Vvar__2___24Anonymous__955
& Vvar__1___24Anonymous__952 = Vvar__1___24Anonymous__953
& Vvar__0__C__950 = Vvar__0__C__951 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__10496,Vvar__0___24Anonymous__10497,Vvar__1___24Anonymous__10498,Vvar__1___24Anonymous__10499] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__10496,Vvar__1___24Anonymous__10498) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__10497,Vvar__1___24Anonymous__10499)
=> ( Vvar__1___24Anonymous__10498 = Vvar__1___24Anonymous__10499
& Vvar__0___24Anonymous__10496 = Vvar__0___24Anonymous__10497 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__10492,Vvar__0___24Anonymous__10493,Vvar__1___24Anonymous__10494,Vvar__1___24Anonymous__10495] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__10492,Vvar__1___24Anonymous__10494) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__10493,Vvar__1___24Anonymous__10495)
=> ( Vvar__1___24Anonymous__10494 = Vvar__1___24Anonymous__10495
& Vvar__0___24Anonymous__10492 = Vvar__0___24Anonymous__10493 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__30000,Vvar__0__R__30001,Vvar__1__req__30002,Vvar__1__req__30003,Vvar__2__reqb__30004,Vvar__2__reqb__30005,Vvar__3___24Anonymous__30006,Vvar__3___24Anonymous__30007] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__30000,Vvar__1__req__30002,Vvar__2__reqb__30004) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__30001,Vvar__1__req__30003,Vvar__2__reqb__30005)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__30004 = Vvar__2__reqb__30005
& Vvar__1__req__30002 = Vvar__1__req__30003
& Vvar__0__R__30000 = Vvar__0__R__30001 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__30008,Vvar__0__R__30009,Vvar__1__rO__30010,Vvar__1__rO__30011,Vvar__2__rI__30012,Vvar__2__rI__30013,Vvar__3__radd__30014,Vvar__3__radd__30015,Vvar__4__rmul__30016,Vvar__4__rmul__30017,Vvar__5__rsub__30018,Vvar__5__rsub__30019,Vvar__6__ropp__30020,Vvar__6__ropp__30021,Vvar__7__req__30022,Vvar__7__req__30023,Vvar__8__C__30024,Vvar__8__C__30025,Vvar__9__cO__30026,Vvar__9__cO__30027,Vvar__10__cI__30028,Vvar__10__cI__30029,Vvar__11__cadd__30030,Vvar__11__cadd__30031,Vvar__12__cmul__30032,Vvar__12__cmul__30033,Vvar__13__csub__30034,Vvar__13__csub__30035,Vvar__14__copp__30036,Vvar__14__copp__30037,Vvar__15__ceqb__30038,Vvar__15__ceqb__30039,Vvar__16__phi__30040,Vvar__16__phi__30041,Vvar__17___24Anonymous__30042,Vvar__17___24Anonymous__30043] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__30008,Vvar__1__rO__30010,Vvar__2__rI__30012,Vvar__3__radd__30014,Vvar__4__rmul__30016,Vvar__5__rsub__30018,Vvar__6__ropp__30020,Vvar__7__req__30022,Vvar__8__C__30024,Vvar__9__cO__30026,Vvar__10__cI__30028,Vvar__11__cadd__30030,Vvar__12__cmul__30032,Vvar__13__csub__30034,Vvar__14__copp__30036,Vvar__15__ceqb__30038,Vvar__16__phi__30040) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__30009,Vvar__1__rO__30011,Vvar__2__rI__30013,Vvar__3__radd__30015,Vvar__4__rmul__30017,Vvar__5__rsub__30019,Vvar__6__ropp__30021,Vvar__7__req__30023,Vvar__8__C__30025,Vvar__9__cO__30027,Vvar__10__cI__30029,Vvar__11__cadd__30031,Vvar__12__cmul__30033,Vvar__13__csub__30035,Vvar__14__copp__30037,Vvar__15__ceqb__30039,Vvar__16__phi__30041)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__30040 = Vvar__16__phi__30041
& Vvar__15__ceqb__30038 = Vvar__15__ceqb__30039
& Vvar__14__copp__30036 = Vvar__14__copp__30037
& Vvar__13__csub__30034 = Vvar__13__csub__30035
& Vvar__12__cmul__30032 = Vvar__12__cmul__30033
& Vvar__11__cadd__30030 = Vvar__11__cadd__30031
& Vvar__10__cI__30028 = Vvar__10__cI__30029
& Vvar__9__cO__30026 = Vvar__9__cO__30027
& Vvar__8__C__30024 = Vvar__8__C__30025
& Vvar__7__req__30022 = Vvar__7__req__30023
& Vvar__6__ropp__30020 = Vvar__6__ropp__30021
& Vvar__5__rsub__30018 = Vvar__5__rsub__30019
& Vvar__4__rmul__30016 = Vvar__4__rmul__30017
& Vvar__3__radd__30014 = Vvar__3__radd__30015
& Vvar__2__rI__30012 = Vvar__2__rI__30013
& Vvar__1__rO__30010 = Vvar__1__rO__30011
& Vvar__0__R__30008 = Vvar__0__R__30009 ) ) ).
fof('$_inj_hahn.HahnBase.Equality.Mixin',axiom,
! [Vvar__0__T__30660,Vvar__0__T__30661,Vvar__1__op__30662,Vvar__1__op__30663,Vvar__2___24Anonymous__30664,Vvar__2___24Anonymous__30665] :
( chahn_2eHahnBase_2eEquality_2eMixin___24a3(Vvar__0__T__30660,Vvar__1__op__30662,Vvar__2___24Anonymous__30664) = chahn_2eHahnBase_2eEquality_2eMixin___24a3(Vvar__0__T__30661,Vvar__1__op__30663,Vvar__2___24Anonymous__30665)
=> ( Vvar__2___24Anonymous__30664 = Vvar__2___24Anonymous__30665
& Vvar__1__op__30662 = Vvar__1__op__30663
& Vvar__0__T__30660 = Vvar__0__T__30661 ) ) ).
fof('$_inj_hahn.HahnBase.Equality.Pack',axiom,
! [Vvar__0__sort__30670,Vvar__0__sort__30671,Vvar__1___24Anonymous__30672,Vvar__1___24Anonymous__30673,Vvar__2___24Anonymous__30674,Vvar__2___24Anonymous__30675] :
( chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__30670,Vvar__1___24Anonymous__30672,Vvar__2___24Anonymous__30674) = chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__30671,Vvar__1___24Anonymous__30673,Vvar__2___24Anonymous__30675)
=> ( Vvar__2___24Anonymous__30674 = Vvar__2___24Anonymous__30675
& Vvar__1___24Anonymous__30672 = Vvar__1___24Anonymous__30673
& Vvar__0__sort__30670 = Vvar__0__sort__30671 ) ) ).
fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
! [Vvar__0__P__18249,Vvar__1__Q__18251,Vvar__2__init__18254,Vvar__3___24Anonymous__18255,Vvar__4___24Anonymous__18256] :
( c_24__type__18282___24t(Vvar__0__P__18249,Vvar__1__Q__18251,Vvar__2__init__18254,Vvar__3___24Anonymous__18255,Vvar__4___24Anonymous__18256,Vvar__0__P__18249)
=> ( c_24__type__18290___24t(Vvar__0__P__18249,Vvar__1__Q__18251,Vvar__2__init__18254,Vvar__3___24Anonymous__18255,Vvar__4___24Anonymous__18256,Vvar__1__Q__18251)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__18254)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__18255)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__18256)
=> ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__18249,Vvar__1__Q__18251,Vvar__2__init__18254,Vvar__3___24Anonymous__18255,Vvar__4___24Anonymous__18256)
=> ( ( Vvar__4___24Anonymous__18256 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__3___24Anonymous__18255 = Vvar__2__init__18254 )
| ? [Vvar__3__k__18270] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__18270)
& ? [Vvar__4__l__18271] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__18271)
& ? [Vvar__5__n__18272] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__18272)
& cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__18249,Vvar__1__Q__18251,Vvar__2__init__18254,Vvar__3__k__18270,Vvar__5__n__18272)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__18249,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__18270),Vvar__4__l__18271)
& p(happ(Vvar__1__Q__18251,Vvar__4__l__18271))
& Vvar__4___24Anonymous__18256 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__18272)
& Vvar__3___24Anonymous__18255 = Vvar__4__l__18271 ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__18209,Vvar__1__k__18211,Vvar__2___24Anonymous__18212] :
( c_24__type__18226___24t(Vvar__0__P__18209,Vvar__1__k__18211,Vvar__2___24Anonymous__18212,Vvar__0__P__18209)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__18211)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__18212)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__18209,Vvar__1__k__18211,Vvar__2___24Anonymous__18212)
=> ( Vvar__2___24Anonymous__18212 = Vvar__1__k__18211
| ? [Vvar__2__l__18220] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__18220)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__18209,Vvar__1__k__18211,Vvar__2__l__18220)
& p(happ(Vvar__0__P__18209,Vvar__2__l__18220))
& Vvar__2___24Anonymous__18212 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__18220) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__18228,Vvar__1__k__18230,Vvar__2___24Anonymous__18231] :
( c_24__type__18247___24t(Vvar__0__Q__18228,Vvar__1__k__18230,Vvar__2___24Anonymous__18231,Vvar__0__Q__18228)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__18230)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__18231)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__18228,Vvar__1__k__18230,Vvar__2___24Anonymous__18231)
=> ( ? [Vvar__2__l__18236] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__18236)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__18228,Vvar__1__k__18230,Vvar__2__l__18236)
& Vvar__2___24Anonymous__18231 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__18236) )
| ? [Vvar__2__l__18241] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__18241)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__18230,Vvar__2__l__18241)
& p(happ(Vvar__0__Q__18228,Vvar__2__l__18241))
& Vvar__2___24Anonymous__18231 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__18241) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__6568] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6568)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__6568)
=> ( Vvar__0___24Anonymous__6568 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__6570] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__6570)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__6570)
& Vvar__0___24Anonymous__6568 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__6570) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__6572] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6572)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__6572)
=> ? [Vvar__0__n__6574] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__6574)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__6574)
& Vvar__0___24Anonymous__6572 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__6574) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__4997,Vvar__1___24Anonymous__4998,VX4999] :
( cProp___24t(Vvar__0__P__4997)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__4998)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__4997,Vvar__1___24Anonymous__4998,VX4999)
=> ( ( p(Vvar__0__P__4997)
& Vvar__1___24Anonymous__4998 = cCoq_2eInit_2eDatatypes_2etrue
& VX4999 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__4997) )
| ( ~ p(Vvar__0__P__4997)
& Vvar__1___24Anonymous__4998 = cCoq_2eInit_2eDatatypes_2efalse
& VX4999 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__4997) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
! [Vvar__0___24Anonymous__16574,Vvar__1___24Anonymous__16575,Vvar__2___24Anonymous__16576] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__16574)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__16575)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__16576)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__16574,Vvar__1___24Anonymous__16575,Vvar__2___24Anonymous__16576)
=> ( ? [Vvar__0__x__16578] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__16578)
& Vvar__2___24Anonymous__16576 = Vvar__0__x__16578
& Vvar__1___24Anonymous__16575 = Vvar__0__x__16578
& Vvar__0___24Anonymous__16574 = Vvar__0__x__16578 )
| ? [Vvar__0__x__16579] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__16579)
& Vvar__2___24Anonymous__16576 = Vvar__0__x__16579
& Vvar__1___24Anonymous__16575 = cCoq_2eInit_2eDatatypes_2eEq
& Vvar__0___24Anonymous__16574 = Vvar__0__x__16579 )
| ? [Vvar__0__x__16580] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__16580)
& Vvar__2___24Anonymous__16576 = Vvar__0__x__16580
& Vvar__1___24Anonymous__16575 = Vvar__0__x__16580
& Vvar__0___24Anonymous__16574 = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0__x__16581] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__16581)
& Vvar__2___24Anonymous__16576 = Vvar__0__x__16581
& Vvar__1___24Anonymous__16575 = cCoq_2eInit_2eDatatypes_2eLt
& Vvar__0___24Anonymous__16574 = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0__x__16582] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__16582)
& Vvar__2___24Anonymous__16576 = Vvar__0__x__16582
& Vvar__1___24Anonymous__16575 = cCoq_2eInit_2eDatatypes_2eGt
& Vvar__0___24Anonymous__16574 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX16368] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX16368)
=> ( VX16368 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__16369] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__16369)
& ? [Vvar__1___24Anonymous__16370] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__16370)
& ? [Vvar__2___24Anonymous__16371] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__16371)
& VX16368 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__16369,Vvar__1___24Anonymous__16370,Vvar__2___24Anonymous__16371) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX5027] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX5027)
=> ( VX5027 = cCoq_2eInit_2eByte_2ex00
| VX5027 = cCoq_2eInit_2eByte_2ex01
| VX5027 = cCoq_2eInit_2eByte_2ex02
| VX5027 = cCoq_2eInit_2eByte_2ex03
| VX5027 = cCoq_2eInit_2eByte_2ex04
| VX5027 = cCoq_2eInit_2eByte_2ex05
| VX5027 = cCoq_2eInit_2eByte_2ex06
| VX5027 = cCoq_2eInit_2eByte_2ex07
| VX5027 = cCoq_2eInit_2eByte_2ex08
| VX5027 = cCoq_2eInit_2eByte_2ex09
| VX5027 = cCoq_2eInit_2eByte_2ex0a
| VX5027 = cCoq_2eInit_2eByte_2ex0b
| VX5027 = cCoq_2eInit_2eByte_2ex0c
| VX5027 = cCoq_2eInit_2eByte_2ex0d
| VX5027 = cCoq_2eInit_2eByte_2ex0e
| VX5027 = cCoq_2eInit_2eByte_2ex0f
| VX5027 = cCoq_2eInit_2eByte_2ex10
| VX5027 = cCoq_2eInit_2eByte_2ex11
| VX5027 = cCoq_2eInit_2eByte_2ex12
| VX5027 = cCoq_2eInit_2eByte_2ex13
| VX5027 = cCoq_2eInit_2eByte_2ex14
| VX5027 = cCoq_2eInit_2eByte_2ex15
| VX5027 = cCoq_2eInit_2eByte_2ex16
| VX5027 = cCoq_2eInit_2eByte_2ex17
| VX5027 = cCoq_2eInit_2eByte_2ex18
| VX5027 = cCoq_2eInit_2eByte_2ex19
| VX5027 = cCoq_2eInit_2eByte_2ex1a
| VX5027 = cCoq_2eInit_2eByte_2ex1b
| VX5027 = cCoq_2eInit_2eByte_2ex1c
| VX5027 = cCoq_2eInit_2eByte_2ex1d
| VX5027 = cCoq_2eInit_2eByte_2ex1e
| VX5027 = cCoq_2eInit_2eByte_2ex1f
| VX5027 = cCoq_2eInit_2eByte_2ex20
| VX5027 = cCoq_2eInit_2eByte_2ex21
| VX5027 = cCoq_2eInit_2eByte_2ex22
| VX5027 = cCoq_2eInit_2eByte_2ex23
| VX5027 = cCoq_2eInit_2eByte_2ex24
| VX5027 = cCoq_2eInit_2eByte_2ex25
| VX5027 = cCoq_2eInit_2eByte_2ex26
| VX5027 = cCoq_2eInit_2eByte_2ex27
| VX5027 = cCoq_2eInit_2eByte_2ex28
| VX5027 = cCoq_2eInit_2eByte_2ex29
| VX5027 = cCoq_2eInit_2eByte_2ex2a
| VX5027 = cCoq_2eInit_2eByte_2ex2b
| VX5027 = cCoq_2eInit_2eByte_2ex2c
| VX5027 = cCoq_2eInit_2eByte_2ex2d
| VX5027 = cCoq_2eInit_2eByte_2ex2e
| VX5027 = cCoq_2eInit_2eByte_2ex2f
| VX5027 = cCoq_2eInit_2eByte_2ex30
| VX5027 = cCoq_2eInit_2eByte_2ex31
| VX5027 = cCoq_2eInit_2eByte_2ex32
| VX5027 = cCoq_2eInit_2eByte_2ex33
| VX5027 = cCoq_2eInit_2eByte_2ex34
| VX5027 = cCoq_2eInit_2eByte_2ex35
| VX5027 = cCoq_2eInit_2eByte_2ex36
| VX5027 = cCoq_2eInit_2eByte_2ex37
| VX5027 = cCoq_2eInit_2eByte_2ex38
| VX5027 = cCoq_2eInit_2eByte_2ex39
| VX5027 = cCoq_2eInit_2eByte_2ex3a
| VX5027 = cCoq_2eInit_2eByte_2ex3b
| VX5027 = cCoq_2eInit_2eByte_2ex3c
| VX5027 = cCoq_2eInit_2eByte_2ex3d
| VX5027 = cCoq_2eInit_2eByte_2ex3e
| VX5027 = cCoq_2eInit_2eByte_2ex3f
| VX5027 = cCoq_2eInit_2eByte_2ex40
| VX5027 = cCoq_2eInit_2eByte_2ex41
| VX5027 = cCoq_2eInit_2eByte_2ex42
| VX5027 = cCoq_2eInit_2eByte_2ex43
| VX5027 = cCoq_2eInit_2eByte_2ex44
| VX5027 = cCoq_2eInit_2eByte_2ex45
| VX5027 = cCoq_2eInit_2eByte_2ex46
| VX5027 = cCoq_2eInit_2eByte_2ex47
| VX5027 = cCoq_2eInit_2eByte_2ex48
| VX5027 = cCoq_2eInit_2eByte_2ex49
| VX5027 = cCoq_2eInit_2eByte_2ex4a
| VX5027 = cCoq_2eInit_2eByte_2ex4b
| VX5027 = cCoq_2eInit_2eByte_2ex4c
| VX5027 = cCoq_2eInit_2eByte_2ex4d
| VX5027 = cCoq_2eInit_2eByte_2ex4e
| VX5027 = cCoq_2eInit_2eByte_2ex4f
| VX5027 = cCoq_2eInit_2eByte_2ex50
| VX5027 = cCoq_2eInit_2eByte_2ex51
| VX5027 = cCoq_2eInit_2eByte_2ex52
| VX5027 = cCoq_2eInit_2eByte_2ex53
| VX5027 = cCoq_2eInit_2eByte_2ex54
| VX5027 = cCoq_2eInit_2eByte_2ex55
| VX5027 = cCoq_2eInit_2eByte_2ex56
| VX5027 = cCoq_2eInit_2eByte_2ex57
| VX5027 = cCoq_2eInit_2eByte_2ex58
| VX5027 = cCoq_2eInit_2eByte_2ex59
| VX5027 = cCoq_2eInit_2eByte_2ex5a
| VX5027 = cCoq_2eInit_2eByte_2ex5b
| VX5027 = cCoq_2eInit_2eByte_2ex5c
| VX5027 = cCoq_2eInit_2eByte_2ex5d
| VX5027 = cCoq_2eInit_2eByte_2ex5e
| VX5027 = cCoq_2eInit_2eByte_2ex5f
| VX5027 = cCoq_2eInit_2eByte_2ex60
| VX5027 = cCoq_2eInit_2eByte_2ex61
| VX5027 = cCoq_2eInit_2eByte_2ex62
| VX5027 = cCoq_2eInit_2eByte_2ex63
| VX5027 = cCoq_2eInit_2eByte_2ex64
| VX5027 = cCoq_2eInit_2eByte_2ex65
| VX5027 = cCoq_2eInit_2eByte_2ex66
| VX5027 = cCoq_2eInit_2eByte_2ex67
| VX5027 = cCoq_2eInit_2eByte_2ex68
| VX5027 = cCoq_2eInit_2eByte_2ex69
| VX5027 = cCoq_2eInit_2eByte_2ex6a
| VX5027 = cCoq_2eInit_2eByte_2ex6b
| VX5027 = cCoq_2eInit_2eByte_2ex6c
| VX5027 = cCoq_2eInit_2eByte_2ex6d
| VX5027 = cCoq_2eInit_2eByte_2ex6e
| VX5027 = cCoq_2eInit_2eByte_2ex6f
| VX5027 = cCoq_2eInit_2eByte_2ex70
| VX5027 = cCoq_2eInit_2eByte_2ex71
| VX5027 = cCoq_2eInit_2eByte_2ex72
| VX5027 = cCoq_2eInit_2eByte_2ex73
| VX5027 = cCoq_2eInit_2eByte_2ex74
| VX5027 = cCoq_2eInit_2eByte_2ex75
| VX5027 = cCoq_2eInit_2eByte_2ex76
| VX5027 = cCoq_2eInit_2eByte_2ex77
| VX5027 = cCoq_2eInit_2eByte_2ex78
| VX5027 = cCoq_2eInit_2eByte_2ex79
| VX5027 = cCoq_2eInit_2eByte_2ex7a
| VX5027 = cCoq_2eInit_2eByte_2ex7b
| VX5027 = cCoq_2eInit_2eByte_2ex7c
| VX5027 = cCoq_2eInit_2eByte_2ex7d
| VX5027 = cCoq_2eInit_2eByte_2ex7e
| VX5027 = cCoq_2eInit_2eByte_2ex7f
| VX5027 = cCoq_2eInit_2eByte_2ex80
| VX5027 = cCoq_2eInit_2eByte_2ex81
| VX5027 = cCoq_2eInit_2eByte_2ex82
| VX5027 = cCoq_2eInit_2eByte_2ex83
| VX5027 = cCoq_2eInit_2eByte_2ex84
| VX5027 = cCoq_2eInit_2eByte_2ex85
| VX5027 = cCoq_2eInit_2eByte_2ex86
| VX5027 = cCoq_2eInit_2eByte_2ex87
| VX5027 = cCoq_2eInit_2eByte_2ex88
| VX5027 = cCoq_2eInit_2eByte_2ex89
| VX5027 = cCoq_2eInit_2eByte_2ex8a
| VX5027 = cCoq_2eInit_2eByte_2ex8b
| VX5027 = cCoq_2eInit_2eByte_2ex8c
| VX5027 = cCoq_2eInit_2eByte_2ex8d
| VX5027 = cCoq_2eInit_2eByte_2ex8e
| VX5027 = cCoq_2eInit_2eByte_2ex8f
| VX5027 = cCoq_2eInit_2eByte_2ex90
| VX5027 = cCoq_2eInit_2eByte_2ex91
| VX5027 = cCoq_2eInit_2eByte_2ex92
| VX5027 = cCoq_2eInit_2eByte_2ex93
| VX5027 = cCoq_2eInit_2eByte_2ex94
| VX5027 = cCoq_2eInit_2eByte_2ex95
| VX5027 = cCoq_2eInit_2eByte_2ex96
| VX5027 = cCoq_2eInit_2eByte_2ex97
| VX5027 = cCoq_2eInit_2eByte_2ex98
| VX5027 = cCoq_2eInit_2eByte_2ex99
| VX5027 = cCoq_2eInit_2eByte_2ex9a
| VX5027 = cCoq_2eInit_2eByte_2ex9b
| VX5027 = cCoq_2eInit_2eByte_2ex9c
| VX5027 = cCoq_2eInit_2eByte_2ex9d
| VX5027 = cCoq_2eInit_2eByte_2ex9e
| VX5027 = cCoq_2eInit_2eByte_2ex9f
| VX5027 = cCoq_2eInit_2eByte_2exa0
| VX5027 = cCoq_2eInit_2eByte_2exa1
| VX5027 = cCoq_2eInit_2eByte_2exa2
| VX5027 = cCoq_2eInit_2eByte_2exa3
| VX5027 = cCoq_2eInit_2eByte_2exa4
| VX5027 = cCoq_2eInit_2eByte_2exa5
| VX5027 = cCoq_2eInit_2eByte_2exa6
| VX5027 = cCoq_2eInit_2eByte_2exa7
| VX5027 = cCoq_2eInit_2eByte_2exa8
| VX5027 = cCoq_2eInit_2eByte_2exa9
| VX5027 = cCoq_2eInit_2eByte_2exaa
| VX5027 = cCoq_2eInit_2eByte_2exab
| VX5027 = cCoq_2eInit_2eByte_2exac
| VX5027 = cCoq_2eInit_2eByte_2exad
| VX5027 = cCoq_2eInit_2eByte_2exae
| VX5027 = cCoq_2eInit_2eByte_2exaf
| VX5027 = cCoq_2eInit_2eByte_2exb0
| VX5027 = cCoq_2eInit_2eByte_2exb1
| VX5027 = cCoq_2eInit_2eByte_2exb2
| VX5027 = cCoq_2eInit_2eByte_2exb3
| VX5027 = cCoq_2eInit_2eByte_2exb4
| VX5027 = cCoq_2eInit_2eByte_2exb5
| VX5027 = cCoq_2eInit_2eByte_2exb6
| VX5027 = cCoq_2eInit_2eByte_2exb7
| VX5027 = cCoq_2eInit_2eByte_2exb8
| VX5027 = cCoq_2eInit_2eByte_2exb9
| VX5027 = cCoq_2eInit_2eByte_2exba
| VX5027 = cCoq_2eInit_2eByte_2exbb
| VX5027 = cCoq_2eInit_2eByte_2exbc
| VX5027 = cCoq_2eInit_2eByte_2exbd
| VX5027 = cCoq_2eInit_2eByte_2exbe
| VX5027 = cCoq_2eInit_2eByte_2exbf
| VX5027 = cCoq_2eInit_2eByte_2exc0
| VX5027 = cCoq_2eInit_2eByte_2exc1
| VX5027 = cCoq_2eInit_2eByte_2exc2
| VX5027 = cCoq_2eInit_2eByte_2exc3
| VX5027 = cCoq_2eInit_2eByte_2exc4
| VX5027 = cCoq_2eInit_2eByte_2exc5
| VX5027 = cCoq_2eInit_2eByte_2exc6
| VX5027 = cCoq_2eInit_2eByte_2exc7
| VX5027 = cCoq_2eInit_2eByte_2exc8
| VX5027 = cCoq_2eInit_2eByte_2exc9
| VX5027 = cCoq_2eInit_2eByte_2exca
| VX5027 = cCoq_2eInit_2eByte_2excb
| VX5027 = cCoq_2eInit_2eByte_2excc
| VX5027 = cCoq_2eInit_2eByte_2excd
| VX5027 = cCoq_2eInit_2eByte_2exce
| VX5027 = cCoq_2eInit_2eByte_2excf
| VX5027 = cCoq_2eInit_2eByte_2exd0
| VX5027 = cCoq_2eInit_2eByte_2exd1
| VX5027 = cCoq_2eInit_2eByte_2exd2
| VX5027 = cCoq_2eInit_2eByte_2exd3
| VX5027 = cCoq_2eInit_2eByte_2exd4
| VX5027 = cCoq_2eInit_2eByte_2exd5
| VX5027 = cCoq_2eInit_2eByte_2exd6
| VX5027 = cCoq_2eInit_2eByte_2exd7
| VX5027 = cCoq_2eInit_2eByte_2exd8
| VX5027 = cCoq_2eInit_2eByte_2exd9
| VX5027 = cCoq_2eInit_2eByte_2exda
| VX5027 = cCoq_2eInit_2eByte_2exdb
| VX5027 = cCoq_2eInit_2eByte_2exdc
| VX5027 = cCoq_2eInit_2eByte_2exdd
| VX5027 = cCoq_2eInit_2eByte_2exde
| VX5027 = cCoq_2eInit_2eByte_2exdf
| VX5027 = cCoq_2eInit_2eByte_2exe0
| VX5027 = cCoq_2eInit_2eByte_2exe1
| VX5027 = cCoq_2eInit_2eByte_2exe2
| VX5027 = cCoq_2eInit_2eByte_2exe3
| VX5027 = cCoq_2eInit_2eByte_2exe4
| VX5027 = cCoq_2eInit_2eByte_2exe5
| VX5027 = cCoq_2eInit_2eByte_2exe6
| VX5027 = cCoq_2eInit_2eByte_2exe7
| VX5027 = cCoq_2eInit_2eByte_2exe8
| VX5027 = cCoq_2eInit_2eByte_2exe9
| VX5027 = cCoq_2eInit_2eByte_2exea
| VX5027 = cCoq_2eInit_2eByte_2exeb
| VX5027 = cCoq_2eInit_2eByte_2exec
| VX5027 = cCoq_2eInit_2eByte_2exed
| VX5027 = cCoq_2eInit_2eByte_2exee
| VX5027 = cCoq_2eInit_2eByte_2exef
| VX5027 = cCoq_2eInit_2eByte_2exf0
| VX5027 = cCoq_2eInit_2eByte_2exf1
| VX5027 = cCoq_2eInit_2eByte_2exf2
| VX5027 = cCoq_2eInit_2eByte_2exf3
| VX5027 = cCoq_2eInit_2eByte_2exf4
| VX5027 = cCoq_2eInit_2eByte_2exf5
| VX5027 = cCoq_2eInit_2eByte_2exf6
| VX5027 = cCoq_2eInit_2eByte_2exf7
| VX5027 = cCoq_2eInit_2eByte_2exf8
| VX5027 = cCoq_2eInit_2eByte_2exf9
| VX5027 = cCoq_2eInit_2eByte_2exfa
| VX5027 = cCoq_2eInit_2eByte_2exfb
| VX5027 = cCoq_2eInit_2eByte_2exfc
| VX5027 = cCoq_2eInit_2eByte_2exfd
| VX5027 = cCoq_2eInit_2eByte_2exfe
| VX5027 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__5735,Vvar__1__Q__5736,Vvar__2___24Anonymous__5737] :
( cProp___24t(Vvar__0__P__5735)
=> ( cProp___24t(Vvar__1__Q__5736)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__5737)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__5735,Vvar__1__Q__5736,Vvar__2___24Anonymous__5737)
=> ( ( p(Vvar__0__P__5735)
& Vvar__2___24Anonymous__5737 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__5736)
& Vvar__2___24Anonymous__5737 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__5868,Vvar__1__Plt__5869,Vvar__2__Pgt__5870,Vvar__3___24Anonymous__5871] :
( cProp___24t(Vvar__0__Peq__5868)
=> ( cProp___24t(Vvar__1__Plt__5869)
=> ( cProp___24t(Vvar__2__Pgt__5870)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__5871)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__5868,Vvar__1__Plt__5869,Vvar__2__Pgt__5870,Vvar__3___24Anonymous__5871)
=> ( ( p(Vvar__0__Peq__5868)
& Vvar__3___24Anonymous__5871 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__5869)
& Vvar__3___24Anonymous__5871 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__5870)
& Vvar__3___24Anonymous__5871 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__18577,Vvar__1__Plt__18578,Vvar__2__Pgt__18579,Vvar__3___24Anonymous__18580,VX18581] :
( cProp___24t(Vvar__0__Peq__18577)
=> ( cProp___24t(Vvar__1__Plt__18578)
=> ( cProp___24t(Vvar__2__Pgt__18579)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__18580)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__18577,Vvar__1__Plt__18578,Vvar__2__Pgt__18579,Vvar__3___24Anonymous__18580,VX18581)
=> ( ( p(Vvar__0__Peq__18577)
& Vvar__3___24Anonymous__18580 = cCoq_2eInit_2eDatatypes_2eEq
& VX18581 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__18577,Vvar__1__Plt__18578,Vvar__2__Pgt__18579) )
| ( p(Vvar__1__Plt__18578)
& Vvar__3___24Anonymous__18580 = cCoq_2eInit_2eDatatypes_2eLt
& VX18581 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__18577,Vvar__1__Plt__18578,Vvar__2__Pgt__18579) )
| ( p(Vvar__2__Pgt__18579)
& Vvar__3___24Anonymous__18580 = cCoq_2eInit_2eDatatypes_2eGt
& VX18581 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__18577,Vvar__1__Plt__18578,Vvar__2__Pgt__18579) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX777] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX777)
=> ( VX777 = cCoq_2eInit_2eDatatypes_2etrue
| VX777 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX5865] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX5865)
=> ( VX5865 = cCoq_2eInit_2eDatatypes_2eEq
| VX5865 = cCoq_2eInit_2eDatatypes_2eLt
| VX5865 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
! [Vvar__0___24Anonymous__18513] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__18513)
=> ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__18513)
=> Vvar__0___24Anonymous__18513 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
! [Vvar__0__A__18650,Vvar__1__a__18651,Vvar__2___24Anonymous__18652] :
( cType___24t(Vvar__0__A__18650)
=> ( t(Vvar__1__a__18651,Vvar__0__A__18650)
=> ( t(Vvar__2___24Anonymous__18652,Vvar__0__A__18650)
=> ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__18650,Vvar__1__a__18651,Vvar__2___24Anonymous__18652)
=> Vvar__2___24Anonymous__18652 = Vvar__1__a__18651 ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__783,VX784] :
( cType___24t(Vvar__0__A__783)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__783,VX784)
=> ( VX784 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__783)
| ? [Vvar__1___24Anonymous__787] :
( t(Vvar__1___24Anonymous__787,Vvar__0__A__783)
& ? [Vvar__2___24Anonymous__788] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__783,Vvar__2___24Anonymous__788)
& VX784 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__783,Vvar__1___24Anonymous__787,Vvar__2___24Anonymous__788) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX1)
=> ( VX1 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2)
& VX1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__5745,VX5746] :
( cType___24t(Vvar__0__A__5745)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__5745,VX5746)
=> ( ? [Vvar__1___24Anonymous__5748] :
( t(Vvar__1___24Anonymous__5748,Vvar__0__A__5745)
& VX5746 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__5745,Vvar__1___24Anonymous__5748) )
| VX5746 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__5745) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__5764,Vvar__1__B__5765,VX5766] :
( cType___24t(Vvar__0__A__5764)
=> ( cType___24t(Vvar__1__B__5765)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__5764,Vvar__1__B__5765,VX5766)
=> ? [Vvar__2___24Anonymous__5769] :
( t(Vvar__2___24Anonymous__5769,Vvar__0__A__5764)
& ? [Vvar__3___24Anonymous__5770] :
( t(Vvar__3___24Anonymous__5770,Vvar__1__B__5765)
& VX5766 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__5764,Vvar__1__B__5765,Vvar__2___24Anonymous__5769,Vvar__3___24Anonymous__5770) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__18515,Vvar__1__B__18516,VX18517] :
( cType___24t(Vvar__0__A__18515)
=> ( cType___24t(Vvar__1__B__18516)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__18515,Vvar__1__B__18516,VX18517)
=> ( ? [Vvar__2___24Anonymous__18520] :
( t(Vvar__2___24Anonymous__18520,Vvar__0__A__18515)
& VX18517 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__18515,Vvar__1__B__18516,Vvar__2___24Anonymous__18520) )
| ? [Vvar__2___24Anonymous__18523] :
( t(Vvar__2___24Anonymous__18523,Vvar__1__B__18516)
& VX18517 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__18515,Vvar__1__B__18516,Vvar__2___24Anonymous__18523) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX776] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX776)
=> VX776 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
! [VX18671] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(VX18671)
=> ( ? [Vvar__0__i__18672] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__18672)
& ? [Vvar__1__f__18673] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__18673)
& VX18671 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__18672,Vvar__1__f__18673) ) )
| ? [Vvar__0__i__18674] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__18674)
& ? [Vvar__1__f__18675] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__18675)
& ? [Vvar__2__e__18676] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__18676)
& VX18671 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__18674,Vvar__1__f__18675,Vvar__2__e__18676) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX18662] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX18662)
=> ( ? [Vvar__0__d__18663] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__18663)
& VX18662 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__18663) )
| ? [Vvar__0__d__18664] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__18664)
& VX18662 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__18664) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX17612] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX17612)
=> ( VX17612 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__17613] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__17613)
& VX17612 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__17613) )
| ? [Vvar__0___24Anonymous__17614] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__17614)
& VX17612 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__17614) )
| ? [Vvar__0___24Anonymous__17615] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__17615)
& VX17612 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__17615) )
| ? [Vvar__0___24Anonymous__17616] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__17616)
& VX17612 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__17616) )
| ? [Vvar__0___24Anonymous__17617] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__17617)
& VX17612 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__17617) )
| ? [Vvar__0___24Anonymous__17618] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__17618)
& VX17612 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__17618) )
| ? [Vvar__0___24Anonymous__17619] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__17619)
& VX17612 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__17619) )
| ? [Vvar__0___24Anonymous__17620] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__17620)
& VX17612 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__17620) )
| ? [Vvar__0___24Anonymous__17621] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__17621)
& VX17612 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__17621) )
| ? [Vvar__0___24Anonymous__17622] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__17622)
& VX17612 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__17622) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__853,Vvar__1___24Anonymous__854] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__853)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__854)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__853,Vvar__1___24Anonymous__854)
=> ( Vvar__1___24Anonymous__854 = Vvar__0__n__853
| ? [Vvar__1__m__858] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__858)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__853,Vvar__1__m__858)
& Vvar__1___24Anonymous__854 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__858) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__13997,Vvar__1__P__13998,VX14001] :
( cType___24t(Vvar__0__A__13997)
=> ( c_24__type__14011___24t(Vvar__0__A__13997,Vvar__1__P__13998,Vvar__1__P__13998)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__13997,Vvar__1__P__13998,VX14001)
=> ? [Vvar__2__x__14006] :
( t(Vvar__2__x__14006,Vvar__0__A__13997)
& p(happ(Vvar__1__P__13998,Vvar__2__x__14006))
& VX14001 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__13997,Vvar__1__P__13998,Vvar__2__x__14006) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__30320,Vvar__1__P__30321,Vvar__2__Q__30324,VX30327] :
( cType___24t(Vvar__0__A__30320)
=> ( c_24__type__30344___24t(Vvar__0__A__30320,Vvar__1__P__30321,Vvar__2__Q__30324,Vvar__1__P__30321)
=> ( c_24__type__30352___24t(Vvar__0__A__30320,Vvar__1__P__30321,Vvar__2__Q__30324,Vvar__2__Q__30324)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__30320,Vvar__1__P__30321,Vvar__2__Q__30324,VX30327)
=> ? [Vvar__3__x__30335] :
( t(Vvar__3__x__30335,Vvar__0__A__30320)
& p(happ(Vvar__1__P__30321,Vvar__3__x__30335))
& p(happ(Vvar__2__Q__30324,Vvar__3__x__30335))
& VX30327 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__30320,Vvar__1__P__30321,Vvar__2__Q__30324,Vvar__3__x__30335) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__18098,Vvar__1__P__18099,VX18102] :
( cType___24t(Vvar__0__A__18098)
=> ( c_24__type__18112___24t(Vvar__0__A__18098,Vvar__1__P__18099,Vvar__1__P__18099)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__18098,Vvar__1__P__18099,VX18102)
=> ? [Vvar__2__x__18107] :
( t(Vvar__2__x__18107,Vvar__0__A__18098)
& ? [Vvar__3___24Anonymous__18108] :
( t(Vvar__3___24Anonymous__18108,happ(Vvar__1__P__18099,Vvar__2__x__18107))
& VX18102 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__18098,Vvar__1__P__18099,Vvar__2__x__18107,Vvar__3___24Anonymous__18108) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__30386,Vvar__1__P__30387,Vvar__2__Q__30390,VX30393] :
( cType___24t(Vvar__0__A__30386)
=> ( c_24__type__30410___24t(Vvar__0__A__30386,Vvar__1__P__30387,Vvar__2__Q__30390,Vvar__1__P__30387)
=> ( c_24__type__30418___24t(Vvar__0__A__30386,Vvar__1__P__30387,Vvar__2__Q__30390,Vvar__2__Q__30390)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__30386,Vvar__1__P__30387,Vvar__2__Q__30390,VX30393)
=> ? [Vvar__3__x__30401] :
( t(Vvar__3__x__30401,Vvar__0__A__30386)
& ? [Vvar__4___24Anonymous__30402] :
( t(Vvar__4___24Anonymous__30402,happ(Vvar__1__P__30387,Vvar__3__x__30401))
& ? [Vvar__5___24Anonymous__30403] :
( t(Vvar__5___24Anonymous__30403,happ(Vvar__2__Q__30390,Vvar__3__x__30401))
& VX30393 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__30386,Vvar__1__P__30387,Vvar__2__Q__30390,Vvar__3__x__30401,Vvar__4___24Anonymous__30402,Vvar__5___24Anonymous__30403) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__14127,Vvar__1__B__14128,VX14129] :
( cProp___24t(Vvar__0__A__14127)
=> ( cProp___24t(Vvar__1__B__14128)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__14127,Vvar__1__B__14128,VX14129)
=> ( ( p(Vvar__0__A__14127)
& VX14129 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__14127,Vvar__1__B__14128) )
| ( p(Vvar__1__B__14128)
& VX14129 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__14127,Vvar__1__B__14128) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__18127,Vvar__1__B__18128,VX18129] :
( cType___24t(Vvar__0__A__18127)
=> ( cProp___24t(Vvar__1__B__18128)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__18127,Vvar__1__B__18128,VX18129)
=> ( ? [Vvar__2___24Anonymous__18132] :
( t(Vvar__2___24Anonymous__18132,Vvar__0__A__18127)
& VX18129 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__18127,Vvar__1__B__18128,Vvar__2___24Anonymous__18132) )
| ( p(Vvar__1__B__18128)
& VX18129 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__18127,Vvar__1__B__18128) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__18157,Vvar__1__R__18158,Vvar__2__x__18163] :
( cType___24t(Vvar__0__A__18157)
=> ( c_24__type__18192___24t(Vvar__0__A__18157,Vvar__1__R__18158,Vvar__2__x__18163,Vvar__1__R__18158)
=> ( t(Vvar__2__x__18163,Vvar__0__A__18157)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__18157,Vvar__1__R__18158,Vvar__2__x__18163)
=> ( ! [Vvar__var__var__var__var__3__y__18173__18175__18177__18179__18181] :
( t(Vvar__var__var__var__var__3__y__18173__18175__18177__18179__18181,Vvar__0__A__18157)
=> ( p(happ(happ(Vvar__1__R__18158,Vvar__var__var__var__var__3__y__18173__18175__18177__18179__18181),Vvar__2__x__18163))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__18157,Vvar__1__R__18158,Vvar__var__var__var__var__3__y__18173__18175__18177__18179__18181) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__20675,Vvar__1__a__20676,Vvar__2___24Anonymous__20677,Vvar__3___24Anonymous__20678] :
( cType___24t(Vvar__0__A__20675)
=> ( t(Vvar__1__a__20676,Vvar__0__A__20675)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__20675,Vvar__2___24Anonymous__20677)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__20675,Vvar__3___24Anonymous__20678)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__20675,Vvar__1__a__20676,Vvar__2___24Anonymous__20677,Vvar__3___24Anonymous__20678)
=> ( ? [Vvar__2__l__20682] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__20675,Vvar__2__l__20682)
& Vvar__3___24Anonymous__20678 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__20675,Vvar__1__a__20676,Vvar__2__l__20682)
& Vvar__2___24Anonymous__20677 = Vvar__2__l__20682 )
| ? [Vvar__2__x__20685] :
( t(Vvar__2__x__20685,Vvar__0__A__20675)
& ? [Vvar__3__l__20686] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__20675,Vvar__3__l__20686)
& ? [Vvar__4__l_27__20687] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__20675,Vvar__4__l_27__20687)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__20675,Vvar__1__a__20676,Vvar__3__l__20686,Vvar__4__l_27__20687)
& Vvar__3___24Anonymous__20678 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__20675,Vvar__2__x__20685,Vvar__4__l_27__20687)
& Vvar__2___24Anonymous__20677 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__20675,Vvar__2__x__20685,Vvar__3__l__20686) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__8724,Vvar__1__P__8725,Vvar__2___24Anonymous__8728] :
( cType___24t(Vvar__0__A__8724)
=> ( c_24__type__8748___24t(Vvar__0__A__8724,Vvar__1__P__8725,Vvar__2___24Anonymous__8728,Vvar__1__P__8725)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8724,Vvar__2___24Anonymous__8728)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__8724,Vvar__1__P__8725,Vvar__2___24Anonymous__8728)
=> ( ? [Vvar__2__x__8734] :
( t(Vvar__2__x__8734,Vvar__0__A__8724)
& ? [Vvar__3__l__8735] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8724,Vvar__3__l__8735)
& p(happ(Vvar__1__P__8725,Vvar__2__x__8734))
& Vvar__2___24Anonymous__8728 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8724,Vvar__2__x__8734,Vvar__3__l__8735) ) )
| ? [Vvar__2__x__8741] :
( t(Vvar__2__x__8741,Vvar__0__A__8724)
& ? [Vvar__3__l__8742] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8724,Vvar__3__l__8742)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__8724,Vvar__1__P__8725,Vvar__3__l__8742)
& Vvar__2___24Anonymous__8728 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8724,Vvar__2__x__8741,Vvar__3__l__8742) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__8751,Vvar__1__P__8752,Vvar__2___24Anonymous__8755] :
( cType___24t(Vvar__0__A__8751)
=> ( c_24__type__8773___24t(Vvar__0__A__8751,Vvar__1__P__8752,Vvar__2___24Anonymous__8755,Vvar__1__P__8752)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8751,Vvar__2___24Anonymous__8755)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__8751,Vvar__1__P__8752,Vvar__2___24Anonymous__8755)
=> ( Vvar__2___24Anonymous__8755 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__8751)
| ? [Vvar__2__x__8765] :
( t(Vvar__2__x__8765,Vvar__0__A__8751)
& ? [Vvar__3__l__8766] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8751,Vvar__3__l__8766)
& p(happ(Vvar__1__P__8752,Vvar__2__x__8765))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__8751,Vvar__1__P__8752,Vvar__3__l__8766)
& Vvar__2___24Anonymous__8755 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8751,Vvar__2__x__8765,Vvar__3__l__8766) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__20689,Vvar__1__B__20690,Vvar__2__R__20691,Vvar__3___24Anonymous__20696,Vvar__4___24Anonymous__20697] :
( cType___24t(Vvar__0__A__20689)
=> ( cType___24t(Vvar__1__B__20690)
=> ( c_24__type__20734___24t(Vvar__0__A__20689,Vvar__1__B__20690,Vvar__2__R__20691,Vvar__3___24Anonymous__20696,Vvar__4___24Anonymous__20697,Vvar__2__R__20691)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__20689,Vvar__3___24Anonymous__20696)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__20690,Vvar__4___24Anonymous__20697)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__20689,Vvar__1__B__20690,Vvar__2__R__20691,Vvar__3___24Anonymous__20696,Vvar__4___24Anonymous__20697)
=> ( ( Vvar__4___24Anonymous__20697 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__20690)
& Vvar__3___24Anonymous__20696 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__20689) )
| ? [Vvar__3__x__20713] :
( t(Vvar__3__x__20713,Vvar__0__A__20689)
& ? [Vvar__4__y__20714] :
( t(Vvar__4__y__20714,Vvar__1__B__20690)
& ? [Vvar__5__l__20715] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__20689,Vvar__5__l__20715)
& ? [Vvar__6__l_27__20716] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__20690,Vvar__6__l_27__20716)
& p(happ(happ(Vvar__2__R__20691,Vvar__3__x__20713),Vvar__4__y__20714))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__20689,Vvar__1__B__20690,Vvar__2__R__20691,Vvar__5__l__20715,Vvar__6__l_27__20716)
& Vvar__4___24Anonymous__20697 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__20690,Vvar__4__y__20714,Vvar__6__l_27__20716)
& Vvar__3___24Anonymous__20696 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__20689,Vvar__3__x__20713,Vvar__5__l__20715) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__20736,Vvar__1__R__20737,Vvar__2___24Anonymous__20742] :
( cType___24t(Vvar__0__A__20736)
=> ( c_24__type__20769___24t(Vvar__0__A__20736,Vvar__1__R__20737,Vvar__2___24Anonymous__20742,Vvar__1__R__20737)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__20736,Vvar__2___24Anonymous__20742)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__20736,Vvar__1__R__20737,Vvar__2___24Anonymous__20742)
=> ( Vvar__2___24Anonymous__20742 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__20736)
| ? [Vvar__2__a__20756] :
( t(Vvar__2__a__20756,Vvar__0__A__20736)
& ? [Vvar__3__l__20757] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__20736,Vvar__3__l__20757)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__20736,happ(Vvar__1__R__20737,Vvar__2__a__20756),Vvar__3__l__20757)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__20736,Vvar__1__R__20737,Vvar__3__l__20757)
& Vvar__2___24Anonymous__20742 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__20736,Vvar__2__a__20756,Vvar__3__l__20757) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__8713,Vvar__1___24Anonymous__8714] :
( cType___24t(Vvar__0__A__8713)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8713,Vvar__1___24Anonymous__8714)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__8713,Vvar__1___24Anonymous__8714)
=> ( Vvar__1___24Anonymous__8714 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__8713)
| ? [Vvar__1__x__8718] :
( t(Vvar__1__x__8718,Vvar__0__A__8713)
& ? [Vvar__2__l__8719] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8713,Vvar__2__l__8719)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__8713,Vvar__1__x__8718,Vvar__2__l__8719)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__8713,Vvar__2__l__8719)
& Vvar__1___24Anonymous__8714 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8713,Vvar__1__x__8718,Vvar__2__l__8719) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__13738,Vvar__1__eqA__13739,Vvar__2__x__13744,Vvar__3___24Anonymous__13745] :
( cType___24t(Vvar__0__A__13738)
=> ( c_24__type__13778___24t(Vvar__0__A__13738,Vvar__1__eqA__13739,Vvar__2__x__13744,Vvar__3___24Anonymous__13745,Vvar__1__eqA__13739)
=> ( t(Vvar__2__x__13744,Vvar__0__A__13738)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13738,Vvar__3___24Anonymous__13745)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__13738,Vvar__1__eqA__13739,Vvar__2__x__13744,Vvar__3___24Anonymous__13745)
=> ( ? [Vvar__3__y__13754] :
( t(Vvar__3__y__13754,Vvar__0__A__13738)
& ? [Vvar__4__l__13755] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13738,Vvar__4__l__13755)
& p(happ(happ(Vvar__1__eqA__13739,Vvar__2__x__13744),Vvar__3__y__13754))
& Vvar__3___24Anonymous__13745 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13738,Vvar__3__y__13754,Vvar__4__l__13755) ) )
| ? [Vvar__3__y__13764] :
( t(Vvar__3__y__13764,Vvar__0__A__13738)
& ? [Vvar__4__l__13765] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13738,Vvar__4__l__13765)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__13738,Vvar__1__eqA__13739,Vvar__2__x__13744,Vvar__4__l__13765)
& Vvar__3___24Anonymous__13745 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13738,Vvar__3__y__13764,Vvar__4__l__13765) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__13780,Vvar__1__eqA__13781,Vvar__2___24Anonymous__13786] :
( cType___24t(Vvar__0__A__13780)
=> ( c_24__type__13813___24t(Vvar__0__A__13780,Vvar__1__eqA__13781,Vvar__2___24Anonymous__13786,Vvar__1__eqA__13781)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13780,Vvar__2___24Anonymous__13786)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__13780,Vvar__1__eqA__13781,Vvar__2___24Anonymous__13786)
=> ( Vvar__2___24Anonymous__13786 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__13780)
| ? [Vvar__2__x__13800] :
( t(Vvar__2__x__13800,Vvar__0__A__13780)
& ? [Vvar__3__l__13801] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13780,Vvar__3__l__13801)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__13780,Vvar__1__eqA__13781,Vvar__2__x__13800,Vvar__3__l__13801)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__13780,Vvar__1__eqA__13781,Vvar__3__l__13801)
& Vvar__2___24Anonymous__13786 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13780,Vvar__2__x__13800,Vvar__3__l__13801) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__30044,Vvar__1__eqA__30045,Vvar__2___24Anonymous__30050,Vvar__3___24Anonymous__30051] :
( cType___24t(Vvar__0__A__30044)
=> ( c_24__type__30082___24t(Vvar__0__A__30044,Vvar__1__eqA__30045,Vvar__2___24Anonymous__30050,Vvar__3___24Anonymous__30051,Vvar__1__eqA__30045)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30044,Vvar__2___24Anonymous__30050)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30044,Vvar__3___24Anonymous__30051)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__30044,Vvar__1__eqA__30045,Vvar__2___24Anonymous__30050,Vvar__3___24Anonymous__30051)
=> ( ( Vvar__3___24Anonymous__30051 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30044)
& Vvar__2___24Anonymous__30050 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30044) )
| ? [Vvar__2__x__30065] :
( t(Vvar__2__x__30065,Vvar__0__A__30044)
& ? [Vvar__3__x_27__30066] :
( t(Vvar__3__x_27__30066,Vvar__0__A__30044)
& ? [Vvar__4__l__30067] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30044,Vvar__4__l__30067)
& ? [Vvar__5__l_27__30068] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30044,Vvar__5__l_27__30068)
& p(happ(happ(Vvar__1__eqA__30045,Vvar__2__x__30065),Vvar__3__x_27__30066))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__30044,Vvar__1__eqA__30045,Vvar__4__l__30067,Vvar__5__l_27__30068)
& Vvar__3___24Anonymous__30051 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30044,Vvar__3__x_27__30066,Vvar__5__l_27__30068)
& Vvar__2___24Anonymous__30050 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30044,Vvar__2__x__30065,Vvar__4__l__30067) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.boolP',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eboolP)
=> p(c_24True) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.has_fixpoint',axiom,
! [Vvar__0__A__18456] :
( cProp___24t(Vvar__0__A__18456)
=> ( cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1(Vvar__0__A__18456)
=> ( ( ( p(Vvar__0__A__18456)
=> p(Vvar__0__A__18456) )
=> p(Vvar__0__A__18456) )
& ( ( p(Vvar__0__A__18456)
=> p(Vvar__0__A__18456) )
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.retract',axiom,
! [Vvar__0__A__18432,Vvar__1__B__18433] :
( cProp___24t(Vvar__0__A__18432)
=> ( cProp___24t(Vvar__1__B__18433)
=> ( cCoq_2eLogic_2eClassicalFacts_2eretract___24a2(Vvar__0__A__18432,Vvar__1__B__18433)
=> ( ( p(Vvar__0__A__18432)
=> p(Vvar__1__B__18433) )
& ( p(Vvar__1__B__18433)
=> p(Vvar__0__A__18432) )
& ( p(Vvar__1__B__18433)
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__17764,Vvar__1__P__17765,Vvar__2__p__17768,Vvar__3__x__17769,Vvar__4__q__17770,Vvar__5___24Anonymous__17771] :
( cType___24t(Vvar__0__U__17764)
=> ( c_24__type__17786___24t(Vvar__0__U__17764,Vvar__1__P__17765,Vvar__2__p__17768,Vvar__3__x__17769,Vvar__4__q__17770,Vvar__5___24Anonymous__17771,Vvar__1__P__17765)
=> ( t(Vvar__2__p__17768,Vvar__0__U__17764)
=> ( t(Vvar__3__x__17769,happ(Vvar__1__P__17765,Vvar__2__p__17768))
=> ( t(Vvar__4__q__17770,Vvar__0__U__17764)
=> ( t(Vvar__5___24Anonymous__17771,happ(Vvar__1__P__17765,Vvar__4__q__17770))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__17764,Vvar__1__P__17765,Vvar__2__p__17768,Vvar__3__x__17769,Vvar__4__q__17770,Vvar__5___24Anonymous__17771)
=> ( Vvar__5___24Anonymous__17771 = Vvar__3__x__17769
& Vvar__4__q__17770 = Vvar__2__p__17768 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__18723,Vvar__1__P__18724,Vvar__2__p__18727,Vvar__3__x__18728,Vvar__4__q__18729,Vvar__5__y__18730] :
( cType___24t(Vvar__0__U__18723)
=> ( c_24__type__18749___24t(Vvar__0__U__18723,Vvar__1__P__18724,Vvar__2__p__18727,Vvar__3__x__18728,Vvar__4__q__18729,Vvar__5__y__18730,Vvar__1__P__18724)
=> ( t(Vvar__2__p__18727,Vvar__0__U__18723)
=> ( t(Vvar__3__x__18728,happ(Vvar__1__P__18724,Vvar__2__p__18727))
=> ( t(Vvar__4__q__18729,Vvar__0__U__18723)
=> ( t(Vvar__5__y__18730,happ(Vvar__1__P__18724,Vvar__4__q__18729))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__18723,Vvar__1__P__18724,Vvar__2__p__18727,Vvar__3__x__18728,Vvar__4__q__18729,Vvar__5__y__18730)
=> ( Vvar__4__q__18729 = Vvar__2__p__18727
& Vvar__3__x__18728 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__18723,Vvar__4__q__18729,Vvar__1__P__18724,Vvar__5__y__18730,Vvar__2__p__18727)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX270] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX270)
=> ( VX270 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__271] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__271)
& VX270 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__271) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX765] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX765)
=> ( VX765 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__766] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__766)
& VX765 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__766) )
| ? [Vvar__0___24Anonymous__767] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__767)
& VX765 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__767) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX754] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX754)
=> ( ? [Vvar__0___24Anonymous__755] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__755)
& VX754 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__755) )
| ? [Vvar__0___24Anonymous__756] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__756)
& VX754 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__756) )
| VX754 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [Vvar__0___24Anonymous__30790,VX30791] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30790)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__30790,VX30791)
=> ( ( Vvar__0___24Anonymous__30790 = cCoq_2eNumbers_2eBinNums_2exH
& VX30791 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
| ? [Vvar__0__p__30792] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__30792)
& ? [Vvar__1___24Anonymous__30793] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__30792,Vvar__1___24Anonymous__30793)
& Vvar__0___24Anonymous__30790 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2430828___24a2(Vvar__0___24Anonymous__30790,Vvar__0__p__30792)
& VX30791 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__30792,Vvar__1___24Anonymous__30793) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
! [Vvar__0__p__30853,Vvar__1__q__30854,Vvar__2___24Anonymous__30855] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__30853)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__30854)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__30855)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__30853,Vvar__1__q__30854,Vvar__2___24Anonymous__30855)
=> ( ( Vvar__0__p__30853 = Vvar__1__q__30854
& Vvar__2___24Anonymous__30855 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
| ? [Vvar__2__r__30862] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__30862)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__30854,Vvar__2__r__30862) = Vvar__0__p__30853
& Vvar__2___24Anonymous__30855 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__30862) )
| ? [Vvar__2__r__30866] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__30866)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__30853,Vvar__2__r__30866) = Vvar__1__q__30854
& Vvar__2___24Anonymous__30855 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX16254] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX16254)
=> ( VX16254 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__16255] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16255)
& VX16254 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__16255) )
| VX16254 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX17820] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX17820)
=> ? [Vvar__0__Qnum__17821] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__17821)
& ? [Vvar__1__Qden__17822] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__17822)
& VX17820 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__17821,Vvar__1__Qden__17822) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
! [VX21523] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(VX21523)
=> ? [Vvar__0__neg__21524] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__21524)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__21524,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX21523 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__21524) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX21502] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX21502)
=> ? [Vvar__0__nonneg__21503] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__21503)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__21503)
& VX21502 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__21503) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
! [VX21516] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX21516)
=> ? [Vvar__0__nonpos__21517] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__21517)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__21517,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX21516 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__21517) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX21530] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX21530)
=> ? [Vvar__0__nonzero__21531] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__21531)
& Vvar__0__nonzero__21531 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX21530 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__21531) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX21509] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX21509)
=> ? [Vvar__0__pos__21510] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__21510)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__21510)
& VX21509 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__21510) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__22579,Vvar__1___24Anonymous__22580,VX22581] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__22579)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__22580)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__22579,Vvar__1___24Anonymous__22580,VX22581)
=> ( ( Vvar__0__x__22579 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__22580 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX22581 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__22579) )
| ? [Vvar__1__n__22585] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__22585)
& Vvar__0__x__22579 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__22585)
& Vvar__1___24Anonymous__22580 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2422605___24a3(Vvar__0__x__22579,Vvar__1___24Anonymous__22580,Vvar__1__n__22585)
& VX22581 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__22579,Vvar__1__n__22585) )
| ? [Vvar__1__n__22590] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__22590)
& Vvar__0__x__22579 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__22590))
& Vvar__1___24Anonymous__22580 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2422622___24a3(Vvar__0__x__22579,Vvar__1___24Anonymous__22580,Vvar__1__n__22590)
& VX22581 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__22579,Vvar__1__n__22590) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
! [Vvar__0__A__559,Vvar__1__R__560] :
( cType___24t(Vvar__0__A__559)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__559,Vvar__1__R__560)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__559,Vvar__1__R__560)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__559,Vvar__1__R__560)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__559,Vvar__1__R__560)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
! [Vvar__0__A__24,Vvar__1__R__25] :
( cType___24t(Vvar__0__A__24)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24,Vvar__1__R__25)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__24,Vvar__1__R__25)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__24,Vvar__1__R__25)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__24,Vvar__1__R__25)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__24,Vvar__1__R__25)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
! [Vvar__0__A__551,Vvar__1__R__552] :
( cType___24t(Vvar__0__A__551)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__551,Vvar__1__R__552)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__551,Vvar__1__R__552)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__551,Vvar__1__R__552)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__551,Vvar__1__R__552)
& cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__551,Vvar__1__R__552)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__276,Vvar__1__R__277] :
( cType___24t(Vvar__0__A__276)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__276,Vvar__1__R__277)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__276,Vvar__1__R__277)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__276,Vvar__1__R__277)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__276,Vvar__1__R__277)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__22060,Vvar__1__leA__22061,Vvar__2___24Anonymous__22066] :
( cType___24t(Vvar__0__A__22060)
=> ( c_24__type__22156___24t(Vvar__0__A__22060,Vvar__1__leA__22061,Vvar__2___24Anonymous__22066,Vvar__1__leA__22061)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22060,Vvar__2___24Anonymous__22066)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__22060,Vvar__1__leA__22061,Vvar__2___24Anonymous__22066)
=> ( Vvar__2___24Anonymous__22066 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22060)
| ? [Vvar__2__x__22080] :
( t(Vvar__2__x__22080,Vvar__0__A__22060)
& Vvar__2___24Anonymous__22066 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22060,Vvar__2__x__22080,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22060)) )
| ? [Vvar__2__x__22087] :
( t(Vvar__2__x__22087,Vvar__0__A__22060)
& ? [Vvar__3__y__22088] :
( t(Vvar__3__y__22088,Vvar__0__A__22060)
& ? [Vvar__4__l__22089] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22060,Vvar__4__l__22089)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__22060,Vvar__1__leA__22061,Vvar__2__x__22087,Vvar__3__y__22088)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__22060,Vvar__1__leA__22061,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__22060,Vvar__4__l__22089,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22060,Vvar__3__y__22088,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22060))))
& Vvar__2___24Anonymous__22066 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2422354___24a6(Vvar__0__A__22060,Vvar__1__leA__22061,Vvar__2___24Anonymous__22066,Vvar__2__x__22087,Vvar__3__y__22088,Vvar__4__l__22089) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__22009,Vvar__1__leA__22010,Vvar__2___24Anonymous__22015,Vvar__3___24Anonymous__22016] :
( cType___24t(Vvar__0__A__22009)
=> ( c_24__type__22058___24t(Vvar__0__A__22009,Vvar__1__leA__22010,Vvar__2___24Anonymous__22015,Vvar__3___24Anonymous__22016,Vvar__1__leA__22010)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22009,Vvar__2___24Anonymous__22015)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22009,Vvar__3___24Anonymous__22016)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__22009,Vvar__1__leA__22010,Vvar__2___24Anonymous__22015,Vvar__3___24Anonymous__22016)
=> ( ? [Vvar__2__a__22024] :
( t(Vvar__2__a__22024,Vvar__0__A__22009)
& ? [Vvar__3__x__22025] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22009,Vvar__3__x__22025)
& Vvar__3___24Anonymous__22016 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22009,Vvar__2__a__22024,Vvar__3__x__22025)
& Vvar__2___24Anonymous__22015 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22009) ) )
| ? [Vvar__2__a__22032] :
( t(Vvar__2__a__22032,Vvar__0__A__22009)
& ? [Vvar__3__b__22033] :
( t(Vvar__3__b__22033,Vvar__0__A__22009)
& p(happ(happ(Vvar__1__leA__22010,Vvar__2__a__22032),Vvar__3__b__22033))
& ? [Vvar__5__x__22035] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22009,Vvar__5__x__22035)
& ? [Vvar__6__y__22036] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22009,Vvar__6__y__22036)
& Vvar__3___24Anonymous__22016 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22009,Vvar__3__b__22033,Vvar__6__y__22036)
& Vvar__2___24Anonymous__22015 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22009,Vvar__2__a__22032,Vvar__5__x__22035) ) ) ) )
| ? [Vvar__2__a__22043] :
( t(Vvar__2__a__22043,Vvar__0__A__22009)
& ? [Vvar__3__x__22044] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22009,Vvar__3__x__22044)
& ? [Vvar__4__y__22045] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22009,Vvar__4__y__22045)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__22009,Vvar__1__leA__22010,Vvar__3__x__22044,Vvar__4__y__22045)
& Vvar__3___24Anonymous__22016 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22009,Vvar__2__a__22043,Vvar__4__y__22045)
& Vvar__2___24Anonymous__22015 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22009,Vvar__2__a__22043,Vvar__3__x__22044) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__296,Vvar__1__R__297,Vvar__2__x__298,Vvar__3___24Anonymous__299] :
( cType___24t(Vvar__0__A__296)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__296,Vvar__1__R__297)
=> ( t(Vvar__2__x__298,Vvar__0__A__296)
=> ( t(Vvar__3___24Anonymous__299,Vvar__0__A__296)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__296,Vvar__1__R__297,Vvar__2__x__298,Vvar__3___24Anonymous__299)
=> ( ? [Vvar__3__y__304] :
( t(Vvar__3__y__304,Vvar__0__A__296)
& p(happ(happ(Vvar__1__R__297,Vvar__2__x__298),Vvar__3__y__304))
& Vvar__3___24Anonymous__299 = Vvar__3__y__304 )
| Vvar__3___24Anonymous__299 = Vvar__2__x__298 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans',axiom,
! [Vvar__0__A__336,Vvar__1__R__337,Vvar__1___24Anonymous__338,Vvar__2___24Anonymous__339] :
( cType___24t(Vvar__0__A__336)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__336,Vvar__1__R__337)
=> ( t(Vvar__1___24Anonymous__338,Vvar__0__A__336)
=> ( t(Vvar__2___24Anonymous__339,Vvar__0__A__336)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__336,Vvar__1__R__337,Vvar__1___24Anonymous__338,Vvar__2___24Anonymous__339)
=> ( ? [Vvar__2__x__343] :
( t(Vvar__2__x__343,Vvar__0__A__336)
& ? [Vvar__3__y__344] :
( t(Vvar__3__y__344,Vvar__0__A__336)
& p(happ(happ(Vvar__1__R__337,Vvar__2__x__343),Vvar__3__y__344))
& Vvar__2___24Anonymous__339 = Vvar__3__y__344
& Vvar__1___24Anonymous__338 = Vvar__2__x__343 ) )
| ? [Vvar__2__x__348] :
( t(Vvar__2__x__348,Vvar__0__A__336)
& Vvar__2___24Anonymous__339 = Vvar__2__x__348
& Vvar__1___24Anonymous__338 = Vvar__2__x__348 )
| ? [Vvar__2__x__351] :
( t(Vvar__2__x__351,Vvar__0__A__336)
& ? [Vvar__3__y__352] :
( t(Vvar__3__y__352,Vvar__0__A__336)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__336,Vvar__1__R__337,Vvar__2__x__351,Vvar__3__y__352)
& Vvar__2___24Anonymous__339 = Vvar__2__x__351
& Vvar__1___24Anonymous__338 = Vvar__3__y__352 ) )
| ? [Vvar__2__x__356] :
( t(Vvar__2__x__356,Vvar__0__A__336)
& ? [Vvar__3__y__357] :
( t(Vvar__3__y__357,Vvar__0__A__336)
& ? [Vvar__4__z__358] :
( t(Vvar__4__z__358,Vvar__0__A__336)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__336,Vvar__1__R__337,Vvar__2__x__356,Vvar__3__y__357)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__336,Vvar__1__R__337,Vvar__3__y__357,Vvar__4__z__358)
& Vvar__2___24Anonymous__339 = Vvar__4__z__358
& Vvar__1___24Anonymous__338 = Vvar__2__x__356 ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
! [Vvar__0__A__168,Vvar__1__R__169,Vvar__2__x__170,Vvar__3___24Anonymous__171] :
( cType___24t(Vvar__0__A__168)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__168,Vvar__1__R__169)
=> ( t(Vvar__2__x__170,Vvar__0__A__168)
=> ( t(Vvar__3___24Anonymous__171,Vvar__0__A__168)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__168,Vvar__1__R__169,Vvar__2__x__170,Vvar__3___24Anonymous__171)
=> ( Vvar__3___24Anonymous__171 = Vvar__2__x__170
| ? [Vvar__3__y__179] :
( t(Vvar__3__y__179,Vvar__0__A__168)
& ? [Vvar__4__z__180] :
( t(Vvar__4__z__180,Vvar__0__A__168)
& ( p(happ(happ(Vvar__1__R__169,Vvar__2__x__170),Vvar__3__y__179))
| p(happ(happ(Vvar__1__R__169,Vvar__3__y__179),Vvar__2__x__170)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__168,Vvar__1__R__169,Vvar__3__y__179,Vvar__4__z__180)
& Vvar__3___24Anonymous__171 = Vvar__4__z__180 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
! [Vvar__0__A__630,Vvar__1__R__631,Vvar__2__x__632,Vvar__3___24Anonymous__633] :
( cType___24t(Vvar__0__A__630)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__630,Vvar__1__R__631)
=> ( t(Vvar__2__x__632,Vvar__0__A__630)
=> ( t(Vvar__3___24Anonymous__633,Vvar__0__A__630)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__630,Vvar__1__R__631,Vvar__2__x__632,Vvar__3___24Anonymous__633)
=> ( Vvar__3___24Anonymous__633 = Vvar__2__x__632
| ? [Vvar__3__y__641] :
( t(Vvar__3__y__641,Vvar__0__A__630)
& ? [Vvar__4__z__642] :
( t(Vvar__4__z__642,Vvar__0__A__630)
& ( p(happ(happ(Vvar__1__R__631,Vvar__3__y__641),Vvar__4__z__642))
| p(happ(happ(Vvar__1__R__631,Vvar__4__z__642),Vvar__3__y__641)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__630,Vvar__1__R__631,Vvar__2__x__632,Vvar__3__y__641)
& Vvar__3___24Anonymous__633 = Vvar__4__z__642 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
! [Vvar__0__A__86,Vvar__1__R__87,Vvar__2__x__88,Vvar__3___24Anonymous__89] :
( cType___24t(Vvar__0__A__86)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__86,Vvar__1__R__87)
=> ( t(Vvar__2__x__88,Vvar__0__A__86)
=> ( t(Vvar__3___24Anonymous__89,Vvar__0__A__86)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__86,Vvar__1__R__87,Vvar__2__x__88,Vvar__3___24Anonymous__89)
=> ( ? [Vvar__3__y__94] :
( t(Vvar__3__y__94,Vvar__0__A__86)
& p(happ(happ(Vvar__1__R__87,Vvar__2__x__88),Vvar__3__y__94))
& Vvar__3___24Anonymous__89 = Vvar__3__y__94 )
| Vvar__3___24Anonymous__89 = Vvar__2__x__88
| ? [Vvar__3__y__102] :
( t(Vvar__3__y__102,Vvar__0__A__86)
& ? [Vvar__4__z__103] :
( t(Vvar__4__z__103,Vvar__0__A__86)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__86,Vvar__1__R__87,Vvar__2__x__88,Vvar__3__y__102)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__86,Vvar__1__R__87,Vvar__3__y__102,Vvar__4__z__103)
& Vvar__3___24Anonymous__89 = Vvar__4__z__103 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
! [Vvar__0__A__120,Vvar__1__R__121,Vvar__2__x__122,Vvar__3___24Anonymous__123] :
( cType___24t(Vvar__0__A__120)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__120,Vvar__1__R__121)
=> ( t(Vvar__2__x__122,Vvar__0__A__120)
=> ( t(Vvar__3___24Anonymous__123,Vvar__0__A__120)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__120,Vvar__1__R__121,Vvar__2__x__122,Vvar__3___24Anonymous__123)
=> ( Vvar__3___24Anonymous__123 = Vvar__2__x__122
| ? [Vvar__3__y__131] :
( t(Vvar__3__y__131,Vvar__0__A__120)
& ? [Vvar__4__z__132] :
( t(Vvar__4__z__132,Vvar__0__A__120)
& p(happ(happ(Vvar__1__R__121,Vvar__2__x__122),Vvar__3__y__131))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__120,Vvar__1__R__121,Vvar__3__y__131,Vvar__4__z__132)
& Vvar__3___24Anonymous__123 = Vvar__4__z__132 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
! [Vvar__0__A__145,Vvar__1__R__146,Vvar__2__x__147,Vvar__3___24Anonymous__148] :
( cType___24t(Vvar__0__A__145)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__145,Vvar__1__R__146)
=> ( t(Vvar__2__x__147,Vvar__0__A__145)
=> ( t(Vvar__3___24Anonymous__148,Vvar__0__A__145)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__145,Vvar__1__R__146,Vvar__2__x__147,Vvar__3___24Anonymous__148)
=> ( Vvar__3___24Anonymous__148 = Vvar__2__x__147
| ? [Vvar__3__y__156] :
( t(Vvar__3__y__156,Vvar__0__A__145)
& ? [Vvar__4__z__157] :
( t(Vvar__4__z__157,Vvar__0__A__145)
& p(happ(happ(Vvar__1__R__146,Vvar__3__y__156),Vvar__4__z__157))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__145,Vvar__1__R__146,Vvar__2__x__147,Vvar__3__y__156)
& Vvar__3___24Anonymous__148 = Vvar__4__z__157 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
! [Vvar__0__A__40,Vvar__1__R__41,Vvar__2__x__42,Vvar__3___24Anonymous__43] :
( cType___24t(Vvar__0__A__40)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__40,Vvar__1__R__41)
=> ( t(Vvar__2__x__42,Vvar__0__A__40)
=> ( t(Vvar__3___24Anonymous__43,Vvar__0__A__40)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__40,Vvar__1__R__41,Vvar__2__x__42,Vvar__3___24Anonymous__43)
=> ( ? [Vvar__3__y__48] :
( t(Vvar__3__y__48,Vvar__0__A__40)
& p(happ(happ(Vvar__1__R__41,Vvar__2__x__42),Vvar__3__y__48))
& Vvar__3___24Anonymous__43 = Vvar__3__y__48 )
| ? [Vvar__3__y__53] :
( t(Vvar__3__y__53,Vvar__0__A__40)
& ? [Vvar__4__z__54] :
( t(Vvar__4__z__54,Vvar__0__A__40)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__40,Vvar__1__R__41,Vvar__2__x__42,Vvar__3__y__53)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__40,Vvar__1__R__41,Vvar__3__y__53,Vvar__4__z__54)
& Vvar__3___24Anonymous__43 = Vvar__4__z__54 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
! [Vvar__0__A__57,Vvar__1__R__58,Vvar__2__x__59,Vvar__3___24Anonymous__60] :
( cType___24t(Vvar__0__A__57)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__57,Vvar__1__R__58)
=> ( t(Vvar__2__x__59,Vvar__0__A__57)
=> ( t(Vvar__3___24Anonymous__60,Vvar__0__A__57)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__57,Vvar__1__R__58,Vvar__2__x__59,Vvar__3___24Anonymous__60)
=> ( ? [Vvar__3__y__65] :
( t(Vvar__3__y__65,Vvar__0__A__57)
& p(happ(happ(Vvar__1__R__58,Vvar__2__x__59),Vvar__3__y__65))
& Vvar__3___24Anonymous__60 = Vvar__3__y__65 )
| ? [Vvar__3__y__70] :
( t(Vvar__3__y__70,Vvar__0__A__57)
& ? [Vvar__4__z__71] :
( t(Vvar__4__z__71,Vvar__0__A__57)
& p(happ(happ(Vvar__1__R__58,Vvar__2__x__59),Vvar__3__y__70))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__57,Vvar__1__R__58,Vvar__3__y__70,Vvar__4__z__71)
& Vvar__3___24Anonymous__60 = Vvar__4__z__71 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
! [Vvar__0__A__602,Vvar__1__R__603,Vvar__2__x__604,Vvar__3___24Anonymous__605] :
( cType___24t(Vvar__0__A__602)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__602,Vvar__1__R__603)
=> ( t(Vvar__2__x__604,Vvar__0__A__602)
=> ( t(Vvar__3___24Anonymous__605,Vvar__0__A__602)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__602,Vvar__1__R__603,Vvar__2__x__604,Vvar__3___24Anonymous__605)
=> ( ? [Vvar__3__y__610] :
( t(Vvar__3__y__610,Vvar__0__A__602)
& p(happ(happ(Vvar__1__R__603,Vvar__2__x__604),Vvar__3__y__610))
& Vvar__3___24Anonymous__605 = Vvar__3__y__610 )
| ? [Vvar__3__y__615] :
( t(Vvar__3__y__615,Vvar__0__A__602)
& ? [Vvar__4__z__616] :
( t(Vvar__4__z__616,Vvar__0__A__602)
& p(happ(happ(Vvar__1__R__603,Vvar__3__y__615),Vvar__4__z__616))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__602,Vvar__1__R__603,Vvar__2__x__604,Vvar__3__y__615)
& Vvar__3___24Anonymous__605 = Vvar__4__z__616 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.swapprod',axiom,
! [Vvar__0__A__21967,Vvar__1__R__21968,Vvar__2___24Anonymous__21973,Vvar__3___24Anonymous__21974] :
( cType___24t(Vvar__0__A__21967)
=> ( c_24__type__22007___24t(Vvar__0__A__21967,Vvar__1__R__21968,Vvar__2___24Anonymous__21973,Vvar__3___24Anonymous__21974,Vvar__1__R__21968)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__21967,Vvar__0__A__21967,Vvar__2___24Anonymous__21973)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__21967,Vvar__0__A__21967,Vvar__3___24Anonymous__21974)
=> ( cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(Vvar__0__A__21967,Vvar__1__R__21968,Vvar__2___24Anonymous__21973,Vvar__3___24Anonymous__21974)
=> ( ? [Vvar__2__x__21982] :
( t(Vvar__2__x__21982,Vvar__0__A__21967)
& ? [Vvar__3__y__21983] :
( t(Vvar__3__y__21983,Vvar__0__A__21967)
& ? [Vvar__4__p__21984] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__21967,Vvar__0__A__21967,Vvar__4__p__21984)
& cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__21967,Vvar__0__A__21967,Vvar__1__R__21968,Vvar__1__R__21968,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__21967,Vvar__0__A__21967,Vvar__2__x__21982,Vvar__3__y__21983),Vvar__4__p__21984)
& Vvar__3___24Anonymous__21974 = Vvar__4__p__21984
& Vvar__2___24Anonymous__21973 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__21967,Vvar__0__A__21967,Vvar__2__x__21982,Vvar__3__y__21983) ) ) )
| ? [Vvar__2__x__21992] :
( t(Vvar__2__x__21992,Vvar__0__A__21967)
& ? [Vvar__3__y__21993] :
( t(Vvar__3__y__21993,Vvar__0__A__21967)
& ? [Vvar__4__p__21994] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__21967,Vvar__0__A__21967,Vvar__4__p__21994)
& cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__21967,Vvar__0__A__21967,Vvar__1__R__21968,Vvar__1__R__21968,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__21967,Vvar__0__A__21967,Vvar__2__x__21992,Vvar__3__y__21993),Vvar__4__p__21994)
& Vvar__3___24Anonymous__21974 = Vvar__4__p__21994
& Vvar__2___24Anonymous__21973 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__21967,Vvar__0__A__21967,Vvar__3__y__21993,Vvar__2__x__21992) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.symprod',axiom,
! [Vvar__0__A__21870,Vvar__1__B__21871,Vvar__2__leA__21872,Vvar__3__leB__21877,Vvar__4___24Anonymous__21882,Vvar__5___24Anonymous__21883] :
( cType___24t(Vvar__0__A__21870)
=> ( cType___24t(Vvar__1__B__21871)
=> ( c_24__type__21940___24t(Vvar__0__A__21870,Vvar__1__B__21871,Vvar__2__leA__21872,Vvar__3__leB__21877,Vvar__4___24Anonymous__21882,Vvar__5___24Anonymous__21883,Vvar__2__leA__21872)
=> ( c_24__type__21965___24t(Vvar__0__A__21870,Vvar__1__B__21871,Vvar__2__leA__21872,Vvar__3__leB__21877,Vvar__4___24Anonymous__21882,Vvar__5___24Anonymous__21883,Vvar__3__leB__21877)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__21870,Vvar__1__B__21871,Vvar__4___24Anonymous__21882)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__21870,Vvar__1__B__21871,Vvar__5___24Anonymous__21883)
=> ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__21870,Vvar__1__B__21871,Vvar__2__leA__21872,Vvar__3__leB__21877,Vvar__4___24Anonymous__21882,Vvar__5___24Anonymous__21883)
=> ( ? [Vvar__4__x__21897] :
( t(Vvar__4__x__21897,Vvar__0__A__21870)
& ? [Vvar__5__x_27__21898] :
( t(Vvar__5__x_27__21898,Vvar__0__A__21870)
& p(happ(happ(Vvar__2__leA__21872,Vvar__4__x__21897),Vvar__5__x_27__21898))
& ? [Vvar__7__y__21900] :
( t(Vvar__7__y__21900,Vvar__1__B__21871)
& Vvar__5___24Anonymous__21883 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__21870,Vvar__1__B__21871,Vvar__5__x_27__21898,Vvar__7__y__21900)
& Vvar__4___24Anonymous__21882 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__21870,Vvar__1__B__21871,Vvar__4__x__21897,Vvar__7__y__21900) ) ) )
| ? [Vvar__4__y__21913] :
( t(Vvar__4__y__21913,Vvar__1__B__21871)
& ? [Vvar__5__y_27__21914] :
( t(Vvar__5__y_27__21914,Vvar__1__B__21871)
& p(happ(happ(Vvar__3__leB__21877,Vvar__4__y__21913),Vvar__5__y_27__21914))
& ? [Vvar__7__x__21916] :
( t(Vvar__7__x__21916,Vvar__0__A__21870)
& Vvar__5___24Anonymous__21883 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__21870,Vvar__1__B__21871,Vvar__7__x__21916,Vvar__5__y_27__21914)
& Vvar__4___24Anonymous__21882 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__21870,Vvar__1__B__21871,Vvar__7__x__21916,Vvar__4__y__21913) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Permutation.Permutation',axiom,
! [Vvar__0__A__21464,Vvar__1___24Anonymous__21465,Vvar__2___24Anonymous__21466] :
( cType___24t(Vvar__0__A__21464)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21464,Vvar__1___24Anonymous__21465)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21464,Vvar__2___24Anonymous__21466)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__21464,Vvar__1___24Anonymous__21465,Vvar__2___24Anonymous__21466)
=> ( ( Vvar__2___24Anonymous__21466 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__21464)
& Vvar__1___24Anonymous__21465 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__21464) )
| ? [Vvar__1__x__21470] :
( t(Vvar__1__x__21470,Vvar__0__A__21464)
& ? [Vvar__2__l__21471] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21464,Vvar__2__l__21471)
& ? [Vvar__3__l_27__21472] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21464,Vvar__3__l_27__21472)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__21464,Vvar__2__l__21471,Vvar__3__l_27__21472)
& Vvar__2___24Anonymous__21466 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21464,Vvar__1__x__21470,Vvar__3__l_27__21472)
& Vvar__1___24Anonymous__21465 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21464,Vvar__1__x__21470,Vvar__2__l__21471) ) ) )
| ? [Vvar__1__x__21475] :
( t(Vvar__1__x__21475,Vvar__0__A__21464)
& ? [Vvar__2__y__21476] :
( t(Vvar__2__y__21476,Vvar__0__A__21464)
& ? [Vvar__3__l__21477] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21464,Vvar__3__l__21477)
& Vvar__2___24Anonymous__21466 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21464,Vvar__1__x__21475,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21464,Vvar__2__y__21476,Vvar__3__l__21477))
& Vvar__1___24Anonymous__21465 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21464,Vvar__2__y__21476,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21464,Vvar__1__x__21475,Vvar__3__l__21477)) ) ) )
| ? [Vvar__1__l__21479] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21464,Vvar__1__l__21479)
& ? [Vvar__2__l_27__21480] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21464,Vvar__2__l_27__21480)
& ? [Vvar__3__l_27_27__21481] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21464,Vvar__3__l_27_27__21481)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__21464,Vvar__1__l__21479,Vvar__2__l_27__21480)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__21464,Vvar__2__l_27__21480,Vvar__3__l_27_27__21481)
& Vvar__2___24Anonymous__21466 = Vvar__3__l_27_27__21481
& Vvar__1___24Anonymous__21465 = Vvar__1__l__21479 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__30211,Vvar__1__R__30212,Vvar__2__a__30217,Vvar__3___24Anonymous__30218] :
( cType___24t(Vvar__0__A__30211)
=> ( c_24__type__30248___24t(Vvar__0__A__30211,Vvar__1__R__30212,Vvar__2__a__30217,Vvar__3___24Anonymous__30218,Vvar__1__R__30212)
=> ( t(Vvar__2__a__30217,Vvar__0__A__30211)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30211,Vvar__3___24Anonymous__30218)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__30211,Vvar__1__R__30212,Vvar__2__a__30217,Vvar__3___24Anonymous__30218)
=> ( Vvar__3___24Anonymous__30218 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30211)
| ? [Vvar__3__b__30234] :
( t(Vvar__3__b__30234,Vvar__0__A__30211)
& ? [Vvar__4__l__30235] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30211,Vvar__4__l__30235)
& p(happ(happ(Vvar__1__R__30212,Vvar__2__a__30217),Vvar__3__b__30234))
& Vvar__3___24Anonymous__30218 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30211,Vvar__3__b__30234,Vvar__4__l__30235) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__13943,Vvar__1__R__13944,Vvar__2___24Anonymous__13949] :
( cType___24t(Vvar__0__A__13943)
=> ( c_24__type__13984___24t(Vvar__0__A__13943,Vvar__1__R__13944,Vvar__2___24Anonymous__13949,Vvar__1__R__13944)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13943,Vvar__2___24Anonymous__13949)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__13943,Vvar__1__R__13944,Vvar__2___24Anonymous__13949)
=> ( Vvar__2___24Anonymous__13949 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__13943)
| ? [Vvar__2__a__13963] :
( t(Vvar__2__a__13963,Vvar__0__A__13943)
& Vvar__2___24Anonymous__13949 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13943,Vvar__2__a__13963,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__13943)) )
| ? [Vvar__2__a__13970] :
( t(Vvar__2__a__13970,Vvar__0__A__13943)
& ? [Vvar__3__b__13971] :
( t(Vvar__3__b__13971,Vvar__0__A__13943)
& ? [Vvar__4__l__13972] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13943,Vvar__4__l__13972)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__13943,Vvar__1__R__13944,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13943,Vvar__3__b__13971,Vvar__4__l__13972))
& p(happ(happ(Vvar__1__R__13944,Vvar__2__a__13970),Vvar__3__b__13971))
& Vvar__2___24Anonymous__13949 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13943,Vvar__2__a__13970,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13943,Vvar__3__b__13971,Vvar__4__l__13972)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__30250,Vvar__1__R__30251,Vvar__2___24Anonymous__30256] :
( cType___24t(Vvar__0__A__30250)
=> ( c_24__type__30283___24t(Vvar__0__A__30250,Vvar__1__R__30251,Vvar__2___24Anonymous__30256,Vvar__1__R__30251)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30250,Vvar__2___24Anonymous__30256)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__30250,Vvar__1__R__30251,Vvar__2___24Anonymous__30256)
=> ( Vvar__2___24Anonymous__30256 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30250)
| ? [Vvar__2__a__30270] :
( t(Vvar__2__a__30270,Vvar__0__A__30250)
& ? [Vvar__3__l__30271] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30250,Vvar__3__l__30271)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__30250,Vvar__1__R__30251,Vvar__3__l__30271)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__30250,Vvar__1__R__30251,Vvar__2__a__30270,Vvar__3__l__30271)
& Vvar__2___24Anonymous__30256 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30250,Vvar__2__a__30270,Vvar__3__l__30271) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__30285,Vvar__1__R__30286,Vvar__2___24Anonymous__30291] :
( cType___24t(Vvar__0__A__30285)
=> ( c_24__type__30318___24t(Vvar__0__A__30285,Vvar__1__R__30286,Vvar__2___24Anonymous__30291,Vvar__1__R__30286)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30285,Vvar__2___24Anonymous__30291)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__30285,Vvar__1__R__30286,Vvar__2___24Anonymous__30291)
=> ( Vvar__2___24Anonymous__30291 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30285)
| ? [Vvar__2__a__30305] :
( t(Vvar__2__a__30305,Vvar__0__A__30285)
& ? [Vvar__3__l__30306] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30285,Vvar__3__l__30306)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__30285,Vvar__1__R__30286,Vvar__3__l__30306)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__30285,happ(Vvar__1__R__30286,Vvar__2__a__30305),Vvar__3__l__30306)
& Vvar__2___24Anonymous__30291 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30285,Vvar__2__a__30305,Vvar__3__l__30306) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX4911] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX4911)
=> ? [Vvar__0___24Anonymous__4912] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__4912)
& ? [Vvar__1___24Anonymous__4913] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__4913)
& ? [Vvar__2___24Anonymous__4914] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__4914)
& ? [Vvar__3___24Anonymous__4915] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__4915)
& ? [Vvar__4___24Anonymous__4916] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__4916)
& ? [Vvar__5___24Anonymous__4917] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__4917)
& ? [Vvar__6___24Anonymous__4918] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__4918)
& ? [Vvar__7___24Anonymous__4919] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__4919)
& VX4911 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4912,Vvar__1___24Anonymous__4913,Vvar__2___24Anonymous__4914,Vvar__3___24Anonymous__4915,Vvar__4___24Anonymous__4916,Vvar__5___24Anonymous__4917,Vvar__6___24Anonymous__4918,Vvar__7___24Anonymous__4919) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX14173] :
( cCoq_2eStrings_2eString_2estring___24t(VX14173)
=> ( VX14173 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__14174] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__14174)
& ? [Vvar__1___24Anonymous__14175] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__14175)
& VX14173 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__14174,Vvar__1___24Anonymous__14175) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__21270,Vvar__1__lt__21271,Vvar__2__eq__21276,Vvar__3__x__21281,Vvar__4__y__21282,VX21283] :
( cType___24t(Vvar__0__X__21270)
=> ( c_24__type__21343___24t(Vvar__0__X__21270,Vvar__1__lt__21271,Vvar__2__eq__21276,Vvar__3__x__21281,Vvar__4__y__21282,Vvar__1__lt__21271)
=> ( c_24__type__21362___24t(Vvar__0__X__21270,Vvar__1__lt__21271,Vvar__2__eq__21276,Vvar__3__x__21281,Vvar__4__y__21282,Vvar__2__eq__21276)
=> ( t(Vvar__3__x__21281,Vvar__0__X__21270)
=> ( t(Vvar__4__y__21282,Vvar__0__X__21270)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__21270,Vvar__1__lt__21271,Vvar__2__eq__21276,Vvar__3__x__21281,Vvar__4__y__21282,VX21283)
=> ( ( p(happ(happ(Vvar__1__lt__21271,Vvar__3__x__21281),Vvar__4__y__21282))
& VX21283 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__21270,Vvar__1__lt__21271,Vvar__2__eq__21276,Vvar__3__x__21281,Vvar__4__y__21282) )
| ( p(happ(happ(Vvar__2__eq__21276,Vvar__3__x__21281),Vvar__4__y__21282))
& VX21283 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__21270,Vvar__1__lt__21271,Vvar__2__eq__21276,Vvar__3__x__21281,Vvar__4__y__21282) )
| ( p(happ(happ(Vvar__1__lt__21271,Vvar__4__y__21282),Vvar__3__x__21281))
& VX21283 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__21270,Vvar__1__lt__21271,Vvar__2__eq__21276,Vvar__3__x__21281,Vvar__4__y__21282) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__16787,Vvar__1___24Anonymous__16788] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__16787)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__16788)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__16787,Vvar__1___24Anonymous__16788)
=> ( ? [Vvar__0__a__16790] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__16790)
& ? [Vvar__1__s__16791] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__16791)
& Vvar__1___24Anonymous__16788 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__16790,Vvar__1__s__16791)
& Vvar__0___24Anonymous__16787 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__16792] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__16792)
& ? [Vvar__1__s1__16793] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__16793)
& ? [Vvar__2__s2__16794] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__16794)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__16793,Vvar__2__s2__16794)
& Vvar__1___24Anonymous__16788 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__16792,Vvar__2__s2__16794)
& Vvar__0___24Anonymous__16787 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__16792,Vvar__1__s1__16793) ) ) )
| ? [Vvar__0__a__16796] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__16796)
& ? [Vvar__1__b__16797] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__16797)
& ? [Vvar__2__s1__16798] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__16798)
& ? [Vvar__3__s2__16799] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__16799)
& cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__16796),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__16797))
& Vvar__1___24Anonymous__16788 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__16797,Vvar__3__s2__16799)
& Vvar__0___24Anonymous__16787 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__16796,Vvar__2__s1__16798) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX10143] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX10143)
=> ( VX10143 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX10143 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX10143 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__20253,VX20254] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20253)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__20253,VX20254)
=> ( ? [Vvar__0__n__20255] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__20255)
& Vvar__0___24Anonymous__20253 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__20255)
& VX20254 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__20255) )
| ? [Vvar__0__n__20256] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__20256)
& ? [Vvar__1___24Anonymous__20257] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__20256,Vvar__1___24Anonymous__20257)
& Vvar__0___24Anonymous__20253 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__20256)
& VX20254 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__20256,Vvar__1___24Anonymous__20257) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__14851,Vvar__1___24Anonymous__14852,VX14853] :
( cType___24t(Vvar__0__A__14851)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__14852)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__14851,Vvar__1___24Anonymous__14852,VX14853)
=> ( ( Vvar__1___24Anonymous__14852 = cCoq_2eInit_2eDatatypes_2eO
& VX14853 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__14851) )
| ? [Vvar__1__h__14856] :
( t(Vvar__1__h__14856,Vvar__0__A__14851)
& ? [Vvar__2__n__14857] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__14857)
& ? [Vvar__3___24Anonymous__14858] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__14851,Vvar__2__n__14857,Vvar__3___24Anonymous__14858)
& Vvar__1___24Anonymous__14852 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__14857)
& VX14853 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__14851,Vvar__1__h__14856,Vvar__2__n__14857,Vvar__3___24Anonymous__14858) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__30618,Vvar__1__b__30619,Vvar__2__d__30620] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__30618)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__30619)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__30620)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__30618,Vvar__1__b__30619,Vvar__2__d__30620)
=> ? [Vvar__3__u__30625] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__30625)
& ? [Vvar__4__v__30626] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__30626)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__30625,Vvar__0__a__30618),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__30626,Vvar__1__b__30619)) = Vvar__2__d__30620
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__30593,Vvar__1__b__30594,VX30595] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__30593)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__30594)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__30593,Vvar__1__b__30594,VX30595)
=> ? [Vvar__2__u__30598] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__30598)
& ? [Vvar__3__v__30599] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__30599)
& ? [Vvar__4__d__30600] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__30600)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__30598,Vvar__0__a__30593),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__30599,Vvar__1__b__30594)) = Vvar__4__d__30600
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__30593,Vvar__1__b__30594,Vvar__4__d__30600)
& VX30595 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__30593,Vvar__1__b__30594,Vvar__2__u__30598,Vvar__3__v__30599,Vvar__4__d__30600) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__15802,Vvar__1__b__15803,Vvar__2__g__15804] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__15802)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__15803)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__15804)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__15802,Vvar__1__b__15803,Vvar__2__g__15804)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__15804,Vvar__0__a__15802)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__15804,Vvar__1__b__15803)
& ! [Vvar__var__var__var__var__5__x__15812__15815__15818__15821__15824] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__15812__15815__15818__15821__15824)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__15812__15815__15818__15821__15824,Vvar__0__a__15802)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__15812__15815__15818__15821__15824,Vvar__1__b__15803)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__15812__15815__15818__15821__15824,Vvar__2__g__15804) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__18196] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__18196)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__18196)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__18196)
& ! [Vvar__var__var__2__n__18201__18203__18205] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__18201__18203__18205)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__18201__18203__18205)
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__18201__18203__18205,Vvar__0__p__18196) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__18201__18203__18205,Vvar__0__p__18196) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__16008,Vvar__1__p__16009,VX16010] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__16008)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__16009)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__16008,Vvar__1__p__16009,VX16010)
=> ? [Vvar__2__q__16013] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__16013)
& ? [Vvar__3__r__16014] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__16014)
& Vvar__0__x__16008 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__16013,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__16009)),Vvar__3__r__16014)
& cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__16014)
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__16014,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__16009))
& VX16010 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__16008,Vvar__1__p__16009,Vvar__2__q__16013,Vvar__3__r__16014) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
! [Vvar__0__T__18703,Vvar__1__F__18704] :
( cType___24t(Vvar__0__T__18703)
=> ( t(Vvar__1__F__18704,Vvar__0__T__18703)
=> ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__18703,Vvar__1__F__18704)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
! [Vvar__0__T__18708,Vvar__1__F__18709] :
( cType___24t(Vvar__0__T__18708)
=> ( t(Vvar__1__F__18709,Vvar__0__T__18708)
=> ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__18708,Vvar__1__F__18709)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX17743] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX17743)
=> ( VX17743 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__17744] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17744)
& ? [Vvar__1___24Anonymous__17745] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__17745)
& VX17743 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__17744,Vvar__1___24Anonymous__17745) ) )
| ? [Vvar__0___24Anonymous__17746] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17746)
& ? [Vvar__1___24Anonymous__17747] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__17747)
& VX17743 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__17746,Vvar__1___24Anonymous__17747) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__5909,VX5910] :
( cType___24t(Vvar__0__C__5909)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5909,VX5910)
=> ( ? [Vvar__1___24Anonymous__5912] :
( t(Vvar__1___24Anonymous__5912,Vvar__0__C__5909)
& VX5910 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__5909,Vvar__1___24Anonymous__5912) )
| ? [Vvar__1___24Anonymous__5914] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5914)
& VX5910 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__5909,Vvar__1___24Anonymous__5914) )
| ? [Vvar__1___24Anonymous__5916] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5909,Vvar__1___24Anonymous__5916)
& ? [Vvar__2___24Anonymous__5917] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5909,Vvar__2___24Anonymous__5917)
& VX5910 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__5909,Vvar__1___24Anonymous__5916,Vvar__2___24Anonymous__5917) ) )
| ? [Vvar__1___24Anonymous__5919] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5909,Vvar__1___24Anonymous__5919)
& ? [Vvar__2___24Anonymous__5920] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5909,Vvar__2___24Anonymous__5920)
& VX5910 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__5909,Vvar__1___24Anonymous__5919,Vvar__2___24Anonymous__5920) ) )
| ? [Vvar__1___24Anonymous__5922] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5909,Vvar__1___24Anonymous__5922)
& ? [Vvar__2___24Anonymous__5923] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5909,Vvar__2___24Anonymous__5923)
& VX5910 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__5909,Vvar__1___24Anonymous__5922,Vvar__2___24Anonymous__5923) ) )
| ? [Vvar__1___24Anonymous__5925] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5909,Vvar__1___24Anonymous__5925)
& VX5910 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__5909,Vvar__1___24Anonymous__5925) )
| ? [Vvar__1___24Anonymous__5927] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5909,Vvar__1___24Anonymous__5927)
& ? [Vvar__2___24Anonymous__5928] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__5928)
& VX5910 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__5909,Vvar__1___24Anonymous__5927,Vvar__2___24Anonymous__5928) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__6073,VX6074] :
( cType___24t(Vvar__0__C__6073)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__6073,VX6074)
=> ( ? [Vvar__1___24Anonymous__6076] :
( t(Vvar__1___24Anonymous__6076,Vvar__0__C__6073)
& VX6074 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__6073,Vvar__1___24Anonymous__6076) )
| ? [Vvar__1___24Anonymous__6078] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6078)
& ? [Vvar__2___24Anonymous__6079] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__6073,Vvar__2___24Anonymous__6079)
& VX6074 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__6073,Vvar__1___24Anonymous__6078,Vvar__2___24Anonymous__6079) ) )
| ? [Vvar__1___24Anonymous__6081] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__6073,Vvar__1___24Anonymous__6081)
& ? [Vvar__2___24Anonymous__6082] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__6082)
& ? [Vvar__3___24Anonymous__6083] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__6073,Vvar__3___24Anonymous__6083)
& VX6074 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__6073,Vvar__1___24Anonymous__6081,Vvar__2___24Anonymous__6082,Vvar__3___24Anonymous__6083) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__8890,Vvar__1__rO__8891,Vvar__2__rI__8892,Vvar__3__rplus__8893,Vvar__4__rtimes__8898,Vvar__5__rminus__8903,Vvar__6__ropp__8908,Vvar__7__req__8911,Vvar__8__rle__8916,Vvar__9__rlt__8921] :
( cType___24t(Vvar__0__R__8890)
=> ( t(Vvar__1__rO__8891,Vvar__0__R__8890)
=> ( t(Vvar__2__rI__8892,Vvar__0__R__8890)
=> ( c_24__type__9322___24t(Vvar__0__R__8890,Vvar__1__rO__8891,Vvar__2__rI__8892,Vvar__3__rplus__8893,Vvar__4__rtimes__8898,Vvar__5__rminus__8903,Vvar__6__ropp__8908,Vvar__7__req__8911,Vvar__8__rle__8916,Vvar__9__rlt__8921,Vvar__3__rplus__8893)
=> ( c_24__type__9423___24t(Vvar__0__R__8890,Vvar__1__rO__8891,Vvar__2__rI__8892,Vvar__3__rplus__8893,Vvar__4__rtimes__8898,Vvar__5__rminus__8903,Vvar__6__ropp__8908,Vvar__7__req__8911,Vvar__8__rle__8916,Vvar__9__rlt__8921,Vvar__4__rtimes__8898)
=> ( c_24__type__9524___24t(Vvar__0__R__8890,Vvar__1__rO__8891,Vvar__2__rI__8892,Vvar__3__rplus__8893,Vvar__4__rtimes__8898,Vvar__5__rminus__8903,Vvar__6__ropp__8908,Vvar__7__req__8911,Vvar__8__rle__8916,Vvar__9__rlt__8921,Vvar__5__rminus__8903)
=> ( c_24__type__9614___24t(Vvar__0__R__8890,Vvar__1__rO__8891,Vvar__2__rI__8892,Vvar__3__rplus__8893,Vvar__4__rtimes__8898,Vvar__5__rminus__8903,Vvar__6__ropp__8908,Vvar__7__req__8911,Vvar__8__rle__8916,Vvar__9__rlt__8921,Vvar__6__ropp__8908)
=> ( c_24__type__9715___24t(Vvar__0__R__8890,Vvar__1__rO__8891,Vvar__2__rI__8892,Vvar__3__rplus__8893,Vvar__4__rtimes__8898,Vvar__5__rminus__8903,Vvar__6__ropp__8908,Vvar__7__req__8911,Vvar__8__rle__8916,Vvar__9__rlt__8921,Vvar__7__req__8911)
=> ( c_24__type__9816___24t(Vvar__0__R__8890,Vvar__1__rO__8891,Vvar__2__rI__8892,Vvar__3__rplus__8893,Vvar__4__rtimes__8898,Vvar__5__rminus__8903,Vvar__6__ropp__8908,Vvar__7__req__8911,Vvar__8__rle__8916,Vvar__9__rlt__8921,Vvar__8__rle__8916)
=> ( c_24__type__9917___24t(Vvar__0__R__8890,Vvar__1__rO__8891,Vvar__2__rI__8892,Vvar__3__rplus__8893,Vvar__4__rtimes__8898,Vvar__5__rminus__8903,Vvar__6__ropp__8908,Vvar__7__req__8911,Vvar__8__rle__8916,Vvar__9__rlt__8921,Vvar__9__rlt__8921)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__8890,Vvar__1__rO__8891,Vvar__2__rI__8892,Vvar__3__rplus__8893,Vvar__4__rtimes__8898,Vvar__5__rminus__8903,Vvar__6__ropp__8908,Vvar__7__req__8911,Vvar__8__rle__8916,Vvar__9__rlt__8921)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__8890,Vvar__7__req__8911)
& ! [Vvar__var__var__var__var__11__x1__8965__8971__9076__9082__9088] :
( t(Vvar__var__var__var__var__11__x1__8965__8971__9076__9082__9088,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__12__x2__8966__8972__9077__9083__9089] :
( t(Vvar__var__var__var__var__12__x2__8966__8972__9077__9083__9089,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__7__req__8911,Vvar__var__var__var__var__11__x1__8965__8971__9076__9082__9088),Vvar__var__var__var__var__12__x2__8966__8972__9077__9083__9089))
=> ! [Vvar__var__var__var__var__14__y1__8967__8973__9078__9084__9090] :
( t(Vvar__var__var__var__var__14__y1__8967__8973__9078__9084__9090,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__15__y2__8968__8974__9079__9085__9091] :
( t(Vvar__var__var__var__var__15__y2__8968__8974__9079__9085__9091,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__7__req__8911,Vvar__var__var__var__var__14__y1__8967__8973__9078__9084__9090),Vvar__var__var__var__var__15__y2__8968__8974__9079__9085__9091))
=> p(happ(happ(Vvar__7__req__8911,happ(happ(Vvar__3__rplus__8893,Vvar__var__var__var__var__11__x1__8965__8971__9076__9082__9088),Vvar__var__var__var__var__14__y1__8967__8973__9078__9084__9090)),happ(happ(Vvar__3__rplus__8893,Vvar__var__var__var__var__12__x2__8966__8972__9077__9083__9089),Vvar__var__var__var__var__15__y2__8968__8974__9079__9085__9091))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__8978__8984__9094__9100__9106] :
( t(Vvar__var__var__var__var__12__x1__8978__8984__9094__9100__9106,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__13__x2__8979__8985__9095__9101__9107] :
( t(Vvar__var__var__var__var__13__x2__8979__8985__9095__9101__9107,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__7__req__8911,Vvar__var__var__var__var__12__x1__8978__8984__9094__9100__9106),Vvar__var__var__var__var__13__x2__8979__8985__9095__9101__9107))
=> ! [Vvar__var__var__var__var__15__y1__8980__8986__9096__9102__9108] :
( t(Vvar__var__var__var__var__15__y1__8980__8986__9096__9102__9108,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__16__y2__8981__8987__9097__9103__9109] :
( t(Vvar__var__var__var__var__16__y2__8981__8987__9097__9103__9109,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__7__req__8911,Vvar__var__var__var__var__15__y1__8980__8986__9096__9102__9108),Vvar__var__var__var__var__16__y2__8981__8987__9097__9103__9109))
=> p(happ(happ(Vvar__7__req__8911,happ(happ(Vvar__4__rtimes__8898,Vvar__var__var__var__var__12__x1__8978__8984__9094__9100__9106),Vvar__var__var__var__var__15__y1__8980__8986__9096__9102__9108)),happ(happ(Vvar__4__rtimes__8898,Vvar__var__var__var__var__13__x2__8979__8985__9095__9101__9107),Vvar__var__var__var__var__16__y2__8981__8987__9097__9103__9109))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__8991__8994__9112__9115__9118] :
( t(Vvar__var__var__var__var__13__x1__8991__8994__9112__9115__9118,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__14__x2__8992__8995__9113__9116__9119] :
( t(Vvar__var__var__var__var__14__x2__8992__8995__9113__9116__9119,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__7__req__8911,Vvar__var__var__var__var__13__x1__8991__8994__9112__9115__9118),Vvar__var__var__var__var__14__x2__8992__8995__9113__9116__9119))
=> p(happ(happ(Vvar__7__req__8911,happ(Vvar__6__ropp__8908,Vvar__var__var__var__var__13__x1__8991__8994__9112__9115__9118)),happ(Vvar__6__ropp__8908,Vvar__var__var__var__var__14__x2__8992__8995__9113__9116__9119))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__8998__9004__9121__9127__9133] :
( t(Vvar__var__var__var__var__14__x1__8998__9004__9121__9127__9133,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__15__x2__8999__9005__9122__9128__9134] :
( t(Vvar__var__var__var__var__15__x2__8999__9005__9122__9128__9134,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__7__req__8911,Vvar__var__var__var__var__14__x1__8998__9004__9121__9127__9133),Vvar__var__var__var__var__15__x2__8999__9005__9122__9128__9134))
=> ! [Vvar__var__var__var__var__17__y1__9000__9006__9123__9129__9135] :
( t(Vvar__var__var__var__var__17__y1__9000__9006__9123__9129__9135,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__18__y2__9001__9007__9124__9130__9136] :
( t(Vvar__var__var__var__var__18__y2__9001__9007__9124__9130__9136,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__7__req__8911,Vvar__var__var__var__var__17__y1__9000__9006__9123__9129__9135),Vvar__var__var__var__var__18__y2__9001__9007__9124__9130__9136))
=> ( p(happ(happ(Vvar__8__rle__8916,Vvar__var__var__var__var__14__x1__8998__9004__9121__9127__9133),Vvar__var__var__var__var__17__y1__9000__9006__9123__9129__9135))
<=> p(happ(happ(Vvar__8__rle__8916,Vvar__var__var__var__var__15__x2__8999__9005__9122__9128__9134),Vvar__var__var__var__var__18__y2__9001__9007__9124__9130__9136)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__9011__9017__9139__9145__9151] :
( t(Vvar__var__var__var__var__15__x1__9011__9017__9139__9145__9151,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__16__x2__9012__9018__9140__9146__9152] :
( t(Vvar__var__var__var__var__16__x2__9012__9018__9140__9146__9152,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__7__req__8911,Vvar__var__var__var__var__15__x1__9011__9017__9139__9145__9151),Vvar__var__var__var__var__16__x2__9012__9018__9140__9146__9152))
=> ! [Vvar__var__var__var__var__18__y1__9013__9019__9141__9147__9153] :
( t(Vvar__var__var__var__var__18__y1__9013__9019__9141__9147__9153,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__19__y2__9014__9020__9142__9148__9154] :
( t(Vvar__var__var__var__var__19__y2__9014__9020__9142__9148__9154,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__7__req__8911,Vvar__var__var__var__var__18__y1__9013__9019__9141__9147__9153),Vvar__var__var__var__var__19__y2__9014__9020__9142__9148__9154))
=> ( p(happ(happ(Vvar__9__rlt__8921,Vvar__var__var__var__var__15__x1__9011__9017__9139__9145__9151),Vvar__var__var__var__var__18__y1__9013__9019__9141__9147__9153))
<=> p(happ(happ(Vvar__9__rlt__8921,Vvar__var__var__var__var__16__x2__9012__9018__9140__9146__9152),Vvar__var__var__var__var__19__y2__9014__9020__9142__9148__9154)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__8890,Vvar__1__rO__8891,Vvar__2__rI__8892,Vvar__3__rplus__8893,Vvar__4__rtimes__8898,Vvar__5__rminus__8903,Vvar__6__ropp__8908,Vvar__7__req__8911)
& ! [Vvar__var__var__var__17__n__9025__9026__9157__9158] :
( t(Vvar__var__var__var__17__n__9025__9026__9157__9158,Vvar__0__R__8890)
=> p(happ(happ(Vvar__8__rle__8916,Vvar__var__var__var__17__n__9025__9026__9157__9158),Vvar__var__var__var__17__n__9025__9026__9157__9158)) )
& ! [Vvar__var__var__var__var__18__n__9028__9032__9159__9163__9167] :
( t(Vvar__var__var__var__var__18__n__9028__9032__9159__9163__9167,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__19__m__9029__9033__9160__9164__9168] :
( t(Vvar__var__var__var__var__19__m__9029__9033__9160__9164__9168,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__8__rle__8916,Vvar__var__var__var__var__18__n__9028__9032__9159__9163__9167),Vvar__var__var__var__var__19__m__9029__9033__9160__9164__9168))
=> ( p(happ(happ(Vvar__8__rle__8916,Vvar__var__var__var__var__19__m__9029__9033__9160__9164__9168),Vvar__var__var__var__var__18__n__9028__9032__9159__9163__9167))
=> p(happ(happ(Vvar__7__req__8911,Vvar__var__var__var__var__18__n__9028__9032__9159__9163__9167),Vvar__var__var__var__var__19__m__9029__9033__9160__9164__9168)) ) ) ) )
& ! [Vvar__var__var__var__19__n__9037__9042__9171__9176] :
( t(Vvar__var__var__var__19__n__9037__9042__9171__9176,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__20__m__9038__9043__9172__9177] :
( t(Vvar__var__var__var__20__m__9038__9043__9172__9177,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__21__p__9039__9044__9173__9178] :
( t(Vvar__var__var__var__21__p__9039__9044__9173__9178,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__8__rle__8916,Vvar__var__var__var__19__n__9037__9042__9171__9176),Vvar__var__var__var__20__m__9038__9043__9172__9177))
=> ( p(happ(happ(Vvar__8__rle__8916,Vvar__var__var__var__20__m__9038__9043__9172__9177),Vvar__var__var__var__21__p__9039__9044__9173__9178))
=> p(happ(happ(Vvar__8__rle__8916,Vvar__var__var__var__19__n__9037__9042__9171__9176),Vvar__var__var__var__21__p__9039__9044__9173__9178)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__9048__9050__9181__9183__9185__9187] :
( t(Vvar__var__var__var__var__var__20__n__9048__9050__9181__9183__9185__9187,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__var__21__m__9049__9051__9182__9184__9186__9188] :
( t(Vvar__var__var__var__var__var__21__m__9049__9051__9182__9184__9186__9188,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__9__rlt__8921,Vvar__var__var__var__var__var__20__n__9048__9050__9181__9183__9185__9187),Vvar__var__var__var__var__var__21__m__9049__9051__9182__9184__9186__9188))
<=> ( p(happ(happ(Vvar__8__rle__8916,Vvar__var__var__var__var__var__20__n__9048__9050__9181__9183__9185__9187),Vvar__var__var__var__var__var__21__m__9049__9051__9182__9184__9186__9188))
& ~ p(happ(happ(Vvar__7__req__8911,Vvar__var__var__var__var__var__20__n__9048__9050__9181__9183__9185__9187),Vvar__var__var__var__var__var__21__m__9049__9051__9182__9184__9186__9188)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__9053__9055__9189__9191__9193] :
( t(Vvar__var__var__var__var__21__n__9053__9055__9189__9191__9193,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__22__m__9054__9056__9190__9192__9194] :
( t(Vvar__var__var__var__var__22__m__9054__9056__9190__9192__9194,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__9__rlt__8921,Vvar__var__var__var__var__21__n__9053__9055__9189__9191__9193),Vvar__var__var__var__var__22__m__9054__9056__9190__9192__9194))
| p(happ(happ(Vvar__7__req__8911,Vvar__var__var__var__var__21__n__9053__9055__9189__9191__9193),Vvar__var__var__var__var__22__m__9054__9056__9190__9192__9194))
| p(happ(happ(Vvar__9__rlt__8921,Vvar__var__var__var__var__22__m__9054__9056__9190__9192__9194),Vvar__var__var__var__var__21__n__9053__9055__9189__9191__9193)) ) ) )
& ! [Vvar__var__var__var__var__22__n__9058__9062__9195__9199__9203] :
( t(Vvar__var__var__var__var__22__n__9058__9062__9195__9199__9203,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__23__m__9059__9063__9196__9200__9204] :
( t(Vvar__var__var__var__var__23__m__9059__9063__9196__9200__9204,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__24__p__9060__9064__9197__9201__9205] :
( t(Vvar__var__var__var__var__24__p__9060__9064__9197__9201__9205,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__8__rle__8916,Vvar__var__var__var__var__22__n__9058__9062__9195__9199__9203),Vvar__var__var__var__var__23__m__9059__9063__9196__9200__9204))
=> p(happ(happ(Vvar__8__rle__8916,happ(happ(Vvar__3__rplus__8893,Vvar__var__var__var__var__24__p__9060__9064__9197__9201__9205),Vvar__var__var__var__var__22__n__9058__9062__9195__9199__9203)),happ(happ(Vvar__3__rplus__8893,Vvar__var__var__var__var__24__p__9060__9064__9197__9201__9205),Vvar__var__var__var__var__23__m__9059__9063__9196__9200__9204))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__9067__9071__9207__9211__9215__9219] :
( t(Vvar__var__var__var__var__var__23__n__9067__9071__9207__9211__9215__9219,Vvar__0__R__8890)
=> ! [Vvar__var__var__var__var__var__24__m__9068__9072__9208__9212__9216__9220] :
( t(Vvar__var__var__var__var__var__24__m__9068__9072__9208__9212__9216__9220,Vvar__0__R__8890)
=> ( p(happ(happ(Vvar__9__rlt__8921,Vvar__1__rO__8891),Vvar__var__var__var__var__var__23__n__9067__9071__9207__9211__9215__9219))
=> ( p(happ(happ(Vvar__9__rlt__8921,Vvar__1__rO__8891),Vvar__var__var__var__var__var__24__m__9068__9072__9208__9212__9216__9220))
=> p(happ(happ(Vvar__9__rlt__8921,Vvar__1__rO__8891),happ(happ(Vvar__4__rtimes__8898,Vvar__var__var__var__var__var__23__n__9067__9071__9207__9211__9215__9219),Vvar__var__var__var__var__var__24__m__9068__9072__9208__9212__9216__9220))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__8911,Vvar__1__rO__8891),Vvar__2__rI__8892))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX21537] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX21537)
=> ( VX21537 = cCoq_2emicromega_2eRMicromega_2eC0
| VX21537 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__21538] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__21538)
& VX21537 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__21538) )
| ? [Vvar__0__r__21539] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__21539)
& VX21537 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__21539) )
| ? [Vvar__0__r1__21540] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__21540)
& ? [Vvar__1__r2__21541] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__21541)
& VX21537 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__21540,Vvar__1__r2__21541) ) )
| ? [Vvar__0__r1__21542] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__21542)
& ? [Vvar__1__r2__21543] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__21543)
& VX21537 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__21542,Vvar__1__r2__21543) ) )
| ? [Vvar__0__r1__21544] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__21544)
& ? [Vvar__1__r2__21545] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__21545)
& VX21537 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__21544,Vvar__1__r2__21545) ) )
| ? [Vvar__0__r1__21546] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__21546)
& ? [Vvar__1__z__21547] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__21547)
& VX21537 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__21546,Vvar__1__z__21547) ) )
| ? [Vvar__0__r__21548] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__21548)
& VX21537 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__21548) )
| ? [Vvar__0__r__21549] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__21549)
& VX21537 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__21549) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__28108,VX28109] :
( cType___24t(Vvar__0__T__28108)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__28108,VX28109)
=> ? [Vvar__1__Flhs__28111] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__28108,Vvar__1__Flhs__28111)
& ? [Vvar__2__Fop__28112] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__28112)
& ? [Vvar__3__Frhs__28113] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__28108,Vvar__3__Frhs__28113)
& VX28109 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__28108,Vvar__1__Flhs__28111,Vvar__2__Fop__28112,Vvar__3__Frhs__28113) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX27961] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX27961)
=> ( VX27961 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX27961 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX27961 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX27961 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX17833] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX17833)
=> ( VX17833 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX17833 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX17833 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX17833 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX17833 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX17833 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__27962,VX27963] :
( cType___24t(Vvar__0__C__27962)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27962,VX27963)
=> ( ? [Vvar__1___24Anonymous__27965] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__27965)
& VX27963 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__27962,Vvar__1___24Anonymous__27965) )
| ? [Vvar__1___24Anonymous__27967] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__27962,Vvar__1___24Anonymous__27967)
& VX27963 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__27962,Vvar__1___24Anonymous__27967) )
| ? [Vvar__1___24Anonymous__27969] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__27962,Vvar__1___24Anonymous__27969)
& ? [Vvar__2___24Anonymous__27970] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27962,Vvar__2___24Anonymous__27970)
& VX27963 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__27962,Vvar__1___24Anonymous__27969,Vvar__2___24Anonymous__27970) ) )
| ? [Vvar__1___24Anonymous__27972] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27962,Vvar__1___24Anonymous__27972)
& ? [Vvar__2___24Anonymous__27973] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27962,Vvar__2___24Anonymous__27973)
& VX27963 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__27962,Vvar__1___24Anonymous__27972,Vvar__2___24Anonymous__27973) ) )
| ? [Vvar__1___24Anonymous__27975] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27962,Vvar__1___24Anonymous__27975)
& ? [Vvar__2___24Anonymous__27976] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27962,Vvar__2___24Anonymous__27976)
& VX27963 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__27962,Vvar__1___24Anonymous__27975,Vvar__2___24Anonymous__27976) ) )
| ? [Vvar__1___24Anonymous__27978] :
( t(Vvar__1___24Anonymous__27978,Vvar__0__C__27962)
& VX27963 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__27962,Vvar__1___24Anonymous__27978) )
| VX27963 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__27962) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737] :
( cType___24t(Vvar__0__R__22668)
=> ( t(Vvar__1__rO__22669,Vvar__0__R__22668)
=> ( t(Vvar__2__rI__22670,Vvar__0__R__22668)
=> ( c_24__type__23201___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__3__rplus__22671)
=> ( c_24__type__23547___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__4__rtimes__22676)
=> ( c_24__type__23893___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__5__rminus__22681)
=> ( c_24__type__24216___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__6__ropp__22686)
=> ( c_24__type__24562___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__7__req__22689)
=> ( c_24__type__24908___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__8__rle__22694)
=> ( cType___24t(Vvar__9__C__22699)
=> ( t(Vvar__10__cO__22700,Vvar__9__C__22699)
=> ( t(Vvar__11__cI__22701,Vvar__9__C__22699)
=> ( c_24__type__25254___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__12__cplus__22702)
=> ( c_24__type__25600___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__13__ctimes__22707)
=> ( c_24__type__25946___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__14__cminus__22712)
=> ( c_24__type__26269___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__15__copp__22717)
=> ( c_24__type__26615___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__16__ceqb__22720)
=> ( c_24__type__26961___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__17__cleb__22725)
=> ( c_24__type__27284___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__18__phi__22730)
=> ( cType___24t(Vvar__19__E__22733)
=> ( c_24__type__27607___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__20__pow__phi__22734)
=> ( c_24__type__27953___24t(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737,Vvar__21__rpow__22737)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__8__rle__22694,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__17__cleb__22725,Vvar__18__phi__22730,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__22668,Vvar__1__rO__22669,Vvar__2__rI__22670,Vvar__3__rplus__22671,Vvar__4__rtimes__22676,Vvar__5__rminus__22681,Vvar__6__ropp__22686,Vvar__7__req__22689,Vvar__9__C__22699,Vvar__10__cO__22700,Vvar__11__cI__22701,Vvar__12__cplus__22702,Vvar__13__ctimes__22707,Vvar__14__cminus__22712,Vvar__15__copp__22717,Vvar__16__ceqb__22720,Vvar__18__phi__22730)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__22668,Vvar__2__rI__22670,Vvar__4__rtimes__22676,Vvar__7__req__22689,Vvar__19__E__22733,Vvar__20__pow__phi__22734,Vvar__21__rpow__22737)
& ! [Vvar__var__var__var__var__var__24__x__22820__22823__22833__22836__22839__22842] :
( t(Vvar__var__var__var__var__var__24__x__22820__22823__22833__22836__22839__22842,Vvar__9__C__22699)
=> ! [Vvar__var__var__var__var__var__25__y__22821__22824__22834__22837__22840__22843] :
( t(Vvar__var__var__var__var__var__25__y__22821__22824__22834__22837__22840__22843,Vvar__9__C__22699)
=> ( happ(happ(Vvar__16__ceqb__22720,Vvar__var__var__var__var__var__24__x__22820__22823__22833__22836__22839__22842),Vvar__var__var__var__var__var__25__y__22821__22824__22834__22837__22840__22843) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__22689,happ(Vvar__18__phi__22730,Vvar__var__var__var__var__var__24__x__22820__22823__22833__22836__22839__22842)),happ(Vvar__18__phi__22730,Vvar__var__var__var__var__var__25__y__22821__22824__22834__22837__22840__22843))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__22827__22830__22845__22848__22851__22854] :
( t(Vvar__var__var__var__var__var__25__x__22827__22830__22845__22848__22851__22854,Vvar__9__C__22699)
=> ! [Vvar__var__var__var__var__var__26__y__22828__22831__22846__22849__22852__22855] :
( t(Vvar__var__var__var__var__var__26__y__22828__22831__22846__22849__22852__22855,Vvar__9__C__22699)
=> ( happ(happ(Vvar__17__cleb__22725,Vvar__var__var__var__var__var__25__x__22827__22830__22845__22848__22851__22854),Vvar__var__var__var__var__var__26__y__22828__22831__22846__22849__22852__22855) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__22694,happ(Vvar__18__phi__22730,Vvar__var__var__var__var__var__25__x__22827__22830__22845__22848__22851__22854)),happ(Vvar__18__phi__22730,Vvar__var__var__var__var__var__26__y__22828__22831__22846__22849__22852__22855))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,VX14243] :
( cType___24t(Vvar__0__TA__14239)
=> ( cType___24t(Vvar__1__TX__14240)
=> ( cType___24t(Vvar__2__AA__14241)
=> ( cType___24t(Vvar__3__AF__14242)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,VX14243)
=> ( VX14243 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242)
| VX14243 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242)
| ? [Vvar__4___24Anonymous__14256] :
( t(Vvar__4___24Anonymous__14256,Vvar__1__TX__14240)
& VX14243 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__4___24Anonymous__14256) )
| ? [Vvar__4___24Anonymous__14261] :
( t(Vvar__4___24Anonymous__14261,Vvar__0__TA__14239)
& ? [Vvar__5___24Anonymous__14262] :
( t(Vvar__5___24Anonymous__14262,Vvar__2__AA__14241)
& VX14243 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__4___24Anonymous__14261,Vvar__5___24Anonymous__14262) ) )
| ? [Vvar__4___24Anonymous__14267] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__4___24Anonymous__14267)
& ? [Vvar__5___24Anonymous__14268] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__5___24Anonymous__14268)
& VX14243 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__4___24Anonymous__14267,Vvar__5___24Anonymous__14268) ) )
| ? [Vvar__4___24Anonymous__14273] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__4___24Anonymous__14273)
& ? [Vvar__5___24Anonymous__14274] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__5___24Anonymous__14274)
& VX14243 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__4___24Anonymous__14273,Vvar__5___24Anonymous__14274) ) )
| ? [Vvar__4___24Anonymous__14279] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__4___24Anonymous__14279)
& VX14243 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__4___24Anonymous__14279) )
| ? [Vvar__4___24Anonymous__14284] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__4___24Anonymous__14284)
& ? [Vvar__5___24Anonymous__14285] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__14242,Vvar__5___24Anonymous__14285)
& ? [Vvar__6___24Anonymous__14286] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__6___24Anonymous__14286)
& VX14243 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__14239,Vvar__1__TX__14240,Vvar__2__AA__14241,Vvar__3__AF__14242,Vvar__4___24Anonymous__14284,Vvar__5___24Anonymous__14285,Vvar__6___24Anonymous__14286) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__30446,VX30447] :
( cType___24t(Vvar__0__A__30446)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__30446,VX30447)
=> ( VX30447 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__30446)
| ? [Vvar__1___24Anonymous__30450] :
( t(Vvar__1___24Anonymous__30450,Vvar__0__A__30446)
& VX30447 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__30446,Vvar__1___24Anonymous__30450) )
| ? [Vvar__1___24Anonymous__30452] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__30446,Vvar__1___24Anonymous__30452)
& ? [Vvar__2___24Anonymous__30453] :
( t(Vvar__2___24Anonymous__30453,Vvar__0__A__30446)
& ? [Vvar__3___24Anonymous__30454] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__30446,Vvar__3___24Anonymous__30454)
& VX30447 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__30446,Vvar__1___24Anonymous__30452,Vvar__2___24Anonymous__30453,Vvar__3___24Anonymous__30454) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
! [Vvar__0___24Anonymous__30707] :
( cProp___24t(Vvar__0___24Anonymous__30707)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__30707)
=> ( ? [Vvar__0__P__30709] :
( cProp___24t(Vvar__0__P__30709)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__30709)
& Vvar__0___24Anonymous__30707 = Vvar__0__P__30709 )
| ? [Vvar__0__s__30711] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__30711)
& Vvar__0___24Anonymous__30707 = c_24__prop__30720___24a2(Vvar__0___24Anonymous__30707,Vvar__0__s__30711) )
| ? [Vvar__0__s1__30713] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__30713)
& ? [Vvar__1__s2__30714] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__30714)
& Vvar__0___24Anonymous__30707 = c_24__prop__30721___24a3(Vvar__0___24Anonymous__30707,Vvar__0__s1__30713,Vvar__1__s2__30714) ) )
| ? [Vvar__0__s1__30717] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__30717)
& ? [Vvar__1__s2__30718] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__30718)
& Vvar__0___24Anonymous__30707 = c_24__prop__30722___24a3(Vvar__0___24Anonymous__30707,Vvar__0__s1__30717,Vvar__1__s2__30718) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__30676] :
( cProp___24t(Vvar__0___24Anonymous__30676)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__30676)
=> ( ? [Vvar__0__S__30678] :
( cType___24t(Vvar__0__S__30678)
& ? [Vvar__1__x__30679] :
( t(Vvar__1__x__30679,Vvar__0__S__30678)
& ? [Vvar__2__y__30680] :
( t(Vvar__2__y__30680,Vvar__0__S__30678)
& Vvar__0___24Anonymous__30676 = c_24__prop__30700___24a4(Vvar__0___24Anonymous__30676,Vvar__0__S__30678,Vvar__1__x__30679,Vvar__2__y__30680) ) ) )
| ? [Vvar__0__x__30681] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__30681)
& ? [Vvar__1__y__30682] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__30682)
& Vvar__0___24Anonymous__30676 = c_24__prop__30701___24a3(Vvar__0___24Anonymous__30676,Vvar__0__x__30681,Vvar__1__y__30682) ) )
| ? [Vvar__0__x__30683] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__30683)
& ? [Vvar__1__s__30684] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__30684)
& Vvar__0___24Anonymous__30676 = c_24__prop__30702___24a3(Vvar__0___24Anonymous__30676,Vvar__0__x__30683,Vvar__1__s__30684) ) )
| Vvar__0___24Anonymous__30676 = c_24True
| Vvar__0___24Anonymous__30676 = c_24False
| ? [Vvar__0__P__30685] :
( cProp___24t(Vvar__0__P__30685)
& ? [Vvar__1__Q__30686] :
( cProp___24t(Vvar__1__Q__30686)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__30685)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__30686)
& Vvar__0___24Anonymous__30676 = c_24__prop__30703___24a3(Vvar__0___24Anonymous__30676,Vvar__0__P__30685,Vvar__1__Q__30686) ) )
| ? [Vvar__0__P__30689] :
( cProp___24t(Vvar__0__P__30689)
& ? [Vvar__1__Q__30690] :
( cProp___24t(Vvar__1__Q__30690)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__30689)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__30690)
& Vvar__0___24Anonymous__30676 = c_24__prop__30704___24a3(Vvar__0___24Anonymous__30676,Vvar__0__P__30689,Vvar__1__Q__30690) ) )
| ? [Vvar__0__P__30693] :
( cProp___24t(Vvar__0__P__30693)
& ? [Vvar__1__Q__30694] :
( cProp___24t(Vvar__1__Q__30694)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__30693)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__30694)
& Vvar__0___24Anonymous__30676 = c_24__prop__30705___24a3(Vvar__0___24Anonymous__30676,Vvar__0__P__30693,Vvar__1__Q__30694) ) )
| ? [Vvar__0__P__30698] :
( cProp___24t(Vvar__0__P__30698)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__30698)
& Vvar__0___24Anonymous__30676 = c_24__prop__30706___24a2(Vvar__0___24Anonymous__30676,Vvar__0__P__30698) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX30533] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX30533)
=> ( VX30533 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__30534] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__30534)
& ? [Vvar__1___24Anonymous__30535] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__30535)
& VX30533 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__30534,Vvar__1___24Anonymous__30535) ) )
| ? [Vvar__0___24Anonymous__30536] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__30536)
& ? [Vvar__1___24Anonymous__30537] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__30537)
& VX30533 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__30536,Vvar__1___24Anonymous__30537) ) )
| ? [Vvar__0___24Anonymous__30538] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__30538)
& ? [Vvar__1___24Anonymous__30539] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__30539)
& ? [Vvar__2___24Anonymous__30540] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__30540)
& VX30533 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__30538,Vvar__1___24Anonymous__30539,Vvar__2___24Anonymous__30540) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__15690,Vvar__1__env__15691,Vvar__2__env_27__15694,Vvar__3__x__15697] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__15690)
=> ( c_24__type__15718___24t(Vvar__0__fr__15690,Vvar__1__env__15691,Vvar__2__env_27__15694,Vvar__3__x__15697,Vvar__1__env__15691)
=> ( c_24__type__15727___24t(Vvar__0__fr__15690,Vvar__1__env__15691,Vvar__2__env_27__15694,Vvar__3__x__15697,Vvar__2__env_27__15694)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__15697)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__15690,Vvar__1__env__15691,Vvar__2__env_27__15694,Vvar__3__x__15697)
=> ( happ(Vvar__1__env__15691,Vvar__3__x__15697) = happ(Vvar__2__env_27__15694,Vvar__3__x__15697)
& happ(Vvar__1__env__15691,Vvar__3__x__15697) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__15694,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__15690,Vvar__3__x__15697))),happ(Vvar__2__env_27__15694,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__15690,Vvar__3__x__15697))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__15694,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__15690,Vvar__3__x__15697))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__15694,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__15690,Vvar__3__x__15697))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__18759,VX18760] :
( cType___24t(Vvar__0__C__18759)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18759,VX18760)
=> ( VX18760 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__18759)
| VX18760 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__18759)
| ? [Vvar__1___24Anonymous__18764] :
( t(Vvar__1___24Anonymous__18764,Vvar__0__C__18759)
& VX18760 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__18759,Vvar__1___24Anonymous__18764) )
| ? [Vvar__1___24Anonymous__18766] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__18766)
& VX18760 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__18759,Vvar__1___24Anonymous__18766) )
| ? [Vvar__1___24Anonymous__18768] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18759,Vvar__1___24Anonymous__18768)
& ? [Vvar__2___24Anonymous__18769] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18759,Vvar__2___24Anonymous__18769)
& VX18760 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__18759,Vvar__1___24Anonymous__18768,Vvar__2___24Anonymous__18769) ) )
| ? [Vvar__1___24Anonymous__18771] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18759,Vvar__1___24Anonymous__18771)
& ? [Vvar__2___24Anonymous__18772] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18759,Vvar__2___24Anonymous__18772)
& VX18760 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__18759,Vvar__1___24Anonymous__18771,Vvar__2___24Anonymous__18772) ) )
| ? [Vvar__1___24Anonymous__18774] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18759,Vvar__1___24Anonymous__18774)
& ? [Vvar__2___24Anonymous__18775] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18759,Vvar__2___24Anonymous__18775)
& VX18760 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__18759,Vvar__1___24Anonymous__18774,Vvar__2___24Anonymous__18775) ) )
| ? [Vvar__1___24Anonymous__18777] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18759,Vvar__1___24Anonymous__18777)
& VX18760 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__18759,Vvar__1___24Anonymous__18777) )
| ? [Vvar__1___24Anonymous__18779] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18759,Vvar__1___24Anonymous__18779)
& VX18760 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__18759,Vvar__1___24Anonymous__18779) )
| ? [Vvar__1___24Anonymous__18781] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18759,Vvar__1___24Anonymous__18781)
& ? [Vvar__2___24Anonymous__18782] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18759,Vvar__2___24Anonymous__18782)
& VX18760 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__18759,Vvar__1___24Anonymous__18781,Vvar__2___24Anonymous__18782) ) )
| ? [Vvar__1___24Anonymous__18784] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18759,Vvar__1___24Anonymous__18784)
& ? [Vvar__2___24Anonymous__18785] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__18785)
& VX18760 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__18759,Vvar__1___24Anonymous__18784,Vvar__2___24Anonymous__18785) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__6576,Vvar__1__rO__6577,Vvar__2__rI__6578,Vvar__3__radd__6579,Vvar__4__rmul__6584,Vvar__5__rsub__6589,Vvar__6__ropp__6594,Vvar__7__rdiv__6597,Vvar__8__rinv__6602,Vvar__9__req__6605] :
( cType___24t(Vvar__0__R__6576)
=> ( t(Vvar__1__rO__6577,Vvar__0__R__6576)
=> ( t(Vvar__2__rI__6578,Vvar__0__R__6576)
=> ( c_24__type__6770___24t(Vvar__0__R__6576,Vvar__1__rO__6577,Vvar__2__rI__6578,Vvar__3__radd__6579,Vvar__4__rmul__6584,Vvar__5__rsub__6589,Vvar__6__ropp__6594,Vvar__7__rdiv__6597,Vvar__8__rinv__6602,Vvar__9__req__6605,Vvar__3__radd__6579)
=> ( c_24__type__6863___24t(Vvar__0__R__6576,Vvar__1__rO__6577,Vvar__2__rI__6578,Vvar__3__radd__6579,Vvar__4__rmul__6584,Vvar__5__rsub__6589,Vvar__6__ropp__6594,Vvar__7__rdiv__6597,Vvar__8__rinv__6602,Vvar__9__req__6605,Vvar__4__rmul__6584)
=> ( c_24__type__6956___24t(Vvar__0__R__6576,Vvar__1__rO__6577,Vvar__2__rI__6578,Vvar__3__radd__6579,Vvar__4__rmul__6584,Vvar__5__rsub__6589,Vvar__6__ropp__6594,Vvar__7__rdiv__6597,Vvar__8__rinv__6602,Vvar__9__req__6605,Vvar__5__rsub__6589)
=> ( c_24__type__7038___24t(Vvar__0__R__6576,Vvar__1__rO__6577,Vvar__2__rI__6578,Vvar__3__radd__6579,Vvar__4__rmul__6584,Vvar__5__rsub__6589,Vvar__6__ropp__6594,Vvar__7__rdiv__6597,Vvar__8__rinv__6602,Vvar__9__req__6605,Vvar__6__ropp__6594)
=> ( c_24__type__7131___24t(Vvar__0__R__6576,Vvar__1__rO__6577,Vvar__2__rI__6578,Vvar__3__radd__6579,Vvar__4__rmul__6584,Vvar__5__rsub__6589,Vvar__6__ropp__6594,Vvar__7__rdiv__6597,Vvar__8__rinv__6602,Vvar__9__req__6605,Vvar__7__rdiv__6597)
=> ( c_24__type__7213___24t(Vvar__0__R__6576,Vvar__1__rO__6577,Vvar__2__rI__6578,Vvar__3__radd__6579,Vvar__4__rmul__6584,Vvar__5__rsub__6589,Vvar__6__ropp__6594,Vvar__7__rdiv__6597,Vvar__8__rinv__6602,Vvar__9__req__6605,Vvar__8__rinv__6602)
=> ( c_24__type__7306___24t(Vvar__0__R__6576,Vvar__1__rO__6577,Vvar__2__rI__6578,Vvar__3__radd__6579,Vvar__4__rmul__6584,Vvar__5__rsub__6589,Vvar__6__ropp__6594,Vvar__7__rdiv__6597,Vvar__8__rinv__6602,Vvar__9__req__6605,Vvar__9__req__6605)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__6576,Vvar__1__rO__6577,Vvar__2__rI__6578,Vvar__3__radd__6579,Vvar__4__rmul__6584,Vvar__5__rsub__6589,Vvar__6__ropp__6594,Vvar__7__rdiv__6597,Vvar__8__rinv__6602,Vvar__9__req__6605)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__6576,Vvar__1__rO__6577,Vvar__2__rI__6578,Vvar__3__radd__6579,Vvar__4__rmul__6584,Vvar__5__rsub__6589,Vvar__6__ropp__6594,Vvar__9__req__6605)
& ~ p(happ(happ(Vvar__9__req__6605,Vvar__2__rI__6578),Vvar__1__rO__6577))
& ! [Vvar__var__var__var__var__var__var__12__p__6648__6650__6657__6659__6661__6663__6665] :
( t(Vvar__var__var__var__var__var__var__12__p__6648__6650__6657__6659__6661__6663__6665,Vvar__0__R__6576)
=> ! [Vvar__var__var__var__var__var__var__13__q__6649__6651__6658__6660__6662__6664__6666] :
( t(Vvar__var__var__var__var__var__var__13__q__6649__6651__6658__6660__6662__6664__6666,Vvar__0__R__6576)
=> p(happ(happ(Vvar__9__req__6605,happ(happ(Vvar__7__rdiv__6597,Vvar__var__var__var__var__var__var__12__p__6648__6650__6657__6659__6661__6663__6665),Vvar__var__var__var__var__var__var__13__q__6649__6651__6658__6660__6662__6664__6666)),happ(happ(Vvar__4__rmul__6584,Vvar__var__var__var__var__var__var__12__p__6648__6650__6657__6659__6661__6663__6665),happ(Vvar__8__rinv__6602,Vvar__var__var__var__var__var__var__13__q__6649__6651__6658__6660__6662__6664__6666)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__6653__6655__6667__6669__6671__6673__6675__6677] :
( t(Vvar__var__var__var__var__var__var__var__13__p__6653__6655__6667__6669__6671__6673__6675__6677,Vvar__0__R__6576)
=> ( ~ p(happ(happ(Vvar__9__req__6605,Vvar__var__var__var__var__var__var__var__13__p__6653__6655__6667__6669__6671__6673__6675__6677),Vvar__1__rO__6577))
=> p(happ(happ(Vvar__9__req__6605,happ(happ(Vvar__4__rmul__6584,happ(Vvar__8__rinv__6602,Vvar__var__var__var__var__var__var__var__13__p__6653__6655__6667__6669__6671__6673__6675__6677)),Vvar__var__var__var__var__var__var__var__13__p__6653__6655__6667__6669__6671__6673__6675__6677)),Vvar__2__rI__6578)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__19120,Vvar__1__rO__19121,Vvar__2__rI__19122,Vvar__3__radd__19123,Vvar__4__rmul__19128,Vvar__5__rsub__19133,Vvar__6__ropp__19138,Vvar__7__rdiv__19141,Vvar__8__rinv__19146,Vvar__9__req__19149] :
( cType___24t(Vvar__0__R__19120)
=> ( t(Vvar__1__rO__19121,Vvar__0__R__19120)
=> ( t(Vvar__2__rI__19122,Vvar__0__R__19120)
=> ( c_24__type__19314___24t(Vvar__0__R__19120,Vvar__1__rO__19121,Vvar__2__rI__19122,Vvar__3__radd__19123,Vvar__4__rmul__19128,Vvar__5__rsub__19133,Vvar__6__ropp__19138,Vvar__7__rdiv__19141,Vvar__8__rinv__19146,Vvar__9__req__19149,Vvar__3__radd__19123)
=> ( c_24__type__19407___24t(Vvar__0__R__19120,Vvar__1__rO__19121,Vvar__2__rI__19122,Vvar__3__radd__19123,Vvar__4__rmul__19128,Vvar__5__rsub__19133,Vvar__6__ropp__19138,Vvar__7__rdiv__19141,Vvar__8__rinv__19146,Vvar__9__req__19149,Vvar__4__rmul__19128)
=> ( c_24__type__19500___24t(Vvar__0__R__19120,Vvar__1__rO__19121,Vvar__2__rI__19122,Vvar__3__radd__19123,Vvar__4__rmul__19128,Vvar__5__rsub__19133,Vvar__6__ropp__19138,Vvar__7__rdiv__19141,Vvar__8__rinv__19146,Vvar__9__req__19149,Vvar__5__rsub__19133)
=> ( c_24__type__19582___24t(Vvar__0__R__19120,Vvar__1__rO__19121,Vvar__2__rI__19122,Vvar__3__radd__19123,Vvar__4__rmul__19128,Vvar__5__rsub__19133,Vvar__6__ropp__19138,Vvar__7__rdiv__19141,Vvar__8__rinv__19146,Vvar__9__req__19149,Vvar__6__ropp__19138)
=> ( c_24__type__19675___24t(Vvar__0__R__19120,Vvar__1__rO__19121,Vvar__2__rI__19122,Vvar__3__radd__19123,Vvar__4__rmul__19128,Vvar__5__rsub__19133,Vvar__6__ropp__19138,Vvar__7__rdiv__19141,Vvar__8__rinv__19146,Vvar__9__req__19149,Vvar__7__rdiv__19141)
=> ( c_24__type__19757___24t(Vvar__0__R__19120,Vvar__1__rO__19121,Vvar__2__rI__19122,Vvar__3__radd__19123,Vvar__4__rmul__19128,Vvar__5__rsub__19133,Vvar__6__ropp__19138,Vvar__7__rdiv__19141,Vvar__8__rinv__19146,Vvar__9__req__19149,Vvar__8__rinv__19146)
=> ( c_24__type__19850___24t(Vvar__0__R__19120,Vvar__1__rO__19121,Vvar__2__rI__19122,Vvar__3__radd__19123,Vvar__4__rmul__19128,Vvar__5__rsub__19133,Vvar__6__ropp__19138,Vvar__7__rdiv__19141,Vvar__8__rinv__19146,Vvar__9__req__19149,Vvar__9__req__19149)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__19120,Vvar__1__rO__19121,Vvar__2__rI__19122,Vvar__3__radd__19123,Vvar__4__rmul__19128,Vvar__5__rsub__19133,Vvar__6__ropp__19138,Vvar__7__rdiv__19141,Vvar__8__rinv__19146,Vvar__9__req__19149)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__19120,Vvar__1__rO__19121,Vvar__2__rI__19122,Vvar__3__radd__19123,Vvar__4__rmul__19128,Vvar__5__rsub__19133,Vvar__6__ropp__19138,Vvar__9__req__19149)
& ~ p(happ(happ(Vvar__9__req__19149,Vvar__2__rI__19122),Vvar__1__rO__19121))
& ! [Vvar__var__var__var__var__var__var__12__p__19192__19194__19201__19203__19205__19207__19209] :
( t(Vvar__var__var__var__var__var__var__12__p__19192__19194__19201__19203__19205__19207__19209,Vvar__0__R__19120)
=> ! [Vvar__var__var__var__var__var__var__13__q__19193__19195__19202__19204__19206__19208__19210] :
( t(Vvar__var__var__var__var__var__var__13__q__19193__19195__19202__19204__19206__19208__19210,Vvar__0__R__19120)
=> p(happ(happ(Vvar__9__req__19149,happ(happ(Vvar__7__rdiv__19141,Vvar__var__var__var__var__var__var__12__p__19192__19194__19201__19203__19205__19207__19209),Vvar__var__var__var__var__var__var__13__q__19193__19195__19202__19204__19206__19208__19210)),happ(happ(Vvar__4__rmul__19128,Vvar__var__var__var__var__var__var__12__p__19192__19194__19201__19203__19205__19207__19209),happ(Vvar__8__rinv__19146,Vvar__var__var__var__var__var__var__13__q__19193__19195__19202__19204__19206__19208__19210)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__19197__19199__19211__19213__19215__19217__19219__19221] :
( t(Vvar__var__var__var__var__var__var__var__13__p__19197__19199__19211__19213__19215__19217__19219__19221,Vvar__0__R__19120)
=> ( ~ p(happ(happ(Vvar__9__req__19149,Vvar__var__var__var__var__var__var__var__13__p__19197__19199__19211__19213__19215__19217__19219__19221),Vvar__1__rO__19121))
=> p(happ(happ(Vvar__9__req__19149,happ(happ(Vvar__4__rmul__19128,happ(Vvar__8__rinv__19146,Vvar__var__var__var__var__var__var__var__13__p__19197__19199__19211__19213__19215__19217__19219__19221)),Vvar__var__var__var__var__var__var__var__13__p__19197__19199__19211__19213__19215__19217__19219__19221)),Vvar__2__rI__19122)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__19092,VX19093] :
( cType___24t(Vvar__0__C__19092)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__19092,VX19093)
=> ? [Vvar__1__num__19095] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19092,Vvar__1__num__19095)
& ? [Vvar__2__denum__19096] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19092,Vvar__2__denum__19096)
& ? [Vvar__3__condition__19097] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__19092),Vvar__3__condition__19097)
& VX19093 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__19092,Vvar__1__num__19095,Vvar__2__denum__19096,Vvar__3__condition__19097) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__19106,VX19107] :
( cType___24t(Vvar__0__C__19106)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__19106,VX19107)
=> ? [Vvar__1__rsplit__left__19109] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19106,Vvar__1__rsplit__left__19109)
& ? [Vvar__2__rsplit__common__19110] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19106,Vvar__2__rsplit__common__19110)
& ? [Vvar__3__rsplit__right__19111] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__19106,Vvar__3__rsplit__right__19111)
& VX19107 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__19106,Vvar__1__rsplit__left__19109,Vvar__2__rsplit__common__19110,Vvar__3__rsplit__right__19111) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__19856,Vvar__1__rO__19857,Vvar__2__rI__19858,Vvar__3__radd__19859,Vvar__4__rmul__19864,Vvar__5__rdiv__19869,Vvar__6__rinv__19874,Vvar__7__req__19877] :
( cType___24t(Vvar__0__R__19856)
=> ( t(Vvar__1__rO__19857,Vvar__0__R__19856)
=> ( t(Vvar__2__rI__19858,Vvar__0__R__19856)
=> ( c_24__type__20004___24t(Vvar__0__R__19856,Vvar__1__rO__19857,Vvar__2__rI__19858,Vvar__3__radd__19859,Vvar__4__rmul__19864,Vvar__5__rdiv__19869,Vvar__6__rinv__19874,Vvar__7__req__19877,Vvar__3__radd__19859)
=> ( c_24__type__20067___24t(Vvar__0__R__19856,Vvar__1__rO__19857,Vvar__2__rI__19858,Vvar__3__radd__19859,Vvar__4__rmul__19864,Vvar__5__rdiv__19869,Vvar__6__rinv__19874,Vvar__7__req__19877,Vvar__4__rmul__19864)
=> ( c_24__type__20130___24t(Vvar__0__R__19856,Vvar__1__rO__19857,Vvar__2__rI__19858,Vvar__3__radd__19859,Vvar__4__rmul__19864,Vvar__5__rdiv__19869,Vvar__6__rinv__19874,Vvar__7__req__19877,Vvar__5__rdiv__19869)
=> ( c_24__type__20184___24t(Vvar__0__R__19856,Vvar__1__rO__19857,Vvar__2__rI__19858,Vvar__3__radd__19859,Vvar__4__rmul__19864,Vvar__5__rdiv__19869,Vvar__6__rinv__19874,Vvar__7__req__19877,Vvar__6__rinv__19874)
=> ( c_24__type__20247___24t(Vvar__0__R__19856,Vvar__1__rO__19857,Vvar__2__rI__19858,Vvar__3__radd__19859,Vvar__4__rmul__19864,Vvar__5__rdiv__19869,Vvar__6__rinv__19874,Vvar__7__req__19877,Vvar__7__req__19877)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__19856,Vvar__1__rO__19857,Vvar__2__rI__19858,Vvar__3__radd__19859,Vvar__4__rmul__19864,Vvar__5__rdiv__19869,Vvar__6__rinv__19874,Vvar__7__req__19877)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__19856,Vvar__1__rO__19857,Vvar__2__rI__19858,Vvar__3__radd__19859,Vvar__4__rmul__19864,Vvar__7__req__19877)
& ~ p(happ(happ(Vvar__7__req__19877,Vvar__2__rI__19858),Vvar__1__rO__19857))
& ! [Vvar__var__var__var__var__var__var__10__p__19912__19914__19921__19923__19925__19927__19929] :
( t(Vvar__var__var__var__var__var__var__10__p__19912__19914__19921__19923__19925__19927__19929,Vvar__0__R__19856)
=> ! [Vvar__var__var__var__var__var__var__11__q__19913__19915__19922__19924__19926__19928__19930] :
( t(Vvar__var__var__var__var__var__var__11__q__19913__19915__19922__19924__19926__19928__19930,Vvar__0__R__19856)
=> p(happ(happ(Vvar__7__req__19877,happ(happ(Vvar__5__rdiv__19869,Vvar__var__var__var__var__var__var__10__p__19912__19914__19921__19923__19925__19927__19929),Vvar__var__var__var__var__var__var__11__q__19913__19915__19922__19924__19926__19928__19930)),happ(happ(Vvar__4__rmul__19864,Vvar__var__var__var__var__var__var__10__p__19912__19914__19921__19923__19925__19927__19929),happ(Vvar__6__rinv__19874,Vvar__var__var__var__var__var__var__11__q__19913__19915__19922__19924__19926__19928__19930)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__19917__19919__19931__19933__19935__19937__19939__19941] :
( t(Vvar__var__var__var__var__var__var__var__11__p__19917__19919__19931__19933__19935__19937__19939__19941,Vvar__0__R__19856)
=> ( ~ p(happ(happ(Vvar__7__req__19877,Vvar__var__var__var__var__var__var__var__11__p__19917__19919__19931__19933__19935__19937__19939__19941),Vvar__1__rO__19857))
=> p(happ(happ(Vvar__7__req__19877,happ(happ(Vvar__4__rmul__19864,happ(Vvar__6__rinv__19874,Vvar__var__var__var__var__var__var__var__11__p__19917__19919__19931__19933__19935__19937__19939__19941)),Vvar__var__var__var__var__var__var__var__11__p__19917__19919__19931__19933__19935__19937__19939__19941)),Vvar__2__rI__19858)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
! [VX20556] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX20556)
=> ? [Vvar__0__hypo__type__20557] :
( cType___24t(Vvar__0__hypo__type__20557)
& ? [Vvar__1__hypo__proof__20558] :
( t(Vvar__1__hypo__proof__20558,Vvar__0__hypo__type__20557)
& VX20556 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__20557,Vvar__1__hypo__proof__20558) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX10479] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX10479)
=> ( VX10479 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__10480] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10480)
& ? [Vvar__1___24Anonymous__10481] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__10481)
& VX10479 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__10480,Vvar__1___24Anonymous__10481) ) )
| ? [Vvar__0___24Anonymous__10482] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10482)
& ? [Vvar__1___24Anonymous__10483] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__10483)
& VX10479 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__10482,Vvar__1___24Anonymous__10483) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__10512,VX10513] :
( cType___24t(Vvar__0__C__10512)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10512,VX10513)
=> ( VX10513 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10512)
| VX10513 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10512)
| ? [Vvar__1___24Anonymous__10517] :
( t(Vvar__1___24Anonymous__10517,Vvar__0__C__10512)
& VX10513 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__10512,Vvar__1___24Anonymous__10517) )
| ? [Vvar__1___24Anonymous__10519] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10519)
& VX10513 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__10512,Vvar__1___24Anonymous__10519) )
| ? [Vvar__1___24Anonymous__10521] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10512,Vvar__1___24Anonymous__10521)
& ? [Vvar__2___24Anonymous__10522] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10512,Vvar__2___24Anonymous__10522)
& VX10513 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__10512,Vvar__1___24Anonymous__10521,Vvar__2___24Anonymous__10522) ) )
| ? [Vvar__1___24Anonymous__10524] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10512,Vvar__1___24Anonymous__10524)
& ? [Vvar__2___24Anonymous__10525] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10512,Vvar__2___24Anonymous__10525)
& VX10513 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__10512,Vvar__1___24Anonymous__10524,Vvar__2___24Anonymous__10525) ) )
| ? [Vvar__1___24Anonymous__10527] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10512,Vvar__1___24Anonymous__10527)
& ? [Vvar__2___24Anonymous__10528] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10512,Vvar__2___24Anonymous__10528)
& VX10513 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__10512,Vvar__1___24Anonymous__10527,Vvar__2___24Anonymous__10528) ) )
| ? [Vvar__1___24Anonymous__10530] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10512,Vvar__1___24Anonymous__10530)
& VX10513 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__10512,Vvar__1___24Anonymous__10530) )
| ? [Vvar__1___24Anonymous__10532] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10512,Vvar__1___24Anonymous__10532)
& ? [Vvar__2___24Anonymous__10533] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__10533)
& VX10513 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__10512,Vvar__1___24Anonymous__10532,Vvar__2___24Anonymous__10533) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__917,VX918] :
( cType___24t(Vvar__0__C__917)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__917,VX918)
=> ( ? [Vvar__1___24Anonymous__920] :
( t(Vvar__1___24Anonymous__920,Vvar__0__C__917)
& VX918 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__917,Vvar__1___24Anonymous__920) )
| ? [Vvar__1___24Anonymous__922] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__922)
& ? [Vvar__2___24Anonymous__923] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__917,Vvar__2___24Anonymous__923)
& VX918 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__917,Vvar__1___24Anonymous__922,Vvar__2___24Anonymous__923) ) )
| ? [Vvar__1___24Anonymous__925] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__917,Vvar__1___24Anonymous__925)
& ? [Vvar__2___24Anonymous__926] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__926)
& ? [Vvar__3___24Anonymous__927] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__917,Vvar__3___24Anonymous__927)
& VX918 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__917,Vvar__1___24Anonymous__925,Vvar__2___24Anonymous__926,Vvar__3___24Anonymous__927) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__1294,Vvar__1__rO__1295,Vvar__2__rI__1296,Vvar__3__radd__1297,Vvar__4__rmul__1302,Vvar__5__rsub__1307,Vvar__6__ropp__1312,Vvar__7__req__1315] :
( cType___24t(Vvar__0__R__1294)
=> ( t(Vvar__1__rO__1295,Vvar__0__R__1294)
=> ( t(Vvar__2__rI__1296,Vvar__0__R__1294)
=> ( c_24__type__1543___24t(Vvar__0__R__1294,Vvar__1__rO__1295,Vvar__2__rI__1296,Vvar__3__radd__1297,Vvar__4__rmul__1302,Vvar__5__rsub__1307,Vvar__6__ropp__1312,Vvar__7__req__1315,Vvar__3__radd__1297)
=> ( c_24__type__1606___24t(Vvar__0__R__1294,Vvar__1__rO__1295,Vvar__2__rI__1296,Vvar__3__radd__1297,Vvar__4__rmul__1302,Vvar__5__rsub__1307,Vvar__6__ropp__1312,Vvar__7__req__1315,Vvar__4__rmul__1302)
=> ( c_24__type__1669___24t(Vvar__0__R__1294,Vvar__1__rO__1295,Vvar__2__rI__1296,Vvar__3__radd__1297,Vvar__4__rmul__1302,Vvar__5__rsub__1307,Vvar__6__ropp__1312,Vvar__7__req__1315,Vvar__5__rsub__1307)
=> ( c_24__type__1723___24t(Vvar__0__R__1294,Vvar__1__rO__1295,Vvar__2__rI__1296,Vvar__3__radd__1297,Vvar__4__rmul__1302,Vvar__5__rsub__1307,Vvar__6__ropp__1312,Vvar__7__req__1315,Vvar__6__ropp__1312)
=> ( c_24__type__1786___24t(Vvar__0__R__1294,Vvar__1__rO__1295,Vvar__2__rI__1296,Vvar__3__radd__1297,Vvar__4__rmul__1302,Vvar__5__rsub__1307,Vvar__6__ropp__1312,Vvar__7__req__1315,Vvar__7__req__1315)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__1294,Vvar__1__rO__1295,Vvar__2__rI__1296,Vvar__3__radd__1297,Vvar__4__rmul__1302,Vvar__5__rsub__1307,Vvar__6__ropp__1312,Vvar__7__req__1315)
=> ( ! [Vvar__var__var__var__var__var__8__x__1348__1349__1402__1403__1404__1405] :
( t(Vvar__var__var__var__var__var__8__x__1348__1349__1402__1403__1404__1405,Vvar__0__R__1294)
=> p(happ(happ(Vvar__7__req__1315,happ(happ(Vvar__3__radd__1297,Vvar__1__rO__1295),Vvar__var__var__var__var__var__8__x__1348__1349__1402__1403__1404__1405)),Vvar__var__var__var__var__var__8__x__1348__1349__1402__1403__1404__1405)) )
& ! [Vvar__var__var__var__var__9__x__1351__1353__1406__1408__1410] :
( t(Vvar__var__var__var__var__9__x__1351__1353__1406__1408__1410,Vvar__0__R__1294)
=> ! [Vvar__var__var__var__var__10__y__1352__1354__1407__1409__1411] :
( t(Vvar__var__var__var__var__10__y__1352__1354__1407__1409__1411,Vvar__0__R__1294)
=> p(happ(happ(Vvar__7__req__1315,happ(happ(Vvar__3__radd__1297,Vvar__var__var__var__var__9__x__1351__1353__1406__1408__1410),Vvar__var__var__var__var__10__y__1352__1354__1407__1409__1411)),happ(happ(Vvar__3__radd__1297,Vvar__var__var__var__var__10__y__1352__1354__1407__1409__1411),Vvar__var__var__var__var__9__x__1351__1353__1406__1408__1410))) ) )
& ! [Vvar__var__var__var__var__10__x__1356__1359__1412__1415__1418] :
( t(Vvar__var__var__var__var__10__x__1356__1359__1412__1415__1418,Vvar__0__R__1294)
=> ! [Vvar__var__var__var__var__11__y__1357__1360__1413__1416__1419] :
( t(Vvar__var__var__var__var__11__y__1357__1360__1413__1416__1419,Vvar__0__R__1294)
=> ! [Vvar__var__var__var__var__12__z__1358__1361__1414__1417__1420] :
( t(Vvar__var__var__var__var__12__z__1358__1361__1414__1417__1420,Vvar__0__R__1294)
=> p(happ(happ(Vvar__7__req__1315,happ(happ(Vvar__3__radd__1297,Vvar__var__var__var__var__10__x__1356__1359__1412__1415__1418),happ(happ(Vvar__3__radd__1297,Vvar__var__var__var__var__11__y__1357__1360__1413__1416__1419),Vvar__var__var__var__var__12__z__1358__1361__1414__1417__1420))),happ(happ(Vvar__3__radd__1297,happ(happ(Vvar__3__radd__1297,Vvar__var__var__var__var__10__x__1356__1359__1412__1415__1418),Vvar__var__var__var__var__11__y__1357__1360__1413__1416__1419)),Vvar__var__var__var__var__12__z__1358__1361__1414__1417__1420))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__1363__1364__1421__1422__1423__1424] :
( t(Vvar__var__var__var__var__var__11__x__1363__1364__1421__1422__1423__1424,Vvar__0__R__1294)
=> p(happ(happ(Vvar__7__req__1315,happ(happ(Vvar__4__rmul__1302,Vvar__2__rI__1296),Vvar__var__var__var__var__var__11__x__1363__1364__1421__1422__1423__1424)),Vvar__var__var__var__var__var__11__x__1363__1364__1421__1422__1423__1424)) )
& ! [Vvar__var__var__var__var__var__12__x__1366__1367__1425__1426__1427__1428] :
( t(Vvar__var__var__var__var__var__12__x__1366__1367__1425__1426__1427__1428,Vvar__0__R__1294)
=> p(happ(happ(Vvar__7__req__1315,happ(happ(Vvar__4__rmul__1302,Vvar__1__rO__1295),Vvar__var__var__var__var__var__12__x__1366__1367__1425__1426__1427__1428)),Vvar__1__rO__1295)) )
& ! [Vvar__var__var__var__var__13__x__1369__1371__1429__1431__1433] :
( t(Vvar__var__var__var__var__13__x__1369__1371__1429__1431__1433,Vvar__0__R__1294)
=> ! [Vvar__var__var__var__var__14__y__1370__1372__1430__1432__1434] :
( t(Vvar__var__var__var__var__14__y__1370__1372__1430__1432__1434,Vvar__0__R__1294)
=> p(happ(happ(Vvar__7__req__1315,happ(happ(Vvar__4__rmul__1302,Vvar__var__var__var__var__13__x__1369__1371__1429__1431__1433),Vvar__var__var__var__var__14__y__1370__1372__1430__1432__1434)),happ(happ(Vvar__4__rmul__1302,Vvar__var__var__var__var__14__y__1370__1372__1430__1432__1434),Vvar__var__var__var__var__13__x__1369__1371__1429__1431__1433))) ) )
& ! [Vvar__var__var__var__var__14__x__1374__1377__1435__1438__1441] :
( t(Vvar__var__var__var__var__14__x__1374__1377__1435__1438__1441,Vvar__0__R__1294)
=> ! [Vvar__var__var__var__var__15__y__1375__1378__1436__1439__1442] :
( t(Vvar__var__var__var__var__15__y__1375__1378__1436__1439__1442,Vvar__0__R__1294)
=> ! [Vvar__var__var__var__var__16__z__1376__1379__1437__1440__1443] :
( t(Vvar__var__var__var__var__16__z__1376__1379__1437__1440__1443,Vvar__0__R__1294)
=> p(happ(happ(Vvar__7__req__1315,happ(happ(Vvar__4__rmul__1302,Vvar__var__var__var__var__14__x__1374__1377__1435__1438__1441),happ(happ(Vvar__4__rmul__1302,Vvar__var__var__var__var__15__y__1375__1378__1436__1439__1442),Vvar__var__var__var__var__16__z__1376__1379__1437__1440__1443))),happ(happ(Vvar__4__rmul__1302,happ(happ(Vvar__4__rmul__1302,Vvar__var__var__var__var__14__x__1374__1377__1435__1438__1441),Vvar__var__var__var__var__15__y__1375__1378__1436__1439__1442)),Vvar__var__var__var__var__16__z__1376__1379__1437__1440__1443))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__1381__1384__1444__1447__1450__1453] :
( t(Vvar__var__var__var__var__var__15__x__1381__1384__1444__1447__1450__1453,Vvar__0__R__1294)
=> ! [Vvar__var__var__var__var__var__16__y__1382__1385__1445__1448__1451__1454] :
( t(Vvar__var__var__var__var__var__16__y__1382__1385__1445__1448__1451__1454,Vvar__0__R__1294)
=> ! [Vvar__var__var__var__var__var__17__z__1383__1386__1446__1449__1452__1455] :
( t(Vvar__var__var__var__var__var__17__z__1383__1386__1446__1449__1452__1455,Vvar__0__R__1294)
=> p(happ(happ(Vvar__7__req__1315,happ(happ(Vvar__4__rmul__1302,happ(happ(Vvar__3__radd__1297,Vvar__var__var__var__var__var__15__x__1381__1384__1444__1447__1450__1453),Vvar__var__var__var__var__var__16__y__1382__1385__1445__1448__1451__1454)),Vvar__var__var__var__var__var__17__z__1383__1386__1446__1449__1452__1455)),happ(happ(Vvar__3__radd__1297,happ(happ(Vvar__4__rmul__1302,Vvar__var__var__var__var__var__15__x__1381__1384__1444__1447__1450__1453),Vvar__var__var__var__var__var__17__z__1383__1386__1446__1449__1452__1455)),happ(happ(Vvar__4__rmul__1302,Vvar__var__var__var__var__var__16__y__1382__1385__1445__1448__1451__1454),Vvar__var__var__var__var__var__17__z__1383__1386__1446__1449__1452__1455)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__1388__1390__1456__1458__1460__1462] :
( t(Vvar__var__var__var__var__var__16__x__1388__1390__1456__1458__1460__1462,Vvar__0__R__1294)
=> ! [Vvar__var__var__var__var__var__17__y__1389__1391__1457__1459__1461__1463] :
( t(Vvar__var__var__var__var__var__17__y__1389__1391__1457__1459__1461__1463,Vvar__0__R__1294)
=> p(happ(happ(Vvar__7__req__1315,happ(Vvar__6__ropp__1312,happ(happ(Vvar__4__rmul__1302,Vvar__var__var__var__var__var__16__x__1388__1390__1456__1458__1460__1462),Vvar__var__var__var__var__var__17__y__1389__1391__1457__1459__1461__1463))),happ(happ(Vvar__4__rmul__1302,happ(Vvar__6__ropp__1312,Vvar__var__var__var__var__var__16__x__1388__1390__1456__1458__1460__1462)),Vvar__var__var__var__var__var__17__y__1389__1391__1457__1459__1461__1463))) ) )
& ! [Vvar__var__var__var__var__var__17__x__1393__1395__1464__1466__1468__1470] :
( t(Vvar__var__var__var__var__var__17__x__1393__1395__1464__1466__1468__1470,Vvar__0__R__1294)
=> ! [Vvar__var__var__var__var__var__18__y__1394__1396__1465__1467__1469__1471] :
( t(Vvar__var__var__var__var__var__18__y__1394__1396__1465__1467__1469__1471,Vvar__0__R__1294)
=> p(happ(happ(Vvar__7__req__1315,happ(Vvar__6__ropp__1312,happ(happ(Vvar__3__radd__1297,Vvar__var__var__var__var__var__17__x__1393__1395__1464__1466__1468__1470),Vvar__var__var__var__var__var__18__y__1394__1396__1465__1467__1469__1471))),happ(happ(Vvar__3__radd__1297,happ(Vvar__6__ropp__1312,Vvar__var__var__var__var__var__17__x__1393__1395__1464__1466__1468__1470)),happ(Vvar__6__ropp__1312,Vvar__var__var__var__var__var__18__y__1394__1396__1465__1467__1469__1471)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__1398__1400__1472__1474__1476__1478__1480] :
( t(Vvar__var__var__var__var__var__var__18__x__1398__1400__1472__1474__1476__1478__1480,Vvar__0__R__1294)
=> ! [Vvar__var__var__var__var__var__var__19__y__1399__1401__1473__1475__1477__1479__1481] :
( t(Vvar__var__var__var__var__var__var__19__y__1399__1401__1473__1475__1477__1479__1481,Vvar__0__R__1294)
=> p(happ(happ(Vvar__7__req__1315,happ(happ(Vvar__5__rsub__1307,Vvar__var__var__var__var__var__var__18__x__1398__1400__1472__1474__1476__1478__1480),Vvar__var__var__var__var__var__var__19__y__1399__1401__1473__1475__1477__1479__1481)),happ(happ(Vvar__3__radd__1297,Vvar__var__var__var__var__var__var__18__x__1398__1400__1472__1474__1476__1478__1480),happ(Vvar__6__ropp__1312,Vvar__var__var__var__var__var__var__19__y__1399__1401__1473__1475__1477__1479__1481)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__29402,Vvar__1__req__29403,Vvar__2__C__29408,Vvar__3__cadd__29409,Vvar__4__cmul__29414,Vvar__5__phi__29419,Vvar__6__cdiv__29422] :
( cType___24t(Vvar__0__R__29402)
=> ( c_24__type__29542___24t(Vvar__0__R__29402,Vvar__1__req__29403,Vvar__2__C__29408,Vvar__3__cadd__29409,Vvar__4__cmul__29414,Vvar__5__phi__29419,Vvar__6__cdiv__29422,Vvar__1__req__29403)
=> ( cType___24t(Vvar__2__C__29408)
=> ( c_24__type__29592___24t(Vvar__0__R__29402,Vvar__1__req__29403,Vvar__2__C__29408,Vvar__3__cadd__29409,Vvar__4__cmul__29414,Vvar__5__phi__29419,Vvar__6__cdiv__29422,Vvar__3__cadd__29409)
=> ( c_24__type__29642___24t(Vvar__0__R__29402,Vvar__1__req__29403,Vvar__2__C__29408,Vvar__3__cadd__29409,Vvar__4__cmul__29414,Vvar__5__phi__29419,Vvar__6__cdiv__29422,Vvar__4__cmul__29414)
=> ( c_24__type__29684___24t(Vvar__0__R__29402,Vvar__1__req__29403,Vvar__2__C__29408,Vvar__3__cadd__29409,Vvar__4__cmul__29414,Vvar__5__phi__29419,Vvar__6__cdiv__29422,Vvar__5__phi__29419)
=> ( c_24__type__29734___24t(Vvar__0__R__29402,Vvar__1__req__29403,Vvar__2__C__29408,Vvar__3__cadd__29409,Vvar__4__cmul__29414,Vvar__5__phi__29419,Vvar__6__cdiv__29422,Vvar__6__cdiv__29422)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__29402,Vvar__1__req__29403,Vvar__2__C__29408,Vvar__3__cadd__29409,Vvar__4__cmul__29414,Vvar__5__phi__29419,Vvar__6__cdiv__29422)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__29454__29459__29464__29469__29474__29479__29484__29489] :
( t(Vvar__var__var__var__var__var__var__var__7__a__29454__29459__29464__29469__29474__29479__29484__29489,Vvar__2__C__29408)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__29455__29460__29465__29470__29475__29480__29485__29490] :
( t(Vvar__var__var__var__var__var__var__var__8__b__29455__29460__29465__29470__29475__29480__29485__29490,Vvar__2__C__29408)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2429797___24a9(Vvar__0__R__29402,Vvar__1__req__29403,Vvar__2__C__29408,Vvar__3__cadd__29409,Vvar__4__cmul__29414,Vvar__5__phi__29419,Vvar__6__cdiv__29422,Vvar__var__var__var__var__var__var__var__7__a__29454__29459__29464__29469__29474__29479__29484__29489,Vvar__var__var__var__var__var__var__var__8__b__29455__29460__29465__29470__29475__29480__29485__29490) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__13454,Vvar__1__rI__13455,Vvar__2__rmul__13456,Vvar__3__req__13461,Vvar__4__Cpow__13466,Vvar__5__Cp__phi__13467,Vvar__6__rpow__13470] :
( cType___24t(Vvar__0__R__13454)
=> ( t(Vvar__1__rI__13455,Vvar__0__R__13454)
=> ( c_24__type__13556___24t(Vvar__0__R__13454,Vvar__1__rI__13455,Vvar__2__rmul__13456,Vvar__3__req__13461,Vvar__4__Cpow__13466,Vvar__5__Cp__phi__13467,Vvar__6__rpow__13470,Vvar__2__rmul__13456)
=> ( c_24__type__13600___24t(Vvar__0__R__13454,Vvar__1__rI__13455,Vvar__2__rmul__13456,Vvar__3__req__13461,Vvar__4__Cpow__13466,Vvar__5__Cp__phi__13467,Vvar__6__rpow__13470,Vvar__3__req__13461)
=> ( cType___24t(Vvar__4__Cpow__13466)
=> ( c_24__type__13636___24t(Vvar__0__R__13454,Vvar__1__rI__13455,Vvar__2__rmul__13456,Vvar__3__req__13461,Vvar__4__Cpow__13466,Vvar__5__Cp__phi__13467,Vvar__6__rpow__13470,Vvar__5__Cp__phi__13467)
=> ( c_24__type__13680___24t(Vvar__0__R__13454,Vvar__1__rI__13455,Vvar__2__rmul__13456,Vvar__3__req__13461,Vvar__4__Cpow__13466,Vvar__5__Cp__phi__13467,Vvar__6__rpow__13470,Vvar__6__rpow__13470)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__13454,Vvar__1__rI__13455,Vvar__2__rmul__13456,Vvar__3__req__13461,Vvar__4__Cpow__13466,Vvar__5__Cp__phi__13467,Vvar__6__rpow__13470)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__13498__13500__13502__13504__13506__13508__13510__13512] :
( t(Vvar__var__var__var__var__var__var__var__7__r__13498__13500__13502__13504__13506__13508__13510__13512,Vvar__0__R__13454)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__13499__13501__13503__13505__13507__13509__13511__13513] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__13499__13501__13503__13505__13507__13509__13511__13513)
=> p(happ(happ(Vvar__3__req__13461,happ(happ(Vvar__6__rpow__13470,Vvar__var__var__var__var__var__var__var__7__r__13498__13500__13502__13504__13506__13508__13510__13512),happ(Vvar__5__Cp__phi__13467,Vvar__var__var__var__var__var__var__var__8__n__13499__13501__13503__13505__13507__13509__13511__13513))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__13454,Vvar__1__rI__13455,Vvar__2__rmul__13456,Vvar__var__var__var__var__var__var__var__7__r__13498__13500__13502__13504__13506__13508__13510__13512,Vvar__var__var__var__var__var__var__var__8__n__13499__13501__13503__13505__13507__13509__13511__13513))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__1823,Vvar__1__radd__1824,Vvar__2__rmul__1829,Vvar__3__ropp__1834,Vvar__4__req__1837] :
( cType___24t(Vvar__0__R__1823)
=> ( c_24__type__1928___24t(Vvar__0__R__1823,Vvar__1__radd__1824,Vvar__2__rmul__1829,Vvar__3__ropp__1834,Vvar__4__req__1837,Vvar__1__radd__1824)
=> ( c_24__type__1958___24t(Vvar__0__R__1823,Vvar__1__radd__1824,Vvar__2__rmul__1829,Vvar__3__ropp__1834,Vvar__4__req__1837,Vvar__2__rmul__1829)
=> ( c_24__type__1982___24t(Vvar__0__R__1823,Vvar__1__radd__1824,Vvar__2__rmul__1829,Vvar__3__ropp__1834,Vvar__4__req__1837,Vvar__3__ropp__1834)
=> ( c_24__type__2012___24t(Vvar__0__R__1823,Vvar__1__radd__1824,Vvar__2__rmul__1829,Vvar__3__ropp__1834,Vvar__4__req__1837,Vvar__4__req__1837)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__1823,Vvar__1__radd__1824,Vvar__2__rmul__1829,Vvar__3__ropp__1834,Vvar__4__req__1837)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2042___24a5(Vvar__0__R__1823,Vvar__1__radd__1824,Vvar__2__rmul__1829,Vvar__3__ropp__1834,Vvar__4__req__1837),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__1823,c_24__type__2066___24a5(Vvar__0__R__1823,Vvar__1__radd__1824,Vvar__2__rmul__1829,Vvar__3__ropp__1834,Vvar__4__req__1837),Vvar__4__req__1837,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__1823,Vvar__0__R__1823,Vvar__4__req__1837,Vvar__4__req__1837)),Vvar__1__radd__1824)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2099___24a5(Vvar__0__R__1823,Vvar__1__radd__1824,Vvar__2__rmul__1829,Vvar__3__ropp__1834,Vvar__4__req__1837),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__1823,c_24__type__2123___24a5(Vvar__0__R__1823,Vvar__1__radd__1824,Vvar__2__rmul__1829,Vvar__3__ropp__1834,Vvar__4__req__1837),Vvar__4__req__1837,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__1823,Vvar__0__R__1823,Vvar__4__req__1837,Vvar__4__req__1837)),Vvar__2__rmul__1829)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2150___24a5(Vvar__0__R__1823,Vvar__1__radd__1824,Vvar__2__rmul__1829,Vvar__3__ropp__1834,Vvar__4__req__1837),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__1823,Vvar__0__R__1823,Vvar__4__req__1837,Vvar__4__req__1837),Vvar__3__ropp__1834)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX29835] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX29835)
=> ( VX29835 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__29836] :
( cType___24t(Vvar__0__R__29836)
& ? [Vvar__1__req__29837] :
( c_24__type__15___24t(Vvar__0__R__29836,Vvar__1__req__29837)
& ? [Vvar__2__reqb__29842] :
( c_24__type__1030___24t(Vvar__0__R__29836,Vvar__2__reqb__29842)
& ! [Vvar__var__3__x__29848__29851] :
( t(Vvar__var__3__x__29848__29851,Vvar__0__R__29836)
=> ! [Vvar__var__4__y__29849__29852] :
( t(Vvar__var__4__y__29849__29852,Vvar__0__R__29836)
=> ( happ(happ(Vvar__2__reqb__29842,Vvar__var__3__x__29848__29851),Vvar__var__4__y__29849__29852) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__29837,Vvar__var__3__x__29848__29851),Vvar__var__4__y__29849__29852)) ) ) )
& VX29835 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__29836,Vvar__1__req__29837,Vvar__2__reqb__29842) ) ) )
| ? [Vvar__0__R__29854] :
( cType___24t(Vvar__0__R__29854)
& ? [Vvar__1__rO__29855] :
( t(Vvar__1__rO__29855,Vvar__0__R__29854)
& ? [Vvar__2__rI__29856] :
( t(Vvar__2__rI__29856,Vvar__0__R__29854)
& ? [Vvar__3__radd__29857] :
( c_24__type__890___24t(Vvar__0__R__29854,Vvar__3__radd__29857)
& ? [Vvar__4__rmul__29862] :
( c_24__type__890___24t(Vvar__0__R__29854,Vvar__4__rmul__29862)
& ? [Vvar__5__rsub__29867] :
( c_24__type__890___24t(Vvar__0__R__29854,Vvar__5__rsub__29867)
& ? [Vvar__6__ropp__29872] :
( c_24__type__247___24t(Vvar__0__R__29854,Vvar__6__ropp__29872)
& ? [Vvar__7__req__29875] :
( c_24__type__15___24t(Vvar__0__R__29854,Vvar__7__req__29875)
& ? [Vvar__8__C__29880] :
( cType___24t(Vvar__8__C__29880)
& ? [Vvar__9__cO__29881] :
( t(Vvar__9__cO__29881,Vvar__8__C__29880)
& ? [Vvar__10__cI__29882] :
( t(Vvar__10__cI__29882,Vvar__8__C__29880)
& ? [Vvar__11__cadd__29883] :
( c_24__type__1211___24t(Vvar__0__R__29854,Vvar__8__C__29880,Vvar__11__cadd__29883)
& ? [Vvar__12__cmul__29888] :
( c_24__type__1211___24t(Vvar__0__R__29854,Vvar__8__C__29880,Vvar__12__cmul__29888)
& ? [Vvar__13__csub__29893] :
( c_24__type__1211___24t(Vvar__0__R__29854,Vvar__8__C__29880,Vvar__13__csub__29893)
& ? [Vvar__14__copp__29898] :
( c_24__type__1225___24t(Vvar__0__R__29854,Vvar__8__C__29880,Vvar__14__copp__29898)
& ? [Vvar__15__ceqb__29901] :
( c_24__type__1232___24t(Vvar__0__R__29854,Vvar__8__C__29880,Vvar__15__ceqb__29901)
& ? [Vvar__16__phi__29906] :
( c_24__type__1180___24t(Vvar__0__R__29854,Vvar__8__C__29880,Vvar__16__phi__29906)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__29854,Vvar__1__rO__29855,Vvar__2__rI__29856,Vvar__3__radd__29857,Vvar__4__rmul__29862,Vvar__5__rsub__29867,Vvar__6__ropp__29872,Vvar__7__req__29875,Vvar__8__C__29880,Vvar__9__cO__29881,Vvar__10__cI__29882,Vvar__11__cadd__29883,Vvar__12__cmul__29888,Vvar__13__csub__29893,Vvar__14__copp__29898,Vvar__15__ceqb__29901,Vvar__16__phi__29906)
& VX29835 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__29854,Vvar__1__rO__29855,Vvar__2__rI__29856,Vvar__3__radd__29857,Vvar__4__rmul__29862,Vvar__5__rsub__29867,Vvar__6__ropp__29872,Vvar__7__req__29875,Vvar__8__C__29880,Vvar__9__cO__29881,Vvar__10__cI__29882,Vvar__11__cadd__29883,Vvar__12__cmul__29888,Vvar__13__csub__29893,Vvar__14__copp__29898,Vvar__15__ceqb__29901,Vvar__16__phi__29906) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233] :
( cType___24t(Vvar__0__R__2181)
=> ( t(Vvar__1__rO__2182,Vvar__0__R__2181)
=> ( t(Vvar__2__rI__2183,Vvar__0__R__2181)
=> ( c_24__type__2577___24t(Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233,Vvar__3__radd__2184)
=> ( c_24__type__2790___24t(Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233,Vvar__4__rmul__2189)
=> ( c_24__type__3003___24t(Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233,Vvar__5__rsub__2194)
=> ( c_24__type__3198___24t(Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233,Vvar__6__ropp__2199)
=> ( c_24__type__3411___24t(Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233,Vvar__7__req__2202)
=> ( cType___24t(Vvar__8__C__2207)
=> ( t(Vvar__9__cO__2208,Vvar__8__C__2207)
=> ( t(Vvar__10__cI__2209,Vvar__8__C__2207)
=> ( c_24__type__3624___24t(Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233,Vvar__11__cadd__2210)
=> ( c_24__type__3837___24t(Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233,Vvar__12__cmul__2215)
=> ( c_24__type__4050___24t(Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233,Vvar__13__csub__2220)
=> ( c_24__type__4245___24t(Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233,Vvar__14__copp__2225)
=> ( c_24__type__4458___24t(Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233,Vvar__15__ceqb__2228)
=> ( c_24__type__4653___24t(Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233,Vvar__16__phi__2233)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__2181,Vvar__1__rO__2182,Vvar__2__rI__2183,Vvar__3__radd__2184,Vvar__4__rmul__2189,Vvar__5__rsub__2194,Vvar__6__ropp__2199,Vvar__7__req__2202,Vvar__8__C__2207,Vvar__9__cO__2208,Vvar__10__cI__2209,Vvar__11__cadd__2210,Vvar__12__cmul__2215,Vvar__13__csub__2220,Vvar__14__copp__2225,Vvar__15__ceqb__2228,Vvar__16__phi__2233)
=> ( p(happ(happ(Vvar__7__req__2202,happ(Vvar__16__phi__2233,Vvar__9__cO__2208)),Vvar__1__rO__2182))
& p(happ(happ(Vvar__7__req__2202,happ(Vvar__16__phi__2233,Vvar__10__cI__2209)),Vvar__2__rI__2183))
& ! [Vvar__var__var__var__var__var__var__19__x__2295__2297__2319__2321__2323__2325__2327] :
( t(Vvar__var__var__var__var__var__var__19__x__2295__2297__2319__2321__2323__2325__2327,Vvar__8__C__2207)
=> ! [Vvar__var__var__var__var__var__var__20__y__2296__2298__2320__2322__2324__2326__2328] :
( t(Vvar__var__var__var__var__var__var__20__y__2296__2298__2320__2322__2324__2326__2328,Vvar__8__C__2207)
=> p(happ(happ(Vvar__7__req__2202,happ(Vvar__16__phi__2233,happ(happ(Vvar__11__cadd__2210,Vvar__var__var__var__var__var__var__19__x__2295__2297__2319__2321__2323__2325__2327),Vvar__var__var__var__var__var__var__20__y__2296__2298__2320__2322__2324__2326__2328))),happ(happ(Vvar__3__radd__2184,happ(Vvar__16__phi__2233,Vvar__var__var__var__var__var__var__19__x__2295__2297__2319__2321__2323__2325__2327)),happ(Vvar__16__phi__2233,Vvar__var__var__var__var__var__var__20__y__2296__2298__2320__2322__2324__2326__2328)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__2300__2302__2329__2331__2333__2335__2337] :
( t(Vvar__var__var__var__var__var__var__20__x__2300__2302__2329__2331__2333__2335__2337,Vvar__8__C__2207)
=> ! [Vvar__var__var__var__var__var__var__21__y__2301__2303__2330__2332__2334__2336__2338] :
( t(Vvar__var__var__var__var__var__var__21__y__2301__2303__2330__2332__2334__2336__2338,Vvar__8__C__2207)
=> p(happ(happ(Vvar__7__req__2202,happ(Vvar__16__phi__2233,happ(happ(Vvar__13__csub__2220,Vvar__var__var__var__var__var__var__20__x__2300__2302__2329__2331__2333__2335__2337),Vvar__var__var__var__var__var__var__21__y__2301__2303__2330__2332__2334__2336__2338))),happ(happ(Vvar__5__rsub__2194,happ(Vvar__16__phi__2233,Vvar__var__var__var__var__var__var__20__x__2300__2302__2329__2331__2333__2335__2337)),happ(Vvar__16__phi__2233,Vvar__var__var__var__var__var__var__21__y__2301__2303__2330__2332__2334__2336__2338)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__2305__2307__2339__2341__2343__2345__2347] :
( t(Vvar__var__var__var__var__var__var__21__x__2305__2307__2339__2341__2343__2345__2347,Vvar__8__C__2207)
=> ! [Vvar__var__var__var__var__var__var__22__y__2306__2308__2340__2342__2344__2346__2348] :
( t(Vvar__var__var__var__var__var__var__22__y__2306__2308__2340__2342__2344__2346__2348,Vvar__8__C__2207)
=> p(happ(happ(Vvar__7__req__2202,happ(Vvar__16__phi__2233,happ(happ(Vvar__12__cmul__2215,Vvar__var__var__var__var__var__var__21__x__2305__2307__2339__2341__2343__2345__2347),Vvar__var__var__var__var__var__var__22__y__2306__2308__2340__2342__2344__2346__2348))),happ(happ(Vvar__4__rmul__2189,happ(Vvar__16__phi__2233,Vvar__var__var__var__var__var__var__21__x__2305__2307__2339__2341__2343__2345__2347)),happ(Vvar__16__phi__2233,Vvar__var__var__var__var__var__var__22__y__2306__2308__2340__2342__2344__2346__2348)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__2310__2311__2349__2350__2351__2352__2353] :
( t(Vvar__var__var__var__var__var__var__22__x__2310__2311__2349__2350__2351__2352__2353,Vvar__8__C__2207)
=> p(happ(happ(Vvar__7__req__2202,happ(Vvar__16__phi__2233,happ(Vvar__14__copp__2225,Vvar__var__var__var__var__var__var__22__x__2310__2311__2349__2350__2351__2352__2353))),happ(Vvar__6__ropp__2199,happ(Vvar__16__phi__2233,Vvar__var__var__var__var__var__var__22__x__2310__2311__2349__2350__2351__2352__2353)))) )
& ! [Vvar__var__var__var__var__var__23__x__2313__2316__2354__2357__2360__2363] :
( t(Vvar__var__var__var__var__var__23__x__2313__2316__2354__2357__2360__2363,Vvar__8__C__2207)
=> ! [Vvar__var__var__var__var__var__24__y__2314__2317__2355__2358__2361__2364] :
( t(Vvar__var__var__var__var__var__24__y__2314__2317__2355__2358__2361__2364,Vvar__8__C__2207)
=> ( happ(happ(Vvar__15__ceqb__2228,Vvar__var__var__var__var__var__23__x__2313__2316__2354__2357__2360__2363),Vvar__var__var__var__var__var__24__y__2314__2317__2355__2358__2361__2364) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__2202,happ(Vvar__16__phi__2233,Vvar__var__var__var__var__var__23__x__2313__2316__2354__2357__2360__2363)),happ(Vvar__16__phi__2233,Vvar__var__var__var__var__var__24__y__2314__2317__2355__2358__2361__2364))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__12742,Vvar__1__rO__12743,Vvar__2__rI__12744,Vvar__3__radd__12745,Vvar__4__rmul__12750,Vvar__5__rsub__12755,Vvar__6__ropp__12760,Vvar__7__req__12763] :
( cType___24t(Vvar__0__R__12742)
=> ( t(Vvar__1__rO__12743,Vvar__0__R__12742)
=> ( t(Vvar__2__rI__12744,Vvar__0__R__12742)
=> ( c_24__type__12966___24t(Vvar__0__R__12742,Vvar__1__rO__12743,Vvar__2__rI__12744,Vvar__3__radd__12745,Vvar__4__rmul__12750,Vvar__5__rsub__12755,Vvar__6__ropp__12760,Vvar__7__req__12763,Vvar__3__radd__12745)
=> ( c_24__type__13029___24t(Vvar__0__R__12742,Vvar__1__rO__12743,Vvar__2__rI__12744,Vvar__3__radd__12745,Vvar__4__rmul__12750,Vvar__5__rsub__12755,Vvar__6__ropp__12760,Vvar__7__req__12763,Vvar__4__rmul__12750)
=> ( c_24__type__13092___24t(Vvar__0__R__12742,Vvar__1__rO__12743,Vvar__2__rI__12744,Vvar__3__radd__12745,Vvar__4__rmul__12750,Vvar__5__rsub__12755,Vvar__6__ropp__12760,Vvar__7__req__12763,Vvar__5__rsub__12755)
=> ( c_24__type__13146___24t(Vvar__0__R__12742,Vvar__1__rO__12743,Vvar__2__rI__12744,Vvar__3__radd__12745,Vvar__4__rmul__12750,Vvar__5__rsub__12755,Vvar__6__ropp__12760,Vvar__7__req__12763,Vvar__6__ropp__12760)
=> ( c_24__type__13209___24t(Vvar__0__R__12742,Vvar__1__rO__12743,Vvar__2__rI__12744,Vvar__3__radd__12745,Vvar__4__rmul__12750,Vvar__5__rsub__12755,Vvar__6__ropp__12760,Vvar__7__req__12763,Vvar__7__req__12763)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__12742,Vvar__1__rO__12743,Vvar__2__rI__12744,Vvar__3__radd__12745,Vvar__4__rmul__12750,Vvar__5__rsub__12755,Vvar__6__ropp__12760,Vvar__7__req__12763)
=> ( ! [Vvar__var__var__var__var__var__8__x__12796__12797__12840__12841__12842__12843] :
( t(Vvar__var__var__var__var__var__8__x__12796__12797__12840__12841__12842__12843,Vvar__0__R__12742)
=> p(happ(happ(Vvar__7__req__12763,happ(happ(Vvar__3__radd__12745,Vvar__1__rO__12743),Vvar__var__var__var__var__var__8__x__12796__12797__12840__12841__12842__12843)),Vvar__var__var__var__var__var__8__x__12796__12797__12840__12841__12842__12843)) )
& ! [Vvar__var__var__var__var__9__x__12799__12801__12844__12846__12848] :
( t(Vvar__var__var__var__var__9__x__12799__12801__12844__12846__12848,Vvar__0__R__12742)
=> ! [Vvar__var__var__var__var__10__y__12800__12802__12845__12847__12849] :
( t(Vvar__var__var__var__var__10__y__12800__12802__12845__12847__12849,Vvar__0__R__12742)
=> p(happ(happ(Vvar__7__req__12763,happ(happ(Vvar__3__radd__12745,Vvar__var__var__var__var__9__x__12799__12801__12844__12846__12848),Vvar__var__var__var__var__10__y__12800__12802__12845__12847__12849)),happ(happ(Vvar__3__radd__12745,Vvar__var__var__var__var__10__y__12800__12802__12845__12847__12849),Vvar__var__var__var__var__9__x__12799__12801__12844__12846__12848))) ) )
& ! [Vvar__var__var__var__var__10__x__12804__12807__12850__12853__12856] :
( t(Vvar__var__var__var__var__10__x__12804__12807__12850__12853__12856,Vvar__0__R__12742)
=> ! [Vvar__var__var__var__var__11__y__12805__12808__12851__12854__12857] :
( t(Vvar__var__var__var__var__11__y__12805__12808__12851__12854__12857,Vvar__0__R__12742)
=> ! [Vvar__var__var__var__var__12__z__12806__12809__12852__12855__12858] :
( t(Vvar__var__var__var__var__12__z__12806__12809__12852__12855__12858,Vvar__0__R__12742)
=> p(happ(happ(Vvar__7__req__12763,happ(happ(Vvar__3__radd__12745,Vvar__var__var__var__var__10__x__12804__12807__12850__12853__12856),happ(happ(Vvar__3__radd__12745,Vvar__var__var__var__var__11__y__12805__12808__12851__12854__12857),Vvar__var__var__var__var__12__z__12806__12809__12852__12855__12858))),happ(happ(Vvar__3__radd__12745,happ(happ(Vvar__3__radd__12745,Vvar__var__var__var__var__10__x__12804__12807__12850__12853__12856),Vvar__var__var__var__var__11__y__12805__12808__12851__12854__12857)),Vvar__var__var__var__var__12__z__12806__12809__12852__12855__12858))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__12811__12812__12859__12860__12861__12862] :
( t(Vvar__var__var__var__var__var__11__x__12811__12812__12859__12860__12861__12862,Vvar__0__R__12742)
=> p(happ(happ(Vvar__7__req__12763,happ(happ(Vvar__4__rmul__12750,Vvar__2__rI__12744),Vvar__var__var__var__var__var__11__x__12811__12812__12859__12860__12861__12862)),Vvar__var__var__var__var__var__11__x__12811__12812__12859__12860__12861__12862)) )
& ! [Vvar__var__var__var__var__12__x__12814__12816__12863__12865__12867] :
( t(Vvar__var__var__var__var__12__x__12814__12816__12863__12865__12867,Vvar__0__R__12742)
=> ! [Vvar__var__var__var__var__13__y__12815__12817__12864__12866__12868] :
( t(Vvar__var__var__var__var__13__y__12815__12817__12864__12866__12868,Vvar__0__R__12742)
=> p(happ(happ(Vvar__7__req__12763,happ(happ(Vvar__4__rmul__12750,Vvar__var__var__var__var__12__x__12814__12816__12863__12865__12867),Vvar__var__var__var__var__13__y__12815__12817__12864__12866__12868)),happ(happ(Vvar__4__rmul__12750,Vvar__var__var__var__var__13__y__12815__12817__12864__12866__12868),Vvar__var__var__var__var__12__x__12814__12816__12863__12865__12867))) ) )
& ! [Vvar__var__var__var__var__13__x__12819__12822__12869__12872__12875] :
( t(Vvar__var__var__var__var__13__x__12819__12822__12869__12872__12875,Vvar__0__R__12742)
=> ! [Vvar__var__var__var__var__14__y__12820__12823__12870__12873__12876] :
( t(Vvar__var__var__var__var__14__y__12820__12823__12870__12873__12876,Vvar__0__R__12742)
=> ! [Vvar__var__var__var__var__15__z__12821__12824__12871__12874__12877] :
( t(Vvar__var__var__var__var__15__z__12821__12824__12871__12874__12877,Vvar__0__R__12742)
=> p(happ(happ(Vvar__7__req__12763,happ(happ(Vvar__4__rmul__12750,Vvar__var__var__var__var__13__x__12819__12822__12869__12872__12875),happ(happ(Vvar__4__rmul__12750,Vvar__var__var__var__var__14__y__12820__12823__12870__12873__12876),Vvar__var__var__var__var__15__z__12821__12824__12871__12874__12877))),happ(happ(Vvar__4__rmul__12750,happ(happ(Vvar__4__rmul__12750,Vvar__var__var__var__var__13__x__12819__12822__12869__12872__12875),Vvar__var__var__var__var__14__y__12820__12823__12870__12873__12876)),Vvar__var__var__var__var__15__z__12821__12824__12871__12874__12877))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__12826__12829__12878__12881__12884__12887] :
( t(Vvar__var__var__var__var__var__14__x__12826__12829__12878__12881__12884__12887,Vvar__0__R__12742)
=> ! [Vvar__var__var__var__var__var__15__y__12827__12830__12879__12882__12885__12888] :
( t(Vvar__var__var__var__var__var__15__y__12827__12830__12879__12882__12885__12888,Vvar__0__R__12742)
=> ! [Vvar__var__var__var__var__var__16__z__12828__12831__12880__12883__12886__12889] :
( t(Vvar__var__var__var__var__var__16__z__12828__12831__12880__12883__12886__12889,Vvar__0__R__12742)
=> p(happ(happ(Vvar__7__req__12763,happ(happ(Vvar__4__rmul__12750,happ(happ(Vvar__3__radd__12745,Vvar__var__var__var__var__var__14__x__12826__12829__12878__12881__12884__12887),Vvar__var__var__var__var__var__15__y__12827__12830__12879__12882__12885__12888)),Vvar__var__var__var__var__var__16__z__12828__12831__12880__12883__12886__12889)),happ(happ(Vvar__3__radd__12745,happ(happ(Vvar__4__rmul__12750,Vvar__var__var__var__var__var__14__x__12826__12829__12878__12881__12884__12887),Vvar__var__var__var__var__var__16__z__12828__12831__12880__12883__12886__12889)),happ(happ(Vvar__4__rmul__12750,Vvar__var__var__var__var__var__15__y__12827__12830__12879__12882__12885__12888),Vvar__var__var__var__var__var__16__z__12828__12831__12880__12883__12886__12889)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__12833__12835__12890__12892__12894__12896__12898] :
( t(Vvar__var__var__var__var__var__var__15__x__12833__12835__12890__12892__12894__12896__12898,Vvar__0__R__12742)
=> ! [Vvar__var__var__var__var__var__var__16__y__12834__12836__12891__12893__12895__12897__12899] :
( t(Vvar__var__var__var__var__var__var__16__y__12834__12836__12891__12893__12895__12897__12899,Vvar__0__R__12742)
=> p(happ(happ(Vvar__7__req__12763,happ(happ(Vvar__5__rsub__12755,Vvar__var__var__var__var__var__var__15__x__12833__12835__12890__12892__12894__12896__12898),Vvar__var__var__var__var__var__var__16__y__12834__12836__12891__12893__12895__12897__12899)),happ(happ(Vvar__3__radd__12745,Vvar__var__var__var__var__var__var__15__x__12833__12835__12890__12892__12894__12896__12898),happ(Vvar__6__ropp__12760,Vvar__var__var__var__var__var__var__16__y__12834__12836__12891__12893__12895__12897__12899)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__12838__12839__12900__12901__12902__12903__12904] :
( t(Vvar__var__var__var__var__var__var__16__x__12838__12839__12900__12901__12902__12903__12904,Vvar__0__R__12742)
=> p(happ(happ(Vvar__7__req__12763,happ(happ(Vvar__3__radd__12745,Vvar__var__var__var__var__var__var__16__x__12838__12839__12900__12901__12902__12903__12904),happ(Vvar__6__ropp__12760,Vvar__var__var__var__var__var__var__16__x__12838__12839__12900__12901__12902__12903__12904))),Vvar__1__rO__12743)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__28404,Vvar__1__rO__28405,Vvar__2__rI__28406,Vvar__3__radd__28407,Vvar__4__rmul__28412,Vvar__5__req__28417,Vvar__6__C__28422,Vvar__7__cO__28423,Vvar__8__cI__28424,Vvar__9__cadd__28425,Vvar__10__cmul__28430,Vvar__11__ceqb__28435,Vvar__12__phi__28440] :
( cType___24t(Vvar__0__R__28404)
=> ( t(Vvar__1__rO__28405,Vvar__0__R__28404)
=> ( t(Vvar__2__rI__28406,Vvar__0__R__28404)
=> ( c_24__type__28657___24t(Vvar__0__R__28404,Vvar__1__rO__28405,Vvar__2__rI__28406,Vvar__3__radd__28407,Vvar__4__rmul__28412,Vvar__5__req__28417,Vvar__6__C__28422,Vvar__7__cO__28423,Vvar__8__cI__28424,Vvar__9__cadd__28425,Vvar__10__cmul__28430,Vvar__11__ceqb__28435,Vvar__12__phi__28440,Vvar__3__radd__28407)
=> ( c_24__type__28782___24t(Vvar__0__R__28404,Vvar__1__rO__28405,Vvar__2__rI__28406,Vvar__3__radd__28407,Vvar__4__rmul__28412,Vvar__5__req__28417,Vvar__6__C__28422,Vvar__7__cO__28423,Vvar__8__cI__28424,Vvar__9__cadd__28425,Vvar__10__cmul__28430,Vvar__11__ceqb__28435,Vvar__12__phi__28440,Vvar__4__rmul__28412)
=> ( c_24__type__28907___24t(Vvar__0__R__28404,Vvar__1__rO__28405,Vvar__2__rI__28406,Vvar__3__radd__28407,Vvar__4__rmul__28412,Vvar__5__req__28417,Vvar__6__C__28422,Vvar__7__cO__28423,Vvar__8__cI__28424,Vvar__9__cadd__28425,Vvar__10__cmul__28430,Vvar__11__ceqb__28435,Vvar__12__phi__28440,Vvar__5__req__28417)
=> ( cType___24t(Vvar__6__C__28422)
=> ( t(Vvar__7__cO__28423,Vvar__6__C__28422)
=> ( t(Vvar__8__cI__28424,Vvar__6__C__28422)
=> ( c_24__type__29032___24t(Vvar__0__R__28404,Vvar__1__rO__28405,Vvar__2__rI__28406,Vvar__3__radd__28407,Vvar__4__rmul__28412,Vvar__5__req__28417,Vvar__6__C__28422,Vvar__7__cO__28423,Vvar__8__cI__28424,Vvar__9__cadd__28425,Vvar__10__cmul__28430,Vvar__11__ceqb__28435,Vvar__12__phi__28440,Vvar__9__cadd__28425)
=> ( c_24__type__29157___24t(Vvar__0__R__28404,Vvar__1__rO__28405,Vvar__2__rI__28406,Vvar__3__radd__28407,Vvar__4__rmul__28412,Vvar__5__req__28417,Vvar__6__C__28422,Vvar__7__cO__28423,Vvar__8__cI__28424,Vvar__9__cadd__28425,Vvar__10__cmul__28430,Vvar__11__ceqb__28435,Vvar__12__phi__28440,Vvar__10__cmul__28430)
=> ( c_24__type__29282___24t(Vvar__0__R__28404,Vvar__1__rO__28405,Vvar__2__rI__28406,Vvar__3__radd__28407,Vvar__4__rmul__28412,Vvar__5__req__28417,Vvar__6__C__28422,Vvar__7__cO__28423,Vvar__8__cI__28424,Vvar__9__cadd__28425,Vvar__10__cmul__28430,Vvar__11__ceqb__28435,Vvar__12__phi__28440,Vvar__11__ceqb__28435)
=> ( c_24__type__29393___24t(Vvar__0__R__28404,Vvar__1__rO__28405,Vvar__2__rI__28406,Vvar__3__radd__28407,Vvar__4__rmul__28412,Vvar__5__req__28417,Vvar__6__C__28422,Vvar__7__cO__28423,Vvar__8__cI__28424,Vvar__9__cadd__28425,Vvar__10__cmul__28430,Vvar__11__ceqb__28435,Vvar__12__phi__28440,Vvar__12__phi__28440)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__28404,Vvar__1__rO__28405,Vvar__2__rI__28406,Vvar__3__radd__28407,Vvar__4__rmul__28412,Vvar__5__req__28417,Vvar__6__C__28422,Vvar__7__cO__28423,Vvar__8__cI__28424,Vvar__9__cadd__28425,Vvar__10__cmul__28430,Vvar__11__ceqb__28435,Vvar__12__phi__28440)
=> ( p(happ(happ(Vvar__5__req__28417,happ(Vvar__12__phi__28440,Vvar__7__cO__28423)),Vvar__1__rO__28405))
& p(happ(happ(Vvar__5__req__28417,happ(Vvar__12__phi__28440,Vvar__8__cI__28424)),Vvar__2__rI__28406))
& ! [Vvar__var__var__var__var__var__var__15__x__28486__28488__28502__28504__28506__28508__28510] :
( t(Vvar__var__var__var__var__var__var__15__x__28486__28488__28502__28504__28506__28508__28510,Vvar__6__C__28422)
=> ! [Vvar__var__var__var__var__var__var__16__y__28487__28489__28503__28505__28507__28509__28511] :
( t(Vvar__var__var__var__var__var__var__16__y__28487__28489__28503__28505__28507__28509__28511,Vvar__6__C__28422)
=> p(happ(happ(Vvar__5__req__28417,happ(Vvar__12__phi__28440,happ(happ(Vvar__9__cadd__28425,Vvar__var__var__var__var__var__var__15__x__28486__28488__28502__28504__28506__28508__28510),Vvar__var__var__var__var__var__var__16__y__28487__28489__28503__28505__28507__28509__28511))),happ(happ(Vvar__3__radd__28407,happ(Vvar__12__phi__28440,Vvar__var__var__var__var__var__var__15__x__28486__28488__28502__28504__28506__28508__28510)),happ(Vvar__12__phi__28440,Vvar__var__var__var__var__var__var__16__y__28487__28489__28503__28505__28507__28509__28511)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__28491__28493__28512__28514__28516__28518__28520] :
( t(Vvar__var__var__var__var__var__var__16__x__28491__28493__28512__28514__28516__28518__28520,Vvar__6__C__28422)
=> ! [Vvar__var__var__var__var__var__var__17__y__28492__28494__28513__28515__28517__28519__28521] :
( t(Vvar__var__var__var__var__var__var__17__y__28492__28494__28513__28515__28517__28519__28521,Vvar__6__C__28422)
=> p(happ(happ(Vvar__5__req__28417,happ(Vvar__12__phi__28440,happ(happ(Vvar__10__cmul__28430,Vvar__var__var__var__var__var__var__16__x__28491__28493__28512__28514__28516__28518__28520),Vvar__var__var__var__var__var__var__17__y__28492__28494__28513__28515__28517__28519__28521))),happ(happ(Vvar__4__rmul__28412,happ(Vvar__12__phi__28440,Vvar__var__var__var__var__var__var__16__x__28491__28493__28512__28514__28516__28518__28520)),happ(Vvar__12__phi__28440,Vvar__var__var__var__var__var__var__17__y__28492__28494__28513__28515__28517__28519__28521)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__28496__28499__28522__28525__28528__28531] :
( t(Vvar__var__var__var__var__var__17__x__28496__28499__28522__28525__28528__28531,Vvar__6__C__28422)
=> ! [Vvar__var__var__var__var__var__18__y__28497__28500__28523__28526__28529__28532] :
( t(Vvar__var__var__var__var__var__18__y__28497__28500__28523__28526__28529__28532,Vvar__6__C__28422)
=> ( happ(happ(Vvar__11__ceqb__28435,Vvar__var__var__var__var__var__17__x__28496__28499__28522__28525__28528__28531),Vvar__var__var__var__var__var__18__y__28497__28500__28523__28526__28529__28532) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__28417,happ(Vvar__12__phi__28440,Vvar__var__var__var__var__var__17__x__28496__28499__28522__28525__28528__28531)),happ(Vvar__12__phi__28440,Vvar__var__var__var__var__var__18__y__28497__28500__28523__28526__28529__28532))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__17834,Vvar__1__rO__17835,Vvar__2__rI__17836,Vvar__3__radd__17837,Vvar__4__rmul__17842,Vvar__5__req__17847] :
( cType___24t(Vvar__0__R__17834)
=> ( t(Vvar__1__rO__17835,Vvar__0__R__17834)
=> ( t(Vvar__2__rI__17836,Vvar__0__R__17834)
=> ( c_24__type__18002___24t(Vvar__0__R__17834,Vvar__1__rO__17835,Vvar__2__rI__17836,Vvar__3__radd__17837,Vvar__4__rmul__17842,Vvar__5__req__17847,Vvar__3__radd__17837)
=> ( c_24__type__18041___24t(Vvar__0__R__17834,Vvar__1__rO__17835,Vvar__2__rI__17836,Vvar__3__radd__17837,Vvar__4__rmul__17842,Vvar__5__req__17847,Vvar__4__rmul__17842)
=> ( c_24__type__18080___24t(Vvar__0__R__17834,Vvar__1__rO__17835,Vvar__2__rI__17836,Vvar__3__radd__17837,Vvar__4__rmul__17842,Vvar__5__req__17847,Vvar__5__req__17847)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__17834,Vvar__1__rO__17835,Vvar__2__rI__17836,Vvar__3__radd__17837,Vvar__4__rmul__17842,Vvar__5__req__17847)
=> ( ! [Vvar__var__var__var__var__var__6__n__17872__17873__17911__17912__17913__17914] :
( t(Vvar__var__var__var__var__var__6__n__17872__17873__17911__17912__17913__17914,Vvar__0__R__17834)
=> p(happ(happ(Vvar__5__req__17847,happ(happ(Vvar__3__radd__17837,Vvar__1__rO__17835),Vvar__var__var__var__var__var__6__n__17872__17873__17911__17912__17913__17914)),Vvar__var__var__var__var__var__6__n__17872__17873__17911__17912__17913__17914)) )
& ! [Vvar__var__var__var__var__7__n__17875__17877__17915__17917__17919] :
( t(Vvar__var__var__var__var__7__n__17875__17877__17915__17917__17919,Vvar__0__R__17834)
=> ! [Vvar__var__var__var__var__8__m__17876__17878__17916__17918__17920] :
( t(Vvar__var__var__var__var__8__m__17876__17878__17916__17918__17920,Vvar__0__R__17834)
=> p(happ(happ(Vvar__5__req__17847,happ(happ(Vvar__3__radd__17837,Vvar__var__var__var__var__7__n__17875__17877__17915__17917__17919),Vvar__var__var__var__var__8__m__17876__17878__17916__17918__17920)),happ(happ(Vvar__3__radd__17837,Vvar__var__var__var__var__8__m__17876__17878__17916__17918__17920),Vvar__var__var__var__var__7__n__17875__17877__17915__17917__17919))) ) )
& ! [Vvar__var__var__var__var__8__n__17880__17883__17921__17924__17927] :
( t(Vvar__var__var__var__var__8__n__17880__17883__17921__17924__17927,Vvar__0__R__17834)
=> ! [Vvar__var__var__var__var__9__m__17881__17884__17922__17925__17928] :
( t(Vvar__var__var__var__var__9__m__17881__17884__17922__17925__17928,Vvar__0__R__17834)
=> ! [Vvar__var__var__var__var__10__p__17882__17885__17923__17926__17929] :
( t(Vvar__var__var__var__var__10__p__17882__17885__17923__17926__17929,Vvar__0__R__17834)
=> p(happ(happ(Vvar__5__req__17847,happ(happ(Vvar__3__radd__17837,Vvar__var__var__var__var__8__n__17880__17883__17921__17924__17927),happ(happ(Vvar__3__radd__17837,Vvar__var__var__var__var__9__m__17881__17884__17922__17925__17928),Vvar__var__var__var__var__10__p__17882__17885__17923__17926__17929))),happ(happ(Vvar__3__radd__17837,happ(happ(Vvar__3__radd__17837,Vvar__var__var__var__var__8__n__17880__17883__17921__17924__17927),Vvar__var__var__var__var__9__m__17881__17884__17922__17925__17928)),Vvar__var__var__var__var__10__p__17882__17885__17923__17926__17929))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__17887__17888__17930__17931__17932__17933] :
( t(Vvar__var__var__var__var__var__9__n__17887__17888__17930__17931__17932__17933,Vvar__0__R__17834)
=> p(happ(happ(Vvar__5__req__17847,happ(happ(Vvar__4__rmul__17842,Vvar__2__rI__17836),Vvar__var__var__var__var__var__9__n__17887__17888__17930__17931__17932__17933)),Vvar__var__var__var__var__var__9__n__17887__17888__17930__17931__17932__17933)) )
& ! [Vvar__var__var__var__var__var__10__n__17890__17891__17934__17935__17936__17937] :
( t(Vvar__var__var__var__var__var__10__n__17890__17891__17934__17935__17936__17937,Vvar__0__R__17834)
=> p(happ(happ(Vvar__5__req__17847,happ(happ(Vvar__4__rmul__17842,Vvar__1__rO__17835),Vvar__var__var__var__var__var__10__n__17890__17891__17934__17935__17936__17937)),Vvar__1__rO__17835)) )
& ! [Vvar__var__var__var__var__11__n__17893__17895__17938__17940__17942] :
( t(Vvar__var__var__var__var__11__n__17893__17895__17938__17940__17942,Vvar__0__R__17834)
=> ! [Vvar__var__var__var__var__12__m__17894__17896__17939__17941__17943] :
( t(Vvar__var__var__var__var__12__m__17894__17896__17939__17941__17943,Vvar__0__R__17834)
=> p(happ(happ(Vvar__5__req__17847,happ(happ(Vvar__4__rmul__17842,Vvar__var__var__var__var__11__n__17893__17895__17938__17940__17942),Vvar__var__var__var__var__12__m__17894__17896__17939__17941__17943)),happ(happ(Vvar__4__rmul__17842,Vvar__var__var__var__var__12__m__17894__17896__17939__17941__17943),Vvar__var__var__var__var__11__n__17893__17895__17938__17940__17942))) ) )
& ! [Vvar__var__var__var__var__12__n__17898__17901__17944__17947__17950] :
( t(Vvar__var__var__var__var__12__n__17898__17901__17944__17947__17950,Vvar__0__R__17834)
=> ! [Vvar__var__var__var__var__13__m__17899__17902__17945__17948__17951] :
( t(Vvar__var__var__var__var__13__m__17899__17902__17945__17948__17951,Vvar__0__R__17834)
=> ! [Vvar__var__var__var__var__14__p__17900__17903__17946__17949__17952] :
( t(Vvar__var__var__var__var__14__p__17900__17903__17946__17949__17952,Vvar__0__R__17834)
=> p(happ(happ(Vvar__5__req__17847,happ(happ(Vvar__4__rmul__17842,Vvar__var__var__var__var__12__n__17898__17901__17944__17947__17950),happ(happ(Vvar__4__rmul__17842,Vvar__var__var__var__var__13__m__17899__17902__17945__17948__17951),Vvar__var__var__var__var__14__p__17900__17903__17946__17949__17952))),happ(happ(Vvar__4__rmul__17842,happ(happ(Vvar__4__rmul__17842,Vvar__var__var__var__var__12__n__17898__17901__17944__17947__17950),Vvar__var__var__var__var__13__m__17899__17902__17945__17948__17951)),Vvar__var__var__var__var__14__p__17900__17903__17946__17949__17952))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__17905__17908__17953__17956__17959__17962] :
( t(Vvar__var__var__var__var__var__13__n__17905__17908__17953__17956__17959__17962,Vvar__0__R__17834)
=> ! [Vvar__var__var__var__var__var__14__m__17906__17909__17954__17957__17960__17963] :
( t(Vvar__var__var__var__var__var__14__m__17906__17909__17954__17957__17960__17963,Vvar__0__R__17834)
=> ! [Vvar__var__var__var__var__var__15__p__17907__17910__17955__17958__17961__17964] :
( t(Vvar__var__var__var__var__var__15__p__17907__17910__17955__17958__17961__17964,Vvar__0__R__17834)
=> p(happ(happ(Vvar__5__req__17847,happ(happ(Vvar__4__rmul__17842,happ(happ(Vvar__3__radd__17837,Vvar__var__var__var__var__var__13__n__17905__17908__17953__17956__17959__17962),Vvar__var__var__var__var__var__14__m__17906__17909__17954__17957__17960__17963)),Vvar__var__var__var__var__var__15__p__17907__17910__17955__17958__17961__17964)),happ(happ(Vvar__3__radd__17837,happ(happ(Vvar__4__rmul__17842,Vvar__var__var__var__var__var__13__n__17905__17908__17953__17956__17959__17962),Vvar__var__var__var__var__var__15__p__17907__17910__17955__17958__17961__17964)),happ(happ(Vvar__4__rmul__17842,Vvar__var__var__var__var__var__14__m__17906__17909__17954__17957__17960__17963),Vvar__var__var__var__var__var__15__p__17907__17910__17955__17958__17961__17964)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__28182,Vvar__1__radd__28183,Vvar__2__rmul__28188,Vvar__3__req__28193] :
( cType___24t(Vvar__0__R__28182)
=> ( c_24__type__28268___24t(Vvar__0__R__28182,Vvar__1__radd__28183,Vvar__2__rmul__28188,Vvar__3__req__28193,Vvar__1__radd__28183)
=> ( c_24__type__28291___24t(Vvar__0__R__28182,Vvar__1__radd__28183,Vvar__2__rmul__28188,Vvar__3__req__28193,Vvar__2__rmul__28188)
=> ( c_24__type__28314___24t(Vvar__0__R__28182,Vvar__1__radd__28183,Vvar__2__rmul__28188,Vvar__3__req__28193,Vvar__3__req__28193)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__28182,Vvar__1__radd__28183,Vvar__2__rmul__28188,Vvar__3__req__28193)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__28337___24a4(Vvar__0__R__28182,Vvar__1__radd__28183,Vvar__2__rmul__28188,Vvar__3__req__28193),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__28182,c_24__type__28355___24a4(Vvar__0__R__28182,Vvar__1__radd__28183,Vvar__2__rmul__28188,Vvar__3__req__28193),Vvar__3__req__28193,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__28182,Vvar__0__R__28182,Vvar__3__req__28193,Vvar__3__req__28193)),Vvar__1__radd__28183)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__28381___24a4(Vvar__0__R__28182,Vvar__1__radd__28183,Vvar__2__rmul__28188,Vvar__3__req__28193),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__28182,c_24__type__28399___24a4(Vvar__0__R__28182,Vvar__1__radd__28183,Vvar__2__rmul__28188,Vvar__3__req__28193),Vvar__3__req__28193,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__28182,Vvar__0__R__28182,Vvar__3__req__28193,Vvar__3__req__28193)),Vvar__2__rmul__28188)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [VX21701] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX21701)
=> ( VX21701 = cHammer_2eTactics_2eReconstr_2eEmpty
| VX21701 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).
fof('$_inversion_hahn.HahnBase.Equality.mixin_of',axiom,
! [Vvar__0__T__30646,VX30647] :
( cType___24t(Vvar__0__T__30646)
=> ( chahn_2eHahnBase_2eEquality_2emixin__of___24t(Vvar__0__T__30646,VX30647)
=> ? [Vvar__1__op__30649] :
( c_24__type__1030___24t(Vvar__0__T__30646,Vvar__1__op__30649)
& ? [Vvar__2___24Anonymous__30654] :
( chahn_2eHahnBase_2eEquality_2eaxiom___24t(Vvar__0__T__30646,Vvar__1__op__30649,Vvar__2___24Anonymous__30654)
& VX30647 = chahn_2eHahnBase_2eEquality_2eMixin___24a3(Vvar__0__T__30646,Vvar__1__op__30649,Vvar__2___24Anonymous__30654) ) ) ) ) ).
fof('$_inversion_hahn.HahnBase.Equality.type',axiom,
! [VX30666] :
( chahn_2eHahnBase_2eEquality_2etype___24t(VX30666)
=> ? [Vvar__0__sort__30667] :
( cType___24t(Vvar__0__sort__30667)
& ? [Vvar__1___24Anonymous__30668] :
( chahn_2eHahnBase_2eEquality_2emixin__of___24t(Vvar__0__sort__30667,Vvar__1___24Anonymous__30668)
& ? [Vvar__2___24Anonymous__30669] :
( cType___24t(Vvar__2___24Anonymous__30669)
& VX30666 = chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__30667,Vvar__1___24Anonymous__30668,Vvar__2___24Anonymous__30669) ) ) ) ) ).
fof('$_lam_167045',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__167045___24a1(Vv__CANONICAL__0)
<=> p(c_24True) ) ).
fof('$_lam_18430',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__18430___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_194',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__194___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_20336',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__20336___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_20344',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__20344___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_418',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__418___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> p(happ(happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4)),happ(Vv__CANONICAL__2,Vv__CANONICAL__5))) ) ).
fof('$_lam_491',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__491___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_569',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__569___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_573',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__573___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_701',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__701___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(c_24True) ) ).
fof('$_prop_30700',axiom,
! [Vvar__0___24Anonymous__30676,Vvar__0__S__30678,Vvar__1__x__30679,Vvar__2__y__30680] :
( p(c_24__prop__30700___24a4(Vvar__0___24Anonymous__30676,Vvar__0__S__30678,Vvar__1__x__30679,Vvar__2__y__30680))
<=> Vvar__1__x__30679 = Vvar__2__y__30680 ) ).
fof('$_prop_30701',axiom,
! [Vvar__0___24Anonymous__30676,Vvar__0__x__30681,Vvar__1__y__30682] :
( p(c_24__prop__30701___24a3(Vvar__0___24Anonymous__30676,Vvar__0__x__30681,Vvar__1__y__30682))
<=> Vvar__0__x__30681 = Vvar__1__y__30682 ) ).
fof('$_prop_30702',axiom,
! [Vvar__0___24Anonymous__30676,Vvar__0__x__30683,Vvar__1__s__30684] :
( p(c_24__prop__30702___24a3(Vvar__0___24Anonymous__30676,Vvar__0__x__30683,Vvar__1__s__30684))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__30683,Vvar__1__s__30684) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_30703',axiom,
! [Vvar__0___24Anonymous__30676,Vvar__0__P__30685,Vvar__1__Q__30686] :
( p(c_24__prop__30703___24a3(Vvar__0___24Anonymous__30676,Vvar__0__P__30685,Vvar__1__Q__30686))
<=> ( p(Vvar__0__P__30685)
& p(Vvar__1__Q__30686) ) ) ).
fof('$_prop_30704',axiom,
! [Vvar__0___24Anonymous__30676,Vvar__0__P__30689,Vvar__1__Q__30690] :
( p(c_24__prop__30704___24a3(Vvar__0___24Anonymous__30676,Vvar__0__P__30689,Vvar__1__Q__30690))
<=> ( p(Vvar__0__P__30689)
| p(Vvar__1__Q__30690) ) ) ).
fof('$_prop_30705',axiom,
! [Vvar__0___24Anonymous__30676,Vvar__0__P__30693,Vvar__1__Q__30694] :
( p(c_24__prop__30705___24a3(Vvar__0___24Anonymous__30676,Vvar__0__P__30693,Vvar__1__Q__30694))
<=> ( p(Vvar__0__P__30693)
=> p(Vvar__1__Q__30694) ) ) ).
fof('$_prop_30706',axiom,
! [Vvar__0___24Anonymous__30676,Vvar__0__P__30698] :
( p(c_24__prop__30706___24a2(Vvar__0___24Anonymous__30676,Vvar__0__P__30698))
<=> ~ p(Vvar__0__P__30698) ) ).
fof('$_prop_30720',axiom,
! [Vvar__0___24Anonymous__30707,Vvar__0__s__30711] :
( p(c_24__prop__30720___24a2(Vvar__0___24Anonymous__30707,Vvar__0__s__30711))
<=> ! [Vvar__1__a__30712] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__30712)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__30712,Vvar__0__s__30711) ) ) ).
fof('$_prop_30721',axiom,
! [Vvar__0___24Anonymous__30707,Vvar__0__s1__30713,Vvar__1__s2__30714] :
( p(c_24__prop__30721___24a3(Vvar__0___24Anonymous__30707,Vvar__0__s1__30713,Vvar__1__s2__30714))
<=> ! [Vvar__2__a__30715] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__30715)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__30715,Vvar__0__s1__30713)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__30715,Vvar__1__s2__30714) ) ) ) ).
fof('$_prop_30722',axiom,
! [Vvar__0___24Anonymous__30707,Vvar__0__s1__30717,Vvar__1__s2__30718] :
( p(c_24__prop__30722___24a3(Vvar__0___24Anonymous__30707,Vvar__0__s1__30717,Vvar__1__s2__30718))
<=> ! [Vvar__2__a__30719] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__30719)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__30719,Vvar__0__s1__30717)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__30719,Vvar__1__s2__30718) ) ) ) ).
fof('$_type_10171',axiom,
! [Vvar__10172] :
( c_24__type__10171___24t(Vvar__10172)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__10172,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1030',axiom,
! [Vv__CANONICAL__0,Vvar__1031] :
( c_24__type__1030___24t(Vv__CANONICAL__0,Vvar__1031)
<=> ! [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__1031,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_10501',axiom,
! [Vvar__10502] :
( c_24__type__10501___24t(Vvar__10502)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(happ(happ(Vvar__10502,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10734',axiom,
! [Vvar__10735] :
( c_24__type__10734___24t(Vvar__10735)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__10735,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10737',axiom,
! [Vvar__10738] :
( c_24__type__10737___24t(Vvar__10738)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__10738,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10740',axiom,
! [Vvar__10741] :
( c_24__type__10740___24t(Vvar__10741)
<=> ! [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__10741,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10745',axiom,
! [Vvar__10746] :
( c_24__type__10745___24t(Vvar__10746)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__10746,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_10754',axiom,
! [Vvar__10755] :
( c_24__type__10754___24t(Vvar__10755)
<=> ! [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__10755,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1180',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1181] :
( c_24__type__1180___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1181)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__1181,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_1211',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1212] :
( c_24__type__1211___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1212)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__1212,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_1225',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1226] :
( c_24__type__1225___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1226)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__1226,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_1232',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1233] :
( c_24__type__1232___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1233)
<=> ! [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__1233,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_12698',axiom,
! [Vvar__12699] :
( c_24__type__12698___24t(Vvar__12699)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__890___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__12699,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_1289',axiom,
! [Vvar__1290] :
( c_24__type__1289___24t(Vvar__1290)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__890___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__1290,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_12966',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12967] :
( c_24__type__12966___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12967)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12967,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13029',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__13030] :
( c_24__type__13029___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__13030)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13030,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13092',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__13093] :
( c_24__type__13092___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__13093)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13093,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13146',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__13147] :
( c_24__type__13146___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__13147)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__13147,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_13209',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__13210] :
( c_24__type__13209___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__13210)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__13210,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_13556',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__13557] :
( c_24__type__13556___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__13557)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13557,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13600',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__13601] :
( c_24__type__13600___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__13601)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__13601,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_13636',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__13637] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__13637)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__13637,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_136578',axiom,
! [Vvar__136579] :
( c_24__type__136578___24t(Vvar__136579)
<=> ! [Vv__CANONICAL__0] :
( cB___24t(Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,happ(Vvar__136579,Vv__CANONICAL__0)) ) ) ).
fof('$_type_136580',axiom,
! [Vvar__136581] :
( c_24__type__136580___24t(Vvar__136581)
<=> ! [Vv__CANONICAL__0] :
( cB___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__136581,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13680',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__13681] :
( c_24__type__13680___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__13681)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__13681,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13699',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13700] :
( c_24__type__13699___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13700)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__13700,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13778',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__13779] :
( c_24__type__13778___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__13779)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__13779,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_13813',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13814] :
( c_24__type__13813___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13814)
<=> ! [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__13814,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_13984',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13985] :
( c_24__type__13984___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13985)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__13985,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_14011',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14012] :
( c_24__type__14011___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14012)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__14012,Vv__CANONICAL__2)) ) ) ).
fof('$_type_14015',axiom,
! [Vvar__14016] :
( c_24__type__14015___24t(Vvar__14016)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__14016,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14033',axiom,
! [Vvar__14034] :
( c_24__type__14033___24t(Vvar__14034)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___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__14034,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_14058',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14059] :
( c_24__type__14058___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14059)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__14059,Vv__CANONICAL__2)) ) ) ).
fof('$_type_14064',axiom,
! [Vvar__14065] :
( c_24__type__14064___24t(Vvar__14065)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___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__14065,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_14137',axiom,
! [Vvar__14138] :
( c_24__type__14137___24t(Vvar__14138)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__14138,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14160',axiom,
! [Vvar__14161] :
( c_24__type__14160___24t(Vvar__14161)
<=> ! [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__14161,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_14165',axiom,
! [Vvar__14166] :
( c_24__type__14165___24t(Vvar__14166)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__14166,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_14293',axiom,
! [Vvar__14294] :
( c_24__type__14293___24t(Vvar__14294)
<=> ! [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__14294,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_14860',axiom,
! [Vvar__14861] :
( c_24__type__14860___24t(Vvar__14861)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__14861,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15',axiom,
! [Vv__CANONICAL__0,Vvar__16] :
( c_24__type__15___24t(Vv__CANONICAL__0,Vvar__16)
<=> ! [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__16,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_1543',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1544] :
( c_24__type__1543___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1544)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1544,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15718',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15719] :
( c_24__type__15718___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15719)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__15719,Vv__CANONICAL__4)) ) ) ).
fof('$_type_15727',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15728] :
( c_24__type__15727___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15728)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__15728,Vv__CANONICAL__4)) ) ) ).
fof('$_type_15741',axiom,
! [Vvar__15742] :
( c_24__type__15741___24t(Vvar__15742)
<=> ! [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__15742,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15846',axiom,
! [Vvar__15847] :
( c_24__type__15846___24t(Vvar__15847)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__15847,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16030',axiom,
! [Vvar__16031] :
( c_24__type__16030___24t(Vvar__16031)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__16031,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1606',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1607] :
( c_24__type__1606___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1607)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1607,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16073',axiom,
! [Vvar__16074] :
( c_24__type__16073___24t(Vvar__16074)
<=> ! [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__16074,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_161',axiom,
! [Vv__CANONICAL__0,Vvar__162] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vvar__162)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__162,Vv__CANONICAL__1)) ) ) ).
fof('$_type_16110',axiom,
! [Vvar__16111] :
( c_24__type__16110___24t(Vvar__16111)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__16111,Vv__CANONICAL__0)) ) ) ).
fof('$_type_16190',axiom,
! [Vvar__16191] :
( c_24__type__16190___24t(Vvar__16191)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__16191,Vv__CANONICAL__0)) ) ) ).
fof('$_type_16260',axiom,
! [Vvar__16261] :
( c_24__type__16260___24t(Vvar__16261)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__16261,Vv__CANONICAL__0)) ) ) ).
fof('$_type_16281',axiom,
! [Vvar__16282] :
( c_24__type__16281___24t(Vvar__16282)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__247___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__16282,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_16286',axiom,
! [Vvar__16287] :
( c_24__type__16286___24t(Vvar__16287)
<=> ! [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_2ecomparison___24t(happ(happ(Vvar__16287,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16291',axiom,
! [Vvar__16292] :
( c_24__type__16291___24t(Vvar__16292)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__16292,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16352',axiom,
! [Vvar__16353] :
( c_24__type__16352___24t(Vvar__16353)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__16353,Vv__CANONICAL__0)) ) ) ).
fof('$_type_16571',axiom,
! [Vvar__16572] :
( c_24__type__16571___24t(Vvar__16572)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__16572,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1669',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__1670] :
( c_24__type__1669___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__1670)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1670,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16806',axiom,
! [Vvar__16807] :
( c_24__type__16806___24t(Vvar__16807)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__16807,Vv__CANONICAL__0)) ) ) ).
fof('$_type_16857',axiom,
! [Vvar__16858] :
( c_24__type__16857___24t(Vvar__16858)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__16858,Vv__CANONICAL__0)) ) ) ).
fof('$_type_16861',axiom,
! [Vvar__16862] :
( c_24__type__16861___24t(Vvar__16862)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__16862,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17',axiom,
! [Vvar__18] :
( c_24__type__17___24t(Vvar__18)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__18,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17039',axiom,
! [Vvar__17040] :
( c_24__type__17039___24t(Vvar__17040)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__17040,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17101',axiom,
! [Vvar__17102] :
( c_24__type__17101___24t(Vvar__17102)
<=> ! [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__17102,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1723',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1724] :
( c_24__type__1723___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1724)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__1724,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_17608',axiom,
! [Vvar__17609] :
( c_24__type__17608___24t(Vvar__17609)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__17609,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_17786',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__17787] :
( c_24__type__17786___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__17787)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__17787,Vv__CANONICAL__6)) ) ) ).
fof('$_type_17797',axiom,
! [Vvar__17798] :
( c_24__type__17797___24t(Vvar__17798)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__17798,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_17816',axiom,
! [Vvar__17817] :
( c_24__type__17816___24t(Vvar__17817)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__17817,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17828',axiom,
! [Vvar__17829] :
( c_24__type__17828___24t(Vvar__17829)
<=> ! [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__17829,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1786',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1787] :
( c_24__type__1786___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1787)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1787,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_18002',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__18003] :
( c_24__type__18002___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__18003)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18003,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18041',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__18042] :
( c_24__type__18041___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__18042)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18042,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18080',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__18081] :
( c_24__type__18080___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__18081)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__18081,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_18112',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18113] :
( c_24__type__18112___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18113)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__18113,Vv__CANONICAL__2)) ) ) ).
fof('$_type_18116',axiom,
! [Vvar__18117] :
( c_24__type__18116___24t(Vvar__18117)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6566___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__18117,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18137',axiom,
! [Vvar__18138] :
( c_24__type__18137___24t(Vvar__18138)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__18138,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18192',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18193] :
( c_24__type__18192___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18193)
<=> ! [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__18193,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_18226',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18227] :
( c_24__type__18226___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18227)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__18227,Vv__CANONICAL__3)) ) ) ).
fof('$_type_18247',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18248] :
( c_24__type__18247___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18248)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__18248,Vv__CANONICAL__3)) ) ) ).
fof('$_type_18282',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18283] :
( c_24__type__18282___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18283)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__18283,Vv__CANONICAL__5)) ) ) ).
fof('$_type_18290',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18291] :
( c_24__type__18290___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18291)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__18291,Vv__CANONICAL__5)) ) ) ).
fof('$_type_18293',axiom,
! [Vvar__18294] :
( c_24__type__18293___24t(Vvar__18294)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__18294,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18299',axiom,
! [Vvar__18300] :
( c_24__type__18299___24t(Vvar__18300)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__18300,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_18301',axiom,
! [Vvar__18302] :
( c_24__type__18301___24t(Vvar__18302)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eByte_2ebyte___24t(happ(Vvar__18302,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18315',axiom,
! [Vvar__18316] :
( c_24__type__18315___24t(Vvar__18316)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5680___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__18316,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_18328',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18329] :
( c_24__type__18328___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18329)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cProp___24t(happ(happ(Vvar__18329,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_18335',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18336] :
( c_24__type__18335___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18336)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__18336,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_18339',axiom,
! [Vvar__18340] :
( c_24__type__18339___24t(Vvar__18340)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6566___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__18340,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18345',axiom,
! [Vv__CANONICAL__0,Vvar__18346] :
( c_24__type__18345___24t(Vv__CANONICAL__0,Vvar__18346)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__18346,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_18380',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18381] :
( c_24__type__18380___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18381)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__18381,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_18423',axiom,
! [Vv__CANONICAL__0,Vvar__18424] :
( c_24__type__18423___24t(Vv__CANONICAL__0,Vvar__18424)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__161___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,c_24__lam__18430___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(Vvar__18424,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18493',axiom,
! [Vvar__18494] :
( c_24__type__18493___24t(Vvar__18494)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__8___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__18494,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18563',axiom,
! [Vvar__18564] :
( c_24__type__18563___24t(Vvar__18564)
<=> ! [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__18564,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_18575',axiom,
! [Vvar__18576] :
( c_24__type__18575___24t(Vvar__18576)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__18576,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_18600',axiom,
! [Vvar__18601] :
( c_24__type__18600___24t(Vvar__18601)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cProp___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__18601,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_18657',axiom,
! [Vvar__18658] :
( c_24__type__18657___24t(Vvar__18658)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__18658,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18660',axiom,
! [Vvar__18661] :
( c_24__type__18660___24t(Vvar__18661)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2euint___24t(happ(Vvar__18661,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18714',axiom,
! [Vvar__18715] :
( c_24__type__18714___24t(Vvar__18715)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__18715,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18749',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__18750] :
( c_24__type__18749___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__18750)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__18750,Vv__CANONICAL__6)) ) ) ).
fof('$_type_19087',axiom,
! [Vvar__19088] :
( c_24__type__19087___24t(Vvar__19088)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__19088,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19090',axiom,
! [Vvar__19091] :
( c_24__type__19090___24t(Vvar__19091)
<=> ! [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__19091,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1928',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1929] :
( c_24__type__1928___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1929)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1929,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19314',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__19315] :
( c_24__type__19314___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__19315)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19315,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19407',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19408] :
( c_24__type__19407___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19408)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19408,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19500',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__19501] :
( c_24__type__19500___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__19501)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19501,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1958',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1959] :
( c_24__type__1958___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1959)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1959,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19582',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__19583] :
( c_24__type__19582___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__19583)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__19583,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_19675',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19676] :
( c_24__type__19675___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19676)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19676,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19757',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__19758] :
( c_24__type__19757___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__19758)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__19758,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_1982',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1983] :
( c_24__type__1982___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1983)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__1983,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_19850',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__19851] :
( c_24__type__19850___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__19851)
<=> ! [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__19851,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_20',axiom,
! [Vvar__21] :
( c_24__type__20___24t(Vvar__21)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__21,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20004',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__20005] :
( c_24__type__20004___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__20005)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20005,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20067',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20068] :
( c_24__type__20067___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20068)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20068,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2012',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2013] :
( c_24__type__2012___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2013)
<=> ! [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__2013,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_20130',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20131] :
( c_24__type__20130___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20131)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20131,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20184',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__20185] :
( c_24__type__20184___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__20185)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__20185,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_20247',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20248] :
( c_24__type__20247___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20248)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__20248,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_20272',axiom,
! [Vvar__20273] :
( c_24__type__20272___24t(Vvar__20273)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__268___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__20273,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_20300',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20301] :
( c_24__type__20300___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20301)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__20301,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_20305',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20306] :
( c_24__type__20305___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20306)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__20306,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_20311',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20312] :
( c_24__type__20311___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20312)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__20312,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_20316',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20317] :
( c_24__type__20316___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20317)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__20317,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_20328',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20329] :
( c_24__type__20328___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20329)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__20329,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_20348',axiom,
! [Vv__CANONICAL__0,Vvar__20349] :
( c_24__type__20348___24t(Vv__CANONICAL__0,Vvar__20349)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__20349,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_20359',axiom,
! [Vvar__20360] :
( c_24__type__20359___24t(Vvar__20360)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__20348___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__20360,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_20377',axiom,
! [Vvar__20378] :
( c_24__type__20377___24t(Vvar__20378)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__20378,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20384',axiom,
! [Vvar__20385] :
( c_24__type__20384___24t(Vvar__20385)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__20385,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2042',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2043] :
( c_24__type__2042___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2043)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2043,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20422',axiom,
! [Vvar__20423] :
( c_24__type__20422___24t(Vvar__20423)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__268___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__20428___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__20423,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_20428',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20429] :
( c_24__type__20428___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20429)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__20429,Vv__CANONICAL__2)) ) ) ).
fof('$_type_20445',axiom,
! [Vvar__20446] :
( c_24__type__20445___24t(Vvar__20446)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__268___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__20451___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__20446,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_20451',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20452] :
( c_24__type__20451___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20452)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__20452,Vv__CANONICAL__2)) ) ) ).
fof('$_type_20472',axiom,
! [Vvar__20473] :
( c_24__type__20472___24t(Vvar__20473)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__5680___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__20473,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_20512',axiom,
! [Vvar__20513] :
( c_24__type__20512___24t(Vvar__20513)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__890___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__890___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__20513,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_20564',axiom,
! [Vvar__20565] :
( c_24__type__20564___24t(Vvar__20565)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(happ(happ(Vvar__20565,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20589',axiom,
! [Vvar__20590] :
( c_24__type__20589___24t(Vvar__20590)
<=> ! [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__20590,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_206',axiom,
! [Vvar__207] :
( c_24__type__206___24t(Vvar__207)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__211___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__207,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_20613',axiom,
! [Vvar__20614] :
( c_24__type__20613___24t(Vvar__20614)
<=> ! [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__20614,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_20637',axiom,
! [Vvar__20638] :
( c_24__type__20637___24t(Vvar__20638)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__13699___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(happ(Vvar__20638,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_2066',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2067] :
( c_24__type__2066___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2067)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__2067,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_20666',axiom,
! [Vvar__20667] :
( c_24__type__20666___24t(Vvar__20667)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__20673___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__20667,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_20673',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20674] :
( c_24__type__20673___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__20674)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20674,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20734',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20735] :
( c_24__type__20734___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__20735)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__20735,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_20769',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__20770] :
( c_24__type__20769___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__20770)
<=> ! [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__20770,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_2099',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2100] :
( c_24__type__2099___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2100)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2100,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_211',axiom,
! [Vv__CANONICAL__0,Vvar__212] :
( c_24__type__211___24t(Vv__CANONICAL__0,Vvar__212)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__212,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2123',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2124] :
( c_24__type__2123___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2124)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__2124,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_21343',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__21344] :
( c_24__type__21343___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__21344)
<=> ! [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__21344,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_21362',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__21363] :
( c_24__type__21362___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__21363)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21363,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_21382',axiom,
! [Vvar__21383] :
( c_24__type__21382___24t(Vvar__21383)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__15___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__15___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__21383,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_21488',axiom,
! [Vvar__21489] :
( c_24__type__21488___24t(Vvar__21489)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__21489,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21493',axiom,
! [Vvar__21494] :
( c_24__type__21493___24t(Vvar__21494)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__21494,Vv__CANONICAL__0)) ) ) ).
fof('$_type_21498',axiom,
! [Vvar__21499] :
( c_24__type__21498___24t(Vvar__21499)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__21499,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2150',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2151] :
( c_24__type__2150___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2151)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__2151,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_21500',axiom,
! [Vvar__21501] :
( c_24__type__21500___24t(Vvar__21501)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__21501,Vv__CANONICAL__0)) ) ) ).
fof('$_type_21684',axiom,
! [Vvar__21685] :
( c_24__type__21684___24t(Vvar__21685)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__21685,Vv__CANONICAL__0)) ) ) ).
fof('$_type_21694',axiom,
! [Vvar__21695] :
( c_24__type__21694___24t(Vvar__21695)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__21695,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21697',axiom,
! [Vvar__21698] :
( c_24__type__21697___24t(Vvar__21698)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__21698,Vv__CANONICAL__0)) ) ) ).
fof('$_type_21719',axiom,
! [Vvar__21720] :
( c_24__type__21719___24t(Vvar__21720)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__21720,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_21940',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__21941] :
( c_24__type__21940___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__21941)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21941,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_21965',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__21966] :
( c_24__type__21965___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__21966)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__21966,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_22007',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22008] :
( c_24__type__22007___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22008)
<=> ! [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__22008,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_22058',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22059] :
( c_24__type__22058___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22059)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22059,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_22156',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22157] :
( c_24__type__22156___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22157)
<=> ! [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__22157,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_224',axiom,
! [Vv__CANONICAL__0,Vvar__225] :
( c_24__type__224___24t(Vv__CANONICAL__0,Vvar__225)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__211___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(Vvar__225,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_22634',axiom,
! [Vvar__22635] :
( c_24__type__22634___24t(Vvar__22635)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__22635,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23201',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__23202] :
( c_24__type__23201___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__23202)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23202,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_235',axiom,
! [Vv__CANONICAL__0,Vvar__236] :
( c_24__type__235___24t(Vv__CANONICAL__0,Vvar__236)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__211___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__236,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23547',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__23548] :
( c_24__type__23547___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__23548)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23548,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23893',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__23894] :
( c_24__type__23893___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__23894)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23894,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24216',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24217] :
( c_24__type__24216___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24217)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__24217,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_244',axiom,
! [Vv__CANONICAL__0,Vvar__245] :
( c_24__type__244___24t(Vv__CANONICAL__0,Vvar__245)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__245,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_24562',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24563] :
( c_24__type__24562___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24563)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24563,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_247',axiom,
! [Vv__CANONICAL__0,Vvar__248] :
( c_24__type__247___24t(Vv__CANONICAL__0,Vvar__248)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__248,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_24908',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24909] :
( c_24__type__24908___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24909)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24909,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_25254',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__25255] :
( c_24__type__25254___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__25255)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__25255,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_253',axiom,
! [Vvar__254] :
( c_24__type__253___24t(Vvar__254)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__254,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_25600',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__25601] :
( c_24__type__25600___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__25601)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__25601,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_2577',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__2578] :
( c_24__type__2577___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__2578)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2578,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25946',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__25947] :
( c_24__type__25946___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__25947)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__25947,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_26269',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26270] :
( c_24__type__26269___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26270)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__26270,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_264',axiom,
! [Vvar__265] :
( c_24__type__264___24t(Vvar__265)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__268___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__265,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_26615',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26616] :
( c_24__type__26615___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26616)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__26616,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_268',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__269] :
( c_24__type__268___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__269)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__269,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_26961',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26962] :
( c_24__type__26961___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26962)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__26962,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_27284',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__27285] :
( c_24__type__27284___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__27285)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__27285,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_27607',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27608] :
( c_24__type__27607___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27608)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__27608,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_2790',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__2791] :
( c_24__type__2790___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__2791)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2791,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27953',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27954] :
( c_24__type__27953___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27954)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__27954,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28138',axiom,
! [Vvar__28139] :
( c_24__type__28138___24t(Vvar__28139)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__890___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__28139,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_28268',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28269] :
( c_24__type__28268___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28269)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28269,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28291',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28292] :
( c_24__type__28291___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28292)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28292,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28314',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28315] :
( c_24__type__28314___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28315)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28315,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_28337',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28338] :
( c_24__type__28337___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28338)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28338,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28355',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28356] :
( c_24__type__28355___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28356)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__28356,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_28381',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28382] :
( c_24__type__28381___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28382)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28382,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28399',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28400] :
( c_24__type__28399___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28400)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__28400,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_28657',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__28658] :
( c_24__type__28657___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__28658)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28658,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28782',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__28783] :
( c_24__type__28782___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__28783)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28783,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28907',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__28908] :
( c_24__type__28907___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__28908)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28908,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_29032',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__29033] :
( c_24__type__29032___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__29033)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__29033,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_29157',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__29158] :
( c_24__type__29157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__29158)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__29158,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_29282',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__29283] :
( c_24__type__29282___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__29283)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__29283,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_29393',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__29394] :
( c_24__type__29393___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__29394)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__29394,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_29542',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29543] :
( c_24__type__29542___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29543)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__29543,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_29592',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29593] :
( c_24__type__29592___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29593)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__29593,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_29642',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29643] :
( c_24__type__29642___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29643)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__29643,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_29684',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29685] :
( c_24__type__29684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29685)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__29685,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_29734',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29735] :
( c_24__type__29734___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29735)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__29735,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_29810',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29811] :
( c_24__type__29810___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29811)
<=> ! [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__29811,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_29818',axiom,
! [Vvar__29819] :
( c_24__type__29818___24t(Vvar__29819)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29819,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3003',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__3004] :
( c_24__type__3003___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__3004)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3004,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30082',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30083] :
( c_24__type__30082___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30083)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30083,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_30102',axiom,
! [Vvar__30103] :
( c_24__type__30102___24t(Vvar__30103)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__15___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__30112___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__30103,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30112',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30113] :
( c_24__type__30112___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30113)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__30113,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_30145',axiom,
! [Vvar__30146] :
( c_24__type__30145___24t(Vvar__30146)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__15___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__30155___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__30112___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__30146,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_30155',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30156] :
( c_24__type__30155___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30156)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30156,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_30248',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30249] :
( c_24__type__30248___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30249)
<=> ! [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__30249,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_30283',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30284] :
( c_24__type__30283___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30284)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30284,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_30318',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30319] :
( c_24__type__30318___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30319)
<=> ! [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__30319,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_30344',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30345] :
( c_24__type__30344___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30345)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30345,Vv__CANONICAL__3)) ) ) ).
fof('$_type_30352',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30353] :
( c_24__type__30352___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30353)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30353,Vv__CANONICAL__3)) ) ) ).
fof('$_type_30360',axiom,
! [Vvar__30361] :
( c_24__type__30360___24t(Vvar__30361)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__30361,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30383',axiom,
! [Vvar__30384] :
( c_24__type__30383___24t(Vvar__30384)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6566___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__30384,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30410',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30411] :
( c_24__type__30410___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30411)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__30411,Vv__CANONICAL__3)) ) ) ).
fof('$_type_30418',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30419] :
( c_24__type__30418___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30419)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__30419,Vv__CANONICAL__3)) ) ) ).
fof('$_type_30426',axiom,
! [Vvar__30427] :
( c_24__type__30426___24t(Vvar__30427)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6566___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6566___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__30427,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30443',axiom,
! [Vvar__30444] :
( c_24__type__30443___24t(Vvar__30444)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ( p(c_24False)
=> t(happ(Vvar__30444,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30490',axiom,
! [Vvar__30491] :
( c_24__type__30490___24t(Vvar__30491)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__30493___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__30491,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30493',axiom,
! [Vv__CANONICAL__0,Vvar__30494] :
( c_24__type__30493___24t(Vv__CANONICAL__0,Vvar__30494)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__30494,Vv__CANONICAL__1)) ) ) ).
fof('$_type_30737',axiom,
! [Vvar__30738] :
( c_24__type__30737___24t(Vvar__30738)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__16110___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__16110___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__30738,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30780',axiom,
! [Vvar__30781] :
( c_24__type__30780___24t(Vvar__30781)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__890___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__30781,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_30871',axiom,
! [Vvar__30872] :
( c_24__type__30871___24t(Vvar__30872)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__30872,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30887',axiom,
! [Vvar__30888] :
( c_24__type__30887___24t(Vvar__30888)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__17039___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__17039___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__30888,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30895',axiom,
! [Vvar__30896] :
( c_24__type__30895___24t(Vvar__30896)
<=> ! [Vv__CANONICAL__0] :
( cA___24t(Vv__CANONICAL__0)
=> cB___24t(happ(Vvar__30896,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30897',axiom,
! [Vvar__30898] :
( c_24__type__30897___24t(Vvar__30898)
<=> ! [Vv__CANONICAL__0] :
( cA___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30898,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3198',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3199] :
( c_24__type__3198___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3199)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__3199,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_3411',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__3412] :
( c_24__type__3411___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__3412)
<=> ! [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__3412,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_35',axiom,
! [Vvar__36] :
( c_24__type__35___24t(Vvar__36)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__36,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3624',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__3625] :
( c_24__type__3624___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__3625)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__3625,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_3837',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3838] :
( c_24__type__3837___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3838)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__3838,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_403',axiom,
! [Vvar__404] :
( c_24__type__403___24t(Vvar__404)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__404,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4050',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4051] :
( c_24__type__4050___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4051)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__4051,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_420',axiom,
! [Vvar__421] :
( c_24__type__420___24t(Vvar__421)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__421,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4245',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4246] :
( c_24__type__4245___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4246)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__4246,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_4458',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__4459] :
( c_24__type__4458___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__4459)
<=> ! [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__4459,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_459',axiom,
! [Vv__CANONICAL__0,Vvar__460] :
( c_24__type__459___24t(Vv__CANONICAL__0,Vvar__460)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__460,Vv__CANONICAL__1)) ) ) ).
fof('$_type_4653',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__4654] :
( c_24__type__4653___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__4654)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__4654,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_4719',axiom,
! [Vvar__4720] :
( c_24__type__4719___24t(Vvar__4720)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__15___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4720,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_472',axiom,
! [Vvar__473] :
( c_24__type__472___24t(Vvar__473)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__474___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eN0))
=> ! [Vv__CANONICAL__2] :
( c_24__type__479___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__473,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4728',axiom,
! [Vvar__4729] :
( c_24__type__4728___24t(Vvar__4729)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4729,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_474',axiom,
! [Vvar__475] :
( c_24__type__474___24t(Vvar__475)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__475,Vv__CANONICAL__0)) ) ) ).
fof('$_type_479',axiom,
! [Vv__CANONICAL__0,Vvar__480] :
( c_24__type__479___24t(Vv__CANONICAL__0,Vvar__480)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__480,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_4823',axiom,
! [Vvar__4824] :
( c_24__type__4823___24t(Vvar__4824)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__4825___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4825___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4824,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4825',axiom,
! [Vvar__4826] :
( c_24__type__4825___24t(Vvar__4826)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__4826,Vv__CANONICAL__0)) ) ) ).
fof('$_type_484',axiom,
! [Vv__CANONICAL__0,Vvar__485] :
( c_24__type__484___24t(Vv__CANONICAL__0,Vvar__485)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__485,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_4841',axiom,
! [Vvar__4842] :
( c_24__type__4841___24t(Vvar__4842)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__4842,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4844',axiom,
! [Vvar__4845] :
( c_24__type__4844___24t(Vvar__4845)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__4845,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4847',axiom,
! [Vvar__4848] :
( c_24__type__4847___24t(Vvar__4848)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__4848,Vv__CANONICAL__0)) ) ) ).
fof('$_type_486',axiom,
! [Vvar__487] :
( c_24__type__486___24t(Vvar__487)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__487,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4860',axiom,
! [Vvar__4861] :
( c_24__type__4860___24t(Vvar__4861)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__4861,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4872',axiom,
! [Vvar__4873] :
( c_24__type__4872___24t(Vvar__4873)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__268___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__4873,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4887',axiom,
! [Vvar__4888] :
( c_24__type__4887___24t(Vvar__4888)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__268___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__4888,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4892',axiom,
! [Vvar__4893] :
( c_24__type__4892___24t(Vvar__4893)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__4893,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4899',axiom,
! [Vvar__4900] :
( c_24__type__4899___24t(Vvar__4900)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__268___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__4900,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4964',axiom,
! [Vvar__4965] :
( c_24__type__4964___24t(Vvar__4965)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
=> cCoq_2eStrings_2eAscii_2eascii___24t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__4965,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_4981',axiom,
! [Vvar__4982] :
( c_24__type__4981___24t(Vvar__4982)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__4982,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4983',axiom,
! [Vvar__4984] :
( c_24__type__4983___24t(Vvar__4984)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4984,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4989',axiom,
! [Vvar__4990] :
( c_24__type__4989___24t(Vvar__4990)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__4990,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4991',axiom,
! [Vvar__4992] :
( c_24__type__4991___24t(Vvar__4992)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__4992,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4993',axiom,
! [Vvar__4994] :
( c_24__type__4993___24t(Vvar__4994)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4994,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5005',axiom,
! [Vvar__5006] :
( c_24__type__5005___24t(Vvar__5006)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__5006,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5025',axiom,
! [Vvar__5026] :
( c_24__type__5025___24t(Vvar__5026)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__5026,Vv__CANONICAL__0)) ) ) ).
fof('$_type_503',axiom,
! [Vvar__504] :
( c_24__type__503___24t(Vvar__504)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__508___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__504,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_508',axiom,
! [Vv__CANONICAL__0,Vvar__509] :
( c_24__type__508___24t(Vv__CANONICAL__0,Vvar__509)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__509,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_521',axiom,
! [Vv__CANONICAL__0,Vvar__522] :
( c_24__type__521___24t(Vv__CANONICAL__0,Vvar__522)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__508___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(Vvar__522,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_532',axiom,
! [Vv__CANONICAL__0,Vvar__533] :
( c_24__type__532___24t(Vv__CANONICAL__0,Vvar__533)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__508___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__533,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_541',axiom,
! [Vv__CANONICAL__0,Vvar__542] :
( c_24__type__541___24t(Vv__CANONICAL__0,Vvar__542)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__542,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_5680',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5681] :
( c_24__type__5680___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5681)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__5681,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_5687',axiom,
! [Vvar__5688] :
( c_24__type__5687___24t(Vvar__5688)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__5688,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5760',axiom,
! [Vvar__5761] :
( c_24__type__5760___24t(Vvar__5761)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__5761,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5762',axiom,
! [Vvar__5763] :
( c_24__type__5762___24t(Vvar__5763)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__5763,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5772',axiom,
! [Vvar__5773] :
( c_24__type__5772___24t(Vvar__5773)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__5773,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5788',axiom,
! [Vvar__5789] :
( c_24__type__5788___24t(Vvar__5789)
<=> ! [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__5789,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_5790',axiom,
! [Vvar__5791] :
( c_24__type__5790___24t(Vvar__5791)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__5791,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5795',axiom,
! [Vvar__5796] :
( c_24__type__5795___24t(Vvar__5796)
<=> ! [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__5796,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5851',axiom,
! [Vvar__5852] :
( c_24__type__5851___24t(Vvar__5852)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__5852,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5863',axiom,
! [Vvar__5864] :
( c_24__type__5863___24t(Vvar__5864)
<=> ! [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__5864,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5866',axiom,
! [Vvar__5867] :
( c_24__type__5866___24t(Vvar__5867)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__5867,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5886',axiom,
! [Vv__CANONICAL__0,Vvar__5887] :
( c_24__type__5886___24t(Vv__CANONICAL__0,Vvar__5887)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__5887,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_6',axiom,
! [Vvar__7] :
( c_24__type__6___24t(Vvar__7)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__7,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6121',axiom,
! [Vvar__6122] :
( c_24__type__6121___24t(Vvar__6122)
<=> ! [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__6122,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6551',axiom,
! [Vvar__6552] :
( c_24__type__6551___24t(Vvar__6552)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__6552,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6566',axiom,
! [Vv__CANONICAL__0,Vvar__6567] :
( c_24__type__6566___24t(Vv__CANONICAL__0,Vvar__6567)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__6567,Vv__CANONICAL__1)) ) ) ).
fof('$_type_667',axiom,
! [Vvar__668] :
( c_24__type__667___24t(Vvar__668)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__668,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_6770',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__6771] :
( c_24__type__6770___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__6771)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6771,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6863',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6864] :
( c_24__type__6863___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6864)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6864,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_691',axiom,
! [Vvar__692] :
( c_24__type__691___24t(Vvar__692)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__696___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__692,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_6956',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6957] :
( c_24__type__6956___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6957)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6957,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_696',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__697] :
( c_24__type__696___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__697)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(Vvar__697,Vv__CANONICAL__2)) ) ) ).
fof('$_type_7038',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7039] :
( c_24__type__7038___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7039)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__7039,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_705',axiom,
! [Vvar__706] :
( c_24__type__705___24t(Vvar__706)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__706,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7131',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7132] :
( c_24__type__7131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7132)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7132,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_714',axiom,
! [Vvar__715] :
( c_24__type__714___24t(Vvar__715)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__715,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_721',axiom,
! [Vvar__722] :
( c_24__type__721___24t(Vvar__722)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__722,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7213',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__7214] :
( c_24__type__7213___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__7214)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__7214,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_724',axiom,
! [Vvar__725] :
( c_24__type__724___24t(Vvar__725)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__725,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_729',axiom,
! [Vvar__730] :
( c_24__type__729___24t(Vvar__730)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__730,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7306',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7307] :
( c_24__type__7306___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7307)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__7307,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_735',axiom,
! [Vvar__736] :
( c_24__type__735___24t(Vvar__736)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__736,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_740',axiom,
! [Vvar__741] :
( c_24__type__740___24t(Vvar__741)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__741,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_779',axiom,
! [Vvar__780] :
( c_24__type__779___24t(Vvar__780)
<=> ! [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__780,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_781',axiom,
! [Vvar__782] :
( c_24__type__781___24t(Vvar__782)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__782,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8',axiom,
! [Vvar__9] :
( c_24__type__8___24t(Vvar__9)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__9,Vv__CANONICAL__0)) ) ) ).
fof('$_type_810',axiom,
! [Vvar__811] :
( c_24__type__810___24t(Vvar__811)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__811,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_831',axiom,
! [Vvar__832] :
( c_24__type__831___24t(Vvar__832)
<=> ! [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__832,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_836',axiom,
! [Vvar__837] :
( c_24__type__836___24t(Vvar__837)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__837,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_839',axiom,
! [Vvar__840] :
( c_24__type__839___24t(Vvar__840)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__840,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8493',axiom,
! [Vvar__8494] :
( c_24__type__8493___24t(Vvar__8494)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__8494,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_861',axiom,
! [Vvar__862] :
( c_24__type__861___24t(Vvar__862)
<=> ! [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__862,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8748',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8749] :
( c_24__type__8748___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8749)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__8749,Vv__CANONICAL__3)) ) ) ).
fof('$_type_8773',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8774] :
( c_24__type__8773___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8774)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__8774,Vv__CANONICAL__3)) ) ) ).
fof('$_type_8834',axiom,
! [Vvar__8835] :
( c_24__type__8834___24t(Vvar__8835)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__8835,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8860',axiom,
! [Vvar__8861] :
( c_24__type__8860___24t(Vvar__8861)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__8861,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8871',axiom,
! [Vvar__8872] :
( c_24__type__8871___24t(Vvar__8872)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__8872,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_890',axiom,
! [Vv__CANONICAL__0,Vvar__891] :
( c_24__type__890___24t(Vv__CANONICAL__0,Vvar__891)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__891,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9322',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9323] :
( c_24__type__9322___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9323)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9323,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9423',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__9424] :
( c_24__type__9423___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__9424)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9424,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9524',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9525] :
( c_24__type__9524___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9525)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9525,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9614',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__9615] :
( c_24__type__9614___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__9615)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__9615,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_965',axiom,
! [Vvar__966] :
( c_24__type__965___24t(Vvar__966)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__966,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9715',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__9716] :
( c_24__type__9715___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__9716)
<=> ! [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__9716,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_9816',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9817] :
( c_24__type__9816___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9817)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__9817,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_9917',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__9918] :
( c_24__type__9917___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__9918)
<=> ! [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__9918,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_typeof_A',axiom,
cType___24t(cA) ).
fof('$_typeof_B',axiom,
cType___24t(cB) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__861___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
c_24__type__861___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__4823___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
c_24__type__861___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
c_24__type__861___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__206___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
c_24__type__839___24t(cCoq_2eArith_2ePlus_2etail__plus) ).
fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
c_24__type__30490___24t(cCoq_2eArith_2eWf__nat_2eltof) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__18293___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__779___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
c_24__type__18299___24t(cCoq_2eBool_2eBool_2eifb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__5005___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
c_24__type__5025___24t(cCoq_2eBool_2eBvector_2eBvector) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
c_24__type__30871___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_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.eq',axiom,
c_24__type__16571___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Byte.byte_of_byte',axiom,
c_24__type__18301___24t(cCoq_2eInit_2eByte_2ebyte__of__byte) ).
fof('$_typeof_Coq.Init.Byte.x00',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex00) ).
fof('$_typeof_Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex01) ).
fof('$_typeof_Coq.Init.Byte.x02',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex02) ).
fof('$_typeof_Coq.Init.Byte.x03',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex03) ).
fof('$_typeof_Coq.Init.Byte.x04',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex04) ).
fof('$_typeof_Coq.Init.Byte.x05',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex05) ).
fof('$_typeof_Coq.Init.Byte.x06',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex06) ).
fof('$_typeof_Coq.Init.Byte.x07',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex07) ).
fof('$_typeof_Coq.Init.Byte.x08',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex08) ).
fof('$_typeof_Coq.Init.Byte.x09',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex09) ).
fof('$_typeof_Coq.Init.Byte.x0a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0a) ).
fof('$_typeof_Coq.Init.Byte.x0b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0b) ).
fof('$_typeof_Coq.Init.Byte.x0c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0c) ).
fof('$_typeof_Coq.Init.Byte.x0d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0d) ).
fof('$_typeof_Coq.Init.Byte.x0e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0e) ).
fof('$_typeof_Coq.Init.Byte.x0f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0f) ).
fof('$_typeof_Coq.Init.Byte.x10',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex10) ).
fof('$_typeof_Coq.Init.Byte.x11',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex11) ).
fof('$_typeof_Coq.Init.Byte.x12',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex12) ).
fof('$_typeof_Coq.Init.Byte.x13',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex13) ).
fof('$_typeof_Coq.Init.Byte.x14',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex14) ).
fof('$_typeof_Coq.Init.Byte.x15',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex15) ).
fof('$_typeof_Coq.Init.Byte.x16',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex16) ).
fof('$_typeof_Coq.Init.Byte.x17',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex17) ).
fof('$_typeof_Coq.Init.Byte.x18',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex18) ).
fof('$_typeof_Coq.Init.Byte.x19',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex19) ).
fof('$_typeof_Coq.Init.Byte.x1a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1a) ).
fof('$_typeof_Coq.Init.Byte.x1b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1b) ).
fof('$_typeof_Coq.Init.Byte.x1c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1c) ).
fof('$_typeof_Coq.Init.Byte.x1d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1d) ).
fof('$_typeof_Coq.Init.Byte.x1e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1e) ).
fof('$_typeof_Coq.Init.Byte.x1f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1f) ).
fof('$_typeof_Coq.Init.Byte.x20',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex20) ).
fof('$_typeof_Coq.Init.Byte.x21',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex21) ).
fof('$_typeof_Coq.Init.Byte.x22',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex22) ).
fof('$_typeof_Coq.Init.Byte.x23',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex23) ).
fof('$_typeof_Coq.Init.Byte.x24',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex24) ).
fof('$_typeof_Coq.Init.Byte.x25',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex25) ).
fof('$_typeof_Coq.Init.Byte.x26',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex26) ).
fof('$_typeof_Coq.Init.Byte.x27',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex27) ).
fof('$_typeof_Coq.Init.Byte.x28',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex28) ).
fof('$_typeof_Coq.Init.Byte.x29',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex29) ).
fof('$_typeof_Coq.Init.Byte.x2a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2a) ).
fof('$_typeof_Coq.Init.Byte.x2b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2b) ).
fof('$_typeof_Coq.Init.Byte.x2c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2c) ).
fof('$_typeof_Coq.Init.Byte.x2d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2d) ).
fof('$_typeof_Coq.Init.Byte.x2e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2e) ).
fof('$_typeof_Coq.Init.Byte.x2f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2f) ).
fof('$_typeof_Coq.Init.Byte.x30',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex30) ).
fof('$_typeof_Coq.Init.Byte.x31',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex31) ).
fof('$_typeof_Coq.Init.Byte.x32',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex32) ).
fof('$_typeof_Coq.Init.Byte.x33',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex33) ).
fof('$_typeof_Coq.Init.Byte.x34',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex34) ).
fof('$_typeof_Coq.Init.Byte.x35',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex35) ).
fof('$_typeof_Coq.Init.Byte.x36',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex36) ).
fof('$_typeof_Coq.Init.Byte.x37',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex37) ).
fof('$_typeof_Coq.Init.Byte.x38',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex38) ).
fof('$_typeof_Coq.Init.Byte.x39',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex39) ).
fof('$_typeof_Coq.Init.Byte.x3a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3a) ).
fof('$_typeof_Coq.Init.Byte.x3b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3b) ).
fof('$_typeof_Coq.Init.Byte.x3c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3c) ).
fof('$_typeof_Coq.Init.Byte.x3d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3d) ).
fof('$_typeof_Coq.Init.Byte.x3e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3e) ).
fof('$_typeof_Coq.Init.Byte.x3f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3f) ).
fof('$_typeof_Coq.Init.Byte.x40',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex40) ).
fof('$_typeof_Coq.Init.Byte.x41',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex41) ).
fof('$_typeof_Coq.Init.Byte.x42',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex42) ).
fof('$_typeof_Coq.Init.Byte.x43',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex43) ).
fof('$_typeof_Coq.Init.Byte.x44',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex44) ).
fof('$_typeof_Coq.Init.Byte.x45',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex45) ).
fof('$_typeof_Coq.Init.Byte.x46',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex46) ).
fof('$_typeof_Coq.Init.Byte.x47',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex47) ).
fof('$_typeof_Coq.Init.Byte.x48',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex48) ).
fof('$_typeof_Coq.Init.Byte.x49',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex49) ).
fof('$_typeof_Coq.Init.Byte.x4a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4a) ).
fof('$_typeof_Coq.Init.Byte.x4b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4b) ).
fof('$_typeof_Coq.Init.Byte.x4c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4c) ).
fof('$_typeof_Coq.Init.Byte.x4d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4d) ).
fof('$_typeof_Coq.Init.Byte.x4e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4e) ).
fof('$_typeof_Coq.Init.Byte.x4f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4f) ).
fof('$_typeof_Coq.Init.Byte.x50',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex50) ).
fof('$_typeof_Coq.Init.Byte.x51',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex51) ).
fof('$_typeof_Coq.Init.Byte.x52',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex52) ).
fof('$_typeof_Coq.Init.Byte.x53',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex53) ).
fof('$_typeof_Coq.Init.Byte.x54',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex54) ).
fof('$_typeof_Coq.Init.Byte.x55',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex55) ).
fof('$_typeof_Coq.Init.Byte.x56',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex56) ).
fof('$_typeof_Coq.Init.Byte.x57',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex57) ).
fof('$_typeof_Coq.Init.Byte.x58',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex58) ).
fof('$_typeof_Coq.Init.Byte.x59',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex59) ).
fof('$_typeof_Coq.Init.Byte.x5a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5a) ).
fof('$_typeof_Coq.Init.Byte.x5b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5b) ).
fof('$_typeof_Coq.Init.Byte.x5c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5c) ).
fof('$_typeof_Coq.Init.Byte.x5d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5d) ).
fof('$_typeof_Coq.Init.Byte.x5e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5e) ).
fof('$_typeof_Coq.Init.Byte.x5f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5f) ).
fof('$_typeof_Coq.Init.Byte.x60',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex60) ).
fof('$_typeof_Coq.Init.Byte.x61',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex61) ).
fof('$_typeof_Coq.Init.Byte.x62',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex62) ).
fof('$_typeof_Coq.Init.Byte.x63',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex63) ).
fof('$_typeof_Coq.Init.Byte.x64',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex64) ).
fof('$_typeof_Coq.Init.Byte.x65',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex65) ).
fof('$_typeof_Coq.Init.Byte.x66',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex66) ).
fof('$_typeof_Coq.Init.Byte.x67',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex67) ).
fof('$_typeof_Coq.Init.Byte.x68',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex68) ).
fof('$_typeof_Coq.Init.Byte.x69',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex69) ).
fof('$_typeof_Coq.Init.Byte.x6a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6a) ).
fof('$_typeof_Coq.Init.Byte.x6b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6b) ).
fof('$_typeof_Coq.Init.Byte.x6c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6c) ).
fof('$_typeof_Coq.Init.Byte.x6d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6d) ).
fof('$_typeof_Coq.Init.Byte.x6e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6e) ).
fof('$_typeof_Coq.Init.Byte.x6f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6f) ).
fof('$_typeof_Coq.Init.Byte.x70',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex70) ).
fof('$_typeof_Coq.Init.Byte.x71',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex71) ).
fof('$_typeof_Coq.Init.Byte.x72',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex72) ).
fof('$_typeof_Coq.Init.Byte.x73',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex73) ).
fof('$_typeof_Coq.Init.Byte.x74',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex74) ).
fof('$_typeof_Coq.Init.Byte.x75',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex75) ).
fof('$_typeof_Coq.Init.Byte.x76',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex76) ).
fof('$_typeof_Coq.Init.Byte.x77',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex77) ).
fof('$_typeof_Coq.Init.Byte.x78',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex78) ).
fof('$_typeof_Coq.Init.Byte.x79',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex79) ).
fof('$_typeof_Coq.Init.Byte.x7a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7a) ).
fof('$_typeof_Coq.Init.Byte.x7b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7b) ).
fof('$_typeof_Coq.Init.Byte.x7c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7c) ).
fof('$_typeof_Coq.Init.Byte.x7d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7d) ).
fof('$_typeof_Coq.Init.Byte.x7e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7e) ).
fof('$_typeof_Coq.Init.Byte.x7f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7f) ).
fof('$_typeof_Coq.Init.Byte.x80',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex80) ).
fof('$_typeof_Coq.Init.Byte.x81',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex81) ).
fof('$_typeof_Coq.Init.Byte.x82',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex82) ).
fof('$_typeof_Coq.Init.Byte.x83',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex83) ).
fof('$_typeof_Coq.Init.Byte.x84',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex84) ).
fof('$_typeof_Coq.Init.Byte.x85',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex85) ).
fof('$_typeof_Coq.Init.Byte.x86',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex86) ).
fof('$_typeof_Coq.Init.Byte.x87',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex87) ).
fof('$_typeof_Coq.Init.Byte.x88',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex88) ).
fof('$_typeof_Coq.Init.Byte.x89',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex89) ).
fof('$_typeof_Coq.Init.Byte.x8a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8a) ).
fof('$_typeof_Coq.Init.Byte.x8b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8b) ).
fof('$_typeof_Coq.Init.Byte.x8c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8c) ).
fof('$_typeof_Coq.Init.Byte.x8d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8d) ).
fof('$_typeof_Coq.Init.Byte.x8e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8e) ).
fof('$_typeof_Coq.Init.Byte.x8f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8f) ).
fof('$_typeof_Coq.Init.Byte.x90',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex90) ).
fof('$_typeof_Coq.Init.Byte.x91',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex91) ).
fof('$_typeof_Coq.Init.Byte.x92',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex92) ).
fof('$_typeof_Coq.Init.Byte.x93',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex93) ).
fof('$_typeof_Coq.Init.Byte.x94',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex94) ).
fof('$_typeof_Coq.Init.Byte.x95',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex95) ).
fof('$_typeof_Coq.Init.Byte.x96',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex96) ).
fof('$_typeof_Coq.Init.Byte.x97',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex97) ).
fof('$_typeof_Coq.Init.Byte.x98',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex98) ).
fof('$_typeof_Coq.Init.Byte.x99',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex99) ).
fof('$_typeof_Coq.Init.Byte.x9a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9a) ).
fof('$_typeof_Coq.Init.Byte.x9b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9b) ).
fof('$_typeof_Coq.Init.Byte.x9c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9c) ).
fof('$_typeof_Coq.Init.Byte.x9d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9d) ).
fof('$_typeof_Coq.Init.Byte.x9e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9e) ).
fof('$_typeof_Coq.Init.Byte.x9f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9f) ).
fof('$_typeof_Coq.Init.Byte.xa0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa0) ).
fof('$_typeof_Coq.Init.Byte.xa1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa1) ).
fof('$_typeof_Coq.Init.Byte.xa2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa2) ).
fof('$_typeof_Coq.Init.Byte.xa3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa3) ).
fof('$_typeof_Coq.Init.Byte.xa4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa4) ).
fof('$_typeof_Coq.Init.Byte.xa5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa5) ).
fof('$_typeof_Coq.Init.Byte.xa6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa6) ).
fof('$_typeof_Coq.Init.Byte.xa7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa7) ).
fof('$_typeof_Coq.Init.Byte.xa8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa8) ).
fof('$_typeof_Coq.Init.Byte.xa9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa9) ).
fof('$_typeof_Coq.Init.Byte.xaa',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exaa) ).
fof('$_typeof_Coq.Init.Byte.xab',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exab) ).
fof('$_typeof_Coq.Init.Byte.xac',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exac) ).
fof('$_typeof_Coq.Init.Byte.xad',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exad) ).
fof('$_typeof_Coq.Init.Byte.xae',axiom,
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fof('$_typeof_Coq.Init.Byte.xaf',axiom,
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fof('$_typeof_Coq.Init.Byte.xb0',axiom,
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fof('$_typeof_Coq.Init.Byte.xb1',axiom,
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fof('$_typeof_Coq.Init.Byte.xb2',axiom,
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fof('$_typeof_Coq.Init.Byte.xb3',axiom,
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fof('$_typeof_Coq.Init.Byte.xb4',axiom,
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fof('$_typeof_Coq.Init.Byte.xb5',axiom,
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fof('$_typeof_Coq.Init.Byte.xb6',axiom,
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fof('$_typeof_Coq.Init.Byte.xb7',axiom,
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fof('$_typeof_Coq.Init.Byte.xb8',axiom,
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fof('$_typeof_Coq.Init.Byte.xb9',axiom,
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fof('$_typeof_Coq.Init.Byte.xba',axiom,
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fof('$_typeof_Coq.Init.Byte.xbb',axiom,
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fof('$_typeof_Coq.Init.Byte.xbc',axiom,
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fof('$_typeof_Coq.Init.Byte.xbd',axiom,
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fof('$_typeof_Coq.Init.Byte.xbe',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbe) ).
fof('$_typeof_Coq.Init.Byte.xbf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbf) ).
fof('$_typeof_Coq.Init.Byte.xc0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc0) ).
fof('$_typeof_Coq.Init.Byte.xc1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc1) ).
fof('$_typeof_Coq.Init.Byte.xc2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc2) ).
fof('$_typeof_Coq.Init.Byte.xc3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc3) ).
fof('$_typeof_Coq.Init.Byte.xc4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc4) ).
fof('$_typeof_Coq.Init.Byte.xc5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc5) ).
fof('$_typeof_Coq.Init.Byte.xc6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc6) ).
fof('$_typeof_Coq.Init.Byte.xc7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc7) ).
fof('$_typeof_Coq.Init.Byte.xc8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc8) ).
fof('$_typeof_Coq.Init.Byte.xc9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc9) ).
fof('$_typeof_Coq.Init.Byte.xca',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exca) ).
fof('$_typeof_Coq.Init.Byte.xcb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excb) ).
fof('$_typeof_Coq.Init.Byte.xcc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excc) ).
fof('$_typeof_Coq.Init.Byte.xcd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excd) ).
fof('$_typeof_Coq.Init.Byte.xce',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exce) ).
fof('$_typeof_Coq.Init.Byte.xcf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excf) ).
fof('$_typeof_Coq.Init.Byte.xd0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd0) ).
fof('$_typeof_Coq.Init.Byte.xd1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd1) ).
fof('$_typeof_Coq.Init.Byte.xd2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd2) ).
fof('$_typeof_Coq.Init.Byte.xd3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd3) ).
fof('$_typeof_Coq.Init.Byte.xd4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd4) ).
fof('$_typeof_Coq.Init.Byte.xd5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd5) ).
fof('$_typeof_Coq.Init.Byte.xd6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd6) ).
fof('$_typeof_Coq.Init.Byte.xd7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd7) ).
fof('$_typeof_Coq.Init.Byte.xd8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd8) ).
fof('$_typeof_Coq.Init.Byte.xd9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd9) ).
fof('$_typeof_Coq.Init.Byte.xda',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exda) ).
fof('$_typeof_Coq.Init.Byte.xdb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdb) ).
fof('$_typeof_Coq.Init.Byte.xdc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdc) ).
fof('$_typeof_Coq.Init.Byte.xdd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdd) ).
fof('$_typeof_Coq.Init.Byte.xde',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exde) ).
fof('$_typeof_Coq.Init.Byte.xdf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdf) ).
fof('$_typeof_Coq.Init.Byte.xe0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe0) ).
fof('$_typeof_Coq.Init.Byte.xe1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe1) ).
fof('$_typeof_Coq.Init.Byte.xe2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe2) ).
fof('$_typeof_Coq.Init.Byte.xe3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe3) ).
fof('$_typeof_Coq.Init.Byte.xe4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe4) ).
fof('$_typeof_Coq.Init.Byte.xe5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe5) ).
fof('$_typeof_Coq.Init.Byte.xe6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe6) ).
fof('$_typeof_Coq.Init.Byte.xe7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe7) ).
fof('$_typeof_Coq.Init.Byte.xe8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe8) ).
fof('$_typeof_Coq.Init.Byte.xe9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe9) ).
fof('$_typeof_Coq.Init.Byte.xea',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exea) ).
fof('$_typeof_Coq.Init.Byte.xeb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exeb) ).
fof('$_typeof_Coq.Init.Byte.xec',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exec) ).
fof('$_typeof_Coq.Init.Byte.xed',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exed) ).
fof('$_typeof_Coq.Init.Byte.xee',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exee) ).
fof('$_typeof_Coq.Init.Byte.xef',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exef) ).
fof('$_typeof_Coq.Init.Byte.xf0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf0) ).
fof('$_typeof_Coq.Init.Byte.xf1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf1) ).
fof('$_typeof_Coq.Init.Byte.xf2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf2) ).
fof('$_typeof_Coq.Init.Byte.xf3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf3) ).
fof('$_typeof_Coq.Init.Byte.xf4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf4) ).
fof('$_typeof_Coq.Init.Byte.xf5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf5) ).
fof('$_typeof_Coq.Init.Byte.xf6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf6) ).
fof('$_typeof_Coq.Init.Byte.xf7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf7) ).
fof('$_typeof_Coq.Init.Byte.xf8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf8) ).
fof('$_typeof_Coq.Init.Byte.xf9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf9) ).
fof('$_typeof_Coq.Init.Byte.xfa',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfa) ).
fof('$_typeof_Coq.Init.Byte.xfb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfb) ).
fof('$_typeof_Coq.Init.Byte.xfc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfc) ).
fof('$_typeof_Coq.Init.Byte.xfd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfd) ).
fof('$_typeof_Coq.Init.Byte.xfe',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfe) ).
fof('$_typeof_Coq.Init.Byte.xff',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exff) ).
fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__5866___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__18600___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.Empty_set',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eEmpty__set) ).
fof('$_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.ID',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eID) ).
fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__5762___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__6___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__5760___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__779___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__5863___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__5795___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__18563___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.id',axiom,
cCoq_2eInit_2eDatatypes_2eID___24t(cCoq_2eInit_2eDatatypes_2eid) ).
fof('$_typeof_Coq.Init.Datatypes.implb',axiom,
c_24__type__779___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__5851___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__17___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__781___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__5790___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__17___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__779___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__5788___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__5772___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__18575___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__5772___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__779___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Decimal.D0',axiom,
c_24__type__18660___24t(cCoq_2eInit_2eDecimal_2eD0) ).
fof('$_typeof_Coq.Init.Decimal.D1',axiom,
c_24__type__18660___24t(cCoq_2eInit_2eDecimal_2eD1) ).
fof('$_typeof_Coq.Init.Decimal.D2',axiom,
c_24__type__18660___24t(cCoq_2eInit_2eDecimal_2eD2) ).
fof('$_typeof_Coq.Init.Decimal.D3',axiom,
c_24__type__18660___24t(cCoq_2eInit_2eDecimal_2eD3) ).
fof('$_typeof_Coq.Init.Decimal.D4',axiom,
c_24__type__18660___24t(cCoq_2eInit_2eDecimal_2eD4) ).
fof('$_typeof_Coq.Init.Decimal.D5',axiom,
c_24__type__18660___24t(cCoq_2eInit_2eDecimal_2eD5) ).
fof('$_typeof_Coq.Init.Decimal.D6',axiom,
c_24__type__18660___24t(cCoq_2eInit_2eDecimal_2eD6) ).
fof('$_typeof_Coq.Init.Decimal.D7',axiom,
c_24__type__18660___24t(cCoq_2eInit_2eDecimal_2eD7) ).
fof('$_typeof_Coq.Init.Decimal.D8',axiom,
c_24__type__18660___24t(cCoq_2eInit_2eDecimal_2eD8) ).
fof('$_typeof_Coq.Init.Decimal.D9',axiom,
c_24__type__18660___24t(cCoq_2eInit_2eDecimal_2eD9) ).
fof('$_typeof_Coq.Init.Decimal.Nil',axiom,
cCoq_2eInit_2eDecimal_2euint___24t(cCoq_2eInit_2eDecimal_2eNil) ).
fof('$_typeof_Coq.Init.Decimal.decimal',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2edecimal) ).
fof('$_typeof_Coq.Init.Decimal.int',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2eint) ).
fof('$_typeof_Coq.Init.Decimal.nzhead',axiom,
c_24__type__18660___24t(cCoq_2eInit_2eDecimal_2enzhead) ).
fof('$_typeof_Coq.Init.Decimal.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Decimal.uint_of_uint',axiom,
c_24__type__18660___24t(cCoq_2eInit_2eDecimal_2euint__of__uint) ).
fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
c_24__type__6551___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__839___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__8834___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__836___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__4825___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__836___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.log2_iter',axiom,
c_24__type__8860___24t(cCoq_2eInit_2eNat_2elog2__iter) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__839___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__839___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__839___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__839___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__839___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.succ',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2esucc) ).
fof('$_typeof_Coq.Init.Nat.t',axiom,
cType___24t(cCoq_2eInit_2eNat_2et) ).
fof('$_typeof_Coq.Init.Nat.tail_add',axiom,
c_24__type__839___24t(cCoq_2eInit_2eNat_2etail__add) ).
fof('$_typeof_Coq.Init.Nat.zero',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eNat_2ezero) ).
fof('$_typeof_Coq.Init.Peano.IsSucc',axiom,
c_24__type__8___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__861___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__861___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__861___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.Exc',axiom,
c_24__type__17___24t(cCoq_2eInit_2eSpecif_2eExc) ).
fof('$_typeof_Coq.Init.Specif.except',axiom,
c_24__type__30443___24t(cCoq_2eInit_2eSpecif_2eexcept) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__14033___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__30383___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__14160___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__14064___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__14165___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__14015___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__30360___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__18116___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__30426___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__14137___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__18137___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__4719___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__831___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__20637___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__20666___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__810___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__20613___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__20589___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__30102___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__30102___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__30145___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__30145___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ConstructiveIndefiniteDescription_on',axiom,
c_24__type__17___24t(cCoq_2eLogic_2eChoiceFacts_2eConstructiveIndefiniteDescription__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on',axiom,
c_24__type__18339___24t(cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ExcludedMiddle',axiom,
cProp___24t(cCoq_2eLogic_2eChoiceFacts_2eExcludedMiddle) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalChoice_on',axiom,
c_24__type__5687___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalChoice_on_rel',axiom,
c_24__type__18315___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on',axiom,
c_24__type__6551___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.GeneralizedSetoidFunctionalChoice_on',axiom,
c_24__type__5687___24t(cCoq_2eLogic_2eChoiceFacts_2eGeneralizedSetoidFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ProofIrrelevance',axiom,
cProp___24t(cCoq_2eLogic_2eChoiceFacts_2eProofIrrelevance) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.RepresentativeFunctionalChoice_on',axiom,
c_24__type__6551___24t(cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.SetoidFunctionalChoice_on',axiom,
c_24__type__5687___24t(cCoq_2eLogic_2eChoiceFacts_2eSetoidFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on',axiom,
c_24__type__5687___24t(cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.BoolP',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eBoolP) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.DrinkerParadox',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eDrinkerParadox) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.GodelDummett',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eGodelDummett) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.IndependenceOfGeneralPremises',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eIndependenceOfGeneralPremises) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.Minimal',axiom,
c_24__type__18493___24t(cCoq_2eLogic_2eClassicalFacts_2eMinimal) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.RightDistributivityImplicationOverDisjunction',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eRightDistributivityImplicationOverDisjunction) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eexcluded__middle) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.generalized_excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2egeneralized__excluded__middle) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.proof_irrelevance',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eproof__irrelevance) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.prop_extensionality',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.weak_generalized_excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eweak__generalized__excluded__middle) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__18657___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.FinFun.Bijective',axiom,
c_24__type__20272___24t(cCoq_2eLogic_2eFinFun_2eBijective) ).
fof('$_typeof_Coq.Logic.FinFun.Injective',axiom,
c_24__type__20272___24t(cCoq_2eLogic_2eFinFun_2eInjective) ).
fof('$_typeof_Coq.Logic.FinFun.Surjective',axiom,
c_24__type__20272___24t(cCoq_2eLogic_2eFinFun_2eSurjective) ).
fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
c_24__type__4728___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__30737___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__4728___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__4728___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNat.N.peano_rect',axiom,
c_24__type__472___24t(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect) ).
fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
c_24__type__503___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__8493___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
c_24__type__420___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__16110___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
c_24__type__8493___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__8493___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__8493___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__420___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__420___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.t',axiom,
cType___24t(cCoq_2eNArith_2eBinNatDef_2eN_2et) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__8871___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__16190___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ezero) ).
fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
c_24__type__4823___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).
fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__4989___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__4991___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__4991___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__4981___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__4981___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
c_24__type__16352___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
c_24__type__16073___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNeg',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNul',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
c_24__type__16260___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__16286___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
c_24__type__4981___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
c_24__type__16291___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__16281___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__30780___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
c_24__type__15846___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
c_24__type__15846___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__4981___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.t',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2et) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
c_24__type__21498___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__21488___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__21493___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__21500___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.negreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonnegreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonnegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonposreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonposreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).
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.Rgt',axiom,
c_24__type__17828___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__21500___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__17828___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__17828___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__21694___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__21500___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__21694___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__21697___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__22634___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
c_24__type__20___24t(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.commut',axiom,
c_24__type__35___24t(cCoq_2eRelations_2eRelation__Definitions_2ecommut) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.equiv',axiom,
c_24__type__20___24t(cCoq_2eRelations_2eRelation__Definitions_2eequiv) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.inclusion',axiom,
c_24__type__35___24t(cCoq_2eRelations_2eRelation__Definitions_2einclusion) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__20___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__17___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.same_relation',axiom,
c_24__type__35___24t(cCoq_2eRelations_2eRelation__Definitions_2esame__relation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.symmetric',axiom,
c_24__type__20___24t(cCoq_2eRelations_2eRelation__Definitions_2esymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__20___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Relations.Relation_Operators.transp',axiom,
c_24__type__403___24t(cCoq_2eRelations_2eRelation__Operators_2etransp) ).
fof('$_typeof_Coq.Relations.Relation_Operators.union',axiom,
c_24__type__667___24t(cCoq_2eRelations_2eRelation__Operators_2eunion) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__20___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__17___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
c_24__type__4964___24t(cCoq_2eStrings_2eAscii_2eAscii) ).
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('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.GenericMinMax.gmax',axiom,
c_24__type__20359___24t(cCoq_2eStructures_2eGenericMinMax_2egmax) ).
fof('$_typeof_Coq.Structures.GenericMinMax.gmin',axiom,
c_24__type__20359___24t(cCoq_2eStructures_2eGenericMinMax_2egmin) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__21382___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__4728___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__4728___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__861___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__861___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
c_24__type__16073___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__16073___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
c_24__type__16073___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
c_24__type__16073___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
c_24__type__16073___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
c_24__type__17101___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
c_24__type__17101___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLE',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLE) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLT) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__5025___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__14860___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
c_24__type__4841___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
c_24__type__4841___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__17101___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
c_24__type__17101___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__30887___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__17101___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__17101___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__17101___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__16806___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__4841___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__4841___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
c_24__type__17039___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__4841___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__4841___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__4841___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__4841___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__17039___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__4847___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__16806___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__4841___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__16806___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.t',axiom,
cType___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2et) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_N',axiom,
c_24__type__16857___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__16861___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ezero) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__15741___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__4993___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__4993___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__4983___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__22634___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__16030___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__17___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__18714___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__17___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__6121___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__17___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.EnvRing.mon0',axiom,
cCoq_2emicromega_2eEnvRing_2eMon___24t(cCoq_2emicromega_2eEnvRing_2emon0) ).
fof('$_typeof_Coq.micromega.RMicromega.C0',axiom,
cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC0) ).
fof('$_typeof_Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC1) ).
fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__21684___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__10171___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__21719___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__17___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_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.OpEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpNEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__17___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__17___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__17___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__14293___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__17___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.DoneProof',axiom,
cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(cCoq_2emicromega_2eZMicromega_2eDoneProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.coneMember',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2econeMember) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_N\'',axiom,
c_24__type__4847___24t(cCoq_2eomega_2ePreOmega_2eZ__of__N_27) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
c_24__type__4844___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zneg\'',axiom,
c_24__type__4991___24t(cCoq_2eomega_2ePreOmega_2eZneg_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zpos\'',axiom,
c_24__type__4991___24t(cCoq_2eomega_2ePreOmega_2eZpos_27) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__19090___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__19087___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__17___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__17___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__17___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.NotConstant',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2esetoid__ring_2eInitialRing_2eNotConstant) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__20512___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__20512___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.hypo',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2ehypo) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.mkhypo',axiom,
c_24__type__20564___24t(cCoq_2esetoid__ring_2eInitialRing_2emkhypo) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__10734___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__10734___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__10740___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__10745___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__10737___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__10745___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__10754___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__10745___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__17___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__965___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__17___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__28138___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
c_24__type__10501___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.Abstract',axiom,
cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(cCoq_2esetoid__ring_2eRing__theory_2eAbstract) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__29818___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__29818___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__420___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__12698___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__1289___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).
fof('$_typeof_HahnRelationsBasic.acyclic',axiom,
c_24__type__20___24t(cHahnRelationsBasic_2eacyclic) ).
fof('$_typeof_HahnRelationsBasic.bunion',axiom,
c_24__type__691___24t(cHahnRelationsBasic_2ebunion) ).
fof('$_typeof_HahnRelationsBasic.clos_refl',axiom,
c_24__type__724___24t(cHahnRelationsBasic_2eclos__refl) ).
fof('$_typeof_HahnRelationsBasic.codom_rel',axiom,
c_24__type__721___24t(cHahnRelationsBasic_2ecodom__rel) ).
fof('$_typeof_HahnRelationsBasic.collect_rel',axiom,
c_24__type__4872___24t(cHahnRelationsBasic_2ecollect__rel) ).
fof('$_typeof_HahnRelationsBasic.cross_rel',axiom,
c_24__type__17608___24t(cHahnRelationsBasic_2ecross__rel) ).
fof('$_typeof_HahnRelationsBasic.dom_rel',axiom,
c_24__type__721___24t(cHahnRelationsBasic_2edom__rel) ).
fof('$_typeof_HahnRelationsBasic.eq_rel',axiom,
c_24__type__4899___24t(cHahnRelationsBasic_2eeq__rel) ).
fof('$_typeof_HahnRelationsBasic.eqv_dom_rel',axiom,
c_24__type__4892___24t(cHahnRelationsBasic_2eeqv__dom__rel) ).
fof('$_typeof_HahnRelationsBasic.eqv_rel',axiom,
c_24__type__740___24t(cHahnRelationsBasic_2eeqv__rel) ).
fof('$_typeof_HahnRelationsBasic.functional',axiom,
c_24__type__20___24t(cHahnRelationsBasic_2efunctional) ).
fof('$_typeof_HahnRelationsBasic.immediate',axiom,
c_24__type__724___24t(cHahnRelationsBasic_2eimmediate) ).
fof('$_typeof_HahnRelationsBasic.inter_rel',axiom,
c_24__type__729___24t(cHahnRelationsBasic_2einter__rel) ).
fof('$_typeof_HahnRelationsBasic.irreflexive',axiom,
c_24__type__20___24t(cHahnRelationsBasic_2eirreflexive) ).
fof('$_typeof_HahnRelationsBasic.is_total',axiom,
c_24__type__253___24t(cHahnRelationsBasic_2eis__total) ).
fof('$_typeof_HahnRelationsBasic.map_rel',axiom,
c_24__type__264___24t(cHahnRelationsBasic_2emap__rel) ).
fof('$_typeof_HahnRelationsBasic.minus_rel',axiom,
c_24__type__729___24t(cHahnRelationsBasic_2eminus__rel) ).
fof('$_typeof_HahnRelationsBasic.pow_rel',axiom,
c_24__type__705___24t(cHahnRelationsBasic_2epow__rel) ).
fof('$_typeof_HahnRelationsBasic.restr_eq_rel',axiom,
c_24__type__4887___24t(cHahnRelationsBasic_2erestr__eq__rel) ).
fof('$_typeof_HahnRelationsBasic.restr_rel',axiom,
c_24__type__735___24t(cHahnRelationsBasic_2erestr__rel) ).
fof('$_typeof_HahnRelationsBasic.restr_subset',axiom,
c_24__type__4860___24t(cHahnRelationsBasic_2erestr__subset) ).
fof('$_typeof_HahnRelationsBasic.seq',axiom,
c_24__type__729___24t(cHahnRelationsBasic_2eseq) ).
fof('$_typeof_HahnRelationsBasic.strict_partial_order',axiom,
c_24__type__20___24t(cHahnRelationsBasic_2estrict__partial__order) ).
fof('$_typeof_HahnRelationsBasic.strict_total_order',axiom,
c_24__type__253___24t(cHahnRelationsBasic_2estrict__total__order) ).
fof('$_typeof_HahnRelationsBasic.upward_closed',axiom,
c_24__type__714___24t(cHahnRelationsBasic_2eupward__closed) ).
fof('$_typeof_Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eAllHyps) ).
fof('$_typeof_Hammer.Tactics.Reconstr.Empty',axiom,
cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eEmpty) ).
fof('$_typeof_Hammer.Tactics.Reconstr.ReconstrT',axiom,
cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).
fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
c_24__type__20377___24t(cHammer_2eTactics_2eReconstr_2erdone) ).
fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
c_24__type__20377___24t(cHammer_2eTactics_2eTactics_2erdone) ).
fof('$_typeof_dom',axiom,
c_24__type__30897___24t(cdom) ).
fof('$_typeof_f',axiom,
c_24__type__30895___24t(cf) ).
fof('$_typeof_hahn.HahnBase.Equality.mixin_of',axiom,
c_24__type__17___24t(chahn_2eHahnBase_2eEquality_2emixin__of) ).
fof('$_typeof_hahn.HahnBase.Equality.type',axiom,
cType___24t(chahn_2eHahnBase_2eEquality_2etype) ).
fof('$_typeof_hahn.HahnSets.set_bunion',axiom,
c_24__type__20472___24t(chahn_2eHahnSets_2eset__bunion) ).
fof('$_typeof_hahn.HahnSets.set_collect',axiom,
c_24__type__20422___24t(chahn_2eHahnSets_2eset__collect) ).
fof('$_typeof_hahn.HahnSets.set_compl',axiom,
c_24__type__20384___24t(chahn_2eHahnSets_2eset__compl) ).
fof('$_typeof_hahn.HahnSets.set_disjoint',axiom,
c_24__type__17816___24t(chahn_2eHahnSets_2eset__disjoint) ).
fof('$_typeof_hahn.HahnSets.set_empty',axiom,
c_24__type__20377___24t(chahn_2eHahnSets_2eset__empty) ).
fof('$_typeof_hahn.HahnSets.set_equiv',axiom,
c_24__type__17816___24t(chahn_2eHahnSets_2eset__equiv) ).
fof('$_typeof_hahn.HahnSets.set_full',axiom,
c_24__type__20377___24t(chahn_2eHahnSets_2eset__full) ).
fof('$_typeof_hahn.HahnSets.set_inter',axiom,
c_24__type__17797___24t(chahn_2eHahnSets_2eset__inter) ).
fof('$_typeof_hahn.HahnSets.set_map',axiom,
c_24__type__20445___24t(chahn_2eHahnSets_2eset__map) ).
fof('$_typeof_hahn.HahnSets.set_minus',axiom,
c_24__type__17797___24t(chahn_2eHahnSets_2eset__minus) ).
fof('$_typeof_hahn.HahnSets.set_subset',axiom,
c_24__type__17816___24t(chahn_2eHahnSets_2eset__subset) ).
fof('$_typeof_hahn.HahnSets.set_union',axiom,
c_24__type__17797___24t(chahn_2eHahnSets_2eset__union) ).
fof('$_typeof_r',axiom,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,cr) ).
fof('$_typeof_r\'',axiom,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,cr_27) ).
fof('$_typeof_r\'\'',axiom,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,cr_27_27) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.induction',axiom,
! [V0__A] :
( c_24__type__8___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e),V0__A)
=> ( p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(happ(V0__A,V3__n))
=> p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n))) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(happ(V0__A,V4__n)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ind',axiom,
! [V0__A] :
( c_24__type__8___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e),V0__A)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__A,V2__n))
=> ( ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V2__n,V4__m)
=> ( p(happ(V0__A,V4__m))
=> p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) )
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V2__n,V5__m)
=> p(happ(V0__A,V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ind_rel',axiom,
! [V0__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cCoq_2eInit_2eDatatypes_2enat,V0__R)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__861,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,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),V0__R)
=> ( ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eO),V2__m)) )
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V3__n,V4__m)
=> ( p(happ(happ(V0__R,V3__n),V4__m))
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V4__n,V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_refl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__861,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,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),cCoq_2eInit_2ePeano_2ele) ).
fof('Coq.Arith.PeanoNat.Nat.lt_exists_pred',axiom,
! [V0__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__z,V1__n)
=> ? [V3__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__k)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(V3__k)
& cCoq_2eInit_2ePeano_2ele___24a2(V0__z,V3__k) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_ind',axiom,
! [V0__A] :
( c_24__type__8___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e),V0__A)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n)))
=> ( ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__n,V4__m)
=> ( p(happ(V0__A,V4__m))
=> p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) )
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__n,V5__m)
=> p(happ(V0__A,V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_ind_rel',axiom,
! [V0__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cCoq_2eInit_2eDatatypes_2enat,V0__R)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__861,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,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),V0__R)
=> ( ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m))) )
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V3__n,V4__m)
=> ( p(happ(happ(V0__R,V3__n),V4__m))
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V4__n,V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.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)
=> ( cCoq_2eInit_2ePeano_2elt___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.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__861,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,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),cCoq_2eInit_2ePeano_2elt) ).
fof('Coq.Arith.PeanoNat.Nat.recursion_succ',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__f] :
( c_24__type__211___24t(V0__A,V3__f)
=> ( p(happ(happ(V1__Aeq,V2__a),V2__a))
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__211___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__247___24a1(V0__A),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),V3__f)
=> ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> p(happ(happ(V1__Aeq,cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4(V0__A,V2__a,V3__f,cCoq_2eInit_2eDatatypes_2eS___24a1(V6__n))),happ(happ(V3__f,V6__n),cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4(V0__A,V2__a,V3__f,V6__n)))) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.recursion_wd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__224___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__235___24a1(V0__A),V1__Aeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__211___24a1(V0__A),c_24__type__244___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__247___24a1(V0__A),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,V0__A,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),V1__Aeq))),cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A)) ) ) ).
fof('Coq.Arith.Wf_nat.lt_wf_ind',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__8___24t(V1__P)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V3__m,V2__n)
=> p(happ(V1__P,V3__m)) ) )
=> p(happ(V1__P,V2__n)) ) )
=> p(happ(V1__P,V0__n)) ) ) ) ).
fof('Coq.Bool.Bool.absurd_eq_bool',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ! [V1__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
=> ( p(c_24False)
=> V0__b = V1__b_27 ) ) ) ).
fof('Coq.Init.Datatypes.idProp',axiom,
p(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__8___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.Logic.ChoiceFacts.proj1_inf',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
& p(V1__B) )
=> p(V0__A) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.FalseP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eBoolP) ).
fof('Coq.Logic.ClassicalFacts.TrueP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eBoolP) ).
fof('Coq.Logic.ClassicalFacts.falseP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eboolP) ).
fof('Coq.Logic.ClassicalFacts.proof_irrelevance_cci',axiom,
( ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
| ~ p(V0__A) ) )
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( p(V1__B)
=> ( p(V1__B)
=> c_24Proof = c_24Proof ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.trueP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eboolP) ).
fof('Coq.Logic.Classical_Pred_Type.ex_not_not_all',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__161___24t(V0__U,V1__P)
=> ( ? [V2__n] :
( t(V2__n,V0__U)
& ~ p(happ(V1__P,V2__n)) )
=> ~ ! [V3__n] :
( t(V3__n,V0__U)
=> p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_all_ex_not',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__161___24t(V0__U,V1__P)
=> ( ~ ! [V2__n] :
( t(V2__n,V0__U)
=> p(happ(V1__P,V2__n)) )
=> ? [V3__n] :
( t(V3__n,V0__U)
& ~ p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_all_not_ex',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__161___24t(V0__U,V1__P)
=> ( ~ ! [V2__n] :
( t(V2__n,V0__U)
=> ~ p(happ(V1__P,V2__n)) )
=> ? [V3__n] :
( t(V3__n,V0__U)
& p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.NNPP',axiom,
! [V0__p] :
( cProp___24t(V0__p)
=> ( ~ ~ p(V0__p)
=> p(V0__p) ) ) ).
fof('Coq.Logic.Classical_Prop.Peirce',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( ( ( p(V0__P)
=> p(c_24False) )
=> p(V0__P) )
=> p(V0__P) ) ) ).
fof('Coq.Logic.Classical_Prop.classic',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_and_or',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( p(V0__P)
=> p(V1__Q) )
=> ( ( p(V0__P)
| p(V1__Q) )
=> p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_and_or2',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ! [V2__R] :
( cProp___24t(V2__R)
=> ( ( p(V0__P)
=> p(V1__Q) )
=> ( ( p(V0__P)
| p(V2__R) )
=> ( p(V1__Q)
| p(V2__R) ) ) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_to_and',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> ( p(V0__P)
& ~ p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_to_or',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( p(V0__P)
=> p(V1__Q) )
=> ( ~ p(V0__P)
| p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_imply_elim',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_imply_elim2',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> ~ p(V1__Q) ) ) ) ).
fof('Coq.Logic.Classical_Prop.or_to_imply',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( ~ p(V0__P)
| p(V1__Q) )
=> ( p(V0__P)
=> p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
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.not_and_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
& p(V1__B) )
=> p(c_24False) )
<=> ( p(V0__A)
=> ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_or_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
| p(V1__B) )
=> p(c_24False) )
<=> ( ( p(V0__A)
=> p(c_24False) )
& ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.equal_f',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__268___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__268___24t(V0__A,V1__B,V3__g)
=> ( V2__f = V3__g
=> ! [V5__x] :
( t(V5__x,V0__A)
=> happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.equal_f_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__6566___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__20300___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__20305___24t(V0__A,V1__B,V3__g)
=> ( V2__f = V3__g
=> ! [V5__x] :
( t(V5__x,V0__A)
=> happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.eta_expansion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__268___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__20344___24a3(V0__A,V1__B,V2__f) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.eta_expansion_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__6566___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__20328___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__20336___24a3(V0__A,V1__B,V2__f) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.functional_extensionality',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__268___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__268___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) )
=> V2__f = V3__g ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.functional_extensionality_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__6566___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__20311___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__20316___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) )
=> V2__f = V3__g ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
fof('Coq.NArith.BinNat.N.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.induction',axiom,
! [V0__A] :
( c_24__type__486___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__486,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e),V0__A)
=> ( p(happ(V0__A,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> ( p(happ(V0__A,V3__n))
=> p(happ(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n))) ) )
=> ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__n)
=> p(happ(V0__A,V4__n)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ).
fof('Coq.NArith.BinNat.N.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
| cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_ind',axiom,
! [V0__A] :
( c_24__type__486___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__486,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e),V0__A)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( p(happ(V0__A,V2__n))
=> ( ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__n,V4__m)
=> ( p(happ(V0__A,V4__m))
=> p(happ(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V4__m))) ) ) )
=> ! [V5__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__n,V5__m)
=> p(happ(V0__A,V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_ind_rel',axiom,
! [V0__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cCoq_2eNumbers_2eBinNums_2eN,V0__R)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4728,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__486,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e)),V0__R)
=> ( ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> p(happ(happ(V0__R,cCoq_2eNumbers_2eBinNums_2eN0),V2__m)) )
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V3__n,V4__m)
=> ( p(happ(happ(V0__R,V3__n),V4__m))
=> p(happ(happ(V0__R,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n)),cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V4__m))) ) ) ) )
=> ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__n)
=> ! [V5__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V4__n,V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.NArith.BinNat.N.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m)
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4728,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__486,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e)),cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('Coq.NArith.BinNat.N.lt_exists_pred',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__z,V1__n)
=> ? [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__k)
& V1__n = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__k)
& cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__z,V3__k) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_ind',axiom,
! [V0__A] :
( c_24__type__486___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__486,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e),V0__A)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( p(happ(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V2__n)))
=> ( ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V2__n,V4__m)
=> ( p(happ(V0__A,V4__m))
=> p(happ(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V4__m))) ) ) )
=> ! [V5__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V2__n,V5__m)
=> p(happ(V0__A,V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_ind_rel',axiom,
! [V0__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cCoq_2eNumbers_2eBinNums_2eN,V0__R)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4728,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__486,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e)),V0__R)
=> ( ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> p(happ(happ(V0__R,cCoq_2eNumbers_2eBinNums_2eN0),cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V2__m))) )
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V3__n,V4__m)
=> ( p(happ(happ(V0__R,V3__n),V4__m))
=> p(happ(happ(V0__R,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n)),cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V4__m))) ) ) ) )
=> ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__n)
=> ! [V5__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V4__n,V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) ) ).
fof('Coq.NArith.BinNat.N.lt_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4728,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__486,cCoq_2eNArith_2eBinNat_2eN_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,cCoq_2eNArith_2eBinNat_2eN_2eeq,c_3c_3d_3e)),cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('Coq.NArith.BinNat.N.peano_ind',axiom,
! [V0__P] :
( c_24__type__486___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.peano_rect_succ',axiom,
! [V0__P] :
( c_24__type__474___24t(V0__P)
=> ! [V1__a] :
( t(V1__a,happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
=> ! [V2__f] :
( c_24__type__484___24t(V0__P,V2__f)
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V0__P,V1__a,V2__f,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n)) = happ(happ(V2__f,V3__n),cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V0__P,V1__a,V2__f,V3__n)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.recursion_succ',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__f] :
( c_24__type__508___24t(V0__A,V3__f)
=> ( p(happ(happ(V1__Aeq,V2__a),V2__a))
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__508___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__247___24a1(V0__A),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),V3__f)
=> ! [V6__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V6__n)
=> p(happ(happ(V1__Aeq,cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4(V0__A,V2__a,V3__f,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V6__n))),happ(happ(V3__f,V6__n),cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4(V0__A,V2__a,V3__f,V6__n)))) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.recursion_wd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__521___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__532___24a1(V0__A),V1__Aeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__508___24a1(V0__A),c_24__type__541___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__247___24a1(V0__A),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,V0__A,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),V1__Aeq))),cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A)) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.Relations.Operators_Properties.clos_r_clos_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a2(V0__A,V1__R),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_refl_trans_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__161___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V6__z)
=> p(happ(V3__P,V6__z)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_refl_trans_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__161___24t(V0__A,V2__P)
=> ! [V3__z] :
( t(V3__z,V0__A)
=> ( p(happ(V2__P,V3__z))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__R,V5__x),V6__y))
=> ( p(happ(V2__P,V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V3__z)
=> p(happ(V2__P,V5__x)) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V3__z)
=> p(happ(V2__P,V6__x)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_idempotent',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_is_equiv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rst1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rst1n_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rstn1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rstn1_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rstn1_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rstn1_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rstn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt1n_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt1n_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_clos_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_idempotent',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_is_preorder',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rt1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rt1n_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rtn1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rtn1_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rtn1_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rtn1_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_t1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_tn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_t1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_t1n_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_tn1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_tn1_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_transp_permute',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__R),V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__R),V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.rt1n_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__161___24t(V0__A,V2__P)
=> ! [V3__z] :
( t(V3__z,V0__A)
=> ( p(happ(V2__P,V3__z))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__R,V5__x),V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V6__y,V3__z)
=> ( p(happ(V2__P,V6__y))
=> p(happ(V2__P,V5__x)) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V6__x,V3__z)
=> p(happ(V2__P,V6__x)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_PER',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V0__A,V1__R) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_equivalence',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_order',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_preorder',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_antisym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.per_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.per_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__161___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( p(happ(V3__P,V2__x))
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__161___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( p(happ(V3__P,V2__x))
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__15___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V4__x),V5__y))
| p(happ(happ(V1__R,V5__y),V4__x)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__15___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V4__x),V5__y))
| p(happ(happ(V1__R,V5__y),V4__x)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__15___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> p(happ(happ(V2__P,V6__y),V5__x)) ) ) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ! [V8__z] :
( t(V8__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V6__x,V7__y)
=> ( p(happ(happ(V2__P,V6__x),V7__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__y,V8__z)
=> ( p(happ(happ(V2__P,V7__y),V8__z))
=> p(happ(happ(V2__P,V6__x),V8__z)) ) ) ) ) ) ) )
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ! [V8__a] :
( t(V8__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__a,V8__a)
=> p(happ(happ(V2__P,V7__a),V8__a)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__161___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V5__y),V6__z))
| p(happ(happ(V1__R,V6__z),V5__y)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__161___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V5__y),V6__z))
| p(happ(happ(V1__R,V6__z),V5__y)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__15___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> p(happ(happ(V2__P,V6__y),V5__x)) ) ) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ! [V8__z] :
( t(V8__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V6__x,V7__y)
=> ( p(happ(happ(V2__P,V6__x),V7__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__y,V8__z)
=> ( p(happ(happ(V2__P,V7__y),V8__z))
=> p(happ(happ(V2__P,V6__x),V8__z)) ) ) ) ) ) ) )
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ! [V8__a] :
( t(V8__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__a,V8__a)
=> p(happ(happ(V2__P,V7__a),V8__a)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_1n_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__15___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_1n_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__15___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__15___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V7__z)
=> ( p(happ(happ(V2__P,V6__y),V7__z))
=> p(happ(happ(V2__P,V5__x),V7__z)) ) ) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V7__a)
=> p(happ(happ(V2__P,V6__x),V7__a)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_n1_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__161___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_n1_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__161___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__15___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V7__z)
=> ( p(happ(happ(V2__P,V6__y),V7__z))
=> p(happ(happ(V2__P,V5__x),V7__z)) ) ) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V7__a)
=> p(happ(happ(V2__P,V6__x),V7__a)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_1n_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__15___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_1n_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__15___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__15___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V4__x,V5__y)
=> ( p(happ(happ(V2__P,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_n1_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__161___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_n1_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__161___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__15___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V4__x,V5__y)
=> ( p(happ(happ(V2__P,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.r_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.r_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst1n_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( ( p(happ(happ(V1__R,V2__x),V3__y))
| p(happ(happ(V1__R,V3__y),V2__x)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rstn1_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rstn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( ( p(happ(happ(V1__R,V3__y),V4__z))
| p(happ(happ(V1__R,V4__z),V3__y)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt1n_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rtn1_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rtn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t1n_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.tn1_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.tn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relations.inverse_image_of_equivalence',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__268___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V1__B,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,c_24__lam__418___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Build_Setoid_Theory',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__A,V1__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V1__Aeq,V3__x),V3__x)) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> p(happ(happ(V1__Aeq,V4__y),V3__x)) ) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ! [V5__z] :
( t(V5__z,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> ( p(happ(happ(V1__Aeq,V4__y),V5__z))
=> p(happ(happ(V1__Aeq,V3__x),V5__z)) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
| cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.le_trans',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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trans',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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_antisymm',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V11__n))
=> p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_gt_cases',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
| p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_lt_trans',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_refl',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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,V11__n),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_trans',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V13__p))
=> p(happ(happ(V8__rle,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_0_1',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> p(happ(happ(V9__rlt,V1__rO),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_le_trans',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_lt_succ',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> p(happ(happ(V9__rlt,V11__n),happ(happ(V3__rplus,V2__rI),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_succ_r',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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(V9__rlt,V11__n),happ(happ(V3__rplus,V2__rI),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_trans',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_trichotomy',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
| p(happ(happ(V7__req,V11__n),V12__m))
| p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_0_l',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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(V7__req,happ(happ(V3__rplus,V1__rO),V11__n)),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_0_r',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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(V7__req,happ(happ(V3__rplus,V11__n),V1__rO)),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_comm',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__rplus,V11__n),V12__m)),happ(happ(V3__rplus,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_le_lt_mono',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V13__p),V14__q))
=> p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_le_mono',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V13__p),V14__q))
=> p(happ(happ(V8__rle,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_lt_le_mono',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V13__p),V14__q))
=> p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_lt_mono',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V13__p),V14__q))
=> p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_nonneg_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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V1__rO),V11__n))
=> ( p(happ(happ(V8__rle,V1__rO),V12__m))
=> p(happ(happ(V8__rle,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_nonneg_pos',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_pos_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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V8__rle,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_pos_pos',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_0_l',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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(V7__req,happ(happ(V4__rtimes,V1__rO),V11__n)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_0_r',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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(V7__req,happ(happ(V4__rtimes,V11__n),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_comm',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V12__m)),happ(happ(V4__rtimes,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_neg_neg',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V1__rO))
=> ( p(happ(happ(V9__rlt,V12__m),V1__rO))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_nonneg_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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V1__rO),V11__n))
=> ( p(happ(happ(V8__rle,V1__rO),V12__m))
=> p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_pos_neg',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V12__m),V1__rO))
=> p(happ(happ(V9__rlt,happ(happ(V4__rtimes,V11__n),V12__m)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_pos_pos',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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.ZCoeff.req_refl',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,V11__x),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZCoeff.req_sym',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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__x] :
( t(V11__x,V0__R)
=> ! [V12__y] :
( t(V12__y,V0__R)
=> ( p(happ(happ(V7__req,V11__x),V12__y))
=> p(happ(happ(V7__req,V12__y),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZCoeff.req_trans',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__890___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__890___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__890___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__15___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__15___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__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,V11__x),V12__y))
=> ( p(happ(happ(V7__req,V12__y),V13__z))
=> p(happ(happ(V7__req,V11__x),V13__z)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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.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__890___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__890___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__890___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___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_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__890___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__890___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__890___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___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_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__890___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__890___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__890___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___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_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__890___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__890___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__890___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__890___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__890___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__890___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___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.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__890___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__890___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__890___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__247___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__15___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('HahnRelationsBasic.BasicProperties.functional_alt',axiom,
( cHahnRelationsBasic_2efunctional___24a2(cA,cr)
<=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2eseq___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(cA,cr),cr),cHahnRelationsBasic_2eeqv__rel___24a2(cA,c_24__lam__167045)) ) ).
fof('HahnRelationsBasic.BasicProperties.functional_eqv_rel',axiom,
cHahnRelationsBasic_2efunctional___24a2(cA,cHahnRelationsBasic_2eeqv__rel___24a2(cA,cdom)) ).
fof('HahnRelationsBasic.BasicProperties.immediateE',axiom,
cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(cA,cHahnRelationsBasic_2eimmediate___24a2(cA,cr),cHahnRelationsBasic_2eminus__rel___24a3(cA,cr,cHahnRelationsBasic_2eseq___24a3(cA,cr,cr))) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_bunion_l',axiom,
! [V0__P] :
( c_24__type__136580___24t(V0__P)
=> ! [V1__rr] :
( c_24__type__136578___24t(V1__rr)
=> ( ! [V2__x] :
( cB___24t(V2__x)
=> ( p(happ(V0__P,V2__x))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,happ(V1__rr,V2__x),cr_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2ebunion___24a4(cB,cA,V0__P,V1__rr),cr_27) ) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_bunion_r',axiom,
! [V0__x] :
( cB___24t(V0__x)
=> ! [V1__P] :
( c_24__type__136580___24t(V1__P)
=> ! [V2__rr] :
( c_24__type__136578___24t(V2__rr)
=> ( p(happ(V1__P,V0__x))
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,happ(V2__rr,V0__x))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cHahnRelationsBasic_2ebunion___24a4(cB,cA,V1__P,V2__rr)) ) ) ) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_inter_mon',axiom,
! [V0__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V0__s)
=> ! [V1__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V1__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cr_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,V0__s,V1__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2einter__rel___24a3(cA,cr,V0__s),cHahnRelationsBasic_2einter__rel___24a3(cA,cr_27,V1__s_27)) ) ) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_minus_l',axiom,
! [V0__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V0__s)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2eminus__rel___24a3(cA,cr,cr_27),V0__s)
<=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,cr_27,V0__s)) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_minus_mon',axiom,
! [V0__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V0__s)
=> ! [V1__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V1__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cr_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,V1__s_27,V0__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2eminus__rel___24a3(cA,cr,V0__s),cHahnRelationsBasic_2eminus__rel___24a3(cA,cr_27,V1__s_27)) ) ) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_refl',axiom,
cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(cA),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(cA)) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_rt_ind_left',axiom,
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(cA,cr_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr,cr_27),cr_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(cA,cr),cr_27) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_rt_ind_right',axiom,
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(cA,cr_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr_27,cr),cr_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(cA,cr),cr_27) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_seq_l',axiom,
( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cr_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(cA,cr_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cHahnRelationsBasic_2eseq___24a3(cA,cr_27,cr_27_27)) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_seq_mon',axiom,
! [V0__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V0__s)
=> ! [V1__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V1__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cr_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,V0__s,V1__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr,V0__s),cHahnRelationsBasic_2eseq___24a3(cA,cr_27,V1__s_27)) ) ) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_seq_r',axiom,
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(cA,cr_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cr_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cHahnRelationsBasic_2eseq___24a3(cA,cr_27,cr_27_27)) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_seq_refl',axiom,
( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cr_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr_27,cr_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(cA,cr_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr,cHahnRelationsBasic_2eclos__refl___24a2(cA,cr_27)),cr_27_27) ) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_seq_rt',axiom,
( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(cA,cr_27_27))
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr_27,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(cA,cr_27_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr,cr_27),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(cA,cr_27_27)) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_seq_trans',axiom,
! [V0__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V0__t)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(cA,V0__t)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,V0__t)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr_27,V0__t)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr,cr_27),V0__t) ) ) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_t_ind_left',axiom,
( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cr_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr,cr_27),cr_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,cr),cr_27) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_t_ind_right',axiom,
( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cr_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr_27,cr),cr_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,cr),cr_27) ) ) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_trans',axiom,
cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(cA),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(cA)) ).
fof('HahnRelationsBasic.BasicProperties.inclusion_union_mon',axiom,
! [V0__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V0__s)
=> ! [V1__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V1__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr,cr_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,V0__s,V1__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,cr,V0__s),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,cr_27,V1__s_27)) ) ) ) ) ).
fof('HahnRelationsBasic.BasicProperties.irreflexive_seqC',axiom,
( cHahnRelationsBasic_2eirreflexive___24a2(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr,cr_27))
<=> cHahnRelationsBasic_2eirreflexive___24a2(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr_27,cr)) ) ).
fof('HahnRelationsBasic.BasicProperties.reflexive_seq',axiom,
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(cA,cr)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(cA,cr_27)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr,cr_27)) ) ) ).
fof('HahnRelationsBasic.BasicProperties.upward_closed_seq',axiom,
! [V0__P] :
( c_24__type__30897___24t(V0__P)
=> ( cHahnRelationsBasic_2eupward__closed___24a3(cA,cr,V0__P)
=> ( cHahnRelationsBasic_2eupward__closed___24a3(cA,cr_27,V0__P)
=> cHahnRelationsBasic_2eupward__closed___24a3(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr,cr_27),V0__P) ) ) ) ).
fof('HahnRelationsBasic.r_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V2__x,V2__x) ) ) ) ).
fof('HahnRelationsBasic.r_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V3__y))
=> cHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V2__x,V3__y) ) ) ) ) ) ).
fof('$adef_HahnRelationsBasic.minus_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cHahnRelationsBasic_2eminus__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cHahnRelationsBasic_2eminus__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Logic.ChoiceFacts.FunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.Ndigits.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eNdigits_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eNdigits_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(V_24X1,V_24X2) ).
fof('$adef_HahnRelationsBasic.map_rel_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cHahnRelationsBasic_2emap__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cHahnRelationsBasic_2emap__rel___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$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_$_case_Coq.Init.Datatypes.nat$22605_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2422605,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2422605___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnSets.set_full_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnSets_2eset__full,V_24X1),V_24X2))
<=> chahn_2eHahnSets_2eset__full___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.preorder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2epreorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_hahn.HahnSets.set_collect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnSets_2eset__collect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnSets_2eset__collect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$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('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
fof('$adef_HahnRelationsBasic.seq_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cHahnRelationsBasic_2eseq,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cHahnRelationsBasic_2eseq___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Init.Decimal.nzhead_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2enzhead,V_24X1) = cCoq_2eInit_2eDecimal_2enzhead___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.Exists_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eExists,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eExists___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$29797_$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_2429797,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_2429797___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_573_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__573,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__573___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_fix_22486_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__22486__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__22486__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$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('$adef_Coq.Init.Logic.ex2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eLogic_2eex2,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eLogic_2eex2___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.implb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eimplb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eimplb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$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('$adef_Coq.micromega.DeclConstant.GT_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eGT,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eDeclConstant_2eGT___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.log2_iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2elog2__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2elog2__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Definitions.symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).
fof('$adef_$_prop_30722_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30722,V_24X1),V_24X2),V_24X3) = c_24__prop__30722___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Relations.Relation_Definitions.inclusion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2einclusion,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.Pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2ePos,V_24X1) = cCoq_2eInit_2eDecimal_2ePos___24a1(V_24X1) ).
fof('$adef_$_let_4_P\'_442_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__4__P_27__442,V_24X1),V_24X2) = c_24__let__4__P_27__442___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Between.P_nth_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eArith_2eBetween_2eP__nth,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eArith_2eBetween_2eP__nth___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).
fof('$adef_$_let_var_6_p_1277_1279_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__1277__1279,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__1277__1279___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_HahnRelationsBasic.collect_rel_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cHahnRelationsBasic_2ecollect__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cHahnRelationsBasic_2ecollect__rel___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_491_$a1',axiom,
! [V_24X1] : happ(c_24__lam__491,V_24X1) = c_24__lam__491___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Init.Datatypes.app_$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('$adef_$_lam_418_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__418,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__418___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$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_hahn.HahnSets.set_disjoint_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnSets_2eset__disjoint,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnSets_2eset__disjoint___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Decimal.D6_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.transp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2etransp,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2etransp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_HahnRelationsBasic.strict_total_order_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cHahnRelationsBasic_2estrict__total__order,V_24X1),V_24X2),V_24X3))
<=> cHahnRelationsBasic_2estrict__total__order___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Operators.symprod_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2esymprod,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$22622_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2422622,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2422622___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$22627_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2422627,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2422627___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D4_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_pow_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_701_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__701,V_24X1),V_24X2))
<=> c_24__lam__701___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_569_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__569,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__569___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$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('$adef_Coq.Reals.RIneq.mknonposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_30703_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30703,V_24X1),V_24X2),V_24X3) = c_24__prop__30703___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.ct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.Relations.Relation_Definitions.commut_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ecommut,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Definitions_2ecommut___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V_24X1) ).
fof('$adef_HahnRelationsBasic.clos_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cHahnRelationsBasic_2eclos__refl,V_24X1),V_24X2) = cHahnRelationsBasic_2eclos__refl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedTypeEx.Z_as_OT.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.hd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2ehd,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2ehd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_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.Structures.OrderedType.LT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_hahn.HahnSets.set_subset_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnSets_2eset__subset,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnSets_2eset__subset___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.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.Arith.Plus.tail_plus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePlus_2etail__plus,V_24X1),V_24X2) = cCoq_2eArith_2ePlus_2etail__plus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Between.exists_between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_HahnRelationsBasic.acyclic_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHahnRelationsBasic_2eacyclic,V_24X1),V_24X2))
<=> cHahnRelationsBasic_2eacyclic___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_hahn.HahnSets.set_union_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnSets_2eset__union,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnSets_2eset__union___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.identity_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eidentity,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eidentity___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.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_hahn.HahnBase.Equality.Pack_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnBase_2eEquality_2ePack,V_24X1),V_24X2),V_24X3) = chahn_2eHahnBase_2eEquality_2ePack___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.FinFun.Surjective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eSurjective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eSurjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_569_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__569,V_24X1),V_24X2),V_24X3) = c_24__lam__569___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Init.Nat.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eeqb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eeqb___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Sorting.Sorted.HdRel_$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('$adef_Hammer.Tactics.Reconstr.rdone_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHammer_2eTactics_2eReconstr_2erdone,V_24X1),V_24X2))
<=> cHammer_2eTactics_2eReconstr_2erdone___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.ChoiceFacts.ConstructiveIndefiniteDescription_on_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLogic_2eChoiceFacts_2eConstructiveIndefiniteDescription__on,V_24X1) = cCoq_2eLogic_2eChoiceFacts_2eConstructiveIndefiniteDescription__on___24a1(V_24X1) ).
fof('$adef_$_prop_30720_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__30720,V_24X1),V_24X2) = c_24__prop__30720___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_6_p_1275_1278_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__1275__1278,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__1275__1278___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.SetoidList.transpose2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose2,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$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('$adef_Coq.Relations.Relation_Operators.clos_trans_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnSets.set_map_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnSets_2eset__map,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnSets_2eset__map___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V_24X1) ).
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('$adef_Coq.Relations.Relation_Operators.union_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eunion,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eRelations_2eRelation__Operators_2eunion___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_lam_20336_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__20336,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__20336___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emax,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.Morphism_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eMorphism,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_hahn.HahnSets.set_empty_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnSets_2eset__empty,V_24X1),V_24X2))
<=> chahn_2eHahnSets_2eset__empty___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).
fof('$adef_$_lam_491_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__491,V_24X1),V_24X2) = c_24__lam__491___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.GenericMinMax.gmax_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eStructures_2eGenericMinMax_2egmax,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Numbers.BinNums.N$456_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eN_24456,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eNumbers_2eBinNums_2eN_24456___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.same_relation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esame__relation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.equiv_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequiv,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
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('$adef_Coq.PArith.BinPosDef.Pos.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V_24X1) ).
fof('$adef_HahnRelationsBasic.eq_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cHahnRelationsBasic_2eeq__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cHahnRelationsBasic_2eeq__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_hahn.HahnBase.Equality.mixin_of_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnBase_2eEquality_2emixin__of,V_24X1) = chahn_2eHahnBase_2eEquality_2emixin__of___24a1(V_24X1) ).
fof('$adef_HahnRelationsBasic.immediate_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cHahnRelationsBasic_2eimmediate,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cHahnRelationsBasic_2eimmediate___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Arith.Even.odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
<=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).
fof('$adef_Coq.Logic.FinFun.Bijective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eBijective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eBijective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Lists.List.ForallOrdPairs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallOrdPairs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Logic_Type.notT_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eLogic__Type_2enotT,V_24X1))
<=> cCoq_2eInit_2eLogic__Type_2enotT___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNat.N.peano_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_hahn.HahnBase.Equality.Mixin_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnBase_2eEquality_2eMixin,V_24X1),V_24X2),V_24X3) = chahn_2eHahnBase_2eEquality_2eMixin___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_HahnRelationsBasic.restr_subset_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cHahnRelationsBasic_2erestr__subset,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cHahnRelationsBasic_2erestr__subset___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_hahn.HahnSets.set_inter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnSets_2eset__inter,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnSets_2eset__inter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Specif.right_$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('$adef_$_fix_30844_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__30844__v__CANONICAL__0,V_24X1) = c_24__fix__30844__v__CANONICAL__0___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ClassicalFacts.retract_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eClassicalFacts_2eretract,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eClassicalFacts_2eretract___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnSets.set_bunion_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnSets_2eset__bunion,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnSets_2eset__bunion___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_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.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Add_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eList_2eAdd,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eList_2eAdd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ifb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eBool_2eifb,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eBool_2eifb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$a13',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.mknegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Relations.Relation_Definitions.inclusion_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2einclusion,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_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.Relations.Relation_Operators.union_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eunion,V_24X1),V_24X2),V_24X3) = cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Operators.Ltl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eLtl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Logic.ChoiceFacts.SetoidFunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eSetoidFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eSetoidFunctionalChoice__on___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2epow,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eSymmetric,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on,V_24X1))
<=> cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on___24a1(V_24X1) ) ).
fof('$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_HahnRelationsBasic.clos_refl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cHahnRelationsBasic_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cHahnRelationsBasic_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_hahn.HahnSets.set_equiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnSets_2eset__equiv,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnSets_2eset__equiv___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.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.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.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_Coq.setoid_ring.Field_theory.semi_field_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Init.Decimal.D8_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.swapprod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eswapprod,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_HahnRelationsBasic.inter_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cHahnRelationsBasic_2einter__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cHahnRelationsBasic_2einter__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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.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.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.NArith.BinNatDef.N.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_HahnRelationsBasic.eqv_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cHahnRelationsBasic_2eeqv__rel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cHahnRelationsBasic_2eeqv__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_194_$a1',axiom,
! [V_24X1] : happ(c_24__lam__194,V_24X1) = c_24__lam__194___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Numbers.BinNums.positive$30828_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2430828,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2430828___24a2(V_24X1,V_24X2) ).
fof('$adef_HahnRelationsBasic.immediate_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cHahnRelationsBasic_2eimmediate,V_24X1),V_24X2) = cHahnRelationsBasic_2eimmediate___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.max_$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('$adef_Coq.Structures.GenericMinMax.gmin_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eStructures_2eGenericMinMax_2egmin,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Decimal.D7_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.FinFun.Injective_$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('$adef_Coq.Arith.Even.even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
<=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$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('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.Relations.Relation_Operators.transp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2etransp,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.PER_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ePER,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D0_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.CompLtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompLtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).
fof('$adef_$_prop_30704_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30704,V_24X1),V_24X2),V_24X3) = c_24__prop__30704___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
<=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).
fof('$adef_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.micromega.VarMap.Branch_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).
fof('$adef_HahnRelationsBasic.eqv_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cHahnRelationsBasic_2eeqv__rel,V_24X1),V_24X2) = cHahnRelationsBasic_2eeqv__rel___24a2(V_24X1,V_24X2) ).
fof('$adef_HahnRelationsBasic.dom_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cHahnRelationsBasic_2edom__rel,V_24X1),V_24X2),V_24X3))
<=> cHahnRelationsBasic_2edom__rel___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V_24X1,V_24X2) ) ).
fof('$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.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_Coq.Init.Specif.Exc_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eSpecif_2eExc,V_24X1) = cCoq_2eInit_2eSpecif_2eExc___24a1(V_24X1) ).
fof('$adef_$_prop_30706_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__30706,V_24X1),V_24X2) = c_24__prop__30706___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_167045_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__167045,V_24X1))
<=> c_24__lam__167045___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_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.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Peano.IsSucc_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2ePeano_2eIsSucc,V_24X1))
<=> cCoq_2eInit_2ePeano_2eIsSucc___24a1(V_24X1) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.eq_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eDatatypes_2eeq__true,V_24X1))
<=> cCoq_2eInit_2eDatatypes_2eeq__true___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_HahnRelationsBasic.minus_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHahnRelationsBasic_2eminus__rel,V_24X1),V_24X2),V_24X3) = cHahnRelationsBasic_2eminus__rel___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.Decimal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDecimal_2eDecimal,V_24X1),V_24X2) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(V_24X1,V_24X2) ).
fof('$adef_HahnRelationsBasic.strict_partial_order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHahnRelationsBasic_2estrict__partial__order,V_24X1),V_24X2))
<=> cHahnRelationsBasic_2estrict__partial__order___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.tail_add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etail__add,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etail__add___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.peano_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1) = cCoq_2eVectors_2eVectorDef_2et___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V_24X1) ).
fof('$adef_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.Structures.OrderedTypeEx.String_as_OT.lts_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zlogarithm.Is_power_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZlogarithm_2eIs__power,V_24X1))
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V_24X1) ) ).
fof('$adef_Coq.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_$_case_Coq.Init.Datatypes.list$22354_$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_2422354,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2422354___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.Reals.RIneq.mknonnegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).
fof('$adef_Coq.Bool.Bool.reflect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2ereflect,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.ChoiceFacts.GeneralizedSetoidFunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eGeneralizedSetoidFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eGeneralizedSetoidFunctionalChoice__on___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Logic.ChoiceFacts.FunctionalChoice_on_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_20344_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__20344,V_24X1),V_24X2),V_24X3) = c_24__lam__20344___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.Between.between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ebetween,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ebetween___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.peano_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_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.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.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_20344_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__20344,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__20344___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNat.N.recursion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$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('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.eqlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Specif.exist2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_HahnRelationsBasic.bunion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cHahnRelationsBasic_2ebunion,V_24X1),V_24X2),V_24X3),V_24X4) = cHahnRelationsBasic_2ebunion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_20336_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__20336,V_24X1),V_24X2),V_24X3) = c_24__lam__20336___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_30701_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30701,V_24X1),V_24X2),V_24X3) = c_24__prop__30701___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Strings.String.String_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequivalence,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_5_f\'_443_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__5__f_27__443,V_24X1),V_24X2),V_24X3) = c_24__let__5__f_27__443___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emin,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V_24X1,V_24X2) ).
fof('$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_hahn.HahnSets.set_compl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnSets_2eset__compl,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnSets_2eset__compl___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Nat.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eleb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Relations.Relation_Definitions.transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_18430_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__18430,V_24X1),V_24X2) = c_24__lam__18430___24a2(V_24X1,V_24X2) ).
fof('$adef_Hammer.Tactics.Tactics.rdone_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHammer_2eTactics_2eTactics_2erdone,V_24X1),V_24X2))
<=> cHammer_2eTactics_2eTactics_2erdone___24a2(V_24X1,V_24X2) ) ).
fof('$adef_HahnRelationsBasic.restr_eq_rel_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cHahnRelationsBasic_2erestr__eq__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cHahnRelationsBasic_2erestr__eq__rel___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$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('$adef_Coq.Init.Peano.ge_$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('$adef_HahnRelationsBasic.functional_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHahnRelationsBasic_2efunctional,V_24X1),V_24X2))
<=> cHahnRelationsBasic_2efunctional___24a2(V_24X1,V_24X2) ) ).
fof('$adef_HahnRelationsBasic.codom_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cHahnRelationsBasic_2ecodom__rel,V_24X1),V_24X2),V_24X3))
<=> cHahnRelationsBasic_2ecodom__rel___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Decimal.Neg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eNeg,V_24X1) = cCoq_2eInit_2eDecimal_2eNeg___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.NoDupA_$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('$adef_Coq.Init.Decimal.D9_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).
fof('$adef_Coq.Init.Byte.byte_of_byte_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eByte_2ebyte__of__byte,V_24X1) = cCoq_2eInit_2eByte_2ebyte__of__byte___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eReflexive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Arith.Wf_nat.ltof_$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('$adef_HahnRelationsBasic.bunion_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cHahnRelationsBasic_2ebunion,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cHahnRelationsBasic_2ebunion___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_30700_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__30700,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__30700___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_HahnRelationsBasic.irreflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHahnRelationsBasic_2eirreflexive,V_24X1),V_24X2))
<=> cHahnRelationsBasic_2eirreflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
<=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.Computational_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eComputational,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_573_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__573,V_24X1),V_24X2),V_24X3) = c_24__lam__573___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_194_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__194,V_24X1),V_24X2) = c_24__lam__194___24a2(V_24X1,V_24X2) ).
fof('$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.Logic.ChoiceFacts.RepresentativeFunctionalChoice_on_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on,V_24X1))
<=> cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on___24a1(V_24X1) ) ).
fof('$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_HahnRelationsBasic.cross_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cHahnRelationsBasic_2ecross__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cHahnRelationsBasic_2ecross__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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.PArith.BinPosDef.Pos.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emax,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_418_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__418,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__418___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_HahnRelationsBasic.pow_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHahnRelationsBasic_2epow__rel,V_24X1),V_24X2),V_24X3) = cHahnRelationsBasic_2epow__rel___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('$adef_Coq.PArith.BinPos.Pos.SubMaskSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2edivide,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$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('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_HahnRelationsBasic.is_total_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cHahnRelationsBasic_2eis__total,V_24X1),V_24X2),V_24X3))
<=> cHahnRelationsBasic_2eis__total___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Forall_$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('$adef_HahnRelationsBasic.eqv_dom_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cHahnRelationsBasic_2eeqv__dom__rel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cHahnRelationsBasic_2eeqv__dom__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_prop_30721_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30721,V_24X1),V_24X2),V_24X3) = c_24__prop__30721___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_HahnRelationsBasic.seq_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHahnRelationsBasic_2eseq,V_24X1),V_24X2),V_24X3) = cHahnRelationsBasic_2eseq___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.D5_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD5,V_24X1) = cCoq_2eInit_2eDecimal_2eD5___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.uint_of_uint_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2euint__of__uint,V_24X1) = cCoq_2eInit_2eDecimal_2euint__of__uint___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ClassicalFacts.has_fixpoint_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint,V_24X1))
<=> cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.VarMap.Empty_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ClassicalFacts.Minimal_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eClassicalFacts_2eMinimal,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eClassicalFacts_2eMinimal___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPos.Pos.PeanoView_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView,V_24X1) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.DecimalExp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDecimal_2eDecimalExp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$22441_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2422441,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2422441___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_30702_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30702,V_24X1),V_24X2),V_24X3) = c_24__prop__30702___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.existT2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).
fof('$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.setoid_ring.InitialRing.mkhypo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eInitialRing_2emkhypo,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_701_$a1',axiom,
! [V_24X1] : happ(c_24__lam__701,V_24X1) = c_24__lam__701___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_5_f\'_443_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__5__f_27__443,V_24X1),V_24X2) = c_24__let__5__f_27__443___24a2(V_24X1,V_24X2) ).
fof('$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_HahnRelationsBasic.upward_closed_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cHahnRelationsBasic_2eupward__closed,V_24X1),V_24X2),V_24X3))
<=> cHahnRelationsBasic_2eupward__closed___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
<=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).
fof('$adef_HahnRelationsBasic.restr_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cHahnRelationsBasic_2erestr__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cHahnRelationsBasic_2erestr__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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_$_lam_18430_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__18430,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__18430___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_HahnRelationsBasic.inter_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHahnRelationsBasic_2einter__rel,V_24X1),V_24X2),V_24X3) = cHahnRelationsBasic_2einter__rel___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).
fof('$adef_$_prop_30705_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30705,V_24X1),V_24X2),V_24X3) = c_24__prop__30705___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
<=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Coq.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.Init.Decimal.D3_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).
fof('$adef_hahn.HahnSets.set_minus_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnSets_2eset__minus,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnSets_2eset__minus___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_let_4_P\'_442_$a1',axiom,
! [V_24X1] : happ(c_24__let__4__P_27__442,V_24X1) = c_24__let__4__P_27__442___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.sig2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2edouble,V_24X1) = cCoq_2eInit_2eNat_2edouble___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_30895',axiom,
! [V_24Y] :
( c_24__type__30895___24t(V_24Y)
<=> t(V_24Y,c_24__type__30895) ) ).
fof('$tdef_$_type_7038',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__7038___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__7038___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_211',axiom,
! [V_24X1,V_24Y] :
( c_24__type__211___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__211___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_Coq.ZArith.Znumtheory.Euclid',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_721',axiom,
! [V_24Y] :
( c_24__type__721___24t(V_24Y)
<=> t(V_24Y,c_24__type__721) ) ).
fof('$tdef_$_type_23547',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__23547___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__23547___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('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).
fof('$tdef_$_type_20451',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__20451___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__20451___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_21940',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__21940___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__21940___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_714',axiom,
! [V_24Y] :
( c_24__type__714___24t(V_24Y)
<=> t(V_24Y,c_24__type__714) ) ).
fof('$tdef_$_type_29157',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__29157___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__29157___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_14015',axiom,
! [V_24Y] :
( c_24__type__14015___24t(V_24Y)
<=> t(V_24Y,c_24__type__14015) ) ).
fof('$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_26269',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__26269___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__26269___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_21498',axiom,
! [V_24Y] :
( c_24__type__21498___24t(V_24Y)
<=> t(V_24Y,c_24__type__21498) ) ).
fof('$tdef_Coq.micromega.VarMap.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonposreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonposreal) ) ).
fof('$tdef_$_type_5687',axiom,
! [V_24Y] :
( c_24__type__5687___24t(V_24Y)
<=> t(V_24Y,c_24__type__5687) ) ).
fof('$tdef_$_type_5005',axiom,
! [V_24Y] :
( c_24__type__5005___24t(V_24Y)
<=> t(V_24Y,c_24__type__5005) ) ).
fof('$tdef_$_type_8493',axiom,
! [V_24Y] :
( c_24__type__8493___24t(V_24Y)
<=> t(V_24Y,c_24__type__8493) ) ).
fof('$tdef_Coq.Init.Specif.sigT2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_30082',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__30082___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__30082___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_161',axiom,
! [V_24X1,V_24Y] :
( c_24__type__161___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__161___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4728',axiom,
! [V_24Y] :
( c_24__type__4728___24t(V_24Y)
<=> t(V_24Y,c_24__type__4728) ) ).
fof('$tdef_$_type_508',axiom,
! [V_24X1,V_24Y] :
( c_24__type__508___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__508___24a1(V_24X1)) ) ).
fof('$tdef_$_type_30383',axiom,
! [V_24Y] :
( c_24__type__30383___24t(V_24Y)
<=> t(V_24Y,c_24__type__30383) ) ).
fof('$tdef_$_type_18575',axiom,
! [V_24Y] :
( c_24__type__18575___24t(V_24Y)
<=> t(V_24Y,c_24__type__18575) ) ).
fof('$tdef_hahn.HahnBase.Equality.axiom',axiom,
! [V_24X1,V_24X2,V_24Y] :
( chahn_2eHahnBase_2eEquality_2eaxiom___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2eaxiom___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_29592',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__29592___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__29592___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.Reals.RIneq.posreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).
fof('$tdef_$_type_14293',axiom,
! [V_24Y] :
( c_24__type__14293___24t(V_24Y)
<=> t(V_24Y,c_24__type__14293) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_Coq.Init.Datatypes.list',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_247',axiom,
! [V_24X1,V_24Y] :
( c_24__type__247___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__247___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8871',axiom,
! [V_24Y] :
( c_24__type__8871___24t(V_24Y)
<=> t(V_24Y,c_24__type__8871) ) ).
fof('$tdef_$_type_503',axiom,
! [V_24Y] :
( c_24__type__503___24t(V_24Y)
<=> t(V_24Y,c_24__type__503) ) ).
fof('$tdef_Coq.Init.Decimal.decimal',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2edecimal) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ) ).
fof('$tdef_$_type_8860',axiom,
! [V_24Y] :
( c_24__type__8860___24t(V_24Y)
<=> t(V_24Y,c_24__type__8860) ) ).
fof('$tdef_$_type_3003',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__3003___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__3003___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.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_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_4964',axiom,
! [V_24Y] :
( c_24__type__4964___24t(V_24Y)
<=> t(V_24Y,c_24__type__4964) ) ).
fof('$tdef_$_type_264',axiom,
! [V_24Y] :
( c_24__type__264___24t(V_24Y)
<=> t(V_24Y,c_24__type__264) ) ).
fof('$tdef_$_type_21382',axiom,
! [V_24Y] :
( c_24__type__21382___24t(V_24Y)
<=> t(V_24Y,c_24__type__21382) ) ).
fof('$tdef_$_type_20613',axiom,
! [V_24Y] :
( c_24__type__20613___24t(V_24Y)
<=> t(V_24Y,c_24__type__20613) ) ).
fof('$tdef_$_type_28314',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28314___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28314___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_729',axiom,
! [V_24Y] :
( c_24__type__729___24t(V_24Y)
<=> t(V_24Y,c_24__type__729) ) ).
fof('$tdef_$_type_4245',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__4245___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__4245___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_1606',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__1606___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__1606___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.PArith.BinPosDef.Pos.t',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2et) ) ).
fof('$tdef_$_type_2123',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__2123___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__2123___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ) ).
fof('$tdef_$_type_4991',axiom,
! [V_24Y] :
( c_24__type__4991___24t(V_24Y)
<=> t(V_24Y,c_24__type__4991) ) ).
fof('$tdef_$_type_28355',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28355___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28355___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_24562',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__24562___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__24562___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_4458',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__4458___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__4458___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_30344',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30344___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30344___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_10737',axiom,
! [V_24Y] :
( c_24__type__10737___24t(V_24Y)
<=> t(V_24Y,c_24__type__10737) ) ).
fof('$tdef_$_type_10734',axiom,
! [V_24Y] :
( c_24__type__10734___24t(V_24Y)
<=> t(V_24Y,c_24__type__10734) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ) ).
fof('$tdef_$_type_4887',axiom,
! [V_24Y] :
( c_24__type__4887___24t(V_24Y)
<=> t(V_24Y,c_24__type__4887) ) ).
fof('$tdef_$_type_17039',axiom,
! [V_24Y] :
( c_24__type__17039___24t(V_24Y)
<=> t(V_24Y,c_24__type__17039) ) ).
fof('$tdef_$_type_25946',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__25946___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__25946___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_20734',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__20734___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__20734___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_18290',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18290___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18290___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_5886',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5886___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5886___24a1(V_24X1)) ) ).
fof('$tdef_$_type_532',axiom,
! [V_24X1,V_24Y] :
( c_24__type__532___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__532___24a1(V_24X1)) ) ).
fof('$tdef_$_type_18226',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__18226___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__18226___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_18660',axiom,
! [V_24Y] :
( c_24__type__18660___24t(V_24Y)
<=> t(V_24Y,c_24__type__18660) ) ).
fof('$tdef_$_type_29818',axiom,
! [V_24Y] :
( c_24__type__29818___24t(V_24Y)
<=> t(V_24Y,c_24__type__29818) ) ).
fof('$tdef_$_type_18002',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__18002___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__18002___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_20666',axiom,
! [V_24Y] :
( c_24__type__20666___24t(V_24Y)
<=> t(V_24Y,c_24__type__20666) ) ).
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_$_type_15727',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__15727___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__15727___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_$_type_20377',axiom,
! [V_24Y] :
( c_24__type__20377___24t(V_24Y)
<=> t(V_24Y,c_24__type__20377) ) ).
fof('$tdef_hahn.HahnBase.Equality.mixin_of',axiom,
! [V_24X1,V_24Y] :
( chahn_2eHahnBase_2eEquality_2emixin__of___24t(V_24X1,V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2emixin__of___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4719',axiom,
! [V_24Y] :
( c_24__type__4719___24t(V_24Y)
<=> t(V_24Y,c_24__type__4719) ) ).
fof('$tdef_$_type_7213',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7213___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7213___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_22156',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22156___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22156___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_18192',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__18192___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__18192___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_21697',axiom,
! [V_24Y] :
( c_24__type__21697___24t(V_24Y)
<=> t(V_24Y,c_24__type__21697) ) ).
fof('$tdef_$_type_2012',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__2012___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__2012___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.N',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).
fof('$tdef_$_type_779',axiom,
! [V_24Y] :
( c_24__type__779___24t(V_24Y)
<=> t(V_24Y,c_24__type__779) ) ).
fof('$tdef_$_type_13984',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__13984___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__13984___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Init.Specif.sig2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.ZArith.BinIntDef.Z.t',axiom,
! [V_24Y] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eBinIntDef_2eZ_2et) ) ).
fof('$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_18749',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__18749___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__18749___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_30887',axiom,
! [V_24Y] :
( c_24__type__30887___24t(V_24Y)
<=> t(V_24Y,c_24__type__30887) ) ).
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_$_type_22058',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__22058___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__22058___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_21965',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__21965___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__21965___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_740',axiom,
! [V_24Y] :
( c_24__type__740___24t(V_24Y)
<=> t(V_24Y,c_24__type__740) ) ).
fof('$tdef_$_type_861',axiom,
! [V_24Y] :
( c_24__type__861___24t(V_24Y)
<=> t(V_24Y,c_24__type__861) ) ).
fof('$tdef_$_type_4872',axiom,
! [V_24Y] :
( c_24__type__4872___24t(V_24Y)
<=> t(V_24Y,c_24__type__4872) ) ).
fof('$tdef_$_type_28337',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28337___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28337___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_18112',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__18112___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__18112___24a2(V_24X1,V_24X2)) ) ).
fof('$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_420',axiom,
! [V_24Y] :
( c_24__type__420___24t(V_24Y)
<=> t(V_24Y,c_24__type__420) ) ).
fof('$tdef_$_type_1723',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__1723___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__1723___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4841',axiom,
! [V_24Y] :
( c_24__type__4841___24t(V_24Y)
<=> t(V_24Y,c_24__type__4841) ) ).
fof('$tdef_$_type_13778',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__13778___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__13778___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_21719',axiom,
! [V_24Y] :
( c_24__type__21719___24t(V_24Y)
<=> t(V_24Y,c_24__type__21719) ) ).
fof('$tdef_$_type_19582',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__19582___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__19582___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_13092',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__13092___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__13092___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_18315',axiom,
! [V_24Y] :
( c_24__type__18315___24t(V_24Y)
<=> t(V_24Y,c_24__type__18315) ) ).
fof('$tdef_$_type_24216',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__24216___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__24216___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_8773',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__8773___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__8773___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_459',axiom,
! [V_24X1,V_24Y] :
( c_24__type__459___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__459___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2790',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__2790___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__2790___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_965',axiom,
! [V_24Y] :
( c_24__type__965___24t(V_24Y)
<=> t(V_24Y,c_24__type__965) ) ).
fof('$tdef_$_type_18116',axiom,
! [V_24Y] :
( c_24__type__18116___24t(V_24Y)
<=> t(V_24Y,c_24__type__18116) ) ).
fof('$tdef_$_type_4653',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__4653___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__4653___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('$tdef_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZArithProof) ) ).
fof('$tdef_$_type_21500',axiom,
! [V_24Y] :
( c_24__type__21500___24t(V_24Y)
<=> t(V_24Y,c_24__type__21500) ) ).
fof('$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('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_$_type_2577',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__2577___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__2577___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_13680',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__13680___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__13680___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_17608',axiom,
! [V_24Y] :
( c_24__type__17608___24t(V_24Y)
<=> t(V_24Y,c_24__type__17608) ) ).
fof('$tdef_$_type_20184',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20184___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__20184___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4892',axiom,
! [V_24Y] :
( c_24__type__4892___24t(V_24Y)
<=> t(V_24Y,c_24__type__4892) ) ).
fof('$tdef_$_type_14860',axiom,
! [V_24Y] :
( c_24__type__14860___24t(V_24Y)
<=> t(V_24Y,c_24__type__14860) ) ).
fof('$tdef_$_type_13209',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__13209___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__13209___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_20004',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20004___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__20004___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_17797',axiom,
! [V_24Y] :
( c_24__type__17797___24t(V_24Y)
<=> t(V_24Y,c_24__type__17797) ) ).
fof('$tdef_$_type_10501',axiom,
! [V_24Y] :
( c_24__type__10501___24t(V_24Y)
<=> t(V_24Y,c_24__type__10501) ) ).
fof('$tdef_$_type_6956',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__6956___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__6956___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_14137',axiom,
! [V_24Y] :
( c_24__type__14137___24t(V_24Y)
<=> t(V_24Y,c_24__type__14137) ) ).
fof('$tdef_$_type_235',axiom,
! [V_24X1,V_24Y] :
( c_24__type__235___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__235___24a1(V_24X1)) ) ).
fof('$tdef_$_type_27607',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__27607___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__27607___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Datatypes.sum',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2esum___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_18080',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__18080___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__18080___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_27953',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__27953___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__27953___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_14011',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__14011___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__14011___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_206',axiom,
! [V_24Y] :
( c_24__type__206___24t(V_24Y)
<=> t(V_24Y,c_24__type__206) ) ).
fof('$tdef_$_type_16291',axiom,
! [V_24Y] :
( c_24__type__16291___24t(V_24Y)
<=> t(V_24Y,c_24__type__16291) ) ).
fof('$tdef_$_type_486',axiom,
! [V_24Y] :
( c_24__type__486___24t(V_24Y)
<=> t(V_24Y,c_24__type__486) ) ).
fof('$tdef_$_type_22634',axiom,
! [V_24Y] :
( c_24__type__22634___24t(V_24Y)
<=> t(V_24Y,c_24__type__22634) ) ).
fof('$tdef_$_type_136578',axiom,
! [V_24Y] :
( c_24__type__136578___24t(V_24Y)
<=> t(V_24Y,c_24__type__136578) ) ).
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_$_type_21493',axiom,
! [V_24Y] :
( c_24__type__21493___24t(V_24Y)
<=> t(V_24Y,c_24__type__21493) ) ).
fof('$tdef_$_type_18137',axiom,
! [V_24Y] :
( c_24__type__18137___24t(V_24Y)
<=> t(V_24Y,c_24__type__18137) ) ).
fof('$tdef_$_type_136580',axiom,
! [V_24Y] :
( c_24__type__136580___24t(V_24Y)
<=> t(V_24Y,c_24__type__136580) ) ).
fof('$tdef_$_type_17101',axiom,
! [V_24Y] :
( c_24__type__17101___24t(V_24Y)
<=> t(V_24Y,c_24__type__17101) ) ).
fof('$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_29393',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__29393___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__29393___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_9423',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__9423___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__9423___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_5025',axiom,
! [V_24Y] :
( c_24__type__5025___24t(V_24Y)
<=> t(V_24Y,c_24__type__5025) ) ).
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_$_type_15',axiom,
! [V_24X1,V_24Y] :
( c_24__type__15___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__15___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22007',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__22007___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__22007___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_14058',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__14058___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__14058___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_20359',axiom,
! [V_24Y] :
( c_24__type__20359___24t(V_24Y)
<=> t(V_24Y,c_24__type__20359) ) ).
fof('$tdef_$_type_14165',axiom,
! [V_24Y] :
( c_24__type__14165___24t(V_24Y)
<=> t(V_24Y,c_24__type__14165) ) ).
fof('$tdef_$_type_28657',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__28657___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__28657___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_Coq.Init.Nat.t',axiom,
! [V_24Y] :
( cCoq_2eInit_2eNat_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eNat_2et) ) ).
fof('$tdef_$_type_472',axiom,
! [V_24Y] :
( c_24__type__472___24t(V_24Y)
<=> t(V_24Y,c_24__type__472) ) ).
fof('$tdef_$_type_19850',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__19850___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__19850___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_12698',axiom,
! [V_24Y] :
( c_24__type__12698___24t(V_24Y)
<=> t(V_24Y,c_24__type__12698) ) ).
fof('$tdef_$_type_20472',axiom,
! [V_24Y] :
( c_24__type__20472___24t(V_24Y)
<=> t(V_24Y,c_24__type__20472) ) ).
fof('$tdef_$_type_16571',axiom,
! [V_24Y] :
( c_24__type__16571___24t(V_24Y)
<=> t(V_24Y,c_24__type__16571) ) ).
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_$_type_4825',axiom,
! [V_24Y] :
( c_24__type__4825___24t(V_24Y)
<=> t(V_24Y,c_24__type__4825) ) ).
fof('$tdef_$_type_13600',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__13600___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__13600___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_13556',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__13556___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__13556___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_23893',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__23893___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__23893___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Decimal.uint',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2euint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2euint) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_26615',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__26615___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__26615___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_25254',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__25254___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__25254___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_1289',axiom,
! [V_24Y] :
( c_24__type__1289___24t(V_24Y)
<=> t(V_24Y,c_24__type__1289) ) ).
fof('$tdef_$_type_21694',axiom,
! [V_24Y] :
( c_24__type__21694___24t(V_24Y)
<=> t(V_24Y,c_24__type__21694) ) ).
fof('$tdef_$_type_18600',axiom,
! [V_24Y] :
( c_24__type__18600___24t(V_24Y)
<=> t(V_24Y,c_24__type__18600) ) ).
fof('$tdef_$_type_18563',axiom,
! [V_24Y] :
( c_24__type__18563___24t(V_24Y)
<=> t(V_24Y,c_24__type__18563) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.hypo',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2ehypo) ) ).
fof('$tdef_$_type_19314',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__19314___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__19314___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_27284',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__27284___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__27284___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('$tdef_Coq.micromega.RingMicromega.Op2',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp2) ) ).
fof('$tdef_$_type_5866',axiom,
! [V_24Y] :
( c_24__type__5866___24t(V_24Y)
<=> t(V_24Y,c_24__type__5866) ) ).
fof('$tdef_$_type_20673',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__20673___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__20673___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6566',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6566___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6566___24a1(V_24X1)) ) ).
fof('$tdef_$_type_14160',axiom,
! [V_24Y] :
( c_24__type__14160___24t(V_24Y)
<=> t(V_24Y,c_24__type__14160) ) ).
fof('$tdef_$_type_831',axiom,
! [V_24Y] :
( c_24__type__831___24t(V_24Y)
<=> t(V_24Y,c_24__type__831) ) ).
fof('$tdef_$_type_18293',axiom,
! [V_24Y] :
( c_24__type__18293___24t(V_24Y)
<=> t(V_24Y,c_24__type__18293) ) ).
fof('$tdef_B',axiom,
! [V_24Y] :
( cB___24t(V_24Y)
<=> t(V_24Y,cB) ) ).
fof('$tdef_$_type_1030',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1030___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1030___24a1(V_24X1)) ) ).
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_$_type_5790',axiom,
! [V_24Y] :
( c_24__type__5790___24t(V_24Y)
<=> t(V_24Y,c_24__type__5790) ) ).
fof('$tdef_$_type_18493',axiom,
! [V_24Y] :
( c_24__type__18493___24t(V_24Y)
<=> t(V_24Y,c_24__type__18493) ) ).
fof('$tdef_$_type_1928',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__1928___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__1928___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Decimal.int',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).
fof('$tdef_$_type_17',axiom,
! [V_24Y] :
( c_24__type__17___24t(V_24Y)
<=> t(V_24Y,c_24__type__17) ) ).
fof('$tdef_$_type_28291',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28291___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28291___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_5863',axiom,
! [V_24Y] :
( c_24__type__5863___24t(V_24Y)
<=> t(V_24Y,c_24__type__5863) ) ).
fof('$tdef_$_type_16286',axiom,
! [V_24Y] :
( c_24__type__16286___24t(V_24Y)
<=> t(V_24Y,c_24__type__16286) ) ).
fof('$tdef_$_type_16110',axiom,
! [V_24Y] :
( c_24__type__16110___24t(V_24Y)
<=> t(V_24Y,c_24__type__16110) ) ).
fof('$tdef_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Strings.String.string',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eString_2estring___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eString_2estring) ) ).
fof('$tdef_$_type_4860',axiom,
! [V_24Y] :
( c_24__type__4860___24t(V_24Y)
<=> t(V_24Y,c_24__type__4860) ) ).
fof('$tdef_$_type_7306',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7306___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7306___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_20512',axiom,
! [V_24Y] :
( c_24__type__20512___24t(V_24Y)
<=> t(V_24Y,c_24__type__20512) ) ).
fof('$tdef_$_type_20272',axiom,
! [V_24Y] :
( c_24__type__20272___24t(V_24Y)
<=> t(V_24Y,c_24__type__20272) ) ).
fof('$tdef_$_type_15718',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__15718___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__15718___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_13813',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__13813___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__13813___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_4050',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__4050___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__4050___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_1958',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__1958___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__1958___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_30318',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30318___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30318___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_20348',axiom,
! [V_24X1,V_24Y] :
( c_24__type__20348___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__20348___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20311',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__20311___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__20311___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_18714',axiom,
! [V_24Y] :
( c_24__type__18714___24t(V_24Y)
<=> t(V_24Y,c_24__type__18714) ) ).
fof('$tdef_$_type_29684',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__29684___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__29684___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_253',axiom,
! [V_24Y] :
( c_24__type__253___24t(V_24Y)
<=> t(V_24Y,c_24__type__253) ) ).
fof('$tdef_$_type_18339',axiom,
! [V_24Y] :
( c_24__type__18339___24t(V_24Y)
<=> t(V_24Y,c_24__type__18339) ) ).
fof('$tdef_$_type_29032',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__29032___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__29032___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_Coq.Init.Datatypes.CompareSpecT',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_403',axiom,
! [V_24Y] :
( c_24__type__403___24t(V_24Y)
<=> t(V_24Y,c_24__type__403) ) ).
fof('$tdef_$_type_13029',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__13029___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__13029___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_7131',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7131___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7131___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_21343',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__21343___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__21343___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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('$tdef_Coq.micromega.ZMicromega.coneMember',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2econeMember___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2econeMember) ) ).
fof('$tdef_$_type_20564',axiom,
! [V_24Y] :
( c_24__type__20564___24t(V_24Y)
<=> t(V_24Y,c_24__type__20564) ) ).
fof('$tdef_$_type_19500',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19500___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19500___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_20316',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__20316___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__20316___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9322',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9322___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9322___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_30352',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30352___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30352___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_A',axiom,
! [V_24Y] :
( cA___24t(V_24Y)
<=> t(V_24Y,cA) ) ).
fof('$tdef_$_type_14064',axiom,
! [V_24Y] :
( c_24__type__14064___24t(V_24Y)
<=> t(V_24Y,c_24__type__14064) ) ).
fof('$tdef_$_type_8748',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__8748___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__8748___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_224',axiom,
! [V_24X1,V_24Y] :
( c_24__type__224___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__224___24a1(V_24X1)) ) ).
fof('$tdef_$_type_30410',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30410___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30410___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1232',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1232___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1232___24a2(V_24X1,V_24X2)) ) ).
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_$_type_5851',axiom,
! [V_24Y] :
( c_24__type__5851___24t(V_24Y)
<=> t(V_24Y,c_24__type__5851) ) ).
fof('$tdef_$_type_1225',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1225___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1225___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2042',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__2042___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__2042___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_18657',axiom,
! [V_24Y] :
( c_24__type__18657___24t(V_24Y)
<=> t(V_24Y,c_24__type__18657) ) ).
fof('$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_244',axiom,
! [V_24X1,V_24Y] :
( c_24__type__244___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__244___24a1(V_24X1)) ) ).
fof('$tdef_$_type_30283',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30283___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30283___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_4847',axiom,
! [V_24Y] :
( c_24__type__4847___24t(V_24Y)
<=> t(V_24Y,c_24__type__4847) ) ).
fof('$tdef_$_type_20637',axiom,
! [V_24Y] :
( c_24__type__20637___24t(V_24Y)
<=> t(V_24Y,c_24__type__20637) ) ).
fof('$tdef_$_type_13636',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__13636___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__13636___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_735',axiom,
! [V_24Y] :
( c_24__type__735___24t(V_24Y)
<=> t(V_24Y,c_24__type__735) ) ).
fof('$tdef_$_type_21684',axiom,
! [V_24Y] :
( c_24__type__21684___24t(V_24Y)
<=> t(V_24Y,c_24__type__21684) ) ).
fof('$tdef_$_type_20445',axiom,
! [V_24Y] :
( c_24__type__20445___24t(V_24Y)
<=> t(V_24Y,c_24__type__20445) ) ).
fof('$tdef_$_type_17816',axiom,
! [V_24Y] :
( c_24__type__17816___24t(V_24Y)
<=> t(V_24Y,c_24__type__17816) ) ).
fof('$tdef_$_type_20305',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__20305___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__20305___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_18328',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__18328___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__18328___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5772',axiom,
! [V_24Y] :
( c_24__type__5772___24t(V_24Y)
<=> t(V_24Y,c_24__type__5772) ) ).
fof('$tdef_$_type_20328',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__20328___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__20328___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_18345',axiom,
! [V_24X1,V_24Y] :
( c_24__type__18345___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__18345___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1669',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__1669___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__1669___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4844',axiom,
! [V_24Y] :
( c_24__type__4844___24t(V_24Y)
<=> t(V_24Y,c_24__type__4844) ) ).
fof('$tdef_$_type_10740',axiom,
! [V_24Y] :
( c_24__type__10740___24t(V_24Y)
<=> t(V_24Y,c_24__type__10740) ) ).
fof('$tdef_$_type_810',axiom,
! [V_24Y] :
( c_24__type__810___24t(V_24Y)
<=> t(V_24Y,c_24__type__810) ) ).
fof('$tdef_Coq.Structures.OrderedType.Compare',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( cCoq_2eStructures_2eOrderedType_2eCompare___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Init.Specif.sumor',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumor___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_268',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__268___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__268___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8834',axiom,
! [V_24Y] :
( c_24__type__8834___24t(V_24Y)
<=> t(V_24Y,c_24__type__8834) ) ).
fof('$tdef_$_type_691',axiom,
! [V_24Y] :
( c_24__type__691___24t(V_24Y)
<=> t(V_24Y,c_24__type__691) ) ).
fof('$tdef_$_type_20',axiom,
! [V_24Y] :
( c_24__type__20___24t(V_24Y)
<=> t(V_24Y,c_24__type__20) ) ).
fof('$tdef_$_type_16190',axiom,
! [V_24Y] :
( c_24__type__16190___24t(V_24Y)
<=> t(V_24Y,c_24__type__16190) ) ).
fof('$tdef_$_type_19407',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__19407___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__19407___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3837',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__3837___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__3837___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_16260',axiom,
! [V_24Y] :
( c_24__type__16260___24t(V_24Y)
<=> t(V_24Y,c_24__type__16260) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ) ).
fof('$tdef_$_type_696',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__696___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__696___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_14033',axiom,
! [V_24Y] :
( c_24__type__14033___24t(V_24Y)
<=> t(V_24Y,c_24__type__14033) ) ).
fof('$tdef_$_type_30443',axiom,
! [V_24Y] :
( c_24__type__30443___24t(V_24Y)
<=> t(V_24Y,c_24__type__30443) ) ).
fof('$tdef_$_type_18299',axiom,
! [V_24Y] :
( c_24__type__18299___24t(V_24Y)
<=> t(V_24Y,c_24__type__18299) ) ).
fof('$tdef_$_type_17786',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__17786___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__17786___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_18380',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__18380___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__18380___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_16073',axiom,
! [V_24Y] :
( c_24__type__16073___24t(V_24Y)
<=> t(V_24Y,c_24__type__16073) ) ).
fof('$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_667',axiom,
! [V_24Y] :
( c_24__type__667___24t(V_24Y)
<=> t(V_24Y,c_24__type__667) ) ).
fof('$tdef_$_type_3624',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__3624___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__3624___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_29734',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__29734___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__29734___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_20247',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20247___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__20247___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_6',axiom,
! [V_24Y] :
( c_24__type__6___24t(V_24Y)
<=> t(V_24Y,c_24__type__6) ) ).
fof('$tdef_$_type_20589',axiom,
! [V_24Y] :
( c_24__type__20589___24t(V_24Y)
<=> t(V_24Y,c_24__type__20589) ) ).
fof('$tdef_$_type_1982',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__1982___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__1982___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_836',axiom,
! [V_24Y] :
( c_24__type__836___24t(V_24Y)
<=> t(V_24Y,c_24__type__836) ) ).
fof('$tdef_$_type_6863',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6863___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6863___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_30493',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30493___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30493___24a1(V_24X1)) ) ).
fof('$tdef_$_type_29542',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__29542___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__29542___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_5680',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5680___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5680___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5760',axiom,
! [V_24Y] :
( c_24__type__5760___24t(V_24Y)
<=> t(V_24Y,c_24__type__5760) ) ).
fof('$tdef_$_type_30737',axiom,
! [V_24Y] :
( c_24__type__30737___24t(V_24Y)
<=> t(V_24Y,c_24__type__30737) ) ).
fof('$tdef_Coq.Numbers.BinNums.Z',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eZ) ) ).
fof('$tdef_$_type_28138',axiom,
! [V_24Y] :
( c_24__type__28138___24t(V_24Y)
<=> t(V_24Y,c_24__type__28138) ) ).
fof('$tdef_$_type_30102',axiom,
! [V_24Y] :
( c_24__type__30102___24t(V_24Y)
<=> t(V_24Y,c_24__type__30102) ) ).
fof('$tdef_$_type_17828',axiom,
! [V_24Y] :
( c_24__type__17828___24t(V_24Y)
<=> t(V_24Y,c_24__type__17828) ) ).
fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_$_type_4989',axiom,
! [V_24Y] :
( c_24__type__4989___24t(V_24Y)
<=> t(V_24Y,c_24__type__4989) ) ).
fof('$tdef_hahn.HahnBase.Equality.type',axiom,
! [V_24Y] :
( chahn_2eHahnBase_2eEquality_2etype___24t(V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2etype) ) ).
fof('$tdef_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [V_24X1,V_24Y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_$_type_5795',axiom,
! [V_24Y] :
( c_24__type__5795___24t(V_24Y)
<=> t(V_24Y,c_24__type__5795) ) ).
fof('$tdef_$_type_5788',axiom,
! [V_24Y] :
( c_24__type__5788___24t(V_24Y)
<=> t(V_24Y,c_24__type__5788) ) ).
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_$_type_521',axiom,
! [V_24X1,V_24Y] :
( c_24__type__521___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__521___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20769',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__20769___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__20769___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_18282',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18282___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18282___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_18301',axiom,
! [V_24Y] :
( c_24__type__18301___24t(V_24Y)
<=> t(V_24Y,c_24__type__18301) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ) ).
fof('$tdef_$_type_724',axiom,
! [V_24Y] :
( c_24__type__724___24t(V_24Y)
<=> t(V_24Y,c_24__type__724) ) ).
fof('$tdef_$_type_19090',axiom,
! [V_24Y] :
( c_24__type__19090___24t(V_24Y)
<=> t(V_24Y,c_24__type__19090) ) ).
fof('$tdef_$_type_6770',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__6770___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__6770___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.prod',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35',axiom,
! [V_24Y] :
( c_24__type__35___24t(V_24Y)
<=> t(V_24Y,c_24__type__35) ) ).
fof('$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_4823',axiom,
! [V_24Y] :
( c_24__type__4823___24t(V_24Y)
<=> t(V_24Y,c_24__type__4823) ) ).
fof('$tdef_$_type_3411',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__3411___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__3411___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_6121',axiom,
! [V_24Y] :
( c_24__type__6121___24t(V_24Y)
<=> t(V_24Y,c_24__type__6121) ) ).
fof('$tdef_$_type_20300',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__20300___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__20300___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.NArith.BinNatDef.N.t',axiom,
! [V_24Y] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNArith_2eBinNatDef_2eN_2et) ) ).
fof('$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_6551',axiom,
! [V_24Y] :
( c_24__type__6551___24t(V_24Y)
<=> t(V_24Y,c_24__type__6551) ) ).
fof('$tdef_$_type_30360',axiom,
! [V_24Y] :
( c_24__type__30360___24t(V_24Y)
<=> t(V_24Y,c_24__type__30360) ) ).
fof('$tdef_$_type_2150',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__2150___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__2150___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [V_24Y] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(V_24Y)
<=> t(V_24Y,cHammer_2eTactics_2eReconstr_2eReconstrT) ) ).
fof('$tdef_$_type_28782',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__28782___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__28782___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_19757',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19757___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19757___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_23201',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__23201___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__23201___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_4993',axiom,
! [V_24Y] :
( c_24__type__4993___24t(V_24Y)
<=> t(V_24Y,c_24__type__4993) ) ).
fof('$tdef_$_type_25600',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__25600___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__25600___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_9816',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9816___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9816___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_30490',axiom,
! [V_24Y] :
( c_24__type__30490___24t(V_24Y)
<=> t(V_24Y,c_24__type__30490) ) ).
fof('$tdef_$_type_1543',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__1543___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__1543___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_20428',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__20428___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__20428___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15741',axiom,
! [V_24Y] :
( c_24__type__15741___24t(V_24Y)
<=> t(V_24Y,c_24__type__15741) ) ).
fof('$tdef_$_type_3198',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__3198___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__3198___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_24908',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__24908___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__24908___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ) ).
fof('$tdef_$_type_18335',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__18335___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__18335___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_781',axiom,
! [V_24Y] :
( c_24__type__781___24t(V_24Y)
<=> t(V_24Y,c_24__type__781) ) ).
fof('$tdef_$_type_2066',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__2066___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__2066___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_16281',axiom,
! [V_24Y] :
( c_24__type__16281___24t(V_24Y)
<=> t(V_24Y,c_24__type__16281) ) ).
fof('$tdef_$_type_16030',axiom,
! [V_24Y] :
( c_24__type__16030___24t(V_24Y)
<=> t(V_24Y,c_24__type__16030) ) ).
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_$_type_484',axiom,
! [V_24X1,V_24Y] :
( c_24__type__484___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__484___24a1(V_24X1)) ) ).
fof('$tdef_$_type_9524',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9524___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9524___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_29282',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__29282___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__29282___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_20067',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20067___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__20067___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_30145',axiom,
! [V_24Y] :
( c_24__type__30145___24t(V_24Y)
<=> t(V_24Y,c_24__type__30145) ) ).
fof('$tdef_$_type_28381',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28381___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28381___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_4983',axiom,
! [V_24Y] :
( c_24__type__4983___24t(V_24Y)
<=> t(V_24Y,c_24__type__4983) ) ).
fof('$tdef_$_type_13699',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__13699___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__13699___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_474',axiom,
! [V_24Y] :
( c_24__type__474___24t(V_24Y)
<=> t(V_24Y,c_24__type__474) ) ).
fof('$tdef_$_type_30871',axiom,
! [V_24Y] :
( c_24__type__30871___24t(V_24Y)
<=> t(V_24Y,c_24__type__30871) ) ).
fof('$tdef_$_type_19087',axiom,
! [V_24Y] :
( c_24__type__19087___24t(V_24Y)
<=> t(V_24Y,c_24__type__19087) ) ).
fof('$tdef_$_type_12966',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12966___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__12966___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_1211',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1211___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1211___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1786',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__1786___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__1786___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_1180',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1180___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1180___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4899',axiom,
! [V_24Y] :
( c_24__type__4899___24t(V_24Y)
<=> t(V_24Y,c_24__type__4899) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
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_$_type_20384',axiom,
! [V_24Y] :
( c_24__type__20384___24t(V_24Y)
<=> t(V_24Y,c_24__type__20384) ) ).
fof('$tdef_$_type_16352',axiom,
! [V_24Y] :
( c_24__type__16352___24t(V_24Y)
<=> t(V_24Y,c_24__type__16352) ) ).
fof('$tdef_$_type_479',axiom,
! [V_24X1,V_24Y] :
( c_24__type__479___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__479___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20130',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20130___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__20130___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_21362',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__21362___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__21362___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_21488',axiom,
! [V_24Y] :
( c_24__type__21488___24t(V_24Y)
<=> t(V_24Y,c_24__type__21488) ) ).
fof('$tdef_$_type_890',axiom,
! [V_24X1,V_24Y] :
( c_24__type__890___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__890___24a1(V_24X1)) ) ).
fof('$tdef_$_type_19675',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19675___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19675___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_26961',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__26961___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__26961___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_839',axiom,
! [V_24Y] :
( c_24__type__839___24t(V_24Y)
<=> t(V_24Y,c_24__type__839) ) ).
fof('$tdef_$_type_8',axiom,
! [V_24Y] :
( c_24__type__8___24t(V_24Y)
<=> t(V_24Y,c_24__type__8) ) ).
fof('$tdef_$_type_30426',axiom,
! [V_24Y] :
( c_24__type__30426___24t(V_24Y)
<=> t(V_24Y,c_24__type__30426) ) ).
fof('$tdef_$_type_16861',axiom,
! [V_24Y] :
( c_24__type__16861___24t(V_24Y)
<=> t(V_24Y,c_24__type__16861) ) ).
fof('$tdef_$_type_28268',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28268___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28268___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_18041',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__18041___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__18041___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).
fof('$tdef_$_type_705',axiom,
! [V_24Y] :
( c_24__type__705___24t(V_24Y)
<=> t(V_24Y,c_24__type__705) ) ).
fof('$tdef_$_type_29642',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__29642___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__29642___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_30112',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30112___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30112___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28399',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28399___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28399___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_10745',axiom,
! [V_24Y] :
( c_24__type__10745___24t(V_24Y)
<=> t(V_24Y,c_24__type__10745) ) ).
fof('$tdef_$_type_16806',axiom,
! [V_24Y] :
( c_24__type__16806___24t(V_24Y)
<=> t(V_24Y,c_24__type__16806) ) ).
fof('$tdef_$_type_9614',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9614___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9614___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_30418',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30418___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30418___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_541',axiom,
! [V_24X1,V_24Y] :
( c_24__type__541___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__541___24a1(V_24X1)) ) ).
fof('$tdef_$_type_18247',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__18247___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__18247___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_29810',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__29810___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__29810___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15846',axiom,
! [V_24Y] :
( c_24__type__15846___24t(V_24Y)
<=> t(V_24Y,c_24__type__15846) ) ).
fof('$tdef_Coq.Reals.RIneq.negreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enegreal) ) ).
fof('$tdef_$_type_30897',axiom,
! [V_24Y] :
( c_24__type__30897___24t(V_24Y)
<=> t(V_24Y,c_24__type__30897) ) ).
fof('$tdef_$_type_30248',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__30248___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__30248___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_18423',axiom,
! [V_24X1,V_24Y] :
( c_24__type__18423___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__18423___24a1(V_24X1)) ) ).
fof('$tdef_$_type_10171',axiom,
! [V_24Y] :
( c_24__type__10171___24t(V_24Y)
<=> t(V_24Y,c_24__type__10171) ) ).
fof('$tdef_$_type_4981',axiom,
! [V_24Y] :
( c_24__type__4981___24t(V_24Y)
<=> t(V_24Y,c_24__type__4981) ) ).
fof('$tdef_$_type_30155',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30155___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30155___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28907',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__28907___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__28907___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_2099',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__2099___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__2099___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_20422',axiom,
! [V_24Y] :
( c_24__type__20422___24t(V_24Y)
<=> t(V_24Y,c_24__type__20422) ) ).
fof('$tdef_$_type_16857',axiom,
! [V_24Y] :
( c_24__type__16857___24t(V_24Y)
<=> t(V_24Y,c_24__type__16857) ) ).
fof('$tdef_$_type_10754',axiom,
! [V_24Y] :
( c_24__type__10754___24t(V_24Y)
<=> t(V_24Y,c_24__type__10754) ) ).
fof('$tdef_$_type_9715',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9715___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9715___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_30780',axiom,
! [V_24Y] :
( c_24__type__30780___24t(V_24Y)
<=> t(V_24Y,c_24__type__30780) ) ).
fof('$tdef_$_type_13146',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__13146___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__13146___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_9917',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9917___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9917___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_5762',axiom,
! [V_24Y] :
( c_24__type__5762___24t(V_24Y)
<=> t(V_24Y,c_24__type__5762) ) ).
fof('_HAMMER_GOAL',conjecture,
( cHahnRelationsBasic_2efunctional___24a2(cA,cr)
=> ( cHahnRelationsBasic_2efunctional___24a2(cA,cr_27)
=> cHahnRelationsBasic_2efunctional___24a2(cA,cHahnRelationsBasic_2eseq___24a3(cA,cr,cr_27)) ) ) ).
%------------------------------------------------------------------------------