TPTP Problem File: SEV616+1.p
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%------------------------------------------------------------------------------
% File : SEV616+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - HahnEquational collect rel empty
% 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 : HahnEquational.collect.rel.empty.p [Kal26]
% Status : Theorem
% Rating : 0.78 v9.3.0
% Syntax : Number of formulae : 2863 (1147 unt; 0 def)
% Number of atoms : 8916 (2223 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 6137 ( 84 ~; 642 |;1404 &)
% (1102 <=>;2905 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 6 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 596 ( 595 usr; 0 prp; 1-23 aty)
% Number of functors : 1621 (1621 usr;1038 con; 0-22 aty)
% Number of variables : 9289 (8735 !; 554 ?)
% 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$33916',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2434003___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2433916___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__33920] :
( t(Vvar__1___24Anonymous__33920,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__33921] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__33921)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2434003___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__33920,Vvar__2___24Anonymous__33921)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2433916___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__33920,c_24__fix__34048__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__33921,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$34003',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2434003___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__34007] :
( t(Vvar__1___24Anonymous__34007,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__34008] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__34008)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__34007,Vvar__2___24Anonymous__34008)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2434003___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__34007,c_24__fix__34048__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__34008,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$34170',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2434170___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__34171] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34171)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34171)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2434170___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__34171)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$34192',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2434192___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__34193] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34193)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34193)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2434192___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__34193)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$28008',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__22688___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__28013] :
( t(Vvar__2___24Anonymous__28013,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__28014] :
( t(Vvar__3___24Anonymous__28014,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__28013,Vvar__3___24Anonymous__28014)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2428008___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__28013)),Vvar__3___24Anonymous__28014)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$34187',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2434192___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2434187___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__34188] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34188)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2434192___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__34188)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2434187___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__34188) )
| ? [Vvar__0___24Anonymous__34189] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34189)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2434192___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__34189)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2434187___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__34189) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.positive$35458',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__35459] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35459)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35459)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435458___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__35474__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__35459)) )
| ? [Vvar__0___24Anonymous__35466] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35466)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35466)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435458___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35466) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435458___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_$_let_var_6_p_22915_22918',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__22914] : c_24__let__var__6__p__22915__22918___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__22914) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__22914) ).
fof('$_def_$_let_var_6_p_22917_22919',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__22916] : c_24__let__var__6__p__22917__22919___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__22916) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__22916) ).
fof('$_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__12175] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12175)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12175)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__12176] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12176)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12176)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__12179] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12179)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12179)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__12176,Vvar__0___24Anonymous__12179) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.Arith.PeanoNat.Nat.recursion',axiom,
! [V0__A] : cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(c_24__lam__10990___24a1(V0__A)) ).
fof('$_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__33431] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33431)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33431)
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__33431,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('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__11192] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__11192)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__11192) ) ).
fof('$_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__11218] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__11218)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__11218) ) ).
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.ID',axiom,
! [Vvar__30716] :
( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__30716)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> t(happ(happ(Vvar__30716,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('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__11945] :
( t(Vvar__1___24Anonymous__11945,V0__A)
& ? [Vvar__2___24Anonymous__11946] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__11946)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__11945,Vvar__2___24Anonymous__11946)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__11945,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__11946,V3__m)) ) ) ) ) ) ).
fof('$_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__3889] :
( t(Vvar__2___24Anonymous__3889,V0__A)
& ? [Vvar__3___24Anonymous__3890] :
( t(Vvar__3___24Anonymous__3890,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__3889,Vvar__3___24Anonymous__3890)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__3889 ) ) ) ) ) ).
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.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__11933] :
( t(Vvar__2___24Anonymous__11933,V0__A)
& ? [Vvar__3___24Anonymous__11934] :
( t(Vvar__3___24Anonymous__11934,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__11933,Vvar__3___24Anonymous__11934)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__11934 ) ) ) ) ) ).
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__39433] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__39433)
& V1__d = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__39433)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = cCoq_2eInit_2eDecimal_2enzhead___24a1(Vvar__0___24Anonymous__39433) )
| ? [Vvar__0___24Anonymous__39434] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__39434)
& V1__d = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__39434)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__39435] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__39435)
& V1__d = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__39435)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__39436] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__39436)
& V1__d = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__39436)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__39437] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__39437)
& V1__d = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__39437)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__39438] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__39438)
& V1__d = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__39438)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__39439] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__39439)
& V1__d = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__39439)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__39440] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__39440)
& V1__d = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__39440)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__39441] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__39441)
& V1__d = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__39441)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__39442] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__39442)
& V1__d = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__39442)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d ) ) ) ).
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__7409] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7409)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7409)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__7409,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.div2',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__12537] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12537)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12537)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12537)
& ( ( Vvar__0___24Anonymous__12537 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__12540] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12540)
& Vvar__0___24Anonymous__12537 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12540)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__12540)) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Nat.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__12515] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12515)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12515)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__12516] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12516)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12516)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__12519] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12519)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12519)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__12516,Vvar__0___24Anonymous__12519) ) ) ) ) ) ) ) ).
fof('$_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__7434] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7434)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7434)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7434)
& ( ( Vvar__0___24Anonymous__7434 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__7437] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7437)
& Vvar__0___24Anonymous__7434 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7437)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__7437) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.leb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__7417] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7417)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7417)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__7420] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7420)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7420)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__7417,Vvar__0___24Anonymous__7420) ) ) ) ) ) ) ) ).
fof('$_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__12522] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12522)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12522)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__12525] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12525)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12525)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__12522,Vvar__0___24Anonymous__12525)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.min',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__12528] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12528)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12528)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__12531] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12531)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12531)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__12528,Vvar__0___24Anonymous__12531)) ) ) ) ) ) ) ) ).
fof('$_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__7414] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7414)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7414)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__7414,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pow',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__7441] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7441)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7441)
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__n,cCoq_2eInit_2eNat_2epow___24a2(V1__n,Vvar__0___24Anonymous__7441)) ) ) ) ).
fof('$_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__7407] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7407)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7407)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__7407 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__12509] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12509)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12509)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__12512] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12512)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12512)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__12509,Vvar__0___24Anonymous__12512) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.succ',axiom,
cCoq_2eInit_2eNat_2esucc = cCoq_2eInit_2eDatatypes_2eS ).
fof('$_def_Coq.Init.Nat.t',axiom,
! [Vvar__33233] :
( cCoq_2eInit_2eNat_2et___24t(Vvar__33233)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__33233) ) ).
fof('$_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__33235] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33235)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33235)
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__33235,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__33429] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33429)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33429)
& ( 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.except',axiom,
cCoq_2eInit_2eSpecif_2eexcept = cCoq_2eInit_2eLogic_2eFalse__rec ).
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__7388] :
( t(Vvar__1___24Anonymous__7388,V0__A)
& ? [Vvar__2___24Anonymous__7389] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7389)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7388,Vvar__2___24Anonymous__7389)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__7388 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__7389) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_left',axiom,
! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
| ? [Vvar__1___24Anonymous__33206] :
( t(Vvar__1___24Anonymous__33206,V1__B)
& ? [Vvar__2___24Anonymous__33207] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__33207)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__33206,Vvar__2___24Anonymous__33207)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__33207,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__33206)) ) ) ) ) ) ) ).
fof('$_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__12319] :
( t(Vvar__1___24Anonymous__12319,V1__B)
& ? [Vvar__2___24Anonymous__12320] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__12320)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__12319,Vvar__2___24Anonymous__12320)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__12319),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__12320)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd',axiom,
! [V0__A,V1__default,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = V1__default )
| ? [Vvar__1___24Anonymous__20812] :
( t(Vvar__1___24Anonymous__20812,V0__A)
& ? [Vvar__2___24Anonymous__20813] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__20813)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__20812,Vvar__2___24Anonymous__20813)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__20812 ) ) ) ) ) ).
fof('$_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__12294] :
( t(Vvar__1___24Anonymous__12294,V0__A)
& ? [Vvar__2___24Anonymous__12295] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12295)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12294,Vvar__2___24Anonymous__12295)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__12294 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__12297] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12297)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12297)
& ( ( 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__12304] :
( t(Vvar__1___24Anonymous__12304,V0__A)
& ? [Vvar__2___24Anonymous__12305] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12305)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12304,Vvar__2___24Anonymous__12305)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__12297,Vvar__2___24Anonymous__12305,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('$_def_Coq.Logic.ChoiceFacts.ConstructiveIndefiniteDescription_on',axiom,
! [V0__A] : cCoq_2eLogic_2eChoiceFacts_2eConstructiveIndefiniteDescription__on___24a1(V0__A) = c_24__type__30624___24a1(V0__A) ).
fof('$_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__30593___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__30600___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__6___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__21___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('$_def_Coq.Logic.ChoiceFacts.FunctionalChoice_on_rel',axiom,
! [V0__A,V1__B,V2__R] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel___24a3(V0__A,V1__B,V2__R)
<=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,V1__B)
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__21___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on',axiom,
! [V0__A] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on___24a1(V0__A)
<=> ! [V1__R] :
( c_24__type__30610___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__11040___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('$_def_Coq.Logic.ChoiceFacts.GeneralizedSetoidFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eGeneralizedSetoidFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__1199___24t(V0__A,V2__R)
=> ! [V3__S] :
( c_24__type__11872___24t(V0__A,V1__B,V3__S)
=> ! [V4__T] :
( c_24__type__6___24t(V0__A,V1__B,V4__T)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V2__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V1__B,V3__S)
=> ( ! [V7__x] :
( t(V7__x,V0__A)
=> ! [V8__x_27] :
( t(V8__x_27,V0__A)
=> ! [V9__y] :
( t(V9__y,V1__B)
=> ! [V10__y_27] :
( t(V10__y_27,V1__B)
=> ( p(happ(happ(V2__R,V7__x),V8__x_27))
=> ( p(happ(happ(V3__S,V9__y),V10__y_27))
=> ( p(happ(happ(V4__T,V7__x),V9__y))
=> p(happ(happ(V4__T,V8__x_27),V10__y_27)) ) ) ) ) ) ) )
=> ( ! [V8__x] :
( t(V8__x,V0__A)
=> ? [V9__y] :
( t(V9__y,V1__B)
& p(happ(happ(V4__T,V8__x),V9__y)) ) )
=> ? [V9__f] :
( c_24__type__21___24t(V0__A,V1__B,V9__f)
& ! [V10__x] :
( t(V10__x,V0__A)
=> ( p(happ(happ(V4__T,V10__x),happ(V9__f,V10__x)))
& ! [V11__x_27] :
( t(V11__x_27,V0__A)
=> ( p(happ(happ(V2__R,V10__x),V11__x_27))
=> p(happ(happ(V3__S,happ(V9__f,V10__x)),happ(V9__f,V11__x_27))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Logic.ChoiceFacts.RepresentativeFunctionalChoice_on',axiom,
! [V0__A] :
( cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on___24a1(V0__A)
<=> ! [V1__R] :
( c_24__type__1199___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__R)
=> ? [V3__f] :
( c_24__type__1194___24t(V0__A,V3__f)
& ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(happ(happ(V1__R,V4__x),happ(V3__f,V4__x)))
& ! [V5__x_27] :
( t(V5__x_27,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__x_27))
=> happ(V3__f,V4__x) = happ(V3__f,V5__x_27) ) ) ) ) ) ) ) ) ).
fof('$_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__1199___24t(V0__A,V2__R)
=> ! [V3__T] :
( c_24__type__6___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__21___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('$_def_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__1199___24t(V0__A,V2__R)
=> ! [V3__T] :
( c_24__type__6___24t(V0__A,V1__B,V3__T)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V2__R)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ? [V6__y] :
( t(V6__y,V1__B)
& ! [V7__x_27] :
( t(V7__x_27,V0__A)
=> ( p(happ(happ(V2__R,V5__x),V7__x_27))
=> p(happ(happ(V3__T,V7__x_27),V6__y)) ) ) ) )
=> ? [V6__f] :
( c_24__type__21___24t(V0__A,V1__B,V6__f)
& ! [V7__x] :
( t(V7__x,V0__A)
=> ( p(happ(happ(V3__T,V7__x),happ(V6__f,V7__x)))
& ! [V8__x_27] :
( t(V8__x_27,V0__A)
=> ( p(happ(happ(V2__R,V7__x),V8__x_27))
=> happ(V6__f,V7__x) = happ(V6__f,V8__x_27) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Logic.ClassicalFacts.DrinkerParadox',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eDrinkerParadox)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1892___24t(V0__A,V1__P)
=> ! [V2___24Anonymous] :
( t(V2___24Anonymous,V0__A)
=> ? [V3__x] :
( t(V3__x,V0__A)
& ( ? [V4__x] :
( t(V4__x,V0__A)
& p(happ(V1__P,V4__x)) )
=> p(happ(V1__P,V3__x)) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Logic.ClassicalFacts.IndependenceOfGeneralPremises',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eIndependenceOfGeneralPremises)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1892___24t(V0__A,V1__P)
=> ! [V2__Q] :
( cProp___24t(V2__Q)
=> ! [V3___24Anonymous] :
( t(V3___24Anonymous,V0__A)
=> ( ( p(V2__Q)
=> ? [V5__x] :
( t(V5__x,V0__A)
& p(happ(V1__P,V5__x)) ) )
=> ? [V5__x] :
( t(V5__x,V0__A)
& ( p(V2__Q)
=> p(happ(V1__P,V5__x)) ) ) ) ) ) ) ) ) ).
fof('$_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__6713___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('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__10821] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10821)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10821)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__10824] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10824)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10824)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__10821,Vvar__0___24Anonymous__10824)) ) ) ) ) ) ) ) ).
fof('$_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__10828] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10828)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10828)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__10831] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10831)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10831)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__10828,Vvar__0___24Anonymous__10831)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__10820] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10820)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10820)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__10820) ) ) ) ).
fof('$_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__5356] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5356)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5356)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__5356)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
! [Vvar__35375] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__35375)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__35375) ) ).
fof('$_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__10864] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10864)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10864)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__10864,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__18603] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18603)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__18603)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__18603) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.zero',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2ezero = cCoq_2eNumbers_2eBinNums_2eN0 ).
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('$_def_Coq.PArith.BinPosDef.Pos.div2',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__35400] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35400)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35400)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__35400 )
| ? [Vvar__0___24Anonymous__35401] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35401)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35401)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__35401 )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.eqb',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__18651] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18651)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18651)
& ( ? [Vvar__0___24Anonymous__18655] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18655)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18655)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__18651,Vvar__0___24Anonymous__18655) )
| ? [Vvar__0___24Anonymous__18656] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18656)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18656)
& 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__18657] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18657)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18657)
& ( ? [Vvar__0___24Anonymous__18661] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18661)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18661)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__18662] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18662)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18662)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__18657,Vvar__0___24Anonymous__18662) )
| ( 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__18663] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18663)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18663)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__18664] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18664)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18664)
& 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('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__35388] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35388)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35388)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__35388),Vvar__0___24Anonymous__35388)) )
| ? [Vvar__0___24Anonymous__35389] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35389)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35389)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__35389),Vvar__0___24Anonymous__35389) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_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__35403] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35403)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35403)
& 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__35403,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__35404] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35404)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35404)
& 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__35404,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('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__18620] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18620)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18620)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__18620)) )
| ? [Vvar__0___24Anonymous__18621] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18621)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18621)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18621) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.t',axiom,
! [Vvar__35386] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__35386)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__35386) ) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__7491] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__7491)
& ? [Vvar__1__Qden__7492] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__7492)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__7491,Vvar__1__Qden__7492)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__7492 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__7486] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__7486)
& ? [Vvar__1__Qden__7487] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__7487)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__7486,Vvar__1__Qden__7487)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__7486 ) ) ) ).
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.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__1199___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('$_def_Coq.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__1199___24a1(V0__U) ).
fof('$_def_Coq.Structures.GenericMinMax.gmax',axiom,
! [V0__A,V1__cmp,V2__x,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__33089___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('$_def_Coq.Structures.GenericMinMax.gmin',axiom,
! [V0__A,V1__cmp,V2__x,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__33089___24t(V0__A,V1__cmp)
=> ( t(V2__x,V0__A)
=> ( t(V3__y,V0__A)
=> ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y ) ) ) ) ) ) ).
fof('$_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__35377] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__35377)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__35377) ) ).
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('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__35383] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__35383)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__35383) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__35282] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35282)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35282)
& ( ? [Vvar__0___24Anonymous__35286] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35286)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35286)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__35282,Vvar__0___24Anonymous__35286) ) )
| ? [Vvar__0___24Anonymous__35287] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35287)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35287)
& ( 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__35288] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35288)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35288)
& ( ? [Vvar__0___24Anonymous__35292] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35292)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35292)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__35293] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35293)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35293)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__35288,Vvar__0___24Anonymous__35293) ) )
| ( 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__35294] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35294)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35294)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__35295] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35295)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35295)
& ( 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('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__35280] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__35280)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__35280) ) ).
fof('$_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__35493] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__35493)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__35493) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__35498] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__35498)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__35498) ) ).
fof('$_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__35514] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__35514)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__35514) ) ).
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('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_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__11595] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11595)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11595)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11595) )
| ? [Vvar__0___24Anonymous__11596] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11596)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11596)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11596) ) ) ) ).
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__2755] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2755)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2755)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__2759] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2759)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2759)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2755,Vvar__0___24Anonymous__2759)) )
| ? [Vvar__0___24Anonymous__2760] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2760)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2760)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__2755,Vvar__0___24Anonymous__2760) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2761] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2761)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2761)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__2765] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2765)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2765)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__2765,Vvar__0___24Anonymous__2761) )
| ? [Vvar__0___24Anonymous__2766] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2766)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2766)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2761,Vvar__0___24Anonymous__2766)) ) ) ) ) ) ) ) ).
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__11607] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__11607)
& ? [Vvar__3___24Anonymous__11608] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__11608)
& 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__11607,Vvar__3___24Anonymous__11608)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__11607 ) ) ) ) ).
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__11619] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11619)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11619)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11619)
& ( ? [Vvar__0___24Anonymous__11623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11623)
& Vvar__0___24Anonymous__11619 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__11623)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__11624] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11624)
& Vvar__0___24Anonymous__11619 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11624)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__11619 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__11625] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11625)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11625)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11625)
& ( ? [Vvar__0___24Anonymous__11629] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11629)
& Vvar__0___24Anonymous__11625 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__11629)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__11630] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11630)
& Vvar__0___24Anonymous__11625 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11630)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__11625 = 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__11615] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__11615)
& ? [Vvar__3___24Anonymous__11616] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__11616)
& 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__11615,Vvar__3___24Anonymous__11616)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__11616 ) ) ) ) ).
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__3774] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3774)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3774)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__3778] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3778)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3778)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3774,Vvar__0___24Anonymous__3778)) )
| ? [Vvar__0___24Anonymous__3779] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3779)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3779)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3774,Vvar__0___24Anonymous__3779)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__3780] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3780)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3780)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__3784] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3784)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3784)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3780,Vvar__0___24Anonymous__3784)) )
| ? [Vvar__0___24Anonymous__3785] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3785)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3785)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3780,Vvar__0___24Anonymous__3785)) ) ) ) ) ) ) ) ).
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__18719] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18719)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18719)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__18719)
& ( ? [Vvar__0___24Anonymous__18723] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18723)
& Vvar__0___24Anonymous__18719 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18723)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__18724] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18724)
& Vvar__0___24Anonymous__18719 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18724)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__18719 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__18725] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18725)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18725)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__18725)
& ( ? [Vvar__0___24Anonymous__18729] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18729)
& Vvar__0___24Anonymous__18725 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18729)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__18730] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18730)
& Vvar__0___24Anonymous__18725 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18730)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__18725 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__11600] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11600)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11600)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11600) ) ) ) ).
fof('$_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__2770] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2770)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2770)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2770) )
| ? [Vvar__0___24Anonymous__2771] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2771)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2771)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2771) ) ) ) ).
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('$_def_Coq.ZArith.BinIntDef.Z.t',axiom,
! [Vvar__35513] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__35513)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__35513) ) ).
fof('$_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__18711] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18711)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__18711)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__18711) )
| ? [Vvar__0___24Anonymous__18712] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18712)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__18712)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__18713] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18713)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__18713)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__18713 )
| ? [Vvar__0___24Anonymous__18714] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18714)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__18714)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_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__18506] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18506)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18506)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__18506)
& ( ? [Vvar__0___24Anonymous__18510] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18510)
& Vvar__0___24Anonymous__18506 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18510)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__18511] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18511)
& Vvar__0___24Anonymous__18506 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18511)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__18506 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__18512] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18512)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18512)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__18512)
& ( ? [Vvar__0___24Anonymous__18516] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18516)
& Vvar__0___24Anonymous__18512 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18516)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__18517] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18517)
& Vvar__0___24Anonymous__18512 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18517)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__18512 = 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__10760] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10760)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10760)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10760)
& ( ? [Vvar__0___24Anonymous__10764] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10764)
& Vvar__0___24Anonymous__10760 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__10764)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__10765] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10765)
& Vvar__0___24Anonymous__10760 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__10765)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__10760 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__10766] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10766)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10766)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10766)
& ( ? [Vvar__0___24Anonymous__10770] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10770)
& Vvar__0___24Anonymous__10766 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__10770)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__10771] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10771)
& Vvar__0___24Anonymous__10766 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__10771)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__10766 = 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__18519] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18519)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18519)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__18520] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18520)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18520)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__18520) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__19670___24a1(V0__D) ).
fof('$_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__12733] :
( t(Vvar__1___24Anonymous__12733,V1__A)
& ? [Vvar__2___24Anonymous__12734] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__12734)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__12734)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__12733,Vvar__2___24Anonymous__12734)
& ( ( Vvar__2___24Anonymous__12734 = 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__12733)) ) )
| ? [Vvar__1___24Anonymous__12745] :
( t(Vvar__1___24Anonymous__12745,V1__A)
& ? [Vvar__2___24Anonymous__12746] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__12746)
& Vvar__2___24Anonymous__12734 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__12745,Vvar__2___24Anonymous__12746)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__12733))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__12734) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__4387] :
( t(Vvar__1___24Anonymous__4387,V1__A)
& ? [Vvar__2___24Anonymous__4388] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__4388)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__4387,Vvar__2___24Anonymous__4388)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__4387))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__4388,V4__goal) ) ) ) ) ) ) ) ).
fof('$_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__35206] :
( cCoq_2emicromega_2eZMicromega_2econeMember___24t(Vvar__35206)
<=> cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__35206) ) ).
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('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
! [Vvar__33201] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__33201)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__33201) ) ).
fof('$_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__33167] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33167)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33167)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33167)
& ( ? [Vvar__0___24Anonymous__33171] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33171)
& Vvar__0___24Anonymous__33167 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33171)
& 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__33167))) )
| ? [Vvar__0___24Anonymous__33172] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33172)
& Vvar__0___24Anonymous__33167 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33172)
& 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__33167))) )
| ( Vvar__0___24Anonymous__33167 = 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__33173] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33173)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33173)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33173)
& ( ? [Vvar__0___24Anonymous__33177] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33177)
& Vvar__0___24Anonymous__33173 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33177)
& 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__33173)) )
| ? [Vvar__0___24Anonymous__33178] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33178)
& Vvar__0___24Anonymous__33173 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33178)
& 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__33173)) )
| ( Vvar__0___24Anonymous__33173 = 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('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__20678] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20678)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20678)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__20678))) )
| ? [Vvar__0___24Anonymous__20679] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20679)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20679)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__20679)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_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__22870] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22870)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22870)
& 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__22870),V4__x,Vvar__0___24Anonymous__22870) )
| ? [Vvar__0___24Anonymous__22871] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22871)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22871)
& 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__22871),V4__x,Vvar__0___24Anonymous__22871) )
| ( 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('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__18143] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18143)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__18143)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__18143) ) ) ) ) ).
fof('$_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__22914] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22914)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22914)
& 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__22915__22918___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__22914)),c_24__let__var__6__p__22915__22918___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__22914))) )
| ? [Vvar__0___24Anonymous__22916] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22916)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22916)
& 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__22917__22919___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__22916)),c_24__let__var__6__p__22917__22919___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__22916)) )
| ( 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('$_def_Hammer.Tactics.Reconstr.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eReconstr_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_Hammer.Tactics.Tactics.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eTactics_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_hahn.HahnRelationsBasic.acyclic',axiom,
! [V0__A,V1__r] :
( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ).
fof('$_def_hahn.HahnRelationsBasic.bunion',axiom,
! [V0__A,V1__B,V2__P,V3__r,V4__x,V5__y] :
( chahn_2eHahnRelationsBasic_2ebunion___24a6(V0__A,V1__B,V2__P,V3__r,V4__x,V5__y)
<=> ? [V6__a] :
( t(V6__a,V0__A)
& p(happ(V2__P,V6__a))
& p(happ(happ(happ(V3__r,V6__a),V4__x),V5__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.clos_refl',axiom,
! [V0__A,V1__r,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ( V2__x = V3__y
| p(happ(happ(V1__r,V2__x),V3__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.collect_rel',axiom,
! [V0__A,V1__B,V2__f,V3__r,V4__x,V5__y] :
( chahn_2eHahnRelationsBasic_2ecollect__rel___24a6(V0__A,V1__B,V2__f,V3__r,V4__x,V5__y)
<=> ? [V6__x_27] :
( t(V6__x_27,V0__A)
& ? [V7__y_27] :
( t(V7__y_27,V0__A)
& p(happ(happ(V3__r,V6__x_27),V7__y_27))
& happ(V2__f,V6__x_27) = V4__x
& happ(V2__f,V7__y_27) = V5__y ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.cross_rel',axiom,
! [V0__A,V1__r,V2__r_27,V3__a,V4__b] :
( chahn_2eHahnRelationsBasic_2ecross__rel___24a5(V0__A,V1__r,V2__r_27,V3__a,V4__b)
<=> ( p(happ(V1__r,V3__a))
& p(happ(V2__r_27,V4__b)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.eqv_dom_rel',axiom,
! [V0__A,V1__dom,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a4(V0__A,V1__dom,V2__x,V3__y)
<=> ( V2__x = V3__y
& cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V1__dom) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.eqv_rel',axiom,
! [V0__A,V1__cond,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4(V0__A,V1__cond,V2__x,V3__y)
<=> ( V2__x = V3__y
& p(happ(V1__cond,V2__x)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.functional',axiom,
! [V0__A,V1__r] :
( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r))
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V3__y))
=> ( p(happ(happ(V1__r,V2__x),V4__z))
=> V3__y = V4__z ) ) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.immediate',axiom,
! [V0__A,V1__r,V2__a,V3__b] :
( chahn_2eHahnRelationsBasic_2eimmediate___24a4(V0__A,V1__r,V2__a,V3__b)
<=> ( p(happ(happ(V1__r,V2__a),V3__b))
& ! [V4__c] :
( t(V4__c,V0__A)
=> ( p(happ(happ(V1__r,V2__a),V4__c))
=> ( p(happ(happ(V1__r,V4__c),V3__b))
=> p(c_24False) ) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.inter_rel',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2einter__rel___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ( p(happ(happ(V1__r,V3__x),V4__y))
& p(happ(happ(V2__r_27,V3__x),V4__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.irreflexive',axiom,
! [V0__A,V1__r] :
( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V2__x))
=> p(c_24False) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.is_total',axiom,
! [V0__A,V1__cond,V2__r] :
( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__cond,V2__r)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(happ(V1__cond,V3__a))
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(V1__cond,V5__b))
=> ( V3__a != V5__b
=> ( p(happ(happ(V2__r,V3__a),V5__b))
| p(happ(happ(V2__r,V5__b),V3__a)) ) ) ) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.map_rel',axiom,
! [V0__A,V1__B,V2__f,V3__r_27_27,V4__x,V5__y] :
( chahn_2eHahnRelationsBasic_2emap__rel___24a6(V0__A,V1__B,V2__f,V3__r_27_27,V4__x,V5__y)
<=> p(happ(happ(V3__r_27_27,happ(V2__f,V4__x)),happ(V2__f,V5__y))) ) ).
fof('$_def_hahn.HahnRelationsBasic.minus_rel',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2eminus__rel___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ( p(happ(happ(V1__r,V3__x),V4__y))
& ~ p(happ(happ(V2__r_27,V3__x),V4__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.pow_rel',axiom,
! [V1__A,V2__r,V3__n] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V3__n) = chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V1__A,c_24__lam__3955___24a1(V1__A)) )
| ? [Vvar__0___24Anonymous__7281] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7281)
& V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7281)
& chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V3__n) = chahn_2eHahnRelationsBasic_2eseq___24a3(V1__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,Vvar__0___24Anonymous__7281),V2__r) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.restr_eq_rel',axiom,
! [V0__A,V1__B,V2__f,V3__r,V4__x,V5__y] :
( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6(V0__A,V1__B,V2__f,V3__r,V4__x,V5__y)
<=> ( p(happ(happ(V3__r,V4__x),V5__y))
& happ(V2__f,V4__x) = happ(V2__f,V5__y) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.restr_rel',axiom,
! [V0__A,V1__cond,V2__r,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2erestr__rel___24a5(V0__A,V1__cond,V2__r,V3__x,V4__y)
<=> ( p(happ(happ(V2__r,V3__x),V4__y))
& p(happ(V1__cond,V3__x))
& p(happ(V1__cond,V4__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.seq',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2eseq___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ? [V5__z] :
( t(V5__z,V0__A)
& p(happ(happ(V1__r,V3__x),V5__z))
& p(happ(happ(V2__r_27,V5__z),V4__y)) ) ) ).
fof('$_def_hahn.HahnSets.set_bunion',axiom,
! [V0__A,V1__B,V2__s,V3__ss,V4__x] :
( chahn_2eHahnSets_2eset__bunion___24a5(V0__A,V1__B,V2__s,V3__ss,V4__x)
<=> ? [V5__y] :
( t(V5__y,V0__A)
& p(happ(V2__s,V5__y))
& p(happ(happ(V3__ss,V5__y),V4__x)) ) ) ).
fof('$_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__1779,Vvar__1___24Anonymous__1780,Vvar__0__P__1781,Vvar__1___24Anonymous__1782] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__1779) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__1781) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__11197,Vvar__1___24Anonymous__11198,Vvar__2___24Anonymous__11199] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__11197,Vvar__1___24Anonymous__11198,Vvar__2___24Anonymous__11199) ).
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__6300,Vvar__1__Plt__6301,Vvar__2__Pgt__6302,Vvar__3___24Anonymous__6303,Vvar__0__Peq__6304,Vvar__1__Plt__6305,Vvar__2__Pgt__6306,Vvar__3___24Anonymous__6307] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__6300,Vvar__1__Plt__6301,Vvar__2__Pgt__6302) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__6304,Vvar__1__Plt__6305,Vvar__2__Pgt__6306) ).
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__3862] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3862) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__30,Vvar__1___24Anonymous__31,Vvar__0__A__32] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__30,Vvar__1___24Anonymous__31) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__32) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__19492,Vvar__1__B__19493,Vvar__2___24Anonymous__19494,Vvar__0__A__19495,Vvar__1__B__19496,Vvar__2___24Anonymous__19497] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__19492,Vvar__1__B__19493,Vvar__2___24Anonymous__19494) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__19495,Vvar__1__B__19496,Vvar__2___24Anonymous__19497) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__68,Vvar__0__A__69,Vvar__1___24Anonymous__70,Vvar__2___24Anonymous__71] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__68) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__69,Vvar__1___24Anonymous__70,Vvar__2___24Anonymous__71) ).
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__30725,Vvar__1__f__30726,Vvar__0__i__30727,Vvar__1__f__30728,Vvar__2__e__30729] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__30725,Vvar__1__f__30726) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__30727,Vvar__1__f__30728,Vvar__2__e__30729) ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__19637] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__19637) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__19661,Vvar__0__d__19662] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__19661) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__19662) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__35065,Vvar__1__B__35066,Vvar__2___24Anonymous__35067,Vvar__0__A__35068,Vvar__1__B__35069,Vvar__2___24Anonymous__35070] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__35065,Vvar__1__B__35066,Vvar__2___24Anonymous__35067) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__35068,Vvar__1__B__35069) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__10129,Vvar__1__B__10130,Vvar__2___24Anonymous__10131,Vvar__0__A__10132,Vvar__1__B__10133,Vvar__2___24Anonymous__10134] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__10129,Vvar__1__B__10130) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__10132,Vvar__1__B__10133) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__3856] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3856) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1762] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1762) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1748,Vvar__0___24Anonymous__1749] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1748) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1749) ).
fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__35477,Vvar__1___24Anonymous__35478] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__35477,Vvar__1___24Anonymous__35478) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__11124] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__11124) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__34212,Vvar__1___24Anonymous__34213,Vvar__0__x__34214,Vvar__1__n__34215,Vvar__2___24Anonymous__34216] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__34212) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__34214,Vvar__1__n__34215) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__18454,Vvar__1___24Anonymous__18455] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__18454,Vvar__1___24Anonymous__18455) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__33381,Vvar__1__lt__33382,Vvar__2__eq__33383,Vvar__3__x__33384,Vvar__4__y__33385,Vvar__5___24Anonymous__33386,Vvar__0__X__33387,Vvar__1__lt__33388,Vvar__2__eq__33389,Vvar__3__x__33390,Vvar__4__y__33391,Vvar__5___24Anonymous__33392] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__33381,Vvar__1__lt__33382,Vvar__2__eq__33383,Vvar__3__x__33384,Vvar__4__y__33385) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__33387,Vvar__1__lt__33388,Vvar__2__eq__33389,Vvar__3__x__33390,Vvar__4__y__33391) ).
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__6761,Vvar__0__n__6762,Vvar__1___24Anonymous__6763] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__6761) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__6762,Vvar__1___24Anonymous__6763) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__10168,Vvar__0__A__10169,Vvar__1__h__10170,Vvar__2__n__10171,Vvar__3___24Anonymous__10172] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__10168) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__10169,Vvar__1__h__10170,Vvar__2__n__10171,Vvar__3___24Anonymous__10172) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__12084,Vvar__1___24Anonymous__12085,Vvar__0__C__12086,Vvar__1___24Anonymous__12087] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__12084,Vvar__1___24Anonymous__12085) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__12086,Vvar__1___24Anonymous__12087) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__12148,Vvar__1___24Anonymous__12149,Vvar__0__C__12150,Vvar__1___24Anonymous__12151,Vvar__2___24Anonymous__12152] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__12148,Vvar__1___24Anonymous__12149) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__12150,Vvar__1___24Anonymous__12151,Vvar__2___24Anonymous__12152) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__30761,Vvar__1___24Anonymous__30762] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__30761,Vvar__1___24Anonymous__30762) ).
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__21227,Vvar__1___24Anonymous__21228,Vvar__0__C__21229,Vvar__1___24Anonymous__21230] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__21227,Vvar__1___24Anonymous__21228) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__21229,Vvar__1___24Anonymous__21230) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__5028,Vvar__1__TX__5029,Vvar__2__AA__5030,Vvar__3__AF__5031,Vvar__0__TA__5032,Vvar__1__TX__5033,Vvar__2__AA__5034,Vvar__3__AF__5035] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__5028,Vvar__1__TX__5029,Vvar__2__AA__5030,Vvar__3__AF__5031) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__5032,Vvar__1__TX__5033,Vvar__2__AA__5034,Vvar__3__AF__5035) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__35107,Vvar__0__A__35108,Vvar__1___24Anonymous__35109] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__35107) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__35108,Vvar__1___24Anonymous__35109) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__35151,Vvar__1___24Anonymous__35152] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__35151,Vvar__1___24Anonymous__35152) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__31810,Vvar__0__C__31811] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__31810) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__31811) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__2297,Vvar__0__C__2298] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2297) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2298) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__1939,Vvar__1___24Anonymous__1940,Vvar__0__C__1941,Vvar__1___24Anonymous__1942,Vvar__2___24Anonymous__1943] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1939,Vvar__1___24Anonymous__1940) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1941,Vvar__1___24Anonymous__1942,Vvar__2___24Anonymous__1943) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__2107,Vvar__1___24Anonymous__2108] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__2107,Vvar__1___24Anonymous__2108) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__34908,Vvar__1__req__34909,Vvar__2__reqb__34910,Vvar__3___24Anonymous__34911] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__34908,Vvar__1__req__34909,Vvar__2__reqb__34910) ).
fof('$_discrim_Hammer.Tactics.Reconstr.Empty$Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eEmpty != cHammer_2eTactics_2eReconstr_2eAllHyps ).
fof('$_fix_34048_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__34048__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__34052] :
( t(Vvar__1___24Anonymous__34052,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__34053] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__34053)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__34052,Vvar__2___24Anonymous__34053)
& c_24__fix__34048__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__34052,c_24__fix__34048__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__34053,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_35474_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__35475] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35475)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35475)
& c_24__fix__35474__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__35474__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__35475)) )
| ? [Vvar__0___24Anonymous__35476] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35476)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35476)
& c_24__fix__35474__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35476) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__35474__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__1787,Vvar__0__P__1788,Vvar__1___24Anonymous__1789,Vvar__1___24Anonymous__1790] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__1787) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__1788)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__1787 = Vvar__0__P__1788 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__1783,Vvar__0__P__1784,Vvar__1___24Anonymous__1785,Vvar__1___24Anonymous__1786] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__1783) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__1784)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__1783 = Vvar__0__P__1784 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__11200,Vvar__0___24Anonymous__11201,Vvar__1___24Anonymous__11202,Vvar__1___24Anonymous__11203,Vvar__2___24Anonymous__11204,Vvar__2___24Anonymous__11205] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__11200,Vvar__1___24Anonymous__11202,Vvar__2___24Anonymous__11204) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__11201,Vvar__1___24Anonymous__11203,Vvar__2___24Anonymous__11205)
=> ( Vvar__2___24Anonymous__11204 = Vvar__2___24Anonymous__11205
& Vvar__1___24Anonymous__11202 = Vvar__1___24Anonymous__11203
& Vvar__0___24Anonymous__11200 = Vvar__0___24Anonymous__11201 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__6308,Vvar__0__Peq__6309,Vvar__1__Plt__6310,Vvar__1__Plt__6311,Vvar__2__Pgt__6312,Vvar__2__Pgt__6313,Vvar__3___24Anonymous__6314,Vvar__3___24Anonymous__6315] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__6308,Vvar__1__Plt__6310,Vvar__2__Pgt__6312) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__6309,Vvar__1__Plt__6311,Vvar__2__Pgt__6313)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__6312 = Vvar__2__Pgt__6313
& Vvar__1__Plt__6310 = Vvar__1__Plt__6311
& Vvar__0__Peq__6308 = Vvar__0__Peq__6309 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__6324,Vvar__0__Peq__6325,Vvar__1__Plt__6326,Vvar__1__Plt__6327,Vvar__2__Pgt__6328,Vvar__2__Pgt__6329,Vvar__3___24Anonymous__6330,Vvar__3___24Anonymous__6331] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__6324,Vvar__1__Plt__6326,Vvar__2__Pgt__6328) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__6325,Vvar__1__Plt__6327,Vvar__2__Pgt__6329)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__6328 = Vvar__2__Pgt__6329
& Vvar__1__Plt__6326 = Vvar__1__Plt__6327
& Vvar__0__Peq__6324 = Vvar__0__Peq__6325 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__6316,Vvar__0__Peq__6317,Vvar__1__Plt__6318,Vvar__1__Plt__6319,Vvar__2__Pgt__6320,Vvar__2__Pgt__6321,Vvar__3___24Anonymous__6322,Vvar__3___24Anonymous__6323] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__6316,Vvar__1__Plt__6318,Vvar__2__Pgt__6320) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__6317,Vvar__1__Plt__6319,Vvar__2__Pgt__6321)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__6320 = Vvar__2__Pgt__6321
& Vvar__1__Plt__6318 = Vvar__1__Plt__6319
& Vvar__0__Peq__6316 = Vvar__0__Peq__6317 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__37,Vvar__0__A__38] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__37) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__38)
=> Vvar__0__A__37 = Vvar__0__A__38 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__3863,Vvar__0___24Anonymous__3864] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3863) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3864)
=> Vvar__0___24Anonymous__3863 = Vvar__0___24Anonymous__3864 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__33,Vvar__0__A__34,Vvar__1___24Anonymous__35,Vvar__1___24Anonymous__36] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__33,Vvar__1___24Anonymous__35) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__34,Vvar__1___24Anonymous__36)
=> ( Vvar__1___24Anonymous__35 = Vvar__1___24Anonymous__36
& Vvar__0__A__33 = Vvar__0__A__34 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__74,Vvar__0__A__75,Vvar__1___24Anonymous__76,Vvar__1___24Anonymous__77,Vvar__2___24Anonymous__78,Vvar__2___24Anonymous__79] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__74,Vvar__1___24Anonymous__76,Vvar__2___24Anonymous__78) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__75,Vvar__1___24Anonymous__77,Vvar__2___24Anonymous__79)
=> ( Vvar__2___24Anonymous__78 = Vvar__2___24Anonymous__79
& Vvar__1___24Anonymous__76 = Vvar__1___24Anonymous__77
& Vvar__0__A__74 = Vvar__0__A__75 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__19498,Vvar__0__A__19499,Vvar__1__B__19500,Vvar__1__B__19501,Vvar__2___24Anonymous__19502,Vvar__2___24Anonymous__19503] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__19498,Vvar__1__B__19500,Vvar__2___24Anonymous__19502) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__19499,Vvar__1__B__19501,Vvar__2___24Anonymous__19503)
=> ( Vvar__2___24Anonymous__19502 = Vvar__2___24Anonymous__19503
& Vvar__1__B__19500 = Vvar__1__B__19501
& Vvar__0__A__19498 = Vvar__0__A__19499 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__19504,Vvar__0__A__19505,Vvar__1__B__19506,Vvar__1__B__19507,Vvar__2___24Anonymous__19508,Vvar__2___24Anonymous__19509] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__19504,Vvar__1__B__19506,Vvar__2___24Anonymous__19508) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__19505,Vvar__1__B__19507,Vvar__2___24Anonymous__19509)
=> ( Vvar__2___24Anonymous__19508 = Vvar__2___24Anonymous__19509
& Vvar__1__B__19506 = Vvar__1__B__19507
& Vvar__0__A__19504 = Vvar__0__A__19505 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__72,Vvar__0__A__73] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__72) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__73)
=> Vvar__0__A__72 = Vvar__0__A__73 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__54,Vvar__0__A__55,Vvar__1__B__56,Vvar__1__B__57,Vvar__2___24Anonymous__58,Vvar__2___24Anonymous__59,Vvar__3___24Anonymous__60,Vvar__3___24Anonymous__61] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__54,Vvar__1__B__56,Vvar__2___24Anonymous__58,Vvar__3___24Anonymous__60) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__55,Vvar__1__B__57,Vvar__2___24Anonymous__59,Vvar__3___24Anonymous__61)
=> ( Vvar__3___24Anonymous__60 = Vvar__3___24Anonymous__61
& Vvar__2___24Anonymous__58 = Vvar__2___24Anonymous__59
& Vvar__1__B__56 = Vvar__1__B__57
& Vvar__0__A__54 = Vvar__0__A__55 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__19638,Vvar__0___24Anonymous__19639] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__19638) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__19639)
=> Vvar__0___24Anonymous__19638 = Vvar__0___24Anonymous__19639 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__19640,Vvar__0___24Anonymous__19641] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__19640) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__19641)
=> Vvar__0___24Anonymous__19640 = Vvar__0___24Anonymous__19641 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__19642,Vvar__0___24Anonymous__19643] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__19642) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__19643)
=> Vvar__0___24Anonymous__19642 = Vvar__0___24Anonymous__19643 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__19644,Vvar__0___24Anonymous__19645] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__19644) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__19645)
=> Vvar__0___24Anonymous__19644 = Vvar__0___24Anonymous__19645 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__19646,Vvar__0___24Anonymous__19647] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__19646) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__19647)
=> Vvar__0___24Anonymous__19646 = Vvar__0___24Anonymous__19647 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__19648,Vvar__0___24Anonymous__19649] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__19648) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__19649)
=> Vvar__0___24Anonymous__19648 = Vvar__0___24Anonymous__19649 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__19650,Vvar__0___24Anonymous__19651] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__19650) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__19651)
=> Vvar__0___24Anonymous__19650 = Vvar__0___24Anonymous__19651 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__19652,Vvar__0___24Anonymous__19653] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__19652) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__19653)
=> Vvar__0___24Anonymous__19652 = Vvar__0___24Anonymous__19653 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__19654,Vvar__0___24Anonymous__19655] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__19654) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__19655)
=> Vvar__0___24Anonymous__19654 = Vvar__0___24Anonymous__19655 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__19656,Vvar__0___24Anonymous__19657] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__19656) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__19657)
=> Vvar__0___24Anonymous__19656 = Vvar__0___24Anonymous__19657 ) ).
fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
! [Vvar__0__i__30730,Vvar__0__i__30731,Vvar__1__f__30732,Vvar__1__f__30733] :
( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__30730,Vvar__1__f__30732) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__30731,Vvar__1__f__30733)
=> ( Vvar__1__f__30732 = Vvar__1__f__30733
& Vvar__0__i__30730 = Vvar__0__i__30731 ) ) ).
fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__30734,Vvar__0__i__30735,Vvar__1__f__30736,Vvar__1__f__30737,Vvar__2__e__30738,Vvar__2__e__30739] :
( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__30734,Vvar__1__f__30736,Vvar__2__e__30738) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__30735,Vvar__1__f__30737,Vvar__2__e__30739)
=> ( Vvar__2__e__30738 = Vvar__2__e__30739
& Vvar__1__f__30736 = Vvar__1__f__30737
& Vvar__0__i__30734 = Vvar__0__i__30735 ) ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__19665,Vvar__0__d__19666] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__19665) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__19666)
=> Vvar__0__d__19665 = Vvar__0__d__19666 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__19663,Vvar__0__d__19664] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__19663) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__19664)
=> Vvar__0__d__19663 = Vvar__0__d__19664 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__3648,Vvar__0__A__3649,Vvar__1__P__3650,Vvar__1__P__3651,Vvar__2__x__3652,Vvar__2__x__3653,Vvar__3___24Anonymous__3654,Vvar__3___24Anonymous__3655] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__3648,Vvar__1__P__3650,Vvar__2__x__3652) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__3649,Vvar__1__P__3651,Vvar__2__x__3653)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__3652 = Vvar__2__x__3653
& Vvar__1__P__3650 = Vvar__1__P__3651
& Vvar__0__A__3648 = Vvar__0__A__3649 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__8080,Vvar__0__A__8081,Vvar__1__P__8082,Vvar__1__P__8083,Vvar__2__Q__8084,Vvar__2__Q__8085,Vvar__3__x__8086,Vvar__3__x__8087,Vvar__4___24Anonymous__8088,Vvar__4___24Anonymous__8089,Vvar__5___24Anonymous__8090,Vvar__5___24Anonymous__8091] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__8080,Vvar__1__P__8082,Vvar__2__Q__8084,Vvar__3__x__8086) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__8081,Vvar__1__P__8083,Vvar__2__Q__8085,Vvar__3__x__8087)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__8086 = Vvar__3__x__8087
& Vvar__2__Q__8084 = Vvar__2__Q__8085
& Vvar__1__P__8082 = Vvar__1__P__8083
& Vvar__0__A__8080 = Vvar__0__A__8081 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__8135,Vvar__0__A__8136,Vvar__1__P__8137,Vvar__1__P__8138,Vvar__2__x__8139,Vvar__2__x__8140,Vvar__3___24Anonymous__8141,Vvar__3___24Anonymous__8142] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__8135,Vvar__1__P__8137,Vvar__2__x__8139,Vvar__3___24Anonymous__8141) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__8136,Vvar__1__P__8138,Vvar__2__x__8140,Vvar__3___24Anonymous__8142)
=> ( Vvar__3___24Anonymous__8141 = Vvar__3___24Anonymous__8142
& Vvar__2__x__8139 = Vvar__2__x__8140
& Vvar__1__P__8137 = Vvar__1__P__8138
& Vvar__0__A__8135 = Vvar__0__A__8136 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__18417,Vvar__0__A__18418,Vvar__1__P__18419,Vvar__1__P__18420,Vvar__2__Q__18421,Vvar__2__Q__18422,Vvar__3__x__18423,Vvar__3__x__18424,Vvar__4___24Anonymous__18425,Vvar__4___24Anonymous__18426,Vvar__5___24Anonymous__18427,Vvar__5___24Anonymous__18428] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__18417,Vvar__1__P__18419,Vvar__2__Q__18421,Vvar__3__x__18423,Vvar__4___24Anonymous__18425,Vvar__5___24Anonymous__18427) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__18418,Vvar__1__P__18420,Vvar__2__Q__18422,Vvar__3__x__18424,Vvar__4___24Anonymous__18426,Vvar__5___24Anonymous__18428)
=> ( Vvar__5___24Anonymous__18427 = Vvar__5___24Anonymous__18428
& Vvar__4___24Anonymous__18425 = Vvar__4___24Anonymous__18426
& Vvar__3__x__18423 = Vvar__3__x__18424
& Vvar__2__Q__18421 = Vvar__2__Q__18422
& Vvar__1__P__18419 = Vvar__1__P__18420
& Vvar__0__A__18417 = Vvar__0__A__18418 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__35071,Vvar__0__A__35072,Vvar__1__B__35073,Vvar__1__B__35074,Vvar__2___24Anonymous__35075,Vvar__2___24Anonymous__35076] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__35071,Vvar__1__B__35073,Vvar__2___24Anonymous__35075) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__35072,Vvar__1__B__35074,Vvar__2___24Anonymous__35076)
=> ( Vvar__2___24Anonymous__35075 = Vvar__2___24Anonymous__35076
& Vvar__1__B__35073 = Vvar__1__B__35074
& Vvar__0__A__35071 = Vvar__0__A__35072 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__35077,Vvar__0__A__35078,Vvar__1__B__35079,Vvar__1__B__35080,Vvar__2___24Anonymous__35081,Vvar__2___24Anonymous__35082] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__35077,Vvar__1__B__35079) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__35078,Vvar__1__B__35080)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__35079 = Vvar__1__B__35080
& Vvar__0__A__35077 = Vvar__0__A__35078 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__10135,Vvar__0__A__10136,Vvar__1__B__10137,Vvar__1__B__10138,Vvar__2___24Anonymous__10139,Vvar__2___24Anonymous__10140] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__10135,Vvar__1__B__10137) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__10136,Vvar__1__B__10138)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__10137 = Vvar__1__B__10138
& Vvar__0__A__10135 = Vvar__0__A__10136 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__10141,Vvar__0__A__10142,Vvar__1__B__10143,Vvar__1__B__10144,Vvar__2___24Anonymous__10145,Vvar__2___24Anonymous__10146] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__10141,Vvar__1__B__10143) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__10142,Vvar__1__B__10144)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__10143 = Vvar__1__B__10144
& Vvar__0__A__10141 = Vvar__0__A__10142 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__3857,Vvar__0___24Anonymous__3858] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3857) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3858)
=> Vvar__0___24Anonymous__3857 = Vvar__0___24Anonymous__3858 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__1765,Vvar__0___24Anonymous__1766] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1765) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1766)
=> Vvar__0___24Anonymous__1765 = Vvar__0___24Anonymous__1766 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1763,Vvar__0___24Anonymous__1764] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1763) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1764)
=> Vvar__0___24Anonymous__1763 = Vvar__0___24Anonymous__1764 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__1750,Vvar__0___24Anonymous__1751] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1750) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1751)
=> Vvar__0___24Anonymous__1750 = Vvar__0___24Anonymous__1751 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1752,Vvar__0___24Anonymous__1753] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1752) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1753)
=> Vvar__0___24Anonymous__1752 = Vvar__0___24Anonymous__1753 ) ).
fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__35479,Vvar__0__p__35480,Vvar__1___24Anonymous__35481,Vvar__1___24Anonymous__35482] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__35479,Vvar__1___24Anonymous__35481) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__35480,Vvar__1___24Anonymous__35482)
=> ( Vvar__1___24Anonymous__35481 = Vvar__1___24Anonymous__35482
& Vvar__0__p__35479 = Vvar__0__p__35480 ) ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__11125,Vvar__0___24Anonymous__11126] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__11125) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__11126)
=> Vvar__0___24Anonymous__11125 = Vvar__0___24Anonymous__11126 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__7479,Vvar__0__Qnum__7480,Vvar__1__Qden__7481,Vvar__1__Qden__7482] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__7479,Vvar__1__Qden__7481) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__7480,Vvar__1__Qden__7482)
=> ( Vvar__1__Qden__7481 = Vvar__1__Qden__7482
& Vvar__0__Qnum__7479 = Vvar__0__Qnum__7480 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
! [Vvar__0__neg__33457,Vvar__0__neg__33458,Vvar__1__cond__neg__33459,Vvar__1__cond__neg__33460] :
( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__33457) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__33458)
=> ( c_24Proof = c_24Proof
& Vvar__0__neg__33457 = Vvar__0__neg__33458 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__33436,Vvar__0__nonneg__33437,Vvar__1__cond__nonneg__33438,Vvar__1__cond__nonneg__33439] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__33436) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__33437)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__33436 = Vvar__0__nonneg__33437 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
! [Vvar__0__nonpos__33450,Vvar__0__nonpos__33451,Vvar__1__cond__nonpos__33452,Vvar__1__cond__nonpos__33453] :
( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__33450) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__33451)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonpos__33450 = Vvar__0__nonpos__33451 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__33464,Vvar__0__nonzero__33465,Vvar__1__cond__nonzero__33466,Vvar__1__cond__nonzero__33467] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__33464) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__33465)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__33464 = Vvar__0__nonzero__33465 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__33443,Vvar__0__pos__33444,Vvar__1__cond__pos__33445,Vvar__1__cond__pos__33446] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__33443) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__33444)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__33443 = Vvar__0__pos__33444 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__34227,Vvar__0__x__34228,Vvar__1__n__34229,Vvar__1__n__34230,Vvar__2___24Anonymous__34231,Vvar__2___24Anonymous__34232] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__34227,Vvar__1__n__34229) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__34228,Vvar__1__n__34230)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__34229 = Vvar__1__n__34230
& Vvar__0__x__34227 = Vvar__0__x__34228 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__34217,Vvar__0__x__34218,Vvar__1___24Anonymous__34219,Vvar__1___24Anonymous__34220] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__34217) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__34218)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__34217 = Vvar__0__x__34218 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__34221,Vvar__0__x__34222,Vvar__1__n__34223,Vvar__1__n__34224,Vvar__2___24Anonymous__34225,Vvar__2___24Anonymous__34226] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__34221,Vvar__1__n__34223) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__34222,Vvar__1__n__34224)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__34223 = Vvar__1__n__34224
& Vvar__0__x__34221 = Vvar__0__x__34222 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__5478,Vvar__0___24Anonymous__5479,Vvar__1___24Anonymous__5480,Vvar__1___24Anonymous__5481,Vvar__2___24Anonymous__5482,Vvar__2___24Anonymous__5483,Vvar__3___24Anonymous__5484,Vvar__3___24Anonymous__5485,Vvar__4___24Anonymous__5486,Vvar__4___24Anonymous__5487,Vvar__5___24Anonymous__5488,Vvar__5___24Anonymous__5489,Vvar__6___24Anonymous__5490,Vvar__6___24Anonymous__5491,Vvar__7___24Anonymous__5492,Vvar__7___24Anonymous__5493] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__5478,Vvar__1___24Anonymous__5480,Vvar__2___24Anonymous__5482,Vvar__3___24Anonymous__5484,Vvar__4___24Anonymous__5486,Vvar__5___24Anonymous__5488,Vvar__6___24Anonymous__5490,Vvar__7___24Anonymous__5492) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__5479,Vvar__1___24Anonymous__5481,Vvar__2___24Anonymous__5483,Vvar__3___24Anonymous__5485,Vvar__4___24Anonymous__5487,Vvar__5___24Anonymous__5489,Vvar__6___24Anonymous__5491,Vvar__7___24Anonymous__5493)
=> ( Vvar__7___24Anonymous__5492 = Vvar__7___24Anonymous__5493
& Vvar__6___24Anonymous__5490 = Vvar__6___24Anonymous__5491
& Vvar__5___24Anonymous__5488 = Vvar__5___24Anonymous__5489
& Vvar__4___24Anonymous__5486 = Vvar__4___24Anonymous__5487
& Vvar__3___24Anonymous__5484 = Vvar__3___24Anonymous__5485
& Vvar__2___24Anonymous__5482 = Vvar__2___24Anonymous__5483
& Vvar__1___24Anonymous__5480 = Vvar__1___24Anonymous__5481
& Vvar__0___24Anonymous__5478 = Vvar__0___24Anonymous__5479 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__18456,Vvar__0___24Anonymous__18457,Vvar__1___24Anonymous__18458,Vvar__1___24Anonymous__18459] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__18456,Vvar__1___24Anonymous__18458) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__18457,Vvar__1___24Anonymous__18459)
=> ( Vvar__1___24Anonymous__18458 = Vvar__1___24Anonymous__18459
& Vvar__0___24Anonymous__18456 = Vvar__0___24Anonymous__18457 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__33405,Vvar__0__X__33406,Vvar__1__lt__33407,Vvar__1__lt__33408,Vvar__2__eq__33409,Vvar__2__eq__33410,Vvar__3__x__33411,Vvar__3__x__33412,Vvar__4__y__33413,Vvar__4__y__33414,Vvar__5___24Anonymous__33415,Vvar__5___24Anonymous__33416] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__33405,Vvar__1__lt__33407,Vvar__2__eq__33409,Vvar__3__x__33411,Vvar__4__y__33413) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__33406,Vvar__1__lt__33408,Vvar__2__eq__33410,Vvar__3__x__33412,Vvar__4__y__33414)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__33413 = Vvar__4__y__33414
& Vvar__3__x__33411 = Vvar__3__x__33412
& Vvar__2__eq__33409 = Vvar__2__eq__33410
& Vvar__1__lt__33407 = Vvar__1__lt__33408
& Vvar__0__X__33405 = Vvar__0__X__33406 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__33417,Vvar__0__X__33418,Vvar__1__lt__33419,Vvar__1__lt__33420,Vvar__2__eq__33421,Vvar__2__eq__33422,Vvar__3__x__33423,Vvar__3__x__33424,Vvar__4__y__33425,Vvar__4__y__33426,Vvar__5___24Anonymous__33427,Vvar__5___24Anonymous__33428] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__33417,Vvar__1__lt__33419,Vvar__2__eq__33421,Vvar__3__x__33423,Vvar__4__y__33425) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__33418,Vvar__1__lt__33420,Vvar__2__eq__33422,Vvar__3__x__33424,Vvar__4__y__33426)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__33425 = Vvar__4__y__33426
& Vvar__3__x__33423 = Vvar__3__x__33424
& Vvar__2__eq__33421 = Vvar__2__eq__33422
& Vvar__1__lt__33419 = Vvar__1__lt__33420
& Vvar__0__X__33417 = Vvar__0__X__33418 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__33393,Vvar__0__X__33394,Vvar__1__lt__33395,Vvar__1__lt__33396,Vvar__2__eq__33397,Vvar__2__eq__33398,Vvar__3__x__33399,Vvar__3__x__33400,Vvar__4__y__33401,Vvar__4__y__33402,Vvar__5___24Anonymous__33403,Vvar__5___24Anonymous__33404] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__33393,Vvar__1__lt__33395,Vvar__2__eq__33397,Vvar__3__x__33399,Vvar__4__y__33401) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__33394,Vvar__1__lt__33396,Vvar__2__eq__33398,Vvar__3__x__33400,Vvar__4__y__33402)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__33401 = Vvar__4__y__33402
& Vvar__3__x__33399 = Vvar__3__x__33400
& Vvar__2__eq__33397 = Vvar__2__eq__33398
& Vvar__1__lt__33395 = Vvar__1__lt__33396
& Vvar__0__X__33393 = Vvar__0__X__33394 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__6764,Vvar__0__n__6765] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__6764) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__6765)
=> Vvar__0__n__6764 = Vvar__0__n__6765 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__6766,Vvar__0__n__6767,Vvar__1___24Anonymous__6768,Vvar__1___24Anonymous__6769] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__6766,Vvar__1___24Anonymous__6768) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__6767,Vvar__1___24Anonymous__6769)
=> ( Vvar__1___24Anonymous__6768 = Vvar__1___24Anonymous__6769
& Vvar__0__n__6766 = Vvar__0__n__6767 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__10175,Vvar__0__A__10176,Vvar__1__h__10177,Vvar__1__h__10178,Vvar__2__n__10179,Vvar__2__n__10180,Vvar__3___24Anonymous__10181,Vvar__3___24Anonymous__10182] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__10175,Vvar__1__h__10177,Vvar__2__n__10179,Vvar__3___24Anonymous__10181) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__10176,Vvar__1__h__10178,Vvar__2__n__10180,Vvar__3___24Anonymous__10182)
=> ( Vvar__3___24Anonymous__10181 = Vvar__3___24Anonymous__10182
& Vvar__2__n__10179 = Vvar__2__n__10180
& Vvar__1__h__10177 = Vvar__1__h__10178
& Vvar__0__A__10175 = Vvar__0__A__10176 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__10173,Vvar__0__A__10174] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__10173) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__10174)
=> Vvar__0__A__10173 = Vvar__0__A__10174 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__35218,Vvar__0__a__35219,Vvar__1__b__35220,Vvar__1__b__35221,Vvar__2__u__35222,Vvar__2__u__35223,Vvar__3__v__35224,Vvar__3__v__35225,Vvar__4__d__35226,Vvar__4__d__35227,Vvar__5___24Anonymous__35228,Vvar__5___24Anonymous__35229,Vvar__6___24Anonymous__35230,Vvar__6___24Anonymous__35231] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__35218,Vvar__1__b__35220,Vvar__2__u__35222,Vvar__3__v__35224,Vvar__4__d__35226) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__35219,Vvar__1__b__35221,Vvar__2__u__35223,Vvar__3__v__35225,Vvar__4__d__35227)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__35226 = Vvar__4__d__35227
& Vvar__3__v__35224 = Vvar__3__v__35225
& Vvar__2__u__35222 = Vvar__2__u__35223
& Vvar__1__b__35220 = Vvar__1__b__35221
& Vvar__0__a__35218 = Vvar__0__a__35219 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__35266,Vvar__0__x__35267,Vvar__1__p__35268,Vvar__1__p__35269,Vvar__2__q__35270,Vvar__2__q__35271,Vvar__3__r__35272,Vvar__3__r__35273,Vvar__4___24Anonymous__35274,Vvar__4___24Anonymous__35275,Vvar__5___24Anonymous__35276,Vvar__5___24Anonymous__35277,Vvar__6___24Anonymous__35278,Vvar__6___24Anonymous__35279] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__35266,Vvar__1__p__35268,Vvar__2__q__35270,Vvar__3__r__35272) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__35267,Vvar__1__p__35269,Vvar__2__q__35271,Vvar__3__r__35273)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__35272 = Vvar__3__r__35273
& Vvar__2__q__35270 = Vvar__2__q__35271
& Vvar__1__p__35268 = Vvar__1__p__35269
& Vvar__0__x__35266 = Vvar__0__x__35267 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__12092,Vvar__0__C__12093,Vvar__1___24Anonymous__12094,Vvar__1___24Anonymous__12095] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__12092,Vvar__1___24Anonymous__12094) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__12093,Vvar__1___24Anonymous__12095)
=> ( Vvar__1___24Anonymous__12094 = Vvar__1___24Anonymous__12095
& Vvar__0__C__12092 = Vvar__0__C__12093 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__12096,Vvar__0__C__12097,Vvar__1___24Anonymous__12098,Vvar__1___24Anonymous__12099,Vvar__2___24Anonymous__12100,Vvar__2___24Anonymous__12101] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__12096,Vvar__1___24Anonymous__12098,Vvar__2___24Anonymous__12100) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__12097,Vvar__1___24Anonymous__12099,Vvar__2___24Anonymous__12101)
=> ( Vvar__2___24Anonymous__12100 = Vvar__2___24Anonymous__12101
& Vvar__1___24Anonymous__12098 = Vvar__1___24Anonymous__12099
& Vvar__0__C__12096 = Vvar__0__C__12097 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__12088,Vvar__0__C__12089,Vvar__1___24Anonymous__12090,Vvar__1___24Anonymous__12091] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__12088,Vvar__1___24Anonymous__12090) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__12089,Vvar__1___24Anonymous__12091)
=> ( Vvar__1___24Anonymous__12090 = Vvar__1___24Anonymous__12091
& Vvar__0__C__12088 = Vvar__0__C__12089 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__12108,Vvar__0__C__12109,Vvar__1___24Anonymous__12110,Vvar__1___24Anonymous__12111,Vvar__2___24Anonymous__12112,Vvar__2___24Anonymous__12113] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__12108,Vvar__1___24Anonymous__12110,Vvar__2___24Anonymous__12112) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__12109,Vvar__1___24Anonymous__12111,Vvar__2___24Anonymous__12113)
=> ( Vvar__2___24Anonymous__12112 = Vvar__2___24Anonymous__12113
& Vvar__1___24Anonymous__12110 = Vvar__1___24Anonymous__12111
& Vvar__0__C__12108 = Vvar__0__C__12109 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__12114,Vvar__0__C__12115,Vvar__1___24Anonymous__12116,Vvar__1___24Anonymous__12117] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__12114,Vvar__1___24Anonymous__12116) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__12115,Vvar__1___24Anonymous__12117)
=> ( Vvar__1___24Anonymous__12116 = Vvar__1___24Anonymous__12117
& Vvar__0__C__12114 = Vvar__0__C__12115 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__12118,Vvar__0__C__12119,Vvar__1___24Anonymous__12120,Vvar__1___24Anonymous__12121,Vvar__2___24Anonymous__12122,Vvar__2___24Anonymous__12123] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__12118,Vvar__1___24Anonymous__12120,Vvar__2___24Anonymous__12122) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__12119,Vvar__1___24Anonymous__12121,Vvar__2___24Anonymous__12123)
=> ( Vvar__2___24Anonymous__12122 = Vvar__2___24Anonymous__12123
& Vvar__1___24Anonymous__12120 = Vvar__1___24Anonymous__12121
& Vvar__0__C__12118 = Vvar__0__C__12119 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__12102,Vvar__0__C__12103,Vvar__1___24Anonymous__12104,Vvar__1___24Anonymous__12105,Vvar__2___24Anonymous__12106,Vvar__2___24Anonymous__12107] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__12102,Vvar__1___24Anonymous__12104,Vvar__2___24Anonymous__12106) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__12103,Vvar__1___24Anonymous__12105,Vvar__2___24Anonymous__12107)
=> ( Vvar__2___24Anonymous__12106 = Vvar__2___24Anonymous__12107
& Vvar__1___24Anonymous__12104 = Vvar__1___24Anonymous__12105
& Vvar__0__C__12102 = Vvar__0__C__12103 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__12163,Vvar__0__C__12164,Vvar__1___24Anonymous__12165,Vvar__1___24Anonymous__12166,Vvar__2___24Anonymous__12167,Vvar__2___24Anonymous__12168,Vvar__3___24Anonymous__12169,Vvar__3___24Anonymous__12170] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__12163,Vvar__1___24Anonymous__12165,Vvar__2___24Anonymous__12167,Vvar__3___24Anonymous__12169) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__12164,Vvar__1___24Anonymous__12166,Vvar__2___24Anonymous__12168,Vvar__3___24Anonymous__12170)
=> ( Vvar__3___24Anonymous__12169 = Vvar__3___24Anonymous__12170
& Vvar__2___24Anonymous__12167 = Vvar__2___24Anonymous__12168
& Vvar__1___24Anonymous__12165 = Vvar__1___24Anonymous__12166
& Vvar__0__C__12163 = Vvar__0__C__12164 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__12153,Vvar__0__C__12154,Vvar__1___24Anonymous__12155,Vvar__1___24Anonymous__12156] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__12153,Vvar__1___24Anonymous__12155) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__12154,Vvar__1___24Anonymous__12156)
=> ( Vvar__1___24Anonymous__12155 = Vvar__1___24Anonymous__12156
& Vvar__0__C__12153 = Vvar__0__C__12154 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__12157,Vvar__0__C__12158,Vvar__1___24Anonymous__12159,Vvar__1___24Anonymous__12160,Vvar__2___24Anonymous__12161,Vvar__2___24Anonymous__12162] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__12157,Vvar__1___24Anonymous__12159,Vvar__2___24Anonymous__12161) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__12158,Vvar__1___24Anonymous__12160,Vvar__2___24Anonymous__12162)
=> ( Vvar__2___24Anonymous__12161 = Vvar__2___24Anonymous__12162
& Vvar__1___24Anonymous__12159 = Vvar__1___24Anonymous__12160
& Vvar__0__C__12157 = Vvar__0__C__12158 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__30767,Vvar__0___24Anonymous__30768,Vvar__1___24Anonymous__30769,Vvar__1___24Anonymous__30770] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__30767,Vvar__1___24Anonymous__30769) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__30768,Vvar__1___24Anonymous__30770)
=> ( Vvar__1___24Anonymous__30769 = Vvar__1___24Anonymous__30770
& Vvar__0___24Anonymous__30767 = Vvar__0___24Anonymous__30768 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__30763,Vvar__0___24Anonymous__30764,Vvar__1___24Anonymous__30765,Vvar__1___24Anonymous__30766] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__30763,Vvar__1___24Anonymous__30765) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__30764,Vvar__1___24Anonymous__30766)
=> ( Vvar__1___24Anonymous__30765 = Vvar__1___24Anonymous__30766
& Vvar__0___24Anonymous__30763 = Vvar__0___24Anonymous__30764 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__12714,Vvar__0__r__12715] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__12714) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__12715)
=> Vvar__0__r__12714 = Vvar__0__r__12715 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__12702,Vvar__0__r1__12703,Vvar__1__r2__12704,Vvar__1__r2__12705] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__12702,Vvar__1__r2__12704) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__12703,Vvar__1__r2__12705)
=> ( Vvar__1__r2__12704 = Vvar__1__r2__12705
& Vvar__0__r1__12702 = Vvar__0__r1__12703 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__12706,Vvar__0__r1__12707,Vvar__1__r2__12708,Vvar__1__r2__12709] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__12706,Vvar__1__r2__12708) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__12707,Vvar__1__r2__12709)
=> ( Vvar__1__r2__12708 = Vvar__1__r2__12709
& Vvar__0__r1__12706 = Vvar__0__r1__12707 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__12716,Vvar__0__r__12717] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__12716) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__12717)
=> Vvar__0__r__12716 = Vvar__0__r__12717 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__12698,Vvar__0__r1__12699,Vvar__1__r2__12700,Vvar__1__r2__12701] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__12698,Vvar__1__r2__12700) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__12699,Vvar__1__r2__12701)
=> ( Vvar__1__r2__12700 = Vvar__1__r2__12701
& Vvar__0__r1__12698 = Vvar__0__r1__12699 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__12710,Vvar__0__r1__12711,Vvar__1__z__12712,Vvar__1__z__12713] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__12710,Vvar__1__z__12712) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__12711,Vvar__1__z__12713)
=> ( Vvar__1__z__12712 = Vvar__1__z__12713
& Vvar__0__r1__12710 = Vvar__0__r1__12711 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__12694,Vvar__0__r__12695] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__12694) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__12695)
=> Vvar__0__r__12694 = Vvar__0__r__12695 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__12696,Vvar__0__r__12697] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__12696) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__12697)
=> Vvar__0__r__12696 = Vvar__0__r__12697 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__18135,Vvar__0__T__18136,Vvar__1__Flhs__18137,Vvar__1__Flhs__18138,Vvar__2__Fop__18139,Vvar__2__Fop__18140,Vvar__3__Frhs__18141,Vvar__3__Frhs__18142] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__18135,Vvar__1__Flhs__18137,Vvar__2__Fop__18139,Vvar__3__Frhs__18141) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__18136,Vvar__1__Flhs__18138,Vvar__2__Fop__18140,Vvar__3__Frhs__18142)
=> ( Vvar__3__Frhs__18141 = Vvar__3__Frhs__18142
& Vvar__2__Fop__18139 = Vvar__2__Fop__18140
& Vvar__1__Flhs__18137 = Vvar__1__Flhs__18138
& Vvar__0__T__18135 = Vvar__0__T__18136 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__21251,Vvar__0__C__21252,Vvar__1___24Anonymous__21253,Vvar__1___24Anonymous__21254,Vvar__2___24Anonymous__21255,Vvar__2___24Anonymous__21256] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__21251,Vvar__1___24Anonymous__21253,Vvar__2___24Anonymous__21255) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__21252,Vvar__1___24Anonymous__21254,Vvar__2___24Anonymous__21256)
=> ( Vvar__2___24Anonymous__21255 = Vvar__2___24Anonymous__21256
& Vvar__1___24Anonymous__21253 = Vvar__1___24Anonymous__21254
& Vvar__0__C__21251 = Vvar__0__C__21252 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__21257,Vvar__0__C__21258,Vvar__1___24Anonymous__21259,Vvar__1___24Anonymous__21260] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__21257,Vvar__1___24Anonymous__21259) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__21258,Vvar__1___24Anonymous__21260)
=> ( Vvar__1___24Anonymous__21259 = Vvar__1___24Anonymous__21260
& Vvar__0__C__21257 = Vvar__0__C__21258 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__21231,Vvar__0__C__21232,Vvar__1___24Anonymous__21233,Vvar__1___24Anonymous__21234] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__21231,Vvar__1___24Anonymous__21233) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__21232,Vvar__1___24Anonymous__21234)
=> ( Vvar__1___24Anonymous__21233 = Vvar__1___24Anonymous__21234
& Vvar__0__C__21231 = Vvar__0__C__21232 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__21239,Vvar__0__C__21240,Vvar__1___24Anonymous__21241,Vvar__1___24Anonymous__21242,Vvar__2___24Anonymous__21243,Vvar__2___24Anonymous__21244] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__21239,Vvar__1___24Anonymous__21241,Vvar__2___24Anonymous__21243) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__21240,Vvar__1___24Anonymous__21242,Vvar__2___24Anonymous__21244)
=> ( Vvar__2___24Anonymous__21243 = Vvar__2___24Anonymous__21244
& Vvar__1___24Anonymous__21241 = Vvar__1___24Anonymous__21242
& Vvar__0__C__21239 = Vvar__0__C__21240 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__21245,Vvar__0__C__21246,Vvar__1___24Anonymous__21247,Vvar__1___24Anonymous__21248,Vvar__2___24Anonymous__21249,Vvar__2___24Anonymous__21250] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__21245,Vvar__1___24Anonymous__21247,Vvar__2___24Anonymous__21249) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__21246,Vvar__1___24Anonymous__21248,Vvar__2___24Anonymous__21250)
=> ( Vvar__2___24Anonymous__21249 = Vvar__2___24Anonymous__21250
& Vvar__1___24Anonymous__21247 = Vvar__1___24Anonymous__21248
& Vvar__0__C__21245 = Vvar__0__C__21246 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__21235,Vvar__0__C__21236,Vvar__1___24Anonymous__21237,Vvar__1___24Anonymous__21238] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__21235,Vvar__1___24Anonymous__21237) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__21236,Vvar__1___24Anonymous__21238)
=> ( Vvar__1___24Anonymous__21237 = Vvar__1___24Anonymous__21238
& Vvar__0__C__21235 = Vvar__0__C__21236 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__21261,Vvar__0__C__21262] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__21261) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__21262)
=> Vvar__0__C__21261 = Vvar__0__C__21262 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__5062,Vvar__0__TA__5063,Vvar__1__TX__5064,Vvar__1__TX__5065,Vvar__2__AA__5066,Vvar__2__AA__5067,Vvar__3__AF__5068,Vvar__3__AF__5069,Vvar__4___24Anonymous__5070,Vvar__4___24Anonymous__5071,Vvar__5___24Anonymous__5072,Vvar__5___24Anonymous__5073] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__5062,Vvar__1__TX__5064,Vvar__2__AA__5066,Vvar__3__AF__5068,Vvar__4___24Anonymous__5070,Vvar__5___24Anonymous__5072) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__5063,Vvar__1__TX__5065,Vvar__2__AA__5067,Vvar__3__AF__5069,Vvar__4___24Anonymous__5071,Vvar__5___24Anonymous__5073)
=> ( Vvar__5___24Anonymous__5072 = Vvar__5___24Anonymous__5073
& Vvar__4___24Anonymous__5070 = Vvar__4___24Anonymous__5071
& Vvar__3__AF__5068 = Vvar__3__AF__5069
& Vvar__2__AA__5066 = Vvar__2__AA__5067
& Vvar__1__TX__5064 = Vvar__1__TX__5065
& Vvar__0__TA__5062 = Vvar__0__TA__5063 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__5074,Vvar__0__TA__5075,Vvar__1__TX__5076,Vvar__1__TX__5077,Vvar__2__AA__5078,Vvar__2__AA__5079,Vvar__3__AF__5080,Vvar__3__AF__5081,Vvar__4___24Anonymous__5082,Vvar__4___24Anonymous__5083,Vvar__5___24Anonymous__5084,Vvar__5___24Anonymous__5085] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__5074,Vvar__1__TX__5076,Vvar__2__AA__5078,Vvar__3__AF__5080,Vvar__4___24Anonymous__5082,Vvar__5___24Anonymous__5084) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__5075,Vvar__1__TX__5077,Vvar__2__AA__5079,Vvar__3__AF__5081,Vvar__4___24Anonymous__5083,Vvar__5___24Anonymous__5085)
=> ( Vvar__5___24Anonymous__5084 = Vvar__5___24Anonymous__5085
& Vvar__4___24Anonymous__5082 = Vvar__4___24Anonymous__5083
& Vvar__3__AF__5080 = Vvar__3__AF__5081
& Vvar__2__AA__5078 = Vvar__2__AA__5079
& Vvar__1__TX__5076 = Vvar__1__TX__5077
& Vvar__0__TA__5074 = Vvar__0__TA__5075 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__5086,Vvar__0__TA__5087,Vvar__1__TX__5088,Vvar__1__TX__5089,Vvar__2__AA__5090,Vvar__2__AA__5091,Vvar__3__AF__5092,Vvar__3__AF__5093,Vvar__4___24Anonymous__5094,Vvar__4___24Anonymous__5095,Vvar__5___24Anonymous__5096,Vvar__5___24Anonymous__5097] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__5086,Vvar__1__TX__5088,Vvar__2__AA__5090,Vvar__3__AF__5092,Vvar__4___24Anonymous__5094,Vvar__5___24Anonymous__5096) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__5087,Vvar__1__TX__5089,Vvar__2__AA__5091,Vvar__3__AF__5093,Vvar__4___24Anonymous__5095,Vvar__5___24Anonymous__5097)
=> ( Vvar__5___24Anonymous__5096 = Vvar__5___24Anonymous__5097
& Vvar__4___24Anonymous__5094 = Vvar__4___24Anonymous__5095
& Vvar__3__AF__5092 = Vvar__3__AF__5093
& Vvar__2__AA__5090 = Vvar__2__AA__5091
& Vvar__1__TX__5088 = Vvar__1__TX__5089
& Vvar__0__TA__5086 = Vvar__0__TA__5087 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__5044,Vvar__0__TA__5045,Vvar__1__TX__5046,Vvar__1__TX__5047,Vvar__2__AA__5048,Vvar__2__AA__5049,Vvar__3__AF__5050,Vvar__3__AF__5051] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__5044,Vvar__1__TX__5046,Vvar__2__AA__5048,Vvar__3__AF__5050) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__5045,Vvar__1__TX__5047,Vvar__2__AA__5049,Vvar__3__AF__5051)
=> ( Vvar__3__AF__5050 = Vvar__3__AF__5051
& Vvar__2__AA__5048 = Vvar__2__AA__5049
& Vvar__1__TX__5046 = Vvar__1__TX__5047
& Vvar__0__TA__5044 = Vvar__0__TA__5045 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__5108,Vvar__0__TA__5109,Vvar__1__TX__5110,Vvar__1__TX__5111,Vvar__2__AA__5112,Vvar__2__AA__5113,Vvar__3__AF__5114,Vvar__3__AF__5115,Vvar__4___24Anonymous__5116,Vvar__4___24Anonymous__5117,Vvar__5___24Anonymous__5118,Vvar__5___24Anonymous__5119,Vvar__6___24Anonymous__5120,Vvar__6___24Anonymous__5121] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__5108,Vvar__1__TX__5110,Vvar__2__AA__5112,Vvar__3__AF__5114,Vvar__4___24Anonymous__5116,Vvar__5___24Anonymous__5118,Vvar__6___24Anonymous__5120) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__5109,Vvar__1__TX__5111,Vvar__2__AA__5113,Vvar__3__AF__5115,Vvar__4___24Anonymous__5117,Vvar__5___24Anonymous__5119,Vvar__6___24Anonymous__5121)
=> ( Vvar__6___24Anonymous__5120 = Vvar__6___24Anonymous__5121
& Vvar__5___24Anonymous__5118 = Vvar__5___24Anonymous__5119
& Vvar__4___24Anonymous__5116 = Vvar__4___24Anonymous__5117
& Vvar__3__AF__5114 = Vvar__3__AF__5115
& Vvar__2__AA__5112 = Vvar__2__AA__5113
& Vvar__1__TX__5110 = Vvar__1__TX__5111
& Vvar__0__TA__5108 = Vvar__0__TA__5109 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__5098,Vvar__0__TA__5099,Vvar__1__TX__5100,Vvar__1__TX__5101,Vvar__2__AA__5102,Vvar__2__AA__5103,Vvar__3__AF__5104,Vvar__3__AF__5105,Vvar__4___24Anonymous__5106,Vvar__4___24Anonymous__5107] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__5098,Vvar__1__TX__5100,Vvar__2__AA__5102,Vvar__3__AF__5104,Vvar__4___24Anonymous__5106) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__5099,Vvar__1__TX__5101,Vvar__2__AA__5103,Vvar__3__AF__5105,Vvar__4___24Anonymous__5107)
=> ( Vvar__4___24Anonymous__5106 = Vvar__4___24Anonymous__5107
& Vvar__3__AF__5104 = Vvar__3__AF__5105
& Vvar__2__AA__5102 = Vvar__2__AA__5103
& Vvar__1__TX__5100 = Vvar__1__TX__5101
& Vvar__0__TA__5098 = Vvar__0__TA__5099 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__5036,Vvar__0__TA__5037,Vvar__1__TX__5038,Vvar__1__TX__5039,Vvar__2__AA__5040,Vvar__2__AA__5041,Vvar__3__AF__5042,Vvar__3__AF__5043] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__5036,Vvar__1__TX__5038,Vvar__2__AA__5040,Vvar__3__AF__5042) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__5037,Vvar__1__TX__5039,Vvar__2__AA__5041,Vvar__3__AF__5043)
=> ( Vvar__3__AF__5042 = Vvar__3__AF__5043
& Vvar__2__AA__5040 = Vvar__2__AA__5041
& Vvar__1__TX__5038 = Vvar__1__TX__5039
& Vvar__0__TA__5036 = Vvar__0__TA__5037 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__5052,Vvar__0__TA__5053,Vvar__1__TX__5054,Vvar__1__TX__5055,Vvar__2__AA__5056,Vvar__2__AA__5057,Vvar__3__AF__5058,Vvar__3__AF__5059,Vvar__4___24Anonymous__5060,Vvar__4___24Anonymous__5061] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__5052,Vvar__1__TX__5054,Vvar__2__AA__5056,Vvar__3__AF__5058,Vvar__4___24Anonymous__5060) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__5053,Vvar__1__TX__5055,Vvar__2__AA__5057,Vvar__3__AF__5059,Vvar__4___24Anonymous__5061)
=> ( Vvar__4___24Anonymous__5060 = Vvar__4___24Anonymous__5061
& Vvar__3__AF__5058 = Vvar__3__AF__5059
& Vvar__2__AA__5056 = Vvar__2__AA__5057
& Vvar__1__TX__5054 = Vvar__1__TX__5055
& Vvar__0__TA__5052 = Vvar__0__TA__5053 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__35116,Vvar__0__A__35117,Vvar__1___24Anonymous__35118,Vvar__1___24Anonymous__35119,Vvar__2___24Anonymous__35120,Vvar__2___24Anonymous__35121,Vvar__3___24Anonymous__35122,Vvar__3___24Anonymous__35123] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__35116,Vvar__1___24Anonymous__35118,Vvar__2___24Anonymous__35120,Vvar__3___24Anonymous__35122) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__35117,Vvar__1___24Anonymous__35119,Vvar__2___24Anonymous__35121,Vvar__3___24Anonymous__35123)
=> ( Vvar__3___24Anonymous__35122 = Vvar__3___24Anonymous__35123
& Vvar__2___24Anonymous__35120 = Vvar__2___24Anonymous__35121
& Vvar__1___24Anonymous__35118 = Vvar__1___24Anonymous__35119
& Vvar__0__A__35116 = Vvar__0__A__35117 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__35112,Vvar__0__A__35113,Vvar__1___24Anonymous__35114,Vvar__1___24Anonymous__35115] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__35112,Vvar__1___24Anonymous__35114) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__35113,Vvar__1___24Anonymous__35115)
=> ( Vvar__1___24Anonymous__35114 = Vvar__1___24Anonymous__35115
& Vvar__0__A__35112 = Vvar__0__A__35113 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__35110,Vvar__0__A__35111] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__35110) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__35111)
=> Vvar__0__A__35110 = Vvar__0__A__35111 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__35157,Vvar__0___24Anonymous__35158,Vvar__1___24Anonymous__35159,Vvar__1___24Anonymous__35160] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__35157,Vvar__1___24Anonymous__35159) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__35158,Vvar__1___24Anonymous__35160)
=> ( Vvar__1___24Anonymous__35159 = Vvar__1___24Anonymous__35160
& Vvar__0___24Anonymous__35157 = Vvar__0___24Anonymous__35158 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__35161,Vvar__0___24Anonymous__35162,Vvar__1___24Anonymous__35163,Vvar__1___24Anonymous__35164,Vvar__2___24Anonymous__35165,Vvar__2___24Anonymous__35166] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__35161,Vvar__1___24Anonymous__35163,Vvar__2___24Anonymous__35165) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__35162,Vvar__1___24Anonymous__35164,Vvar__2___24Anonymous__35166)
=> ( Vvar__2___24Anonymous__35165 = Vvar__2___24Anonymous__35166
& Vvar__1___24Anonymous__35163 = Vvar__1___24Anonymous__35164
& Vvar__0___24Anonymous__35161 = Vvar__0___24Anonymous__35162 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__35153,Vvar__0___24Anonymous__35154,Vvar__1___24Anonymous__35155,Vvar__1___24Anonymous__35156] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__35153,Vvar__1___24Anonymous__35155) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__35154,Vvar__1___24Anonymous__35156)
=> ( Vvar__1___24Anonymous__35155 = Vvar__1___24Anonymous__35156
& Vvar__0___24Anonymous__35153 = Vvar__0___24Anonymous__35154 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__31814,Vvar__0__C__31815] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__31814) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__31815)
=> Vvar__0__C__31814 = Vvar__0__C__31815 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__31812,Vvar__0__C__31813] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__31812) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__31813)
=> Vvar__0__C__31812 = Vvar__0__C__31813 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__31820,Vvar__0__C__31821,Vvar__1___24Anonymous__31822,Vvar__1___24Anonymous__31823] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__31820,Vvar__1___24Anonymous__31822) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__31821,Vvar__1___24Anonymous__31823)
=> ( Vvar__1___24Anonymous__31822 = Vvar__1___24Anonymous__31823
& Vvar__0__C__31820 = Vvar__0__C__31821 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__31824,Vvar__0__C__31825,Vvar__1___24Anonymous__31826,Vvar__1___24Anonymous__31827,Vvar__2___24Anonymous__31828,Vvar__2___24Anonymous__31829] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__31824,Vvar__1___24Anonymous__31826,Vvar__2___24Anonymous__31828) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__31825,Vvar__1___24Anonymous__31827,Vvar__2___24Anonymous__31829)
=> ( Vvar__2___24Anonymous__31828 = Vvar__2___24Anonymous__31829
& Vvar__1___24Anonymous__31826 = Vvar__1___24Anonymous__31827
& Vvar__0__C__31824 = Vvar__0__C__31825 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__31816,Vvar__0__C__31817,Vvar__1___24Anonymous__31818,Vvar__1___24Anonymous__31819] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__31816,Vvar__1___24Anonymous__31818) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__31817,Vvar__1___24Anonymous__31819)
=> ( Vvar__1___24Anonymous__31818 = Vvar__1___24Anonymous__31819
& Vvar__0__C__31816 = Vvar__0__C__31817 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__31850,Vvar__0__C__31851,Vvar__1___24Anonymous__31852,Vvar__1___24Anonymous__31853,Vvar__2___24Anonymous__31854,Vvar__2___24Anonymous__31855] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__31850,Vvar__1___24Anonymous__31852,Vvar__2___24Anonymous__31854) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__31851,Vvar__1___24Anonymous__31853,Vvar__2___24Anonymous__31855)
=> ( Vvar__2___24Anonymous__31854 = Vvar__2___24Anonymous__31855
& Vvar__1___24Anonymous__31852 = Vvar__1___24Anonymous__31853
& Vvar__0__C__31850 = Vvar__0__C__31851 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__31846,Vvar__0__C__31847,Vvar__1___24Anonymous__31848,Vvar__1___24Anonymous__31849] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__31846,Vvar__1___24Anonymous__31848) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__31847,Vvar__1___24Anonymous__31849)
=> ( Vvar__1___24Anonymous__31848 = Vvar__1___24Anonymous__31849
& Vvar__0__C__31846 = Vvar__0__C__31847 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__31836,Vvar__0__C__31837,Vvar__1___24Anonymous__31838,Vvar__1___24Anonymous__31839,Vvar__2___24Anonymous__31840,Vvar__2___24Anonymous__31841] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__31836,Vvar__1___24Anonymous__31838,Vvar__2___24Anonymous__31840) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__31837,Vvar__1___24Anonymous__31839,Vvar__2___24Anonymous__31841)
=> ( Vvar__2___24Anonymous__31840 = Vvar__2___24Anonymous__31841
& Vvar__1___24Anonymous__31838 = Vvar__1___24Anonymous__31839
& Vvar__0__C__31836 = Vvar__0__C__31837 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__31842,Vvar__0__C__31843,Vvar__1___24Anonymous__31844,Vvar__1___24Anonymous__31845] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__31842,Vvar__1___24Anonymous__31844) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__31843,Vvar__1___24Anonymous__31845)
=> ( Vvar__1___24Anonymous__31844 = Vvar__1___24Anonymous__31845
& Vvar__0__C__31842 = Vvar__0__C__31843 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__31856,Vvar__0__C__31857,Vvar__1___24Anonymous__31858,Vvar__1___24Anonymous__31859,Vvar__2___24Anonymous__31860,Vvar__2___24Anonymous__31861] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__31856,Vvar__1___24Anonymous__31858,Vvar__2___24Anonymous__31860) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__31857,Vvar__1___24Anonymous__31859,Vvar__2___24Anonymous__31861)
=> ( Vvar__2___24Anonymous__31860 = Vvar__2___24Anonymous__31861
& Vvar__1___24Anonymous__31858 = Vvar__1___24Anonymous__31859
& Vvar__0__C__31856 = Vvar__0__C__31857 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__31830,Vvar__0__C__31831,Vvar__1___24Anonymous__31832,Vvar__1___24Anonymous__31833,Vvar__2___24Anonymous__31834,Vvar__2___24Anonymous__31835] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__31830,Vvar__1___24Anonymous__31832,Vvar__2___24Anonymous__31834) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__31831,Vvar__1___24Anonymous__31833,Vvar__2___24Anonymous__31835)
=> ( Vvar__2___24Anonymous__31834 = Vvar__2___24Anonymous__31835
& Vvar__1___24Anonymous__31832 = Vvar__1___24Anonymous__31833
& Vvar__0__C__31830 = Vvar__0__C__31831 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__31871,Vvar__0__C__31872,Vvar__1__num__31873,Vvar__1__num__31874,Vvar__2__denum__31875,Vvar__2__denum__31876,Vvar__3__condition__31877,Vvar__3__condition__31878] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__31871,Vvar__1__num__31873,Vvar__2__denum__31875,Vvar__3__condition__31877) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__31872,Vvar__1__num__31874,Vvar__2__denum__31876,Vvar__3__condition__31878)
=> ( Vvar__3__condition__31877 = Vvar__3__condition__31878
& Vvar__2__denum__31875 = Vvar__2__denum__31876
& Vvar__1__num__31873 = Vvar__1__num__31874
& Vvar__0__C__31871 = Vvar__0__C__31872 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__31885,Vvar__0__C__31886,Vvar__1__rsplit__left__31887,Vvar__1__rsplit__left__31888,Vvar__2__rsplit__common__31889,Vvar__2__rsplit__common__31890,Vvar__3__rsplit__right__31891,Vvar__3__rsplit__right__31892] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__31885,Vvar__1__rsplit__left__31887,Vvar__2__rsplit__common__31889,Vvar__3__rsplit__right__31891) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__31886,Vvar__1__rsplit__left__31888,Vvar__2__rsplit__common__31890,Vvar__3__rsplit__right__31892)
=> ( Vvar__3__rsplit__right__31891 = Vvar__3__rsplit__right__31892
& Vvar__2__rsplit__common__31889 = Vvar__2__rsplit__common__31890
& Vvar__1__rsplit__left__31887 = Vvar__1__rsplit__left__31888
& Vvar__0__C__31885 = Vvar__0__C__31886 ) ) ).
fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
! [Vvar__0__hypo__type__20800,Vvar__0__hypo__type__20801,Vvar__1__hypo__proof__20802,Vvar__1__hypo__proof__20803] :
( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__20800,Vvar__1__hypo__proof__20802) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__20801,Vvar__1__hypo__proof__20803)
=> ( Vvar__1__hypo__proof__20802 = Vvar__1__hypo__proof__20803
& Vvar__0__hypo__type__20800 = Vvar__0__hypo__type__20801 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__2301,Vvar__0__C__2302] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2301) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2302)
=> Vvar__0__C__2301 = Vvar__0__C__2302 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__2299,Vvar__0__C__2300] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2299) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2300)
=> Vvar__0__C__2299 = Vvar__0__C__2300 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__2307,Vvar__0__C__2308,Vvar__1___24Anonymous__2309,Vvar__1___24Anonymous__2310] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2307,Vvar__1___24Anonymous__2309) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2308,Vvar__1___24Anonymous__2310)
=> ( Vvar__1___24Anonymous__2309 = Vvar__1___24Anonymous__2310
& Vvar__0__C__2307 = Vvar__0__C__2308 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__2311,Vvar__0__C__2312,Vvar__1___24Anonymous__2313,Vvar__1___24Anonymous__2314,Vvar__2___24Anonymous__2315,Vvar__2___24Anonymous__2316] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2311,Vvar__1___24Anonymous__2313,Vvar__2___24Anonymous__2315) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2312,Vvar__1___24Anonymous__2314,Vvar__2___24Anonymous__2316)
=> ( Vvar__2___24Anonymous__2315 = Vvar__2___24Anonymous__2316
& Vvar__1___24Anonymous__2313 = Vvar__1___24Anonymous__2314
& Vvar__0__C__2311 = Vvar__0__C__2312 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__2303,Vvar__0__C__2304,Vvar__1___24Anonymous__2305,Vvar__1___24Anonymous__2306] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2303,Vvar__1___24Anonymous__2305) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2304,Vvar__1___24Anonymous__2306)
=> ( Vvar__1___24Anonymous__2305 = Vvar__1___24Anonymous__2306
& Vvar__0__C__2303 = Vvar__0__C__2304 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__2323,Vvar__0__C__2324,Vvar__1___24Anonymous__2325,Vvar__1___24Anonymous__2326,Vvar__2___24Anonymous__2327,Vvar__2___24Anonymous__2328] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2323,Vvar__1___24Anonymous__2325,Vvar__2___24Anonymous__2327) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2324,Vvar__1___24Anonymous__2326,Vvar__2___24Anonymous__2328)
=> ( Vvar__2___24Anonymous__2327 = Vvar__2___24Anonymous__2328
& Vvar__1___24Anonymous__2325 = Vvar__1___24Anonymous__2326
& Vvar__0__C__2323 = Vvar__0__C__2324 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__2329,Vvar__0__C__2330,Vvar__1___24Anonymous__2331,Vvar__1___24Anonymous__2332] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2329,Vvar__1___24Anonymous__2331) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2330,Vvar__1___24Anonymous__2332)
=> ( Vvar__1___24Anonymous__2331 = Vvar__1___24Anonymous__2332
& Vvar__0__C__2329 = Vvar__0__C__2330 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__2333,Vvar__0__C__2334,Vvar__1___24Anonymous__2335,Vvar__1___24Anonymous__2336,Vvar__2___24Anonymous__2337,Vvar__2___24Anonymous__2338] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2333,Vvar__1___24Anonymous__2335,Vvar__2___24Anonymous__2337) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2334,Vvar__1___24Anonymous__2336,Vvar__2___24Anonymous__2338)
=> ( Vvar__2___24Anonymous__2337 = Vvar__2___24Anonymous__2338
& Vvar__1___24Anonymous__2335 = Vvar__1___24Anonymous__2336
& Vvar__0__C__2333 = Vvar__0__C__2334 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__2317,Vvar__0__C__2318,Vvar__1___24Anonymous__2319,Vvar__1___24Anonymous__2320,Vvar__2___24Anonymous__2321,Vvar__2___24Anonymous__2322] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2317,Vvar__1___24Anonymous__2319,Vvar__2___24Anonymous__2321) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2318,Vvar__1___24Anonymous__2320,Vvar__2___24Anonymous__2322)
=> ( Vvar__2___24Anonymous__2321 = Vvar__2___24Anonymous__2322
& Vvar__1___24Anonymous__2319 = Vvar__1___24Anonymous__2320
& Vvar__0__C__2317 = Vvar__0__C__2318 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__1954,Vvar__0__C__1955,Vvar__1___24Anonymous__1956,Vvar__1___24Anonymous__1957,Vvar__2___24Anonymous__1958,Vvar__2___24Anonymous__1959,Vvar__3___24Anonymous__1960,Vvar__3___24Anonymous__1961] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1954,Vvar__1___24Anonymous__1956,Vvar__2___24Anonymous__1958,Vvar__3___24Anonymous__1960) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1955,Vvar__1___24Anonymous__1957,Vvar__2___24Anonymous__1959,Vvar__3___24Anonymous__1961)
=> ( Vvar__3___24Anonymous__1960 = Vvar__3___24Anonymous__1961
& Vvar__2___24Anonymous__1958 = Vvar__2___24Anonymous__1959
& Vvar__1___24Anonymous__1956 = Vvar__1___24Anonymous__1957
& Vvar__0__C__1954 = Vvar__0__C__1955 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__1944,Vvar__0__C__1945,Vvar__1___24Anonymous__1946,Vvar__1___24Anonymous__1947] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1944,Vvar__1___24Anonymous__1946) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1945,Vvar__1___24Anonymous__1947)
=> ( Vvar__1___24Anonymous__1946 = Vvar__1___24Anonymous__1947
& Vvar__0__C__1944 = Vvar__0__C__1945 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__1948,Vvar__0__C__1949,Vvar__1___24Anonymous__1950,Vvar__1___24Anonymous__1951,Vvar__2___24Anonymous__1952,Vvar__2___24Anonymous__1953] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1948,Vvar__1___24Anonymous__1950,Vvar__2___24Anonymous__1952) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1949,Vvar__1___24Anonymous__1951,Vvar__2___24Anonymous__1953)
=> ( Vvar__2___24Anonymous__1952 = Vvar__2___24Anonymous__1953
& Vvar__1___24Anonymous__1950 = Vvar__1___24Anonymous__1951
& Vvar__0__C__1948 = Vvar__0__C__1949 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__2113,Vvar__0___24Anonymous__2114,Vvar__1___24Anonymous__2115,Vvar__1___24Anonymous__2116] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__2113,Vvar__1___24Anonymous__2115) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__2114,Vvar__1___24Anonymous__2116)
=> ( Vvar__1___24Anonymous__2115 = Vvar__1___24Anonymous__2116
& Vvar__0___24Anonymous__2113 = Vvar__0___24Anonymous__2114 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__2109,Vvar__0___24Anonymous__2110,Vvar__1___24Anonymous__2111,Vvar__1___24Anonymous__2112] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__2109,Vvar__1___24Anonymous__2111) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__2110,Vvar__1___24Anonymous__2112)
=> ( Vvar__1___24Anonymous__2111 = Vvar__1___24Anonymous__2112
& Vvar__0___24Anonymous__2109 = Vvar__0___24Anonymous__2110 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__34912,Vvar__0__R__34913,Vvar__1__req__34914,Vvar__1__req__34915,Vvar__2__reqb__34916,Vvar__2__reqb__34917,Vvar__3___24Anonymous__34918,Vvar__3___24Anonymous__34919] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__34912,Vvar__1__req__34914,Vvar__2__reqb__34916) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__34913,Vvar__1__req__34915,Vvar__2__reqb__34917)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__34916 = Vvar__2__reqb__34917
& Vvar__1__req__34914 = Vvar__1__req__34915
& Vvar__0__R__34912 = Vvar__0__R__34913 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__34920,Vvar__0__R__34921,Vvar__1__rO__34922,Vvar__1__rO__34923,Vvar__2__rI__34924,Vvar__2__rI__34925,Vvar__3__radd__34926,Vvar__3__radd__34927,Vvar__4__rmul__34928,Vvar__4__rmul__34929,Vvar__5__rsub__34930,Vvar__5__rsub__34931,Vvar__6__ropp__34932,Vvar__6__ropp__34933,Vvar__7__req__34934,Vvar__7__req__34935,Vvar__8__C__34936,Vvar__8__C__34937,Vvar__9__cO__34938,Vvar__9__cO__34939,Vvar__10__cI__34940,Vvar__10__cI__34941,Vvar__11__cadd__34942,Vvar__11__cadd__34943,Vvar__12__cmul__34944,Vvar__12__cmul__34945,Vvar__13__csub__34946,Vvar__13__csub__34947,Vvar__14__copp__34948,Vvar__14__copp__34949,Vvar__15__ceqb__34950,Vvar__15__ceqb__34951,Vvar__16__phi__34952,Vvar__16__phi__34953,Vvar__17___24Anonymous__34954,Vvar__17___24Anonymous__34955] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__34920,Vvar__1__rO__34922,Vvar__2__rI__34924,Vvar__3__radd__34926,Vvar__4__rmul__34928,Vvar__5__rsub__34930,Vvar__6__ropp__34932,Vvar__7__req__34934,Vvar__8__C__34936,Vvar__9__cO__34938,Vvar__10__cI__34940,Vvar__11__cadd__34942,Vvar__12__cmul__34944,Vvar__13__csub__34946,Vvar__14__copp__34948,Vvar__15__ceqb__34950,Vvar__16__phi__34952) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__34921,Vvar__1__rO__34923,Vvar__2__rI__34925,Vvar__3__radd__34927,Vvar__4__rmul__34929,Vvar__5__rsub__34931,Vvar__6__ropp__34933,Vvar__7__req__34935,Vvar__8__C__34937,Vvar__9__cO__34939,Vvar__10__cI__34941,Vvar__11__cadd__34943,Vvar__12__cmul__34945,Vvar__13__csub__34947,Vvar__14__copp__34949,Vvar__15__ceqb__34951,Vvar__16__phi__34953)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__34952 = Vvar__16__phi__34953
& Vvar__15__ceqb__34950 = Vvar__15__ceqb__34951
& Vvar__14__copp__34948 = Vvar__14__copp__34949
& Vvar__13__csub__34946 = Vvar__13__csub__34947
& Vvar__12__cmul__34944 = Vvar__12__cmul__34945
& Vvar__11__cadd__34942 = Vvar__11__cadd__34943
& Vvar__10__cI__34940 = Vvar__10__cI__34941
& Vvar__9__cO__34938 = Vvar__9__cO__34939
& Vvar__8__C__34936 = Vvar__8__C__34937
& Vvar__7__req__34934 = Vvar__7__req__34935
& Vvar__6__ropp__34932 = Vvar__6__ropp__34933
& Vvar__5__rsub__34930 = Vvar__5__rsub__34931
& Vvar__4__rmul__34928 = Vvar__4__rmul__34929
& Vvar__3__radd__34926 = Vvar__3__radd__34927
& Vvar__2__rI__34924 = Vvar__2__rI__34925
& Vvar__1__rO__34922 = Vvar__1__rO__34923
& Vvar__0__R__34920 = Vvar__0__R__34921 ) ) ).
fof('$_inj_hahn.HahnBase.Equality.Mixin',axiom,
! [Vvar__0__T__35312,Vvar__0__T__35313,Vvar__1__op__35314,Vvar__1__op__35315,Vvar__2___24Anonymous__35316,Vvar__2___24Anonymous__35317] :
( chahn_2eHahnBase_2eEquality_2eMixin___24a3(Vvar__0__T__35312,Vvar__1__op__35314,Vvar__2___24Anonymous__35316) = chahn_2eHahnBase_2eEquality_2eMixin___24a3(Vvar__0__T__35313,Vvar__1__op__35315,Vvar__2___24Anonymous__35317)
=> ( Vvar__2___24Anonymous__35316 = Vvar__2___24Anonymous__35317
& Vvar__1__op__35314 = Vvar__1__op__35315
& Vvar__0__T__35312 = Vvar__0__T__35313 ) ) ).
fof('$_inj_hahn.HahnBase.Equality.Pack',axiom,
! [Vvar__0__sort__35322,Vvar__0__sort__35323,Vvar__1___24Anonymous__35324,Vvar__1___24Anonymous__35325,Vvar__2___24Anonymous__35326,Vvar__2___24Anonymous__35327] :
( chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__35322,Vvar__1___24Anonymous__35324,Vvar__2___24Anonymous__35326) = chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__35323,Vvar__1___24Anonymous__35325,Vvar__2___24Anonymous__35327)
=> ( Vvar__2___24Anonymous__35326 = Vvar__2___24Anonymous__35327
& Vvar__1___24Anonymous__35324 = Vvar__1___24Anonymous__35325
& Vvar__0__sort__35322 = Vvar__0__sort__35323 ) ) ).
fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
! [Vvar__0__P__30518,Vvar__1__Q__30520,Vvar__2__init__30523,Vvar__3___24Anonymous__30524,Vvar__4___24Anonymous__30525] :
( c_24__type__30551___24t(Vvar__0__P__30518,Vvar__1__Q__30520,Vvar__2__init__30523,Vvar__3___24Anonymous__30524,Vvar__4___24Anonymous__30525,Vvar__0__P__30518)
=> ( c_24__type__30559___24t(Vvar__0__P__30518,Vvar__1__Q__30520,Vvar__2__init__30523,Vvar__3___24Anonymous__30524,Vvar__4___24Anonymous__30525,Vvar__1__Q__30520)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__30523)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__30524)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__30525)
=> ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__30518,Vvar__1__Q__30520,Vvar__2__init__30523,Vvar__3___24Anonymous__30524,Vvar__4___24Anonymous__30525)
=> ( ( Vvar__4___24Anonymous__30525 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__3___24Anonymous__30524 = Vvar__2__init__30523 )
| ? [Vvar__3__k__30539] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__30539)
& ? [Vvar__4__l__30540] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__30540)
& ? [Vvar__5__n__30541] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__30541)
& cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__30518,Vvar__1__Q__30520,Vvar__2__init__30523,Vvar__3__k__30539,Vvar__5__n__30541)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__30518,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__30539),Vvar__4__l__30540)
& p(happ(Vvar__1__Q__30520,Vvar__4__l__30540))
& Vvar__4___24Anonymous__30525 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__30541)
& Vvar__3___24Anonymous__30524 = Vvar__4__l__30540 ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__30478,Vvar__1__k__30480,Vvar__2___24Anonymous__30481] :
( c_24__type__30495___24t(Vvar__0__P__30478,Vvar__1__k__30480,Vvar__2___24Anonymous__30481,Vvar__0__P__30478)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__30480)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__30481)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__30478,Vvar__1__k__30480,Vvar__2___24Anonymous__30481)
=> ( Vvar__2___24Anonymous__30481 = Vvar__1__k__30480
| ? [Vvar__2__l__30489] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__30489)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__30478,Vvar__1__k__30480,Vvar__2__l__30489)
& p(happ(Vvar__0__P__30478,Vvar__2__l__30489))
& Vvar__2___24Anonymous__30481 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__30489) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__30497,Vvar__1__k__30499,Vvar__2___24Anonymous__30500] :
( c_24__type__30516___24t(Vvar__0__Q__30497,Vvar__1__k__30499,Vvar__2___24Anonymous__30500,Vvar__0__Q__30497)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__30499)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__30500)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__30497,Vvar__1__k__30499,Vvar__2___24Anonymous__30500)
=> ( ? [Vvar__2__l__30505] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__30505)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__30497,Vvar__1__k__30499,Vvar__2__l__30505)
& Vvar__2___24Anonymous__30500 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__30505) )
| ? [Vvar__2__l__30510] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__30510)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__30499,Vvar__2__l__30510)
& p(happ(Vvar__0__Q__30497,Vvar__2__l__30510))
& Vvar__2___24Anonymous__30500 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__30510) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__6471] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6471)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__6471)
=> ( Vvar__0___24Anonymous__6471 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__6473] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__6473)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__6473)
& Vvar__0___24Anonymous__6471 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__6473) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__6475] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6475)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__6475)
=> ? [Vvar__0__n__6477] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__6477)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__6477)
& Vvar__0___24Anonymous__6475 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__6477) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__1769,Vvar__1___24Anonymous__1770,VX1771] :
( cProp___24t(Vvar__0__P__1769)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__1770)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__1769,Vvar__1___24Anonymous__1770,VX1771)
=> ( ( p(Vvar__0__P__1769)
& Vvar__1___24Anonymous__1770 = cCoq_2eInit_2eDatatypes_2etrue
& VX1771 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__1769) )
| ( ~ p(Vvar__0__P__1769)
& Vvar__1___24Anonymous__1770 = cCoq_2eInit_2eDatatypes_2efalse
& VX1771 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__1769) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
! [Vvar__0___24Anonymous__35484,Vvar__1___24Anonymous__35485,Vvar__2___24Anonymous__35486] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__35484)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__35485)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__35486)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__35484,Vvar__1___24Anonymous__35485,Vvar__2___24Anonymous__35486)
=> ( ? [Vvar__0__x__35488] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__35488)
& Vvar__2___24Anonymous__35486 = Vvar__0__x__35488
& Vvar__1___24Anonymous__35485 = Vvar__0__x__35488
& Vvar__0___24Anonymous__35484 = Vvar__0__x__35488 )
| ? [Vvar__0__x__35489] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__35489)
& Vvar__2___24Anonymous__35486 = Vvar__0__x__35489
& Vvar__1___24Anonymous__35485 = cCoq_2eInit_2eDatatypes_2eEq
& Vvar__0___24Anonymous__35484 = Vvar__0__x__35489 )
| ? [Vvar__0__x__35490] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__35490)
& Vvar__2___24Anonymous__35486 = Vvar__0__x__35490
& Vvar__1___24Anonymous__35485 = Vvar__0__x__35490
& Vvar__0___24Anonymous__35484 = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0__x__35491] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__35491)
& Vvar__2___24Anonymous__35486 = Vvar__0__x__35491
& Vvar__1___24Anonymous__35485 = cCoq_2eInit_2eDatatypes_2eLt
& Vvar__0___24Anonymous__35484 = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0__x__35492] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__35492)
& Vvar__2___24Anonymous__35486 = Vvar__0__x__35492
& Vvar__1___24Anonymous__35485 = cCoq_2eInit_2eDatatypes_2eGt
& Vvar__0___24Anonymous__35484 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX11193] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX11193)
=> ( VX11193 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__11194] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__11194)
& ? [Vvar__1___24Anonymous__11195] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__11195)
& ? [Vvar__2___24Anonymous__11196] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__11196)
& VX11193 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__11194,Vvar__1___24Anonymous__11195,Vvar__2___24Anonymous__11196) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX11863] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX11863)
=> ( VX11863 = cCoq_2eInit_2eByte_2ex00
| VX11863 = cCoq_2eInit_2eByte_2ex01
| VX11863 = cCoq_2eInit_2eByte_2ex02
| VX11863 = cCoq_2eInit_2eByte_2ex03
| VX11863 = cCoq_2eInit_2eByte_2ex04
| VX11863 = cCoq_2eInit_2eByte_2ex05
| VX11863 = cCoq_2eInit_2eByte_2ex06
| VX11863 = cCoq_2eInit_2eByte_2ex07
| VX11863 = cCoq_2eInit_2eByte_2ex08
| VX11863 = cCoq_2eInit_2eByte_2ex09
| VX11863 = cCoq_2eInit_2eByte_2ex0a
| VX11863 = cCoq_2eInit_2eByte_2ex0b
| VX11863 = cCoq_2eInit_2eByte_2ex0c
| VX11863 = cCoq_2eInit_2eByte_2ex0d
| VX11863 = cCoq_2eInit_2eByte_2ex0e
| VX11863 = cCoq_2eInit_2eByte_2ex0f
| VX11863 = cCoq_2eInit_2eByte_2ex10
| VX11863 = cCoq_2eInit_2eByte_2ex11
| VX11863 = cCoq_2eInit_2eByte_2ex12
| VX11863 = cCoq_2eInit_2eByte_2ex13
| VX11863 = cCoq_2eInit_2eByte_2ex14
| VX11863 = cCoq_2eInit_2eByte_2ex15
| VX11863 = cCoq_2eInit_2eByte_2ex16
| VX11863 = cCoq_2eInit_2eByte_2ex17
| VX11863 = cCoq_2eInit_2eByte_2ex18
| VX11863 = cCoq_2eInit_2eByte_2ex19
| VX11863 = cCoq_2eInit_2eByte_2ex1a
| VX11863 = cCoq_2eInit_2eByte_2ex1b
| VX11863 = cCoq_2eInit_2eByte_2ex1c
| VX11863 = cCoq_2eInit_2eByte_2ex1d
| VX11863 = cCoq_2eInit_2eByte_2ex1e
| VX11863 = cCoq_2eInit_2eByte_2ex1f
| VX11863 = cCoq_2eInit_2eByte_2ex20
| VX11863 = cCoq_2eInit_2eByte_2ex21
| VX11863 = cCoq_2eInit_2eByte_2ex22
| VX11863 = cCoq_2eInit_2eByte_2ex23
| VX11863 = cCoq_2eInit_2eByte_2ex24
| VX11863 = cCoq_2eInit_2eByte_2ex25
| VX11863 = cCoq_2eInit_2eByte_2ex26
| VX11863 = cCoq_2eInit_2eByte_2ex27
| VX11863 = cCoq_2eInit_2eByte_2ex28
| VX11863 = cCoq_2eInit_2eByte_2ex29
| VX11863 = cCoq_2eInit_2eByte_2ex2a
| VX11863 = cCoq_2eInit_2eByte_2ex2b
| VX11863 = cCoq_2eInit_2eByte_2ex2c
| VX11863 = cCoq_2eInit_2eByte_2ex2d
| VX11863 = cCoq_2eInit_2eByte_2ex2e
| VX11863 = cCoq_2eInit_2eByte_2ex2f
| VX11863 = cCoq_2eInit_2eByte_2ex30
| VX11863 = cCoq_2eInit_2eByte_2ex31
| VX11863 = cCoq_2eInit_2eByte_2ex32
| VX11863 = cCoq_2eInit_2eByte_2ex33
| VX11863 = cCoq_2eInit_2eByte_2ex34
| VX11863 = cCoq_2eInit_2eByte_2ex35
| VX11863 = cCoq_2eInit_2eByte_2ex36
| VX11863 = cCoq_2eInit_2eByte_2ex37
| VX11863 = cCoq_2eInit_2eByte_2ex38
| VX11863 = cCoq_2eInit_2eByte_2ex39
| VX11863 = cCoq_2eInit_2eByte_2ex3a
| VX11863 = cCoq_2eInit_2eByte_2ex3b
| VX11863 = cCoq_2eInit_2eByte_2ex3c
| VX11863 = cCoq_2eInit_2eByte_2ex3d
| VX11863 = cCoq_2eInit_2eByte_2ex3e
| VX11863 = cCoq_2eInit_2eByte_2ex3f
| VX11863 = cCoq_2eInit_2eByte_2ex40
| VX11863 = cCoq_2eInit_2eByte_2ex41
| VX11863 = cCoq_2eInit_2eByte_2ex42
| VX11863 = cCoq_2eInit_2eByte_2ex43
| VX11863 = cCoq_2eInit_2eByte_2ex44
| VX11863 = cCoq_2eInit_2eByte_2ex45
| VX11863 = cCoq_2eInit_2eByte_2ex46
| VX11863 = cCoq_2eInit_2eByte_2ex47
| VX11863 = cCoq_2eInit_2eByte_2ex48
| VX11863 = cCoq_2eInit_2eByte_2ex49
| VX11863 = cCoq_2eInit_2eByte_2ex4a
| VX11863 = cCoq_2eInit_2eByte_2ex4b
| VX11863 = cCoq_2eInit_2eByte_2ex4c
| VX11863 = cCoq_2eInit_2eByte_2ex4d
| VX11863 = cCoq_2eInit_2eByte_2ex4e
| VX11863 = cCoq_2eInit_2eByte_2ex4f
| VX11863 = cCoq_2eInit_2eByte_2ex50
| VX11863 = cCoq_2eInit_2eByte_2ex51
| VX11863 = cCoq_2eInit_2eByte_2ex52
| VX11863 = cCoq_2eInit_2eByte_2ex53
| VX11863 = cCoq_2eInit_2eByte_2ex54
| VX11863 = cCoq_2eInit_2eByte_2ex55
| VX11863 = cCoq_2eInit_2eByte_2ex56
| VX11863 = cCoq_2eInit_2eByte_2ex57
| VX11863 = cCoq_2eInit_2eByte_2ex58
| VX11863 = cCoq_2eInit_2eByte_2ex59
| VX11863 = cCoq_2eInit_2eByte_2ex5a
| VX11863 = cCoq_2eInit_2eByte_2ex5b
| VX11863 = cCoq_2eInit_2eByte_2ex5c
| VX11863 = cCoq_2eInit_2eByte_2ex5d
| VX11863 = cCoq_2eInit_2eByte_2ex5e
| VX11863 = cCoq_2eInit_2eByte_2ex5f
| VX11863 = cCoq_2eInit_2eByte_2ex60
| VX11863 = cCoq_2eInit_2eByte_2ex61
| VX11863 = cCoq_2eInit_2eByte_2ex62
| VX11863 = cCoq_2eInit_2eByte_2ex63
| VX11863 = cCoq_2eInit_2eByte_2ex64
| VX11863 = cCoq_2eInit_2eByte_2ex65
| VX11863 = cCoq_2eInit_2eByte_2ex66
| VX11863 = cCoq_2eInit_2eByte_2ex67
| VX11863 = cCoq_2eInit_2eByte_2ex68
| VX11863 = cCoq_2eInit_2eByte_2ex69
| VX11863 = cCoq_2eInit_2eByte_2ex6a
| VX11863 = cCoq_2eInit_2eByte_2ex6b
| VX11863 = cCoq_2eInit_2eByte_2ex6c
| VX11863 = cCoq_2eInit_2eByte_2ex6d
| VX11863 = cCoq_2eInit_2eByte_2ex6e
| VX11863 = cCoq_2eInit_2eByte_2ex6f
| VX11863 = cCoq_2eInit_2eByte_2ex70
| VX11863 = cCoq_2eInit_2eByte_2ex71
| VX11863 = cCoq_2eInit_2eByte_2ex72
| VX11863 = cCoq_2eInit_2eByte_2ex73
| VX11863 = cCoq_2eInit_2eByte_2ex74
| VX11863 = cCoq_2eInit_2eByte_2ex75
| VX11863 = cCoq_2eInit_2eByte_2ex76
| VX11863 = cCoq_2eInit_2eByte_2ex77
| VX11863 = cCoq_2eInit_2eByte_2ex78
| VX11863 = cCoq_2eInit_2eByte_2ex79
| VX11863 = cCoq_2eInit_2eByte_2ex7a
| VX11863 = cCoq_2eInit_2eByte_2ex7b
| VX11863 = cCoq_2eInit_2eByte_2ex7c
| VX11863 = cCoq_2eInit_2eByte_2ex7d
| VX11863 = cCoq_2eInit_2eByte_2ex7e
| VX11863 = cCoq_2eInit_2eByte_2ex7f
| VX11863 = cCoq_2eInit_2eByte_2ex80
| VX11863 = cCoq_2eInit_2eByte_2ex81
| VX11863 = cCoq_2eInit_2eByte_2ex82
| VX11863 = cCoq_2eInit_2eByte_2ex83
| VX11863 = cCoq_2eInit_2eByte_2ex84
| VX11863 = cCoq_2eInit_2eByte_2ex85
| VX11863 = cCoq_2eInit_2eByte_2ex86
| VX11863 = cCoq_2eInit_2eByte_2ex87
| VX11863 = cCoq_2eInit_2eByte_2ex88
| VX11863 = cCoq_2eInit_2eByte_2ex89
| VX11863 = cCoq_2eInit_2eByte_2ex8a
| VX11863 = cCoq_2eInit_2eByte_2ex8b
| VX11863 = cCoq_2eInit_2eByte_2ex8c
| VX11863 = cCoq_2eInit_2eByte_2ex8d
| VX11863 = cCoq_2eInit_2eByte_2ex8e
| VX11863 = cCoq_2eInit_2eByte_2ex8f
| VX11863 = cCoq_2eInit_2eByte_2ex90
| VX11863 = cCoq_2eInit_2eByte_2ex91
| VX11863 = cCoq_2eInit_2eByte_2ex92
| VX11863 = cCoq_2eInit_2eByte_2ex93
| VX11863 = cCoq_2eInit_2eByte_2ex94
| VX11863 = cCoq_2eInit_2eByte_2ex95
| VX11863 = cCoq_2eInit_2eByte_2ex96
| VX11863 = cCoq_2eInit_2eByte_2ex97
| VX11863 = cCoq_2eInit_2eByte_2ex98
| VX11863 = cCoq_2eInit_2eByte_2ex99
| VX11863 = cCoq_2eInit_2eByte_2ex9a
| VX11863 = cCoq_2eInit_2eByte_2ex9b
| VX11863 = cCoq_2eInit_2eByte_2ex9c
| VX11863 = cCoq_2eInit_2eByte_2ex9d
| VX11863 = cCoq_2eInit_2eByte_2ex9e
| VX11863 = cCoq_2eInit_2eByte_2ex9f
| VX11863 = cCoq_2eInit_2eByte_2exa0
| VX11863 = cCoq_2eInit_2eByte_2exa1
| VX11863 = cCoq_2eInit_2eByte_2exa2
| VX11863 = cCoq_2eInit_2eByte_2exa3
| VX11863 = cCoq_2eInit_2eByte_2exa4
| VX11863 = cCoq_2eInit_2eByte_2exa5
| VX11863 = cCoq_2eInit_2eByte_2exa6
| VX11863 = cCoq_2eInit_2eByte_2exa7
| VX11863 = cCoq_2eInit_2eByte_2exa8
| VX11863 = cCoq_2eInit_2eByte_2exa9
| VX11863 = cCoq_2eInit_2eByte_2exaa
| VX11863 = cCoq_2eInit_2eByte_2exab
| VX11863 = cCoq_2eInit_2eByte_2exac
| VX11863 = cCoq_2eInit_2eByte_2exad
| VX11863 = cCoq_2eInit_2eByte_2exae
| VX11863 = cCoq_2eInit_2eByte_2exaf
| VX11863 = cCoq_2eInit_2eByte_2exb0
| VX11863 = cCoq_2eInit_2eByte_2exb1
| VX11863 = cCoq_2eInit_2eByte_2exb2
| VX11863 = cCoq_2eInit_2eByte_2exb3
| VX11863 = cCoq_2eInit_2eByte_2exb4
| VX11863 = cCoq_2eInit_2eByte_2exb5
| VX11863 = cCoq_2eInit_2eByte_2exb6
| VX11863 = cCoq_2eInit_2eByte_2exb7
| VX11863 = cCoq_2eInit_2eByte_2exb8
| VX11863 = cCoq_2eInit_2eByte_2exb9
| VX11863 = cCoq_2eInit_2eByte_2exba
| VX11863 = cCoq_2eInit_2eByte_2exbb
| VX11863 = cCoq_2eInit_2eByte_2exbc
| VX11863 = cCoq_2eInit_2eByte_2exbd
| VX11863 = cCoq_2eInit_2eByte_2exbe
| VX11863 = cCoq_2eInit_2eByte_2exbf
| VX11863 = cCoq_2eInit_2eByte_2exc0
| VX11863 = cCoq_2eInit_2eByte_2exc1
| VX11863 = cCoq_2eInit_2eByte_2exc2
| VX11863 = cCoq_2eInit_2eByte_2exc3
| VX11863 = cCoq_2eInit_2eByte_2exc4
| VX11863 = cCoq_2eInit_2eByte_2exc5
| VX11863 = cCoq_2eInit_2eByte_2exc6
| VX11863 = cCoq_2eInit_2eByte_2exc7
| VX11863 = cCoq_2eInit_2eByte_2exc8
| VX11863 = cCoq_2eInit_2eByte_2exc9
| VX11863 = cCoq_2eInit_2eByte_2exca
| VX11863 = cCoq_2eInit_2eByte_2excb
| VX11863 = cCoq_2eInit_2eByte_2excc
| VX11863 = cCoq_2eInit_2eByte_2excd
| VX11863 = cCoq_2eInit_2eByte_2exce
| VX11863 = cCoq_2eInit_2eByte_2excf
| VX11863 = cCoq_2eInit_2eByte_2exd0
| VX11863 = cCoq_2eInit_2eByte_2exd1
| VX11863 = cCoq_2eInit_2eByte_2exd2
| VX11863 = cCoq_2eInit_2eByte_2exd3
| VX11863 = cCoq_2eInit_2eByte_2exd4
| VX11863 = cCoq_2eInit_2eByte_2exd5
| VX11863 = cCoq_2eInit_2eByte_2exd6
| VX11863 = cCoq_2eInit_2eByte_2exd7
| VX11863 = cCoq_2eInit_2eByte_2exd8
| VX11863 = cCoq_2eInit_2eByte_2exd9
| VX11863 = cCoq_2eInit_2eByte_2exda
| VX11863 = cCoq_2eInit_2eByte_2exdb
| VX11863 = cCoq_2eInit_2eByte_2exdc
| VX11863 = cCoq_2eInit_2eByte_2exdd
| VX11863 = cCoq_2eInit_2eByte_2exde
| VX11863 = cCoq_2eInit_2eByte_2exdf
| VX11863 = cCoq_2eInit_2eByte_2exe0
| VX11863 = cCoq_2eInit_2eByte_2exe1
| VX11863 = cCoq_2eInit_2eByte_2exe2
| VX11863 = cCoq_2eInit_2eByte_2exe3
| VX11863 = cCoq_2eInit_2eByte_2exe4
| VX11863 = cCoq_2eInit_2eByte_2exe5
| VX11863 = cCoq_2eInit_2eByte_2exe6
| VX11863 = cCoq_2eInit_2eByte_2exe7
| VX11863 = cCoq_2eInit_2eByte_2exe8
| VX11863 = cCoq_2eInit_2eByte_2exe9
| VX11863 = cCoq_2eInit_2eByte_2exea
| VX11863 = cCoq_2eInit_2eByte_2exeb
| VX11863 = cCoq_2eInit_2eByte_2exec
| VX11863 = cCoq_2eInit_2eByte_2exed
| VX11863 = cCoq_2eInit_2eByte_2exee
| VX11863 = cCoq_2eInit_2eByte_2exef
| VX11863 = cCoq_2eInit_2eByte_2exf0
| VX11863 = cCoq_2eInit_2eByte_2exf1
| VX11863 = cCoq_2eInit_2eByte_2exf2
| VX11863 = cCoq_2eInit_2eByte_2exf3
| VX11863 = cCoq_2eInit_2eByte_2exf4
| VX11863 = cCoq_2eInit_2eByte_2exf5
| VX11863 = cCoq_2eInit_2eByte_2exf6
| VX11863 = cCoq_2eInit_2eByte_2exf7
| VX11863 = cCoq_2eInit_2eByte_2exf8
| VX11863 = cCoq_2eInit_2eByte_2exf9
| VX11863 = cCoq_2eInit_2eByte_2exfa
| VX11863 = cCoq_2eInit_2eByte_2exfb
| VX11863 = cCoq_2eInit_2eByte_2exfc
| VX11863 = cCoq_2eInit_2eByte_2exfd
| VX11863 = cCoq_2eInit_2eByte_2exfe
| VX11863 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__30700,Vvar__1__Q__30701,Vvar__2___24Anonymous__30702] :
( cProp___24t(Vvar__0__P__30700)
=> ( cProp___24t(Vvar__1__Q__30701)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__30702)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__30700,Vvar__1__Q__30701,Vvar__2___24Anonymous__30702)
=> ( ( p(Vvar__0__P__30700)
& Vvar__2___24Anonymous__30702 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__30701)
& Vvar__2___24Anonymous__30702 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__19510,Vvar__1__Plt__19511,Vvar__2__Pgt__19512,Vvar__3___24Anonymous__19513] :
( cProp___24t(Vvar__0__Peq__19510)
=> ( cProp___24t(Vvar__1__Plt__19511)
=> ( cProp___24t(Vvar__2__Pgt__19512)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__19513)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__19510,Vvar__1__Plt__19511,Vvar__2__Pgt__19512,Vvar__3___24Anonymous__19513)
=> ( ( p(Vvar__0__Peq__19510)
& Vvar__3___24Anonymous__19513 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__19511)
& Vvar__3___24Anonymous__19513 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__19512)
& Vvar__3___24Anonymous__19513 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__6259,Vvar__1__Plt__6260,Vvar__2__Pgt__6261,Vvar__3___24Anonymous__6262,VX6263] :
( cProp___24t(Vvar__0__Peq__6259)
=> ( cProp___24t(Vvar__1__Plt__6260)
=> ( cProp___24t(Vvar__2__Pgt__6261)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__6262)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__6259,Vvar__1__Plt__6260,Vvar__2__Pgt__6261,Vvar__3___24Anonymous__6262,VX6263)
=> ( ( p(Vvar__0__Peq__6259)
& Vvar__3___24Anonymous__6262 = cCoq_2eInit_2eDatatypes_2eEq
& VX6263 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__6259,Vvar__1__Plt__6260,Vvar__2__Pgt__6261) )
| ( p(Vvar__1__Plt__6260)
& Vvar__3___24Anonymous__6262 = cCoq_2eInit_2eDatatypes_2eLt
& VX6263 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__6259,Vvar__1__Plt__6260,Vvar__2__Pgt__6261) )
| ( p(Vvar__2__Pgt__6261)
& Vvar__3___24Anonymous__6262 = cCoq_2eInit_2eDatatypes_2eGt
& VX6263 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__6259,Vvar__1__Plt__6260,Vvar__2__Pgt__6261) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX1792] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX1792)
=> ( VX1792 = cCoq_2eInit_2eDatatypes_2etrue
| VX1792 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX6256] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX6256)
=> ( VX6256 = cCoq_2eInit_2eDatatypes_2eEq
| VX6256 = cCoq_2eInit_2eDatatypes_2eLt
| VX6256 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
! [Vvar__0___24Anonymous__30698] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__30698)
=> ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__30698)
=> Vvar__0___24Anonymous__30698 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
! [Vvar__0__A__30710,Vvar__1__a__30711,Vvar__2___24Anonymous__30712] :
( cType___24t(Vvar__0__A__30710)
=> ( t(Vvar__1__a__30711,Vvar__0__A__30710)
=> ( t(Vvar__2___24Anonymous__30712,Vvar__0__A__30710)
=> ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__30710,Vvar__1__a__30711,Vvar__2___24Anonymous__30712)
=> Vvar__2___24Anonymous__30712 = Vvar__1__a__30711 ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__62,VX63] :
( cType___24t(Vvar__0__A__62)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__62,VX63)
=> ( VX63 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__62)
| ? [Vvar__1___24Anonymous__66] :
( t(Vvar__1___24Anonymous__66,Vvar__0__A__62)
& ? [Vvar__2___24Anonymous__67] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__62,Vvar__2___24Anonymous__67)
& VX63 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__62,Vvar__1___24Anonymous__66,Vvar__2___24Anonymous__67) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX3860] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX3860)
=> ( VX3860 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__3861] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3861)
& VX3860 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3861) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__23,VX24] :
( cType___24t(Vvar__0__A__23)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__23,VX24)
=> ( ? [Vvar__1___24Anonymous__26] :
( t(Vvar__1___24Anonymous__26,Vvar__0__A__23)
& VX24 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__23,Vvar__1___24Anonymous__26) )
| VX24 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__23) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__44,Vvar__1__B__45,VX46] :
( cType___24t(Vvar__0__A__44)
=> ( cType___24t(Vvar__1__B__45)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__44,Vvar__1__B__45,VX46)
=> ? [Vvar__2___24Anonymous__49] :
( t(Vvar__2___24Anonymous__49,Vvar__0__A__44)
& ? [Vvar__3___24Anonymous__50] :
( t(Vvar__3___24Anonymous__50,Vvar__1__B__45)
& VX46 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__44,Vvar__1__B__45,Vvar__2___24Anonymous__49,Vvar__3___24Anonymous__50) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__19482,Vvar__1__B__19483,VX19484] :
( cType___24t(Vvar__0__A__19482)
=> ( cType___24t(Vvar__1__B__19483)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__19482,Vvar__1__B__19483,VX19484)
=> ( ? [Vvar__2___24Anonymous__19487] :
( t(Vvar__2___24Anonymous__19487,Vvar__0__A__19482)
& VX19484 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__19482,Vvar__1__B__19483,Vvar__2___24Anonymous__19487) )
| ? [Vvar__2___24Anonymous__19490] :
( t(Vvar__2___24Anonymous__19490,Vvar__1__B__19483)
& VX19484 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__19482,Vvar__1__B__19483,Vvar__2___24Anonymous__19490) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX1791] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX1791)
=> VX1791 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
! [VX30719] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(VX30719)
=> ( ? [Vvar__0__i__30720] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__30720)
& ? [Vvar__1__f__30721] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__30721)
& VX30719 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__30720,Vvar__1__f__30721) ) )
| ? [Vvar__0__i__30722] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__30722)
& ? [Vvar__1__f__30723] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__30723)
& ? [Vvar__2__e__30724] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__30724)
& VX30719 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__30722,Vvar__1__f__30723,Vvar__2__e__30724) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX19658] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX19658)
=> ( ? [Vvar__0__d__19659] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__19659)
& VX19658 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__19659) )
| ? [Vvar__0__d__19660] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__19660)
& VX19658 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__19660) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX19527] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX19527)
=> ( VX19527 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__19528] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19528)
& VX19527 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__19528) )
| ? [Vvar__0___24Anonymous__19529] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19529)
& VX19527 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__19529) )
| ? [Vvar__0___24Anonymous__19530] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19530)
& VX19527 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__19530) )
| ? [Vvar__0___24Anonymous__19531] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19531)
& VX19527 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__19531) )
| ? [Vvar__0___24Anonymous__19532] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19532)
& VX19527 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__19532) )
| ? [Vvar__0___24Anonymous__19533] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19533)
& VX19527 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__19533) )
| ? [Vvar__0___24Anonymous__19534] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19534)
& VX19527 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__19534) )
| ? [Vvar__0___24Anonymous__19535] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19535)
& VX19527 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__19535) )
| ? [Vvar__0___24Anonymous__19536] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19536)
& VX19527 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__19536) )
| ? [Vvar__0___24Anonymous__19537] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19537)
& VX19527 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__19537) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__7465,Vvar__1___24Anonymous__7466] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__7465)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__7466)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__7465,Vvar__1___24Anonymous__7466)
=> ( Vvar__1___24Anonymous__7466 = Vvar__0__n__7465
| ? [Vvar__1__m__7470] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__7470)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__7465,Vvar__1__m__7470)
& Vvar__1___24Anonymous__7466 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__7470) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__3627,Vvar__1__P__3628,VX3631] :
( cType___24t(Vvar__0__A__3627)
=> ( c_24__type__3641___24t(Vvar__0__A__3627,Vvar__1__P__3628,Vvar__1__P__3628)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__3627,Vvar__1__P__3628,VX3631)
=> ? [Vvar__2__x__3636] :
( t(Vvar__2__x__3636,Vvar__0__A__3627)
& p(happ(Vvar__1__P__3628,Vvar__2__x__3636))
& VX3631 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__3627,Vvar__1__P__3628,Vvar__2__x__3636) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__8036,Vvar__1__P__8037,Vvar__2__Q__8040,VX8043] :
( cType___24t(Vvar__0__A__8036)
=> ( c_24__type__8060___24t(Vvar__0__A__8036,Vvar__1__P__8037,Vvar__2__Q__8040,Vvar__1__P__8037)
=> ( c_24__type__8068___24t(Vvar__0__A__8036,Vvar__1__P__8037,Vvar__2__Q__8040,Vvar__2__Q__8040)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__8036,Vvar__1__P__8037,Vvar__2__Q__8040,VX8043)
=> ? [Vvar__3__x__8051] :
( t(Vvar__3__x__8051,Vvar__0__A__8036)
& p(happ(Vvar__1__P__8037,Vvar__3__x__8051))
& p(happ(Vvar__2__Q__8040,Vvar__3__x__8051))
& VX8043 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__8036,Vvar__1__P__8037,Vvar__2__Q__8040,Vvar__3__x__8051) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__8114,Vvar__1__P__8115,VX8118] :
( cType___24t(Vvar__0__A__8114)
=> ( c_24__type__8128___24t(Vvar__0__A__8114,Vvar__1__P__8115,Vvar__1__P__8115)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__8114,Vvar__1__P__8115,VX8118)
=> ? [Vvar__2__x__8123] :
( t(Vvar__2__x__8123,Vvar__0__A__8114)
& ? [Vvar__3___24Anonymous__8124] :
( t(Vvar__3___24Anonymous__8124,happ(Vvar__1__P__8115,Vvar__2__x__8123))
& VX8118 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__8114,Vvar__1__P__8115,Vvar__2__x__8123,Vvar__3___24Anonymous__8124) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__18373,Vvar__1__P__18374,Vvar__2__Q__18377,VX18380] :
( cType___24t(Vvar__0__A__18373)
=> ( c_24__type__18397___24t(Vvar__0__A__18373,Vvar__1__P__18374,Vvar__2__Q__18377,Vvar__1__P__18374)
=> ( c_24__type__18405___24t(Vvar__0__A__18373,Vvar__1__P__18374,Vvar__2__Q__18377,Vvar__2__Q__18377)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__18373,Vvar__1__P__18374,Vvar__2__Q__18377,VX18380)
=> ? [Vvar__3__x__18388] :
( t(Vvar__3__x__18388,Vvar__0__A__18373)
& ? [Vvar__4___24Anonymous__18389] :
( t(Vvar__4___24Anonymous__18389,happ(Vvar__1__P__18374,Vvar__3__x__18388))
& ? [Vvar__5___24Anonymous__18390] :
( t(Vvar__5___24Anonymous__18390,happ(Vvar__2__Q__18377,Vvar__3__x__18388))
& VX18380 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__18373,Vvar__1__P__18374,Vvar__2__Q__18377,Vvar__3__x__18388,Vvar__4___24Anonymous__18389,Vvar__5___24Anonymous__18390) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__10117,Vvar__1__B__10118,VX10119] :
( cProp___24t(Vvar__0__A__10117)
=> ( cProp___24t(Vvar__1__B__10118)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__10117,Vvar__1__B__10118,VX10119)
=> ( ( p(Vvar__0__A__10117)
& VX10119 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__10117,Vvar__1__B__10118) )
| ( p(Vvar__1__B__10118)
& VX10119 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__10117,Vvar__1__B__10118) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__35053,Vvar__1__B__35054,VX35055] :
( cType___24t(Vvar__0__A__35053)
=> ( cProp___24t(Vvar__1__B__35054)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__35053,Vvar__1__B__35054,VX35055)
=> ( ? [Vvar__2___24Anonymous__35058] :
( t(Vvar__2___24Anonymous__35058,Vvar__0__A__35053)
& VX35055 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__35053,Vvar__1__B__35054,Vvar__2___24Anonymous__35058) )
| ( p(Vvar__1__B__35054)
& VX35055 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__35053,Vvar__1__B__35054) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__10692,Vvar__1__R__10693,Vvar__2__x__10698] :
( cType___24t(Vvar__0__A__10692)
=> ( c_24__type__10727___24t(Vvar__0__A__10692,Vvar__1__R__10693,Vvar__2__x__10698,Vvar__1__R__10693)
=> ( t(Vvar__2__x__10698,Vvar__0__A__10692)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__10692,Vvar__1__R__10693,Vvar__2__x__10698)
=> ( ! [Vvar__var__var__var__var__3__y__10708__10710__10712__10714__10716] :
( t(Vvar__var__var__var__var__3__y__10708__10710__10712__10714__10716,Vvar__0__A__10692)
=> ( p(happ(happ(Vvar__1__R__10693,Vvar__var__var__var__var__3__y__10708__10710__10712__10714__10716),Vvar__2__x__10698))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__10692,Vvar__1__R__10693,Vvar__var__var__var__var__3__y__10708__10710__10712__10714__10716) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__12351,Vvar__1__a__12352,Vvar__2___24Anonymous__12353,Vvar__3___24Anonymous__12354] :
( cType___24t(Vvar__0__A__12351)
=> ( t(Vvar__1__a__12352,Vvar__0__A__12351)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12351,Vvar__2___24Anonymous__12353)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12351,Vvar__3___24Anonymous__12354)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__12351,Vvar__1__a__12352,Vvar__2___24Anonymous__12353,Vvar__3___24Anonymous__12354)
=> ( ? [Vvar__2__l__12358] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12351,Vvar__2__l__12358)
& Vvar__3___24Anonymous__12354 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12351,Vvar__1__a__12352,Vvar__2__l__12358)
& Vvar__2___24Anonymous__12353 = Vvar__2__l__12358 )
| ? [Vvar__2__x__12361] :
( t(Vvar__2__x__12361,Vvar__0__A__12351)
& ? [Vvar__3__l__12362] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12351,Vvar__3__l__12362)
& ? [Vvar__4__l_27__12363] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12351,Vvar__4__l_27__12363)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__12351,Vvar__1__a__12352,Vvar__3__l__12362,Vvar__4__l_27__12363)
& Vvar__3___24Anonymous__12354 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12351,Vvar__2__x__12361,Vvar__4__l_27__12363)
& Vvar__2___24Anonymous__12353 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12351,Vvar__2__x__12361,Vvar__3__l__12362) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__12374,Vvar__1__P__12375,Vvar__2___24Anonymous__12378] :
( cType___24t(Vvar__0__A__12374)
=> ( c_24__type__12398___24t(Vvar__0__A__12374,Vvar__1__P__12375,Vvar__2___24Anonymous__12378,Vvar__1__P__12375)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12374,Vvar__2___24Anonymous__12378)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__12374,Vvar__1__P__12375,Vvar__2___24Anonymous__12378)
=> ( ? [Vvar__2__x__12384] :
( t(Vvar__2__x__12384,Vvar__0__A__12374)
& ? [Vvar__3__l__12385] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12374,Vvar__3__l__12385)
& p(happ(Vvar__1__P__12375,Vvar__2__x__12384))
& Vvar__2___24Anonymous__12378 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12374,Vvar__2__x__12384,Vvar__3__l__12385) ) )
| ? [Vvar__2__x__12391] :
( t(Vvar__2__x__12391,Vvar__0__A__12374)
& ? [Vvar__3__l__12392] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12374,Vvar__3__l__12392)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__12374,Vvar__1__P__12375,Vvar__3__l__12392)
& Vvar__2___24Anonymous__12378 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12374,Vvar__2__x__12391,Vvar__3__l__12392) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__12400,Vvar__1__P__12401,Vvar__2___24Anonymous__12404] :
( cType___24t(Vvar__0__A__12400)
=> ( c_24__type__12422___24t(Vvar__0__A__12400,Vvar__1__P__12401,Vvar__2___24Anonymous__12404,Vvar__1__P__12401)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12400,Vvar__2___24Anonymous__12404)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__12400,Vvar__1__P__12401,Vvar__2___24Anonymous__12404)
=> ( Vvar__2___24Anonymous__12404 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__12400)
| ? [Vvar__2__x__12414] :
( t(Vvar__2__x__12414,Vvar__0__A__12400)
& ? [Vvar__3__l__12415] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12400,Vvar__3__l__12415)
& p(happ(Vvar__1__P__12401,Vvar__2__x__12414))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__12400,Vvar__1__P__12401,Vvar__3__l__12415)
& Vvar__2___24Anonymous__12404 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12400,Vvar__2__x__12414,Vvar__3__l__12415) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__12425,Vvar__1__B__12426,Vvar__2__R__12427,Vvar__3___24Anonymous__12432,Vvar__4___24Anonymous__12433] :
( cType___24t(Vvar__0__A__12425)
=> ( cType___24t(Vvar__1__B__12426)
=> ( c_24__type__12470___24t(Vvar__0__A__12425,Vvar__1__B__12426,Vvar__2__R__12427,Vvar__3___24Anonymous__12432,Vvar__4___24Anonymous__12433,Vvar__2__R__12427)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12425,Vvar__3___24Anonymous__12432)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__12426,Vvar__4___24Anonymous__12433)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__12425,Vvar__1__B__12426,Vvar__2__R__12427,Vvar__3___24Anonymous__12432,Vvar__4___24Anonymous__12433)
=> ( ( Vvar__4___24Anonymous__12433 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__12426)
& Vvar__3___24Anonymous__12432 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__12425) )
| ? [Vvar__3__x__12449] :
( t(Vvar__3__x__12449,Vvar__0__A__12425)
& ? [Vvar__4__y__12450] :
( t(Vvar__4__y__12450,Vvar__1__B__12426)
& ? [Vvar__5__l__12451] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12425,Vvar__5__l__12451)
& ? [Vvar__6__l_27__12452] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__12426,Vvar__6__l_27__12452)
& p(happ(happ(Vvar__2__R__12427,Vvar__3__x__12449),Vvar__4__y__12450))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__12425,Vvar__1__B__12426,Vvar__2__R__12427,Vvar__5__l__12451,Vvar__6__l_27__12452)
& Vvar__4___24Anonymous__12433 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__12426,Vvar__4__y__12450,Vvar__6__l_27__12452)
& Vvar__3___24Anonymous__12432 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12425,Vvar__3__x__12449,Vvar__5__l__12451) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__12472,Vvar__1__R__12473,Vvar__2___24Anonymous__12478] :
( cType___24t(Vvar__0__A__12472)
=> ( c_24__type__12505___24t(Vvar__0__A__12472,Vvar__1__R__12473,Vvar__2___24Anonymous__12478,Vvar__1__R__12473)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12472,Vvar__2___24Anonymous__12478)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__12472,Vvar__1__R__12473,Vvar__2___24Anonymous__12478)
=> ( Vvar__2___24Anonymous__12478 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__12472)
| ? [Vvar__2__a__12492] :
( t(Vvar__2__a__12492,Vvar__0__A__12472)
& ? [Vvar__3__l__12493] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12472,Vvar__3__l__12493)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__12472,happ(Vvar__1__R__12473,Vvar__2__a__12492),Vvar__3__l__12493)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__12472,Vvar__1__R__12473,Vvar__3__l__12493)
& Vvar__2___24Anonymous__12478 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12472,Vvar__2__a__12492,Vvar__3__l__12493) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__12365,Vvar__1___24Anonymous__12366] :
( cType___24t(Vvar__0__A__12365)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12365,Vvar__1___24Anonymous__12366)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__12365,Vvar__1___24Anonymous__12366)
=> ( Vvar__1___24Anonymous__12366 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__12365)
| ? [Vvar__1__x__12370] :
( t(Vvar__1__x__12370,Vvar__0__A__12365)
& ? [Vvar__2__l__12371] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12365,Vvar__2__l__12371)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__12365,Vvar__1__x__12370,Vvar__2__l__12371)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__12365,Vvar__2__l__12371)
& Vvar__1___24Anonymous__12366 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12365,Vvar__1__x__12370,Vvar__2__l__12371) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__4628,Vvar__1__eqA__4629,Vvar__2__x__4634,Vvar__3___24Anonymous__4635] :
( cType___24t(Vvar__0__A__4628)
=> ( c_24__type__4668___24t(Vvar__0__A__4628,Vvar__1__eqA__4629,Vvar__2__x__4634,Vvar__3___24Anonymous__4635,Vvar__1__eqA__4629)
=> ( t(Vvar__2__x__4634,Vvar__0__A__4628)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4628,Vvar__3___24Anonymous__4635)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__4628,Vvar__1__eqA__4629,Vvar__2__x__4634,Vvar__3___24Anonymous__4635)
=> ( ? [Vvar__3__y__4644] :
( t(Vvar__3__y__4644,Vvar__0__A__4628)
& ? [Vvar__4__l__4645] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4628,Vvar__4__l__4645)
& p(happ(happ(Vvar__1__eqA__4629,Vvar__2__x__4634),Vvar__3__y__4644))
& Vvar__3___24Anonymous__4635 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4628,Vvar__3__y__4644,Vvar__4__l__4645) ) )
| ? [Vvar__3__y__4654] :
( t(Vvar__3__y__4654,Vvar__0__A__4628)
& ? [Vvar__4__l__4655] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4628,Vvar__4__l__4655)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__4628,Vvar__1__eqA__4629,Vvar__2__x__4634,Vvar__4__l__4655)
& Vvar__3___24Anonymous__4635 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4628,Vvar__3__y__4654,Vvar__4__l__4655) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__18167,Vvar__1__eqA__18168,Vvar__2___24Anonymous__18173] :
( cType___24t(Vvar__0__A__18167)
=> ( c_24__type__18200___24t(Vvar__0__A__18167,Vvar__1__eqA__18168,Vvar__2___24Anonymous__18173,Vvar__1__eqA__18168)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18167,Vvar__2___24Anonymous__18173)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__18167,Vvar__1__eqA__18168,Vvar__2___24Anonymous__18173)
=> ( Vvar__2___24Anonymous__18173 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__18167)
| ? [Vvar__2__x__18187] :
( t(Vvar__2__x__18187,Vvar__0__A__18167)
& ? [Vvar__3__l__18188] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18167,Vvar__3__l__18188)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__18167,Vvar__1__eqA__18168,Vvar__2__x__18187,Vvar__3__l__18188)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__18167,Vvar__1__eqA__18168,Vvar__3__l__18188)
& Vvar__2___24Anonymous__18173 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__18167,Vvar__2__x__18187,Vvar__3__l__18188) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__18216,Vvar__1__eqA__18217,Vvar__2___24Anonymous__18222,Vvar__3___24Anonymous__18223] :
( cType___24t(Vvar__0__A__18216)
=> ( c_24__type__18254___24t(Vvar__0__A__18216,Vvar__1__eqA__18217,Vvar__2___24Anonymous__18222,Vvar__3___24Anonymous__18223,Vvar__1__eqA__18217)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18216,Vvar__2___24Anonymous__18222)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18216,Vvar__3___24Anonymous__18223)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__18216,Vvar__1__eqA__18217,Vvar__2___24Anonymous__18222,Vvar__3___24Anonymous__18223)
=> ( ( Vvar__3___24Anonymous__18223 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__18216)
& Vvar__2___24Anonymous__18222 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__18216) )
| ? [Vvar__2__x__18237] :
( t(Vvar__2__x__18237,Vvar__0__A__18216)
& ? [Vvar__3__x_27__18238] :
( t(Vvar__3__x_27__18238,Vvar__0__A__18216)
& ? [Vvar__4__l__18239] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18216,Vvar__4__l__18239)
& ? [Vvar__5__l_27__18240] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18216,Vvar__5__l_27__18240)
& p(happ(happ(Vvar__1__eqA__18217,Vvar__2__x__18237),Vvar__3__x_27__18238))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__18216,Vvar__1__eqA__18217,Vvar__4__l__18239,Vvar__5__l_27__18240)
& Vvar__3___24Anonymous__18223 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__18216,Vvar__3__x_27__18238,Vvar__5__l_27__18240)
& Vvar__2___24Anonymous__18222 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__18216,Vvar__2__x__18237,Vvar__4__l__18239) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.boolP',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eboolP)
=> p(c_24True) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.has_fixpoint',axiom,
! [Vvar__0__A__30656] :
( cProp___24t(Vvar__0__A__30656)
=> ( cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1(Vvar__0__A__30656)
=> ( ( ( p(Vvar__0__A__30656)
=> p(Vvar__0__A__30656) )
=> p(Vvar__0__A__30656) )
& ( ( p(Vvar__0__A__30656)
=> p(Vvar__0__A__30656) )
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.retract',axiom,
! [Vvar__0__A__30632,Vvar__1__B__30633] :
( cProp___24t(Vvar__0__A__30632)
=> ( cProp___24t(Vvar__1__B__30633)
=> ( cCoq_2eLogic_2eClassicalFacts_2eretract___24a2(Vvar__0__A__30632,Vvar__1__B__30633)
=> ( ( p(Vvar__0__A__30632)
=> p(Vvar__1__B__30633) )
& ( p(Vvar__1__B__30633)
=> p(Vvar__0__A__30632) )
& ( p(Vvar__1__B__30633)
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__12181,Vvar__1__P__12182,Vvar__2__p__12185,Vvar__3__x__12186,Vvar__4__q__12187,Vvar__5___24Anonymous__12188] :
( cType___24t(Vvar__0__U__12181)
=> ( c_24__type__12203___24t(Vvar__0__U__12181,Vvar__1__P__12182,Vvar__2__p__12185,Vvar__3__x__12186,Vvar__4__q__12187,Vvar__5___24Anonymous__12188,Vvar__1__P__12182)
=> ( t(Vvar__2__p__12185,Vvar__0__U__12181)
=> ( t(Vvar__3__x__12186,happ(Vvar__1__P__12182,Vvar__2__p__12185))
=> ( t(Vvar__4__q__12187,Vvar__0__U__12181)
=> ( t(Vvar__5___24Anonymous__12188,happ(Vvar__1__P__12182,Vvar__4__q__12187))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__12181,Vvar__1__P__12182,Vvar__2__p__12185,Vvar__3__x__12186,Vvar__4__q__12187,Vvar__5___24Anonymous__12188)
=> ( Vvar__5___24Anonymous__12188 = Vvar__3__x__12186
& Vvar__4__q__12187 = Vvar__2__p__12185 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__30771,Vvar__1__P__30772,Vvar__2__p__30775,Vvar__3__x__30776,Vvar__4__q__30777,Vvar__5__y__30778] :
( cType___24t(Vvar__0__U__30771)
=> ( c_24__type__30797___24t(Vvar__0__U__30771,Vvar__1__P__30772,Vvar__2__p__30775,Vvar__3__x__30776,Vvar__4__q__30777,Vvar__5__y__30778,Vvar__1__P__30772)
=> ( t(Vvar__2__p__30775,Vvar__0__U__30771)
=> ( t(Vvar__3__x__30776,happ(Vvar__1__P__30772,Vvar__2__p__30775))
=> ( t(Vvar__4__q__30777,Vvar__0__U__30771)
=> ( t(Vvar__5__y__30778,happ(Vvar__1__P__30772,Vvar__4__q__30777))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__30771,Vvar__1__P__30772,Vvar__2__p__30775,Vvar__3__x__30776,Vvar__4__q__30777,Vvar__5__y__30778)
=> ( Vvar__4__q__30777 = Vvar__2__p__30775
& Vvar__3__x__30776 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__30771,Vvar__4__q__30777,Vvar__1__P__30772,Vvar__5__y__30778,Vvar__2__p__30775)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX3854] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX3854)
=> ( VX3854 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__3855] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3855)
& VX3854 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3855) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX1756] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX1756)
=> ( VX1756 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__1757] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1757)
& VX1756 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1757) )
| ? [Vvar__0___24Anonymous__1758] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1758)
& VX1756 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1758) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX1743] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1743)
=> ( ? [Vvar__0___24Anonymous__1744] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1744)
& VX1743 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1744) )
| ? [Vvar__0___24Anonymous__1745] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1745)
& VX1743 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1745) )
| VX1743 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [Vvar__0___24Anonymous__35420,VX35421] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35420)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__35420,VX35421)
=> ( ( Vvar__0___24Anonymous__35420 = cCoq_2eNumbers_2eBinNums_2exH
& VX35421 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
| ? [Vvar__0__p__35422] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__35422)
& ? [Vvar__1___24Anonymous__35423] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__35422,Vvar__1___24Anonymous__35423)
& Vvar__0___24Anonymous__35420 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435458___24a2(Vvar__0___24Anonymous__35420,Vvar__0__p__35422)
& VX35421 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__35422,Vvar__1___24Anonymous__35423) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
! [Vvar__0__p__11177,Vvar__1__q__11178,Vvar__2___24Anonymous__11179] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__11177)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__11178)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__11179)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__11177,Vvar__1__q__11178,Vvar__2___24Anonymous__11179)
=> ( ( Vvar__0__p__11177 = Vvar__1__q__11178
& Vvar__2___24Anonymous__11179 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
| ? [Vvar__2__r__11186] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__11186)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__11178,Vvar__2__r__11186) = Vvar__0__p__11177
& Vvar__2___24Anonymous__11179 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__11186) )
| ? [Vvar__2__r__11190] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__11190)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__11177,Vvar__2__r__11190) = Vvar__1__q__11178
& Vvar__2___24Anonymous__11179 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX11121] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX11121)
=> ( VX11121 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__11122] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11122)
& VX11121 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__11122) )
| VX11121 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX7476] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX7476)
=> ? [Vvar__0__Qnum__7477] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__7477)
& ? [Vvar__1__Qden__7478] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__7478)
& VX7476 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__7477,Vvar__1__Qden__7478) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
! [VX33454] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(VX33454)
=> ? [Vvar__0__neg__33455] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__33455)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__33455,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX33454 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__33455) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX33433] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX33433)
=> ? [Vvar__0__nonneg__33434] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__33434)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__33434)
& VX33433 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__33434) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
! [VX33447] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX33447)
=> ? [Vvar__0__nonpos__33448] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__33448)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__33448,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX33447 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__33448) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX33461] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX33461)
=> ? [Vvar__0__nonzero__33462] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__33462)
& Vvar__0__nonzero__33462 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX33461 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__33462) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX33440] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX33440)
=> ? [Vvar__0__pos__33441] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__33441)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__33441)
& VX33440 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__33441) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__34144,Vvar__1___24Anonymous__34145,VX34146] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__34144)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__34145)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__34144,Vvar__1___24Anonymous__34145,VX34146)
=> ( ( Vvar__0__x__34144 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__34145 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX34146 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__34144) )
| ? [Vvar__1__n__34150] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__34150)
& Vvar__0__x__34144 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__34150)
& Vvar__1___24Anonymous__34145 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2434170___24a3(Vvar__0__x__34144,Vvar__1___24Anonymous__34145,Vvar__1__n__34150)
& VX34146 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__34144,Vvar__1__n__34150) )
| ? [Vvar__1__n__34155] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__34155)
& Vvar__0__x__34144 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__34155))
& Vvar__1___24Anonymous__34145 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2434187___24a3(Vvar__0__x__34144,Vvar__1___24Anonymous__34145,Vvar__1__n__34155)
& VX34146 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__34144,Vvar__1__n__34155) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
! [Vvar__0__A__7577,Vvar__1__R__7578] :
( cType___24t(Vvar__0__A__7577)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__7577,Vvar__1__R__7578)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__7577,Vvar__1__R__7578)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__7577,Vvar__1__R__7578)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__7577,Vvar__1__R__7578)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
! [Vvar__0__A__7569,Vvar__1__R__7570] :
( cType___24t(Vvar__0__A__7569)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__7569,Vvar__1__R__7570)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__7569,Vvar__1__R__7570)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__7569,Vvar__1__R__7570)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__7569,Vvar__1__R__7570)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__7569,Vvar__1__R__7570)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
! [Vvar__0__A__7561,Vvar__1__R__7562] :
( cType___24t(Vvar__0__A__7561)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__7561,Vvar__1__R__7562)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__7561,Vvar__1__R__7562)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__7561,Vvar__1__R__7562)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__7561,Vvar__1__R__7562)
& cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__7561,Vvar__1__R__7562)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__7554,Vvar__1__R__7555] :
( cType___24t(Vvar__0__A__7554)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__7554,Vvar__1__R__7555)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__7554,Vvar__1__R__7555)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__7554,Vvar__1__R__7555)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__7554,Vvar__1__R__7555)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__33622,Vvar__1__leA__33623,Vvar__2___24Anonymous__33628] :
( cType___24t(Vvar__0__A__33622)
=> ( c_24__type__33718___24t(Vvar__0__A__33622,Vvar__1__leA__33623,Vvar__2___24Anonymous__33628,Vvar__1__leA__33623)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33622,Vvar__2___24Anonymous__33628)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__33622,Vvar__1__leA__33623,Vvar__2___24Anonymous__33628)
=> ( Vvar__2___24Anonymous__33628 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__33622)
| ? [Vvar__2__x__33642] :
( t(Vvar__2__x__33642,Vvar__0__A__33622)
& Vvar__2___24Anonymous__33628 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__33622,Vvar__2__x__33642,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__33622)) )
| ? [Vvar__2__x__33649] :
( t(Vvar__2__x__33649,Vvar__0__A__33622)
& ? [Vvar__3__y__33650] :
( t(Vvar__3__y__33650,Vvar__0__A__33622)
& ? [Vvar__4__l__33651] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33622,Vvar__4__l__33651)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__33622,Vvar__1__leA__33623,Vvar__2__x__33649,Vvar__3__y__33650)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__33622,Vvar__1__leA__33623,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__33622,Vvar__4__l__33651,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__33622,Vvar__3__y__33650,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__33622))))
& Vvar__2___24Anonymous__33628 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2433916___24a6(Vvar__0__A__33622,Vvar__1__leA__33623,Vvar__2___24Anonymous__33628,Vvar__2__x__33649,Vvar__3__y__33650,Vvar__4__l__33651) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__33571,Vvar__1__leA__33572,Vvar__2___24Anonymous__33577,Vvar__3___24Anonymous__33578] :
( cType___24t(Vvar__0__A__33571)
=> ( c_24__type__33620___24t(Vvar__0__A__33571,Vvar__1__leA__33572,Vvar__2___24Anonymous__33577,Vvar__3___24Anonymous__33578,Vvar__1__leA__33572)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33571,Vvar__2___24Anonymous__33577)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33571,Vvar__3___24Anonymous__33578)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__33571,Vvar__1__leA__33572,Vvar__2___24Anonymous__33577,Vvar__3___24Anonymous__33578)
=> ( ? [Vvar__2__a__33586] :
( t(Vvar__2__a__33586,Vvar__0__A__33571)
& ? [Vvar__3__x__33587] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33571,Vvar__3__x__33587)
& Vvar__3___24Anonymous__33578 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__33571,Vvar__2__a__33586,Vvar__3__x__33587)
& Vvar__2___24Anonymous__33577 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__33571) ) )
| ? [Vvar__2__a__33594] :
( t(Vvar__2__a__33594,Vvar__0__A__33571)
& ? [Vvar__3__b__33595] :
( t(Vvar__3__b__33595,Vvar__0__A__33571)
& p(happ(happ(Vvar__1__leA__33572,Vvar__2__a__33594),Vvar__3__b__33595))
& ? [Vvar__5__x__33597] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33571,Vvar__5__x__33597)
& ? [Vvar__6__y__33598] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33571,Vvar__6__y__33598)
& Vvar__3___24Anonymous__33578 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__33571,Vvar__3__b__33595,Vvar__6__y__33598)
& Vvar__2___24Anonymous__33577 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__33571,Vvar__2__a__33594,Vvar__5__x__33597) ) ) ) )
| ? [Vvar__2__a__33605] :
( t(Vvar__2__a__33605,Vvar__0__A__33571)
& ? [Vvar__3__x__33606] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33571,Vvar__3__x__33606)
& ? [Vvar__4__y__33607] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33571,Vvar__4__y__33607)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__33571,Vvar__1__leA__33572,Vvar__3__x__33606,Vvar__4__y__33607)
& Vvar__3___24Anonymous__33578 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__33571,Vvar__2__a__33605,Vvar__4__y__33607)
& Vvar__2___24Anonymous__33577 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__33571,Vvar__2__a__33605,Vvar__3__x__33606) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__7640,Vvar__1__R__7641,Vvar__2__x__7642,Vvar__3___24Anonymous__7643] :
( cType___24t(Vvar__0__A__7640)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__7640,Vvar__1__R__7641)
=> ( t(Vvar__2__x__7642,Vvar__0__A__7640)
=> ( t(Vvar__3___24Anonymous__7643,Vvar__0__A__7640)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__7640,Vvar__1__R__7641,Vvar__2__x__7642,Vvar__3___24Anonymous__7643)
=> ( ? [Vvar__3__y__7648] :
( t(Vvar__3__y__7648,Vvar__0__A__7640)
& p(happ(happ(Vvar__1__R__7641,Vvar__2__x__7642),Vvar__3__y__7648))
& Vvar__3___24Anonymous__7643 = Vvar__3__y__7648 )
| Vvar__3___24Anonymous__7643 = Vvar__2__x__7642 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
! [Vvar__0__A__4536,Vvar__1__R__4537,Vvar__2__x__4538,Vvar__3___24Anonymous__4539] :
( cType___24t(Vvar__0__A__4536)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__4536,Vvar__1__R__4537)
=> ( t(Vvar__2__x__4538,Vvar__0__A__4536)
=> ( t(Vvar__3___24Anonymous__4539,Vvar__0__A__4536)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__4536,Vvar__1__R__4537,Vvar__2__x__4538,Vvar__3___24Anonymous__4539)
=> ( Vvar__3___24Anonymous__4539 = Vvar__2__x__4538
| ? [Vvar__3__y__4547] :
( t(Vvar__3__y__4547,Vvar__0__A__4536)
& ? [Vvar__4__z__4548] :
( t(Vvar__4__z__4548,Vvar__0__A__4536)
& ( p(happ(happ(Vvar__1__R__4537,Vvar__2__x__4538),Vvar__3__y__4547))
| p(happ(happ(Vvar__1__R__4537,Vvar__3__y__4547),Vvar__2__x__4538)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__4536,Vvar__1__R__4537,Vvar__3__y__4547,Vvar__4__z__4548)
& Vvar__3___24Anonymous__4539 = Vvar__4__z__4548 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
! [Vvar__0__A__4551,Vvar__1__R__4552,Vvar__2__x__4553,Vvar__3___24Anonymous__4554] :
( cType___24t(Vvar__0__A__4551)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__4551,Vvar__1__R__4552)
=> ( t(Vvar__2__x__4553,Vvar__0__A__4551)
=> ( t(Vvar__3___24Anonymous__4554,Vvar__0__A__4551)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__4551,Vvar__1__R__4552,Vvar__2__x__4553,Vvar__3___24Anonymous__4554)
=> ( Vvar__3___24Anonymous__4554 = Vvar__2__x__4553
| ? [Vvar__3__y__4562] :
( t(Vvar__3__y__4562,Vvar__0__A__4551)
& ? [Vvar__4__z__4563] :
( t(Vvar__4__z__4563,Vvar__0__A__4551)
& ( p(happ(happ(Vvar__1__R__4552,Vvar__3__y__4562),Vvar__4__z__4563))
| p(happ(happ(Vvar__1__R__4552,Vvar__4__z__4563),Vvar__3__y__4562)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__4551,Vvar__1__R__4552,Vvar__2__x__4553,Vvar__3__y__4562)
& Vvar__3___24Anonymous__4554 = Vvar__4__z__4563 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
! [Vvar__0__A__4461,Vvar__1__R__4462,Vvar__2__x__4463,Vvar__3___24Anonymous__4464] :
( cType___24t(Vvar__0__A__4461)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__4461,Vvar__1__R__4462)
=> ( t(Vvar__2__x__4463,Vvar__0__A__4461)
=> ( t(Vvar__3___24Anonymous__4464,Vvar__0__A__4461)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__4461,Vvar__1__R__4462,Vvar__2__x__4463,Vvar__3___24Anonymous__4464)
=> ( ? [Vvar__3__y__4469] :
( t(Vvar__3__y__4469,Vvar__0__A__4461)
& p(happ(happ(Vvar__1__R__4462,Vvar__2__x__4463),Vvar__3__y__4469))
& Vvar__3___24Anonymous__4464 = Vvar__3__y__4469 )
| Vvar__3___24Anonymous__4464 = Vvar__2__x__4463
| ? [Vvar__3__y__4477] :
( t(Vvar__3__y__4477,Vvar__0__A__4461)
& ? [Vvar__4__z__4478] :
( t(Vvar__4__z__4478,Vvar__0__A__4461)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__4461,Vvar__1__R__4462,Vvar__2__x__4463,Vvar__3__y__4477)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__4461,Vvar__1__R__4462,Vvar__3__y__4477,Vvar__4__z__4478)
& Vvar__3___24Anonymous__4464 = Vvar__4__z__4478 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
! [Vvar__0__A__4481,Vvar__1__R__4482,Vvar__2__x__4483,Vvar__3___24Anonymous__4484] :
( cType___24t(Vvar__0__A__4481)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__4481,Vvar__1__R__4482)
=> ( t(Vvar__2__x__4483,Vvar__0__A__4481)
=> ( t(Vvar__3___24Anonymous__4484,Vvar__0__A__4481)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__4481,Vvar__1__R__4482,Vvar__2__x__4483,Vvar__3___24Anonymous__4484)
=> ( Vvar__3___24Anonymous__4484 = Vvar__2__x__4483
| ? [Vvar__3__y__4492] :
( t(Vvar__3__y__4492,Vvar__0__A__4481)
& ? [Vvar__4__z__4493] :
( t(Vvar__4__z__4493,Vvar__0__A__4481)
& p(happ(happ(Vvar__1__R__4482,Vvar__2__x__4483),Vvar__3__y__4492))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__4481,Vvar__1__R__4482,Vvar__3__y__4492,Vvar__4__z__4493)
& Vvar__3___24Anonymous__4484 = Vvar__4__z__4493 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
! [Vvar__0__A__4496,Vvar__1__R__4497,Vvar__2__x__4498,Vvar__3___24Anonymous__4499] :
( cType___24t(Vvar__0__A__4496)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__4496,Vvar__1__R__4497)
=> ( t(Vvar__2__x__4498,Vvar__0__A__4496)
=> ( t(Vvar__3___24Anonymous__4499,Vvar__0__A__4496)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__4496,Vvar__1__R__4497,Vvar__2__x__4498,Vvar__3___24Anonymous__4499)
=> ( Vvar__3___24Anonymous__4499 = Vvar__2__x__4498
| ? [Vvar__3__y__4507] :
( t(Vvar__3__y__4507,Vvar__0__A__4496)
& ? [Vvar__4__z__4508] :
( t(Vvar__4__z__4508,Vvar__0__A__4496)
& p(happ(happ(Vvar__1__R__4497,Vvar__3__y__4507),Vvar__4__z__4508))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__4496,Vvar__1__R__4497,Vvar__2__x__4498,Vvar__3__y__4507)
& Vvar__3___24Anonymous__4499 = Vvar__4__z__4508 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
! [Vvar__0__A__1238,Vvar__1__R__1239,Vvar__2__x__1240,Vvar__3___24Anonymous__1241] :
( cType___24t(Vvar__0__A__1238)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__1238,Vvar__1__R__1239)
=> ( t(Vvar__2__x__1240,Vvar__0__A__1238)
=> ( t(Vvar__3___24Anonymous__1241,Vvar__0__A__1238)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__1238,Vvar__1__R__1239,Vvar__2__x__1240,Vvar__3___24Anonymous__1241)
=> ( ? [Vvar__3__y__1246] :
( t(Vvar__3__y__1246,Vvar__0__A__1238)
& p(happ(happ(Vvar__1__R__1239,Vvar__2__x__1240),Vvar__3__y__1246))
& Vvar__3___24Anonymous__1241 = Vvar__3__y__1246 )
| ? [Vvar__3__y__1251] :
( t(Vvar__3__y__1251,Vvar__0__A__1238)
& ? [Vvar__4__z__1252] :
( t(Vvar__4__z__1252,Vvar__0__A__1238)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__1238,Vvar__1__R__1239,Vvar__2__x__1240,Vvar__3__y__1251)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__1238,Vvar__1__R__1239,Vvar__3__y__1251,Vvar__4__z__1252)
& Vvar__3___24Anonymous__1241 = Vvar__4__z__1252 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
! [Vvar__0__A__4419,Vvar__1__R__4420,Vvar__2__x__4421,Vvar__3___24Anonymous__4422] :
( cType___24t(Vvar__0__A__4419)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__4419,Vvar__1__R__4420)
=> ( t(Vvar__2__x__4421,Vvar__0__A__4419)
=> ( t(Vvar__3___24Anonymous__4422,Vvar__0__A__4419)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__4419,Vvar__1__R__4420,Vvar__2__x__4421,Vvar__3___24Anonymous__4422)
=> ( ? [Vvar__3__y__4427] :
( t(Vvar__3__y__4427,Vvar__0__A__4419)
& p(happ(happ(Vvar__1__R__4420,Vvar__2__x__4421),Vvar__3__y__4427))
& Vvar__3___24Anonymous__4422 = Vvar__3__y__4427 )
| ? [Vvar__3__y__4432] :
( t(Vvar__3__y__4432,Vvar__0__A__4419)
& ? [Vvar__4__z__4433] :
( t(Vvar__4__z__4433,Vvar__0__A__4419)
& p(happ(happ(Vvar__1__R__4420,Vvar__2__x__4421),Vvar__3__y__4432))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__4419,Vvar__1__R__4420,Vvar__3__y__4432,Vvar__4__z__4433)
& Vvar__3___24Anonymous__4422 = Vvar__4__z__4433 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
! [Vvar__0__A__4436,Vvar__1__R__4437,Vvar__2__x__4438,Vvar__3___24Anonymous__4439] :
( cType___24t(Vvar__0__A__4436)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__4436,Vvar__1__R__4437)
=> ( t(Vvar__2__x__4438,Vvar__0__A__4436)
=> ( t(Vvar__3___24Anonymous__4439,Vvar__0__A__4436)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__4436,Vvar__1__R__4437,Vvar__2__x__4438,Vvar__3___24Anonymous__4439)
=> ( ? [Vvar__3__y__4444] :
( t(Vvar__3__y__4444,Vvar__0__A__4436)
& p(happ(happ(Vvar__1__R__4437,Vvar__2__x__4438),Vvar__3__y__4444))
& Vvar__3___24Anonymous__4439 = Vvar__3__y__4444 )
| ? [Vvar__3__y__4449] :
( t(Vvar__3__y__4449,Vvar__0__A__4436)
& ? [Vvar__4__z__4450] :
( t(Vvar__4__z__4450,Vvar__0__A__4436)
& p(happ(happ(Vvar__1__R__4437,Vvar__3__y__4449),Vvar__4__z__4450))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__4436,Vvar__1__R__4437,Vvar__2__x__4438,Vvar__3__y__4449)
& Vvar__3___24Anonymous__4439 = Vvar__4__z__4450 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.symprod',axiom,
! [Vvar__0__A__33474,Vvar__1__B__33475,Vvar__2__leA__33476,Vvar__3__leB__33481,Vvar__4___24Anonymous__33486,Vvar__5___24Anonymous__33487] :
( cType___24t(Vvar__0__A__33474)
=> ( cType___24t(Vvar__1__B__33475)
=> ( c_24__type__33544___24t(Vvar__0__A__33474,Vvar__1__B__33475,Vvar__2__leA__33476,Vvar__3__leB__33481,Vvar__4___24Anonymous__33486,Vvar__5___24Anonymous__33487,Vvar__2__leA__33476)
=> ( c_24__type__33569___24t(Vvar__0__A__33474,Vvar__1__B__33475,Vvar__2__leA__33476,Vvar__3__leB__33481,Vvar__4___24Anonymous__33486,Vvar__5___24Anonymous__33487,Vvar__3__leB__33481)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__33474,Vvar__1__B__33475,Vvar__4___24Anonymous__33486)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__33474,Vvar__1__B__33475,Vvar__5___24Anonymous__33487)
=> ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__33474,Vvar__1__B__33475,Vvar__2__leA__33476,Vvar__3__leB__33481,Vvar__4___24Anonymous__33486,Vvar__5___24Anonymous__33487)
=> ( ? [Vvar__4__x__33501] :
( t(Vvar__4__x__33501,Vvar__0__A__33474)
& ? [Vvar__5__x_27__33502] :
( t(Vvar__5__x_27__33502,Vvar__0__A__33474)
& p(happ(happ(Vvar__2__leA__33476,Vvar__4__x__33501),Vvar__5__x_27__33502))
& ? [Vvar__7__y__33504] :
( t(Vvar__7__y__33504,Vvar__1__B__33475)
& Vvar__5___24Anonymous__33487 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__33474,Vvar__1__B__33475,Vvar__5__x_27__33502,Vvar__7__y__33504)
& Vvar__4___24Anonymous__33486 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__33474,Vvar__1__B__33475,Vvar__4__x__33501,Vvar__7__y__33504) ) ) )
| ? [Vvar__4__y__33517] :
( t(Vvar__4__y__33517,Vvar__1__B__33475)
& ? [Vvar__5__y_27__33518] :
( t(Vvar__5__y_27__33518,Vvar__1__B__33475)
& p(happ(happ(Vvar__3__leB__33481,Vvar__4__y__33517),Vvar__5__y_27__33518))
& ? [Vvar__7__x__33520] :
( t(Vvar__7__x__33520,Vvar__0__A__33474)
& Vvar__5___24Anonymous__33487 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__33474,Vvar__1__B__33475,Vvar__7__x__33520,Vvar__5__y_27__33518)
& Vvar__4___24Anonymous__33486 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__33474,Vvar__1__B__33475,Vvar__7__x__33520,Vvar__4__y__33517) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Permutation.Permutation',axiom,
! [Vvar__0__A__12553,Vvar__1___24Anonymous__12554,Vvar__2___24Anonymous__12555] :
( cType___24t(Vvar__0__A__12553)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12553,Vvar__1___24Anonymous__12554)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12553,Vvar__2___24Anonymous__12555)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__12553,Vvar__1___24Anonymous__12554,Vvar__2___24Anonymous__12555)
=> ( ( Vvar__2___24Anonymous__12555 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__12553)
& Vvar__1___24Anonymous__12554 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__12553) )
| ? [Vvar__1__x__12559] :
( t(Vvar__1__x__12559,Vvar__0__A__12553)
& ? [Vvar__2__l__12560] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12553,Vvar__2__l__12560)
& ? [Vvar__3__l_27__12561] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12553,Vvar__3__l_27__12561)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__12553,Vvar__2__l__12560,Vvar__3__l_27__12561)
& Vvar__2___24Anonymous__12555 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12553,Vvar__1__x__12559,Vvar__3__l_27__12561)
& Vvar__1___24Anonymous__12554 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12553,Vvar__1__x__12559,Vvar__2__l__12560) ) ) )
| ? [Vvar__1__x__12564] :
( t(Vvar__1__x__12564,Vvar__0__A__12553)
& ? [Vvar__2__y__12565] :
( t(Vvar__2__y__12565,Vvar__0__A__12553)
& ? [Vvar__3__l__12566] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12553,Vvar__3__l__12566)
& Vvar__2___24Anonymous__12555 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12553,Vvar__1__x__12564,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12553,Vvar__2__y__12565,Vvar__3__l__12566))
& Vvar__1___24Anonymous__12554 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12553,Vvar__2__y__12565,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12553,Vvar__1__x__12564,Vvar__3__l__12566)) ) ) )
| ? [Vvar__1__l__12568] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12553,Vvar__1__l__12568)
& ? [Vvar__2__l_27__12569] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12553,Vvar__2__l_27__12569)
& ? [Vvar__3__l_27_27__12570] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12553,Vvar__3__l_27_27__12570)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__12553,Vvar__1__l__12568,Vvar__2__l_27__12569)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__12553,Vvar__2__l_27__12569,Vvar__3__l_27_27__12570)
& Vvar__2___24Anonymous__12555 = Vvar__3__l_27_27__12570
& Vvar__1___24Anonymous__12554 = Vvar__1__l__12568 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__18299,Vvar__1__R__18300,Vvar__2__a__18305,Vvar__3___24Anonymous__18306] :
( cType___24t(Vvar__0__A__18299)
=> ( c_24__type__18336___24t(Vvar__0__A__18299,Vvar__1__R__18300,Vvar__2__a__18305,Vvar__3___24Anonymous__18306,Vvar__1__R__18300)
=> ( t(Vvar__2__a__18305,Vvar__0__A__18299)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18299,Vvar__3___24Anonymous__18306)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__18299,Vvar__1__R__18300,Vvar__2__a__18305,Vvar__3___24Anonymous__18306)
=> ( Vvar__3___24Anonymous__18306 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__18299)
| ? [Vvar__3__b__18322] :
( t(Vvar__3__b__18322,Vvar__0__A__18299)
& ? [Vvar__4__l__18323] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18299,Vvar__4__l__18323)
& p(happ(happ(Vvar__1__R__18300,Vvar__2__a__18305),Vvar__3__b__18322))
& Vvar__3___24Anonymous__18306 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__18299,Vvar__3__b__18322,Vvar__4__l__18323) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__18256,Vvar__1__R__18257,Vvar__2___24Anonymous__18262] :
( cType___24t(Vvar__0__A__18256)
=> ( c_24__type__18297___24t(Vvar__0__A__18256,Vvar__1__R__18257,Vvar__2___24Anonymous__18262,Vvar__1__R__18257)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18256,Vvar__2___24Anonymous__18262)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__18256,Vvar__1__R__18257,Vvar__2___24Anonymous__18262)
=> ( Vvar__2___24Anonymous__18262 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__18256)
| ? [Vvar__2__a__18276] :
( t(Vvar__2__a__18276,Vvar__0__A__18256)
& Vvar__2___24Anonymous__18262 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__18256,Vvar__2__a__18276,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__18256)) )
| ? [Vvar__2__a__18283] :
( t(Vvar__2__a__18283,Vvar__0__A__18256)
& ? [Vvar__3__b__18284] :
( t(Vvar__3__b__18284,Vvar__0__A__18256)
& ? [Vvar__4__l__18285] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18256,Vvar__4__l__18285)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__18256,Vvar__1__R__18257,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__18256,Vvar__3__b__18284,Vvar__4__l__18285))
& p(happ(happ(Vvar__1__R__18257,Vvar__2__a__18283),Vvar__3__b__18284))
& Vvar__2___24Anonymous__18262 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__18256,Vvar__2__a__18283,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__18256,Vvar__3__b__18284,Vvar__4__l__18285)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__18338,Vvar__1__R__18339,Vvar__2___24Anonymous__18344] :
( cType___24t(Vvar__0__A__18338)
=> ( c_24__type__18371___24t(Vvar__0__A__18338,Vvar__1__R__18339,Vvar__2___24Anonymous__18344,Vvar__1__R__18339)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18338,Vvar__2___24Anonymous__18344)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__18338,Vvar__1__R__18339,Vvar__2___24Anonymous__18344)
=> ( Vvar__2___24Anonymous__18344 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__18338)
| ? [Vvar__2__a__18358] :
( t(Vvar__2__a__18358,Vvar__0__A__18338)
& ? [Vvar__3__l__18359] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18338,Vvar__3__l__18359)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__18338,Vvar__1__R__18339,Vvar__3__l__18359)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__18338,Vvar__1__R__18339,Vvar__2__a__18358,Vvar__3__l__18359)
& Vvar__2___24Anonymous__18344 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__18338,Vvar__2__a__18358,Vvar__3__l__18359) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__28148,Vvar__1__R__28149,Vvar__2___24Anonymous__28154] :
( cType___24t(Vvar__0__A__28148)
=> ( c_24__type__28181___24t(Vvar__0__A__28148,Vvar__1__R__28149,Vvar__2___24Anonymous__28154,Vvar__1__R__28149)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28148,Vvar__2___24Anonymous__28154)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__28148,Vvar__1__R__28149,Vvar__2___24Anonymous__28154)
=> ( Vvar__2___24Anonymous__28154 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28148)
| ? [Vvar__2__a__28168] :
( t(Vvar__2__a__28168,Vvar__0__A__28148)
& ? [Vvar__3__l__28169] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28148,Vvar__3__l__28169)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__28148,Vvar__1__R__28149,Vvar__3__l__28169)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__28148,happ(Vvar__1__R__28149,Vvar__2__a__28168),Vvar__3__l__28169)
& Vvar__2___24Anonymous__28154 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28148,Vvar__2__a__28168,Vvar__3__l__28169) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX5469] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX5469)
=> ? [Vvar__0___24Anonymous__5470] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__5470)
& ? [Vvar__1___24Anonymous__5471] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__5471)
& ? [Vvar__2___24Anonymous__5472] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__5472)
& ? [Vvar__3___24Anonymous__5473] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__5473)
& ? [Vvar__4___24Anonymous__5474] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__5474)
& ? [Vvar__5___24Anonymous__5475] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__5475)
& ? [Vvar__6___24Anonymous__5476] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__5476)
& ? [Vvar__7___24Anonymous__5477] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__5477)
& VX5469 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__5470,Vvar__1___24Anonymous__5471,Vvar__2___24Anonymous__5472,Vvar__3___24Anonymous__5473,Vvar__4___24Anonymous__5474,Vvar__5___24Anonymous__5475,Vvar__6___24Anonymous__5476,Vvar__7___24Anonymous__5477) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX18451] :
( cCoq_2eStrings_2eString_2estring___24t(VX18451)
=> ( VX18451 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__18452] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__18452)
& ? [Vvar__1___24Anonymous__18453] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__18453)
& VX18451 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__18452,Vvar__1___24Anonymous__18453) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__33237,Vvar__1__lt__33238,Vvar__2__eq__33243,Vvar__3__x__33248,Vvar__4__y__33249,VX33250] :
( cType___24t(Vvar__0__X__33237)
=> ( c_24__type__33310___24t(Vvar__0__X__33237,Vvar__1__lt__33238,Vvar__2__eq__33243,Vvar__3__x__33248,Vvar__4__y__33249,Vvar__1__lt__33238)
=> ( c_24__type__33329___24t(Vvar__0__X__33237,Vvar__1__lt__33238,Vvar__2__eq__33243,Vvar__3__x__33248,Vvar__4__y__33249,Vvar__2__eq__33243)
=> ( t(Vvar__3__x__33248,Vvar__0__X__33237)
=> ( t(Vvar__4__y__33249,Vvar__0__X__33237)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__33237,Vvar__1__lt__33238,Vvar__2__eq__33243,Vvar__3__x__33248,Vvar__4__y__33249,VX33250)
=> ( ( p(happ(happ(Vvar__1__lt__33238,Vvar__3__x__33248),Vvar__4__y__33249))
& VX33250 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__33237,Vvar__1__lt__33238,Vvar__2__eq__33243,Vvar__3__x__33248,Vvar__4__y__33249) )
| ( p(happ(happ(Vvar__2__eq__33243,Vvar__3__x__33248),Vvar__4__y__33249))
& VX33250 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__33237,Vvar__1__lt__33238,Vvar__2__eq__33243,Vvar__3__x__33248,Vvar__4__y__33249) )
| ( p(happ(happ(Vvar__1__lt__33238,Vvar__4__y__33249),Vvar__3__x__33248))
& VX33250 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__33237,Vvar__1__lt__33238,Vvar__2__eq__33243,Vvar__3__x__33248,Vvar__4__y__33249) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__35499,Vvar__1___24Anonymous__35500] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__35499)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__35500)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__35499,Vvar__1___24Anonymous__35500)
=> ( ? [Vvar__0__a__35502] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__35502)
& ? [Vvar__1__s__35503] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__35503)
& Vvar__1___24Anonymous__35500 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__35502,Vvar__1__s__35503)
& Vvar__0___24Anonymous__35499 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__35504] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__35504)
& ? [Vvar__1__s1__35505] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__35505)
& ? [Vvar__2__s2__35506] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__35506)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__35505,Vvar__2__s2__35506)
& Vvar__1___24Anonymous__35500 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__35504,Vvar__2__s2__35506)
& Vvar__0___24Anonymous__35499 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__35504,Vvar__1__s1__35505) ) ) )
| ? [Vvar__0__a__35508] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__35508)
& ? [Vvar__1__b__35509] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__35509)
& ? [Vvar__2__s1__35510] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__35510)
& ? [Vvar__3__s2__35511] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__35511)
& cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__35508),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__35509))
& Vvar__1___24Anonymous__35500 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__35509,Vvar__3__s2__35511)
& Vvar__0___24Anonymous__35499 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__35508,Vvar__2__s1__35510) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX21116] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX21116)
=> ( VX21116 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX21116 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX21116 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__6754,VX6755] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6754)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__6754,VX6755)
=> ( ? [Vvar__0__n__6756] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__6756)
& Vvar__0___24Anonymous__6754 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__6756)
& VX6755 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__6756) )
| ? [Vvar__0__n__6757] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__6757)
& ? [Vvar__1___24Anonymous__6758] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__6757,Vvar__1___24Anonymous__6758)
& Vvar__0___24Anonymous__6754 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__6757)
& VX6755 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__6757,Vvar__1___24Anonymous__6758) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__10157,Vvar__1___24Anonymous__10158,VX10159] :
( cType___24t(Vvar__0__A__10157)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__10158)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__10157,Vvar__1___24Anonymous__10158,VX10159)
=> ( ( Vvar__1___24Anonymous__10158 = cCoq_2eInit_2eDatatypes_2eO
& VX10159 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__10157) )
| ? [Vvar__1__h__10162] :
( t(Vvar__1__h__10162,Vvar__0__A__10157)
& ? [Vvar__2__n__10163] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__10163)
& ? [Vvar__3___24Anonymous__10164] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__10157,Vvar__2__n__10163,Vvar__3___24Anonymous__10164)
& Vvar__1___24Anonymous__10158 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__10163)
& VX10159 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__10157,Vvar__1__h__10162,Vvar__2__n__10163,Vvar__3___24Anonymous__10164) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__35232,Vvar__1__b__35233,Vvar__2__d__35234] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__35232)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__35233)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__35234)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__35232,Vvar__1__b__35233,Vvar__2__d__35234)
=> ? [Vvar__3__u__35239] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__35239)
& ? [Vvar__4__v__35240] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__35240)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__35239,Vvar__0__a__35232),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__35240,Vvar__1__b__35233)) = Vvar__2__d__35234
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__35207,Vvar__1__b__35208,VX35209] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__35207)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__35208)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__35207,Vvar__1__b__35208,VX35209)
=> ? [Vvar__2__u__35212] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__35212)
& ? [Vvar__3__v__35213] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__35213)
& ? [Vvar__4__d__35214] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__35214)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__35212,Vvar__0__a__35207),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__35213,Vvar__1__b__35208)) = Vvar__4__d__35214
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__35207,Vvar__1__b__35208,Vvar__4__d__35214)
& VX35209 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__35207,Vvar__1__b__35208,Vvar__2__u__35212,Vvar__3__v__35213,Vvar__4__d__35214) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__18521,Vvar__1__b__18522,Vvar__2__g__18523] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__18521)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__18522)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__18523)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__18521,Vvar__1__b__18522,Vvar__2__g__18523)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__18523,Vvar__0__a__18521)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__18523,Vvar__1__b__18522)
& ! [Vvar__var__var__var__var__5__x__18531__18534__18537__18540__18543] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__18531__18534__18537__18540__18543)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__18531__18534__18537__18540__18543,Vvar__0__a__18521)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__18531__18534__18537__18540__18543,Vvar__1__b__18522)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__18531__18534__18537__18540__18543,Vvar__2__g__18523) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__18549] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__18549)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__18549)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__18549)
& ! [Vvar__var__var__2__n__18554__18556__18558] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__18554__18556__18558)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__18554__18556__18558)
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__18554__18556__18558,Vvar__0__p__18549) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__18554__18556__18558,Vvar__0__p__18549) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__35242,Vvar__1__p__35243,VX35244] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__35242)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__35243)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__35242,Vvar__1__p__35243,VX35244)
=> ? [Vvar__2__q__35247] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__35247)
& ? [Vvar__3__r__35248] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__35248)
& Vvar__0__x__35242 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__35247,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__35243)),Vvar__3__r__35248)
& cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__35248)
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__35248,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__35243))
& VX35244 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__35242,Vvar__1__p__35243,Vvar__2__q__35247,Vvar__3__r__35248) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
! [Vvar__0__T__30740,Vvar__1__F__30741] :
( cType___24t(Vvar__0__T__30740)
=> ( t(Vvar__1__F__30741,Vvar__0__T__30740)
=> ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__30740,Vvar__1__F__30741)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
! [Vvar__0__T__30745,Vvar__1__F__30746] :
( cType___24t(Vvar__0__T__30745)
=> ( t(Vvar__1__F__30746,Vvar__0__T__30745)
=> ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__30745,Vvar__1__F__30746)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX30750] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX30750)
=> ( VX30750 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__30751] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30751)
& ? [Vvar__1___24Anonymous__30752] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__30752)
& VX30750 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__30751,Vvar__1___24Anonymous__30752) ) )
| ? [Vvar__0___24Anonymous__30753] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30753)
& ? [Vvar__1___24Anonymous__30754] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__30754)
& VX30750 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__30753,Vvar__1___24Anonymous__30754) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__11960,VX11961] :
( cType___24t(Vvar__0__C__11960)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__11960,VX11961)
=> ( ? [Vvar__1___24Anonymous__11963] :
( t(Vvar__1___24Anonymous__11963,Vvar__0__C__11960)
& VX11961 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__11960,Vvar__1___24Anonymous__11963) )
| ? [Vvar__1___24Anonymous__11965] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__11965)
& VX11961 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__11960,Vvar__1___24Anonymous__11965) )
| ? [Vvar__1___24Anonymous__11967] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__11960,Vvar__1___24Anonymous__11967)
& ? [Vvar__2___24Anonymous__11968] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__11960,Vvar__2___24Anonymous__11968)
& VX11961 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__11960,Vvar__1___24Anonymous__11967,Vvar__2___24Anonymous__11968) ) )
| ? [Vvar__1___24Anonymous__11970] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__11960,Vvar__1___24Anonymous__11970)
& ? [Vvar__2___24Anonymous__11971] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__11960,Vvar__2___24Anonymous__11971)
& VX11961 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__11960,Vvar__1___24Anonymous__11970,Vvar__2___24Anonymous__11971) ) )
| ? [Vvar__1___24Anonymous__11973] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__11960,Vvar__1___24Anonymous__11973)
& ? [Vvar__2___24Anonymous__11974] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__11960,Vvar__2___24Anonymous__11974)
& VX11961 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__11960,Vvar__1___24Anonymous__11973,Vvar__2___24Anonymous__11974) ) )
| ? [Vvar__1___24Anonymous__11976] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__11960,Vvar__1___24Anonymous__11976)
& VX11961 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__11960,Vvar__1___24Anonymous__11976) )
| ? [Vvar__1___24Anonymous__11978] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__11960,Vvar__1___24Anonymous__11978)
& ? [Vvar__2___24Anonymous__11979] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__11979)
& VX11961 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__11960,Vvar__1___24Anonymous__11978,Vvar__2___24Anonymous__11979) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__12124,VX12125] :
( cType___24t(Vvar__0__C__12124)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__12124,VX12125)
=> ( ? [Vvar__1___24Anonymous__12127] :
( t(Vvar__1___24Anonymous__12127,Vvar__0__C__12124)
& VX12125 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__12124,Vvar__1___24Anonymous__12127) )
| ? [Vvar__1___24Anonymous__12129] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12129)
& ? [Vvar__2___24Anonymous__12130] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__12124,Vvar__2___24Anonymous__12130)
& VX12125 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__12124,Vvar__1___24Anonymous__12129,Vvar__2___24Anonymous__12130) ) )
| ? [Vvar__1___24Anonymous__12132] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__12124,Vvar__1___24Anonymous__12132)
& ? [Vvar__2___24Anonymous__12133] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12133)
& ? [Vvar__3___24Anonymous__12134] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__12124,Vvar__3___24Anonymous__12134)
& VX12125 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__12124,Vvar__1___24Anonymous__12132,Vvar__2___24Anonymous__12133,Vvar__3___24Anonymous__12134) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__104,Vvar__1__rO__105,Vvar__2__rI__106,Vvar__3__rplus__107,Vvar__4__rtimes__112,Vvar__5__rminus__117,Vvar__6__ropp__122,Vvar__7__req__125,Vvar__8__rle__130,Vvar__9__rlt__135] :
( cType___24t(Vvar__0__R__104)
=> ( t(Vvar__1__rO__105,Vvar__0__R__104)
=> ( t(Vvar__2__rI__106,Vvar__0__R__104)
=> ( c_24__type__536___24t(Vvar__0__R__104,Vvar__1__rO__105,Vvar__2__rI__106,Vvar__3__rplus__107,Vvar__4__rtimes__112,Vvar__5__rminus__117,Vvar__6__ropp__122,Vvar__7__req__125,Vvar__8__rle__130,Vvar__9__rlt__135,Vvar__3__rplus__107)
=> ( c_24__type__637___24t(Vvar__0__R__104,Vvar__1__rO__105,Vvar__2__rI__106,Vvar__3__rplus__107,Vvar__4__rtimes__112,Vvar__5__rminus__117,Vvar__6__ropp__122,Vvar__7__req__125,Vvar__8__rle__130,Vvar__9__rlt__135,Vvar__4__rtimes__112)
=> ( c_24__type__738___24t(Vvar__0__R__104,Vvar__1__rO__105,Vvar__2__rI__106,Vvar__3__rplus__107,Vvar__4__rtimes__112,Vvar__5__rminus__117,Vvar__6__ropp__122,Vvar__7__req__125,Vvar__8__rle__130,Vvar__9__rlt__135,Vvar__5__rminus__117)
=> ( c_24__type__828___24t(Vvar__0__R__104,Vvar__1__rO__105,Vvar__2__rI__106,Vvar__3__rplus__107,Vvar__4__rtimes__112,Vvar__5__rminus__117,Vvar__6__ropp__122,Vvar__7__req__125,Vvar__8__rle__130,Vvar__9__rlt__135,Vvar__6__ropp__122)
=> ( c_24__type__929___24t(Vvar__0__R__104,Vvar__1__rO__105,Vvar__2__rI__106,Vvar__3__rplus__107,Vvar__4__rtimes__112,Vvar__5__rminus__117,Vvar__6__ropp__122,Vvar__7__req__125,Vvar__8__rle__130,Vvar__9__rlt__135,Vvar__7__req__125)
=> ( c_24__type__1030___24t(Vvar__0__R__104,Vvar__1__rO__105,Vvar__2__rI__106,Vvar__3__rplus__107,Vvar__4__rtimes__112,Vvar__5__rminus__117,Vvar__6__ropp__122,Vvar__7__req__125,Vvar__8__rle__130,Vvar__9__rlt__135,Vvar__8__rle__130)
=> ( c_24__type__1131___24t(Vvar__0__R__104,Vvar__1__rO__105,Vvar__2__rI__106,Vvar__3__rplus__107,Vvar__4__rtimes__112,Vvar__5__rminus__117,Vvar__6__ropp__122,Vvar__7__req__125,Vvar__8__rle__130,Vvar__9__rlt__135,Vvar__9__rlt__135)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__104,Vvar__1__rO__105,Vvar__2__rI__106,Vvar__3__rplus__107,Vvar__4__rtimes__112,Vvar__5__rminus__117,Vvar__6__ropp__122,Vvar__7__req__125,Vvar__8__rle__130,Vvar__9__rlt__135)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__104,Vvar__7__req__125)
& ! [Vvar__var__var__var__var__11__x1__179__185__290__296__302] :
( t(Vvar__var__var__var__var__11__x1__179__185__290__296__302,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__12__x2__180__186__291__297__303] :
( t(Vvar__var__var__var__var__12__x2__180__186__291__297__303,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__7__req__125,Vvar__var__var__var__var__11__x1__179__185__290__296__302),Vvar__var__var__var__var__12__x2__180__186__291__297__303))
=> ! [Vvar__var__var__var__var__14__y1__181__187__292__298__304] :
( t(Vvar__var__var__var__var__14__y1__181__187__292__298__304,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__15__y2__182__188__293__299__305] :
( t(Vvar__var__var__var__var__15__y2__182__188__293__299__305,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__7__req__125,Vvar__var__var__var__var__14__y1__181__187__292__298__304),Vvar__var__var__var__var__15__y2__182__188__293__299__305))
=> p(happ(happ(Vvar__7__req__125,happ(happ(Vvar__3__rplus__107,Vvar__var__var__var__var__11__x1__179__185__290__296__302),Vvar__var__var__var__var__14__y1__181__187__292__298__304)),happ(happ(Vvar__3__rplus__107,Vvar__var__var__var__var__12__x2__180__186__291__297__303),Vvar__var__var__var__var__15__y2__182__188__293__299__305))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__192__198__308__314__320] :
( t(Vvar__var__var__var__var__12__x1__192__198__308__314__320,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__13__x2__193__199__309__315__321] :
( t(Vvar__var__var__var__var__13__x2__193__199__309__315__321,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__7__req__125,Vvar__var__var__var__var__12__x1__192__198__308__314__320),Vvar__var__var__var__var__13__x2__193__199__309__315__321))
=> ! [Vvar__var__var__var__var__15__y1__194__200__310__316__322] :
( t(Vvar__var__var__var__var__15__y1__194__200__310__316__322,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__16__y2__195__201__311__317__323] :
( t(Vvar__var__var__var__var__16__y2__195__201__311__317__323,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__7__req__125,Vvar__var__var__var__var__15__y1__194__200__310__316__322),Vvar__var__var__var__var__16__y2__195__201__311__317__323))
=> p(happ(happ(Vvar__7__req__125,happ(happ(Vvar__4__rtimes__112,Vvar__var__var__var__var__12__x1__192__198__308__314__320),Vvar__var__var__var__var__15__y1__194__200__310__316__322)),happ(happ(Vvar__4__rtimes__112,Vvar__var__var__var__var__13__x2__193__199__309__315__321),Vvar__var__var__var__var__16__y2__195__201__311__317__323))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__205__208__326__329__332] :
( t(Vvar__var__var__var__var__13__x1__205__208__326__329__332,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__14__x2__206__209__327__330__333] :
( t(Vvar__var__var__var__var__14__x2__206__209__327__330__333,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__7__req__125,Vvar__var__var__var__var__13__x1__205__208__326__329__332),Vvar__var__var__var__var__14__x2__206__209__327__330__333))
=> p(happ(happ(Vvar__7__req__125,happ(Vvar__6__ropp__122,Vvar__var__var__var__var__13__x1__205__208__326__329__332)),happ(Vvar__6__ropp__122,Vvar__var__var__var__var__14__x2__206__209__327__330__333))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__212__218__335__341__347] :
( t(Vvar__var__var__var__var__14__x1__212__218__335__341__347,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__15__x2__213__219__336__342__348] :
( t(Vvar__var__var__var__var__15__x2__213__219__336__342__348,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__7__req__125,Vvar__var__var__var__var__14__x1__212__218__335__341__347),Vvar__var__var__var__var__15__x2__213__219__336__342__348))
=> ! [Vvar__var__var__var__var__17__y1__214__220__337__343__349] :
( t(Vvar__var__var__var__var__17__y1__214__220__337__343__349,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__18__y2__215__221__338__344__350] :
( t(Vvar__var__var__var__var__18__y2__215__221__338__344__350,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__7__req__125,Vvar__var__var__var__var__17__y1__214__220__337__343__349),Vvar__var__var__var__var__18__y2__215__221__338__344__350))
=> ( p(happ(happ(Vvar__8__rle__130,Vvar__var__var__var__var__14__x1__212__218__335__341__347),Vvar__var__var__var__var__17__y1__214__220__337__343__349))
<=> p(happ(happ(Vvar__8__rle__130,Vvar__var__var__var__var__15__x2__213__219__336__342__348),Vvar__var__var__var__var__18__y2__215__221__338__344__350)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__225__231__353__359__365] :
( t(Vvar__var__var__var__var__15__x1__225__231__353__359__365,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__16__x2__226__232__354__360__366] :
( t(Vvar__var__var__var__var__16__x2__226__232__354__360__366,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__7__req__125,Vvar__var__var__var__var__15__x1__225__231__353__359__365),Vvar__var__var__var__var__16__x2__226__232__354__360__366))
=> ! [Vvar__var__var__var__var__18__y1__227__233__355__361__367] :
( t(Vvar__var__var__var__var__18__y1__227__233__355__361__367,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__19__y2__228__234__356__362__368] :
( t(Vvar__var__var__var__var__19__y2__228__234__356__362__368,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__7__req__125,Vvar__var__var__var__var__18__y1__227__233__355__361__367),Vvar__var__var__var__var__19__y2__228__234__356__362__368))
=> ( p(happ(happ(Vvar__9__rlt__135,Vvar__var__var__var__var__15__x1__225__231__353__359__365),Vvar__var__var__var__var__18__y1__227__233__355__361__367))
<=> p(happ(happ(Vvar__9__rlt__135,Vvar__var__var__var__var__16__x2__226__232__354__360__366),Vvar__var__var__var__var__19__y2__228__234__356__362__368)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__104,Vvar__1__rO__105,Vvar__2__rI__106,Vvar__3__rplus__107,Vvar__4__rtimes__112,Vvar__5__rminus__117,Vvar__6__ropp__122,Vvar__7__req__125)
& ! [Vvar__var__var__var__17__n__239__240__371__372] :
( t(Vvar__var__var__var__17__n__239__240__371__372,Vvar__0__R__104)
=> p(happ(happ(Vvar__8__rle__130,Vvar__var__var__var__17__n__239__240__371__372),Vvar__var__var__var__17__n__239__240__371__372)) )
& ! [Vvar__var__var__var__var__18__n__242__246__373__377__381] :
( t(Vvar__var__var__var__var__18__n__242__246__373__377__381,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__19__m__243__247__374__378__382] :
( t(Vvar__var__var__var__var__19__m__243__247__374__378__382,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__8__rle__130,Vvar__var__var__var__var__18__n__242__246__373__377__381),Vvar__var__var__var__var__19__m__243__247__374__378__382))
=> ( p(happ(happ(Vvar__8__rle__130,Vvar__var__var__var__var__19__m__243__247__374__378__382),Vvar__var__var__var__var__18__n__242__246__373__377__381))
=> p(happ(happ(Vvar__7__req__125,Vvar__var__var__var__var__18__n__242__246__373__377__381),Vvar__var__var__var__var__19__m__243__247__374__378__382)) ) ) ) )
& ! [Vvar__var__var__var__19__n__251__256__385__390] :
( t(Vvar__var__var__var__19__n__251__256__385__390,Vvar__0__R__104)
=> ! [Vvar__var__var__var__20__m__252__257__386__391] :
( t(Vvar__var__var__var__20__m__252__257__386__391,Vvar__0__R__104)
=> ! [Vvar__var__var__var__21__p__253__258__387__392] :
( t(Vvar__var__var__var__21__p__253__258__387__392,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__8__rle__130,Vvar__var__var__var__19__n__251__256__385__390),Vvar__var__var__var__20__m__252__257__386__391))
=> ( p(happ(happ(Vvar__8__rle__130,Vvar__var__var__var__20__m__252__257__386__391),Vvar__var__var__var__21__p__253__258__387__392))
=> p(happ(happ(Vvar__8__rle__130,Vvar__var__var__var__19__n__251__256__385__390),Vvar__var__var__var__21__p__253__258__387__392)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__262__264__395__397__399__401] :
( t(Vvar__var__var__var__var__var__20__n__262__264__395__397__399__401,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__var__21__m__263__265__396__398__400__402] :
( t(Vvar__var__var__var__var__var__21__m__263__265__396__398__400__402,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__9__rlt__135,Vvar__var__var__var__var__var__20__n__262__264__395__397__399__401),Vvar__var__var__var__var__var__21__m__263__265__396__398__400__402))
<=> ( p(happ(happ(Vvar__8__rle__130,Vvar__var__var__var__var__var__20__n__262__264__395__397__399__401),Vvar__var__var__var__var__var__21__m__263__265__396__398__400__402))
& ~ p(happ(happ(Vvar__7__req__125,Vvar__var__var__var__var__var__20__n__262__264__395__397__399__401),Vvar__var__var__var__var__var__21__m__263__265__396__398__400__402)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__267__269__403__405__407] :
( t(Vvar__var__var__var__var__21__n__267__269__403__405__407,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__22__m__268__270__404__406__408] :
( t(Vvar__var__var__var__var__22__m__268__270__404__406__408,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__9__rlt__135,Vvar__var__var__var__var__21__n__267__269__403__405__407),Vvar__var__var__var__var__22__m__268__270__404__406__408))
| p(happ(happ(Vvar__7__req__125,Vvar__var__var__var__var__21__n__267__269__403__405__407),Vvar__var__var__var__var__22__m__268__270__404__406__408))
| p(happ(happ(Vvar__9__rlt__135,Vvar__var__var__var__var__22__m__268__270__404__406__408),Vvar__var__var__var__var__21__n__267__269__403__405__407)) ) ) )
& ! [Vvar__var__var__var__var__22__n__272__276__409__413__417] :
( t(Vvar__var__var__var__var__22__n__272__276__409__413__417,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__23__m__273__277__410__414__418] :
( t(Vvar__var__var__var__var__23__m__273__277__410__414__418,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__24__p__274__278__411__415__419] :
( t(Vvar__var__var__var__var__24__p__274__278__411__415__419,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__8__rle__130,Vvar__var__var__var__var__22__n__272__276__409__413__417),Vvar__var__var__var__var__23__m__273__277__410__414__418))
=> p(happ(happ(Vvar__8__rle__130,happ(happ(Vvar__3__rplus__107,Vvar__var__var__var__var__24__p__274__278__411__415__419),Vvar__var__var__var__var__22__n__272__276__409__413__417)),happ(happ(Vvar__3__rplus__107,Vvar__var__var__var__var__24__p__274__278__411__415__419),Vvar__var__var__var__var__23__m__273__277__410__414__418))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__281__285__421__425__429__433] :
( t(Vvar__var__var__var__var__var__23__n__281__285__421__425__429__433,Vvar__0__R__104)
=> ! [Vvar__var__var__var__var__var__24__m__282__286__422__426__430__434] :
( t(Vvar__var__var__var__var__var__24__m__282__286__422__426__430__434,Vvar__0__R__104)
=> ( p(happ(happ(Vvar__9__rlt__135,Vvar__1__rO__105),Vvar__var__var__var__var__var__23__n__281__285__421__425__429__433))
=> ( p(happ(happ(Vvar__9__rlt__135,Vvar__1__rO__105),Vvar__var__var__var__var__var__24__m__282__286__422__426__430__434))
=> p(happ(happ(Vvar__9__rlt__135,Vvar__1__rO__105),happ(happ(Vvar__4__rtimes__112,Vvar__var__var__var__var__var__23__n__281__285__421__425__429__433),Vvar__var__var__var__var__var__24__m__282__286__422__426__430__434))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__125,Vvar__1__rO__105),Vvar__2__rI__106))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX12573] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX12573)
=> ( VX12573 = cCoq_2emicromega_2eRMicromega_2eC0
| VX12573 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__12574] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__12574)
& VX12573 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__12574) )
| ? [Vvar__0__r__12575] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__12575)
& VX12573 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__12575) )
| ? [Vvar__0__r1__12576] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__12576)
& ? [Vvar__1__r2__12577] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__12577)
& VX12573 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__12576,Vvar__1__r2__12577) ) )
| ? [Vvar__0__r1__12578] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__12578)
& ? [Vvar__1__r2__12579] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__12579)
& VX12573 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__12578,Vvar__1__r2__12579) ) )
| ? [Vvar__0__r1__12580] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__12580)
& ? [Vvar__1__r2__12581] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__12581)
& VX12573 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__12580,Vvar__1__r2__12581) ) )
| ? [Vvar__0__r1__12582] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__12582)
& ? [Vvar__1__z__12583] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__12583)
& VX12573 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__12582,Vvar__1__z__12583) ) )
| ? [Vvar__0__r__12584] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__12584)
& VX12573 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__12584) )
| ? [Vvar__0__r__12585] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__12585)
& VX12573 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__12585) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__18129,VX18130] :
( cType___24t(Vvar__0__T__18129)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__18129,VX18130)
=> ? [Vvar__1__Flhs__18132] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__18129,Vvar__1__Flhs__18132)
& ? [Vvar__2__Fop__18133] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__18133)
& ? [Vvar__3__Frhs__18134] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__18129,Vvar__3__Frhs__18134)
& VX18130 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__18129,Vvar__1__Flhs__18132,Vvar__2__Fop__18133,Vvar__3__Frhs__18134) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX18048] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX18048)
=> ( VX18048 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX18048 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX18048 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX18048 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX18049] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX18049)
=> ( VX18049 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX18049 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX18049 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX18049 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX18049 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX18049 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__21117,VX21118] :
( cType___24t(Vvar__0__C__21117)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__21117,VX21118)
=> ( ? [Vvar__1___24Anonymous__21120] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__21120)
& VX21118 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__21117,Vvar__1___24Anonymous__21120) )
| ? [Vvar__1___24Anonymous__21122] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__21117,Vvar__1___24Anonymous__21122)
& VX21118 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__21117,Vvar__1___24Anonymous__21122) )
| ? [Vvar__1___24Anonymous__21124] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__21117,Vvar__1___24Anonymous__21124)
& ? [Vvar__2___24Anonymous__21125] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__21117,Vvar__2___24Anonymous__21125)
& VX21118 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__21117,Vvar__1___24Anonymous__21124,Vvar__2___24Anonymous__21125) ) )
| ? [Vvar__1___24Anonymous__21127] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__21117,Vvar__1___24Anonymous__21127)
& ? [Vvar__2___24Anonymous__21128] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__21117,Vvar__2___24Anonymous__21128)
& VX21118 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__21117,Vvar__1___24Anonymous__21127,Vvar__2___24Anonymous__21128) ) )
| ? [Vvar__1___24Anonymous__21130] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__21117,Vvar__1___24Anonymous__21130)
& ? [Vvar__2___24Anonymous__21131] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__21117,Vvar__2___24Anonymous__21131)
& VX21118 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__21117,Vvar__1___24Anonymous__21130,Vvar__2___24Anonymous__21131) ) )
| ? [Vvar__1___24Anonymous__21133] :
( t(Vvar__1___24Anonymous__21133,Vvar__0__C__21117)
& VX21118 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__21117,Vvar__1___24Anonymous__21133) )
| VX21118 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__21117) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824] :
( cType___24t(Vvar__0__R__12755)
=> ( t(Vvar__1__rO__12756,Vvar__0__R__12755)
=> ( t(Vvar__2__rI__12757,Vvar__0__R__12755)
=> ( c_24__type__13288___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__3__rplus__12758)
=> ( c_24__type__13634___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__4__rtimes__12763)
=> ( c_24__type__13980___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__5__rminus__12768)
=> ( c_24__type__14303___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__6__ropp__12773)
=> ( c_24__type__14649___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__7__req__12776)
=> ( c_24__type__14995___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__8__rle__12781)
=> ( cType___24t(Vvar__9__C__12786)
=> ( t(Vvar__10__cO__12787,Vvar__9__C__12786)
=> ( t(Vvar__11__cI__12788,Vvar__9__C__12786)
=> ( c_24__type__15341___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__12__cplus__12789)
=> ( c_24__type__15687___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__13__ctimes__12794)
=> ( c_24__type__16033___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__14__cminus__12799)
=> ( c_24__type__16356___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__15__copp__12804)
=> ( c_24__type__16702___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__16__ceqb__12807)
=> ( c_24__type__17048___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__17__cleb__12812)
=> ( c_24__type__17371___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__18__phi__12817)
=> ( cType___24t(Vvar__19__E__12820)
=> ( c_24__type__17694___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__20__pow__phi__12821)
=> ( c_24__type__18040___24t(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824,Vvar__21__rpow__12824)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__8__rle__12781,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__17__cleb__12812,Vvar__18__phi__12817,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__12755,Vvar__1__rO__12756,Vvar__2__rI__12757,Vvar__3__rplus__12758,Vvar__4__rtimes__12763,Vvar__5__rminus__12768,Vvar__6__ropp__12773,Vvar__7__req__12776,Vvar__9__C__12786,Vvar__10__cO__12787,Vvar__11__cI__12788,Vvar__12__cplus__12789,Vvar__13__ctimes__12794,Vvar__14__cminus__12799,Vvar__15__copp__12804,Vvar__16__ceqb__12807,Vvar__18__phi__12817)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__12755,Vvar__2__rI__12757,Vvar__4__rtimes__12763,Vvar__7__req__12776,Vvar__19__E__12820,Vvar__20__pow__phi__12821,Vvar__21__rpow__12824)
& ! [Vvar__var__var__var__var__var__24__x__12907__12910__12920__12923__12926__12929] :
( t(Vvar__var__var__var__var__var__24__x__12907__12910__12920__12923__12926__12929,Vvar__9__C__12786)
=> ! [Vvar__var__var__var__var__var__25__y__12908__12911__12921__12924__12927__12930] :
( t(Vvar__var__var__var__var__var__25__y__12908__12911__12921__12924__12927__12930,Vvar__9__C__12786)
=> ( happ(happ(Vvar__16__ceqb__12807,Vvar__var__var__var__var__var__24__x__12907__12910__12920__12923__12926__12929),Vvar__var__var__var__var__var__25__y__12908__12911__12921__12924__12927__12930) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__12776,happ(Vvar__18__phi__12817,Vvar__var__var__var__var__var__24__x__12907__12910__12920__12923__12926__12929)),happ(Vvar__18__phi__12817,Vvar__var__var__var__var__var__25__y__12908__12911__12921__12924__12927__12930))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__12914__12917__12932__12935__12938__12941] :
( t(Vvar__var__var__var__var__var__25__x__12914__12917__12932__12935__12938__12941,Vvar__9__C__12786)
=> ! [Vvar__var__var__var__var__var__26__y__12915__12918__12933__12936__12939__12942] :
( t(Vvar__var__var__var__var__var__26__y__12915__12918__12933__12936__12939__12942,Vvar__9__C__12786)
=> ( happ(happ(Vvar__17__cleb__12812,Vvar__var__var__var__var__var__25__x__12914__12917__12932__12935__12938__12941),Vvar__var__var__var__var__var__26__y__12915__12918__12933__12936__12939__12942) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__12781,happ(Vvar__18__phi__12817,Vvar__var__var__var__var__var__25__x__12914__12917__12932__12935__12938__12941)),happ(Vvar__18__phi__12817,Vvar__var__var__var__var__var__26__y__12915__12918__12933__12936__12939__12942))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,VX4683] :
( cType___24t(Vvar__0__TA__4679)
=> ( cType___24t(Vvar__1__TX__4680)
=> ( cType___24t(Vvar__2__AA__4681)
=> ( cType___24t(Vvar__3__AF__4682)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,VX4683)
=> ( VX4683 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682)
| VX4683 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682)
| ? [Vvar__4___24Anonymous__4696] :
( t(Vvar__4___24Anonymous__4696,Vvar__1__TX__4680)
& VX4683 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__4___24Anonymous__4696) )
| ? [Vvar__4___24Anonymous__4701] :
( t(Vvar__4___24Anonymous__4701,Vvar__0__TA__4679)
& ? [Vvar__5___24Anonymous__4702] :
( t(Vvar__5___24Anonymous__4702,Vvar__2__AA__4681)
& VX4683 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__4___24Anonymous__4701,Vvar__5___24Anonymous__4702) ) )
| ? [Vvar__4___24Anonymous__4707] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__4___24Anonymous__4707)
& ? [Vvar__5___24Anonymous__4708] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__5___24Anonymous__4708)
& VX4683 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__4___24Anonymous__4707,Vvar__5___24Anonymous__4708) ) )
| ? [Vvar__4___24Anonymous__4713] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__4___24Anonymous__4713)
& ? [Vvar__5___24Anonymous__4714] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__5___24Anonymous__4714)
& VX4683 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__4___24Anonymous__4713,Vvar__5___24Anonymous__4714) ) )
| ? [Vvar__4___24Anonymous__4719] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__4___24Anonymous__4719)
& VX4683 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__4___24Anonymous__4719) )
| ? [Vvar__4___24Anonymous__4724] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__4___24Anonymous__4724)
& ? [Vvar__5___24Anonymous__4725] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__4682,Vvar__5___24Anonymous__4725)
& ? [Vvar__6___24Anonymous__4726] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__6___24Anonymous__4726)
& VX4683 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__4679,Vvar__1__TX__4680,Vvar__2__AA__4681,Vvar__3__AF__4682,Vvar__4___24Anonymous__4724,Vvar__5___24Anonymous__4725,Vvar__6___24Anonymous__4726) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__35087,VX35088] :
( cType___24t(Vvar__0__A__35087)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__35087,VX35088)
=> ( VX35088 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__35087)
| ? [Vvar__1___24Anonymous__35091] :
( t(Vvar__1___24Anonymous__35091,Vvar__0__A__35087)
& VX35088 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__35087,Vvar__1___24Anonymous__35091) )
| ? [Vvar__1___24Anonymous__35093] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__35087,Vvar__1___24Anonymous__35093)
& ? [Vvar__2___24Anonymous__35094] :
( t(Vvar__2___24Anonymous__35094,Vvar__0__A__35087)
& ? [Vvar__3___24Anonymous__35095] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__35087,Vvar__3___24Anonymous__35095)
& VX35088 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__35087,Vvar__1___24Anonymous__35093,Vvar__2___24Anonymous__35094,Vvar__3___24Anonymous__35095) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
! [Vvar__0___24Anonymous__35359] :
( cProp___24t(Vvar__0___24Anonymous__35359)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__35359)
=> ( ? [Vvar__0__P__35361] :
( cProp___24t(Vvar__0__P__35361)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__35361)
& Vvar__0___24Anonymous__35359 = Vvar__0__P__35361 )
| ? [Vvar__0__s__35363] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__35363)
& Vvar__0___24Anonymous__35359 = c_24__prop__35372___24a2(Vvar__0___24Anonymous__35359,Vvar__0__s__35363) )
| ? [Vvar__0__s1__35365] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__35365)
& ? [Vvar__1__s2__35366] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__35366)
& Vvar__0___24Anonymous__35359 = c_24__prop__35373___24a3(Vvar__0___24Anonymous__35359,Vvar__0__s1__35365,Vvar__1__s2__35366) ) )
| ? [Vvar__0__s1__35369] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__35369)
& ? [Vvar__1__s2__35370] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__35370)
& Vvar__0___24Anonymous__35359 = c_24__prop__35374___24a3(Vvar__0___24Anonymous__35359,Vvar__0__s1__35369,Vvar__1__s2__35370) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__35328] :
( cProp___24t(Vvar__0___24Anonymous__35328)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__35328)
=> ( ? [Vvar__0__S__35330] :
( cType___24t(Vvar__0__S__35330)
& ? [Vvar__1__x__35331] :
( t(Vvar__1__x__35331,Vvar__0__S__35330)
& ? [Vvar__2__y__35332] :
( t(Vvar__2__y__35332,Vvar__0__S__35330)
& Vvar__0___24Anonymous__35328 = c_24__prop__35352___24a4(Vvar__0___24Anonymous__35328,Vvar__0__S__35330,Vvar__1__x__35331,Vvar__2__y__35332) ) ) )
| ? [Vvar__0__x__35333] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__35333)
& ? [Vvar__1__y__35334] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__35334)
& Vvar__0___24Anonymous__35328 = c_24__prop__35353___24a3(Vvar__0___24Anonymous__35328,Vvar__0__x__35333,Vvar__1__y__35334) ) )
| ? [Vvar__0__x__35335] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__35335)
& ? [Vvar__1__s__35336] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__35336)
& Vvar__0___24Anonymous__35328 = c_24__prop__35354___24a3(Vvar__0___24Anonymous__35328,Vvar__0__x__35335,Vvar__1__s__35336) ) )
| Vvar__0___24Anonymous__35328 = c_24True
| Vvar__0___24Anonymous__35328 = c_24False
| ? [Vvar__0__P__35337] :
( cProp___24t(Vvar__0__P__35337)
& ? [Vvar__1__Q__35338] :
( cProp___24t(Vvar__1__Q__35338)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__35337)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__35338)
& Vvar__0___24Anonymous__35328 = c_24__prop__35355___24a3(Vvar__0___24Anonymous__35328,Vvar__0__P__35337,Vvar__1__Q__35338) ) )
| ? [Vvar__0__P__35341] :
( cProp___24t(Vvar__0__P__35341)
& ? [Vvar__1__Q__35342] :
( cProp___24t(Vvar__1__Q__35342)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__35341)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__35342)
& Vvar__0___24Anonymous__35328 = c_24__prop__35356___24a3(Vvar__0___24Anonymous__35328,Vvar__0__P__35341,Vvar__1__Q__35342) ) )
| ? [Vvar__0__P__35345] :
( cProp___24t(Vvar__0__P__35345)
& ? [Vvar__1__Q__35346] :
( cProp___24t(Vvar__1__Q__35346)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__35345)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__35346)
& Vvar__0___24Anonymous__35328 = c_24__prop__35357___24a3(Vvar__0___24Anonymous__35328,Vvar__0__P__35345,Vvar__1__Q__35346) ) )
| ? [Vvar__0__P__35350] :
( cProp___24t(Vvar__0__P__35350)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__35350)
& Vvar__0___24Anonymous__35328 = c_24__prop__35358___24a2(Vvar__0___24Anonymous__35328,Vvar__0__P__35350) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX35124] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX35124)
=> ( VX35124 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__35125] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__35125)
& ? [Vvar__1___24Anonymous__35126] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__35126)
& VX35124 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__35125,Vvar__1___24Anonymous__35126) ) )
| ? [Vvar__0___24Anonymous__35127] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__35127)
& ? [Vvar__1___24Anonymous__35128] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__35128)
& VX35124 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__35127,Vvar__1___24Anonymous__35128) ) )
| ? [Vvar__0___24Anonymous__35129] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__35129)
& ? [Vvar__1___24Anonymous__35130] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__35130)
& ? [Vvar__2___24Anonymous__35131] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__35131)
& VX35124 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__35129,Vvar__1___24Anonymous__35130,Vvar__2___24Anonymous__35131) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__35167,Vvar__1__env__35168,Vvar__2__env_27__35171,Vvar__3__x__35174] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__35167)
=> ( c_24__type__35195___24t(Vvar__0__fr__35167,Vvar__1__env__35168,Vvar__2__env_27__35171,Vvar__3__x__35174,Vvar__1__env__35168)
=> ( c_24__type__35204___24t(Vvar__0__fr__35167,Vvar__1__env__35168,Vvar__2__env_27__35171,Vvar__3__x__35174,Vvar__2__env_27__35171)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__35174)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__35167,Vvar__1__env__35168,Vvar__2__env_27__35171,Vvar__3__x__35174)
=> ( happ(Vvar__1__env__35168,Vvar__3__x__35174) = happ(Vvar__2__env_27__35171,Vvar__3__x__35174)
& happ(Vvar__1__env__35168,Vvar__3__x__35174) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__35171,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__35167,Vvar__3__x__35174))),happ(Vvar__2__env_27__35171,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__35167,Vvar__3__x__35174))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__35171,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__35167,Vvar__3__x__35174))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__35171,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__35167,Vvar__3__x__35174))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__31535,VX31536] :
( cType___24t(Vvar__0__C__31535)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__31535,VX31536)
=> ( VX31536 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__31535)
| VX31536 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__31535)
| ? [Vvar__1___24Anonymous__31540] :
( t(Vvar__1___24Anonymous__31540,Vvar__0__C__31535)
& VX31536 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__31535,Vvar__1___24Anonymous__31540) )
| ? [Vvar__1___24Anonymous__31542] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__31542)
& VX31536 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__31535,Vvar__1___24Anonymous__31542) )
| ? [Vvar__1___24Anonymous__31544] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__31535,Vvar__1___24Anonymous__31544)
& ? [Vvar__2___24Anonymous__31545] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__31535,Vvar__2___24Anonymous__31545)
& VX31536 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__31535,Vvar__1___24Anonymous__31544,Vvar__2___24Anonymous__31545) ) )
| ? [Vvar__1___24Anonymous__31547] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__31535,Vvar__1___24Anonymous__31547)
& ? [Vvar__2___24Anonymous__31548] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__31535,Vvar__2___24Anonymous__31548)
& VX31536 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__31535,Vvar__1___24Anonymous__31547,Vvar__2___24Anonymous__31548) ) )
| ? [Vvar__1___24Anonymous__31550] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__31535,Vvar__1___24Anonymous__31550)
& ? [Vvar__2___24Anonymous__31551] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__31535,Vvar__2___24Anonymous__31551)
& VX31536 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__31535,Vvar__1___24Anonymous__31550,Vvar__2___24Anonymous__31551) ) )
| ? [Vvar__1___24Anonymous__31553] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__31535,Vvar__1___24Anonymous__31553)
& VX31536 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__31535,Vvar__1___24Anonymous__31553) )
| ? [Vvar__1___24Anonymous__31555] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__31535,Vvar__1___24Anonymous__31555)
& VX31536 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__31535,Vvar__1___24Anonymous__31555) )
| ? [Vvar__1___24Anonymous__31557] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__31535,Vvar__1___24Anonymous__31557)
& ? [Vvar__2___24Anonymous__31558] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__31535,Vvar__2___24Anonymous__31558)
& VX31536 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__31535,Vvar__1___24Anonymous__31557,Vvar__2___24Anonymous__31558) ) )
| ? [Vvar__1___24Anonymous__31560] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__31535,Vvar__1___24Anonymous__31560)
& ? [Vvar__2___24Anonymous__31561] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__31561)
& VX31536 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__31535,Vvar__1___24Anonymous__31560,Vvar__2___24Anonymous__31561) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__30799,Vvar__1__rO__30800,Vvar__2__rI__30801,Vvar__3__radd__30802,Vvar__4__rmul__30807,Vvar__5__rsub__30812,Vvar__6__ropp__30817,Vvar__7__rdiv__30820,Vvar__8__rinv__30825,Vvar__9__req__30828] :
( cType___24t(Vvar__0__R__30799)
=> ( t(Vvar__1__rO__30800,Vvar__0__R__30799)
=> ( t(Vvar__2__rI__30801,Vvar__0__R__30799)
=> ( c_24__type__30993___24t(Vvar__0__R__30799,Vvar__1__rO__30800,Vvar__2__rI__30801,Vvar__3__radd__30802,Vvar__4__rmul__30807,Vvar__5__rsub__30812,Vvar__6__ropp__30817,Vvar__7__rdiv__30820,Vvar__8__rinv__30825,Vvar__9__req__30828,Vvar__3__radd__30802)
=> ( c_24__type__31086___24t(Vvar__0__R__30799,Vvar__1__rO__30800,Vvar__2__rI__30801,Vvar__3__radd__30802,Vvar__4__rmul__30807,Vvar__5__rsub__30812,Vvar__6__ropp__30817,Vvar__7__rdiv__30820,Vvar__8__rinv__30825,Vvar__9__req__30828,Vvar__4__rmul__30807)
=> ( c_24__type__31179___24t(Vvar__0__R__30799,Vvar__1__rO__30800,Vvar__2__rI__30801,Vvar__3__radd__30802,Vvar__4__rmul__30807,Vvar__5__rsub__30812,Vvar__6__ropp__30817,Vvar__7__rdiv__30820,Vvar__8__rinv__30825,Vvar__9__req__30828,Vvar__5__rsub__30812)
=> ( c_24__type__31261___24t(Vvar__0__R__30799,Vvar__1__rO__30800,Vvar__2__rI__30801,Vvar__3__radd__30802,Vvar__4__rmul__30807,Vvar__5__rsub__30812,Vvar__6__ropp__30817,Vvar__7__rdiv__30820,Vvar__8__rinv__30825,Vvar__9__req__30828,Vvar__6__ropp__30817)
=> ( c_24__type__31354___24t(Vvar__0__R__30799,Vvar__1__rO__30800,Vvar__2__rI__30801,Vvar__3__radd__30802,Vvar__4__rmul__30807,Vvar__5__rsub__30812,Vvar__6__ropp__30817,Vvar__7__rdiv__30820,Vvar__8__rinv__30825,Vvar__9__req__30828,Vvar__7__rdiv__30820)
=> ( c_24__type__31436___24t(Vvar__0__R__30799,Vvar__1__rO__30800,Vvar__2__rI__30801,Vvar__3__radd__30802,Vvar__4__rmul__30807,Vvar__5__rsub__30812,Vvar__6__ropp__30817,Vvar__7__rdiv__30820,Vvar__8__rinv__30825,Vvar__9__req__30828,Vvar__8__rinv__30825)
=> ( c_24__type__31529___24t(Vvar__0__R__30799,Vvar__1__rO__30800,Vvar__2__rI__30801,Vvar__3__radd__30802,Vvar__4__rmul__30807,Vvar__5__rsub__30812,Vvar__6__ropp__30817,Vvar__7__rdiv__30820,Vvar__8__rinv__30825,Vvar__9__req__30828,Vvar__9__req__30828)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__30799,Vvar__1__rO__30800,Vvar__2__rI__30801,Vvar__3__radd__30802,Vvar__4__rmul__30807,Vvar__5__rsub__30812,Vvar__6__ropp__30817,Vvar__7__rdiv__30820,Vvar__8__rinv__30825,Vvar__9__req__30828)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__30799,Vvar__1__rO__30800,Vvar__2__rI__30801,Vvar__3__radd__30802,Vvar__4__rmul__30807,Vvar__5__rsub__30812,Vvar__6__ropp__30817,Vvar__9__req__30828)
& ~ p(happ(happ(Vvar__9__req__30828,Vvar__2__rI__30801),Vvar__1__rO__30800))
& ! [Vvar__var__var__var__var__var__var__12__p__30871__30873__30880__30882__30884__30886__30888] :
( t(Vvar__var__var__var__var__var__var__12__p__30871__30873__30880__30882__30884__30886__30888,Vvar__0__R__30799)
=> ! [Vvar__var__var__var__var__var__var__13__q__30872__30874__30881__30883__30885__30887__30889] :
( t(Vvar__var__var__var__var__var__var__13__q__30872__30874__30881__30883__30885__30887__30889,Vvar__0__R__30799)
=> p(happ(happ(Vvar__9__req__30828,happ(happ(Vvar__7__rdiv__30820,Vvar__var__var__var__var__var__var__12__p__30871__30873__30880__30882__30884__30886__30888),Vvar__var__var__var__var__var__var__13__q__30872__30874__30881__30883__30885__30887__30889)),happ(happ(Vvar__4__rmul__30807,Vvar__var__var__var__var__var__var__12__p__30871__30873__30880__30882__30884__30886__30888),happ(Vvar__8__rinv__30825,Vvar__var__var__var__var__var__var__13__q__30872__30874__30881__30883__30885__30887__30889)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__30876__30878__30890__30892__30894__30896__30898__30900] :
( t(Vvar__var__var__var__var__var__var__var__13__p__30876__30878__30890__30892__30894__30896__30898__30900,Vvar__0__R__30799)
=> ( ~ p(happ(happ(Vvar__9__req__30828,Vvar__var__var__var__var__var__var__var__13__p__30876__30878__30890__30892__30894__30896__30898__30900),Vvar__1__rO__30800))
=> p(happ(happ(Vvar__9__req__30828,happ(happ(Vvar__4__rmul__30807,happ(Vvar__8__rinv__30825,Vvar__var__var__var__var__var__var__var__13__p__30876__30878__30890__30892__30894__30896__30898__30900)),Vvar__var__var__var__var__var__var__var__13__p__30876__30878__30890__30892__30894__30896__30898__30900)),Vvar__2__rI__30801)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__31893,Vvar__1__rO__31894,Vvar__2__rI__31895,Vvar__3__radd__31896,Vvar__4__rmul__31901,Vvar__5__rsub__31906,Vvar__6__ropp__31911,Vvar__7__rdiv__31914,Vvar__8__rinv__31919,Vvar__9__req__31922] :
( cType___24t(Vvar__0__R__31893)
=> ( t(Vvar__1__rO__31894,Vvar__0__R__31893)
=> ( t(Vvar__2__rI__31895,Vvar__0__R__31893)
=> ( c_24__type__32087___24t(Vvar__0__R__31893,Vvar__1__rO__31894,Vvar__2__rI__31895,Vvar__3__radd__31896,Vvar__4__rmul__31901,Vvar__5__rsub__31906,Vvar__6__ropp__31911,Vvar__7__rdiv__31914,Vvar__8__rinv__31919,Vvar__9__req__31922,Vvar__3__radd__31896)
=> ( c_24__type__32180___24t(Vvar__0__R__31893,Vvar__1__rO__31894,Vvar__2__rI__31895,Vvar__3__radd__31896,Vvar__4__rmul__31901,Vvar__5__rsub__31906,Vvar__6__ropp__31911,Vvar__7__rdiv__31914,Vvar__8__rinv__31919,Vvar__9__req__31922,Vvar__4__rmul__31901)
=> ( c_24__type__32273___24t(Vvar__0__R__31893,Vvar__1__rO__31894,Vvar__2__rI__31895,Vvar__3__radd__31896,Vvar__4__rmul__31901,Vvar__5__rsub__31906,Vvar__6__ropp__31911,Vvar__7__rdiv__31914,Vvar__8__rinv__31919,Vvar__9__req__31922,Vvar__5__rsub__31906)
=> ( c_24__type__32355___24t(Vvar__0__R__31893,Vvar__1__rO__31894,Vvar__2__rI__31895,Vvar__3__radd__31896,Vvar__4__rmul__31901,Vvar__5__rsub__31906,Vvar__6__ropp__31911,Vvar__7__rdiv__31914,Vvar__8__rinv__31919,Vvar__9__req__31922,Vvar__6__ropp__31911)
=> ( c_24__type__32448___24t(Vvar__0__R__31893,Vvar__1__rO__31894,Vvar__2__rI__31895,Vvar__3__radd__31896,Vvar__4__rmul__31901,Vvar__5__rsub__31906,Vvar__6__ropp__31911,Vvar__7__rdiv__31914,Vvar__8__rinv__31919,Vvar__9__req__31922,Vvar__7__rdiv__31914)
=> ( c_24__type__32530___24t(Vvar__0__R__31893,Vvar__1__rO__31894,Vvar__2__rI__31895,Vvar__3__radd__31896,Vvar__4__rmul__31901,Vvar__5__rsub__31906,Vvar__6__ropp__31911,Vvar__7__rdiv__31914,Vvar__8__rinv__31919,Vvar__9__req__31922,Vvar__8__rinv__31919)
=> ( c_24__type__32623___24t(Vvar__0__R__31893,Vvar__1__rO__31894,Vvar__2__rI__31895,Vvar__3__radd__31896,Vvar__4__rmul__31901,Vvar__5__rsub__31906,Vvar__6__ropp__31911,Vvar__7__rdiv__31914,Vvar__8__rinv__31919,Vvar__9__req__31922,Vvar__9__req__31922)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__31893,Vvar__1__rO__31894,Vvar__2__rI__31895,Vvar__3__radd__31896,Vvar__4__rmul__31901,Vvar__5__rsub__31906,Vvar__6__ropp__31911,Vvar__7__rdiv__31914,Vvar__8__rinv__31919,Vvar__9__req__31922)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__31893,Vvar__1__rO__31894,Vvar__2__rI__31895,Vvar__3__radd__31896,Vvar__4__rmul__31901,Vvar__5__rsub__31906,Vvar__6__ropp__31911,Vvar__9__req__31922)
& ~ p(happ(happ(Vvar__9__req__31922,Vvar__2__rI__31895),Vvar__1__rO__31894))
& ! [Vvar__var__var__var__var__var__var__12__p__31965__31967__31974__31976__31978__31980__31982] :
( t(Vvar__var__var__var__var__var__var__12__p__31965__31967__31974__31976__31978__31980__31982,Vvar__0__R__31893)
=> ! [Vvar__var__var__var__var__var__var__13__q__31966__31968__31975__31977__31979__31981__31983] :
( t(Vvar__var__var__var__var__var__var__13__q__31966__31968__31975__31977__31979__31981__31983,Vvar__0__R__31893)
=> p(happ(happ(Vvar__9__req__31922,happ(happ(Vvar__7__rdiv__31914,Vvar__var__var__var__var__var__var__12__p__31965__31967__31974__31976__31978__31980__31982),Vvar__var__var__var__var__var__var__13__q__31966__31968__31975__31977__31979__31981__31983)),happ(happ(Vvar__4__rmul__31901,Vvar__var__var__var__var__var__var__12__p__31965__31967__31974__31976__31978__31980__31982),happ(Vvar__8__rinv__31919,Vvar__var__var__var__var__var__var__13__q__31966__31968__31975__31977__31979__31981__31983)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__31970__31972__31984__31986__31988__31990__31992__31994] :
( t(Vvar__var__var__var__var__var__var__var__13__p__31970__31972__31984__31986__31988__31990__31992__31994,Vvar__0__R__31893)
=> ( ~ p(happ(happ(Vvar__9__req__31922,Vvar__var__var__var__var__var__var__var__13__p__31970__31972__31984__31986__31988__31990__31992__31994),Vvar__1__rO__31894))
=> p(happ(happ(Vvar__9__req__31922,happ(happ(Vvar__4__rmul__31901,happ(Vvar__8__rinv__31919,Vvar__var__var__var__var__var__var__var__13__p__31970__31972__31984__31986__31988__31990__31992__31994)),Vvar__var__var__var__var__var__var__var__13__p__31970__31972__31984__31986__31988__31990__31992__31994)),Vvar__2__rI__31895)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__31865,VX31866] :
( cType___24t(Vvar__0__C__31865)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__31865,VX31866)
=> ? [Vvar__1__num__31868] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__31865,Vvar__1__num__31868)
& ? [Vvar__2__denum__31869] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__31865,Vvar__2__denum__31869)
& ? [Vvar__3__condition__31870] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__31865),Vvar__3__condition__31870)
& VX31866 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__31865,Vvar__1__num__31868,Vvar__2__denum__31869,Vvar__3__condition__31870) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__31879,VX31880] :
( cType___24t(Vvar__0__C__31879)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__31879,VX31880)
=> ? [Vvar__1__rsplit__left__31882] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__31879,Vvar__1__rsplit__left__31882)
& ? [Vvar__2__rsplit__common__31883] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__31879,Vvar__2__rsplit__common__31883)
& ? [Vvar__3__rsplit__right__31884] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__31879,Vvar__3__rsplit__right__31884)
& VX31880 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__31879,Vvar__1__rsplit__left__31882,Vvar__2__rsplit__common__31883,Vvar__3__rsplit__right__31884) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__32629,Vvar__1__rO__32630,Vvar__2__rI__32631,Vvar__3__radd__32632,Vvar__4__rmul__32637,Vvar__5__rdiv__32642,Vvar__6__rinv__32647,Vvar__7__req__32650] :
( cType___24t(Vvar__0__R__32629)
=> ( t(Vvar__1__rO__32630,Vvar__0__R__32629)
=> ( t(Vvar__2__rI__32631,Vvar__0__R__32629)
=> ( c_24__type__32777___24t(Vvar__0__R__32629,Vvar__1__rO__32630,Vvar__2__rI__32631,Vvar__3__radd__32632,Vvar__4__rmul__32637,Vvar__5__rdiv__32642,Vvar__6__rinv__32647,Vvar__7__req__32650,Vvar__3__radd__32632)
=> ( c_24__type__32840___24t(Vvar__0__R__32629,Vvar__1__rO__32630,Vvar__2__rI__32631,Vvar__3__radd__32632,Vvar__4__rmul__32637,Vvar__5__rdiv__32642,Vvar__6__rinv__32647,Vvar__7__req__32650,Vvar__4__rmul__32637)
=> ( c_24__type__32903___24t(Vvar__0__R__32629,Vvar__1__rO__32630,Vvar__2__rI__32631,Vvar__3__radd__32632,Vvar__4__rmul__32637,Vvar__5__rdiv__32642,Vvar__6__rinv__32647,Vvar__7__req__32650,Vvar__5__rdiv__32642)
=> ( c_24__type__32957___24t(Vvar__0__R__32629,Vvar__1__rO__32630,Vvar__2__rI__32631,Vvar__3__radd__32632,Vvar__4__rmul__32637,Vvar__5__rdiv__32642,Vvar__6__rinv__32647,Vvar__7__req__32650,Vvar__6__rinv__32647)
=> ( c_24__type__33020___24t(Vvar__0__R__32629,Vvar__1__rO__32630,Vvar__2__rI__32631,Vvar__3__radd__32632,Vvar__4__rmul__32637,Vvar__5__rdiv__32642,Vvar__6__rinv__32647,Vvar__7__req__32650,Vvar__7__req__32650)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__32629,Vvar__1__rO__32630,Vvar__2__rI__32631,Vvar__3__radd__32632,Vvar__4__rmul__32637,Vvar__5__rdiv__32642,Vvar__6__rinv__32647,Vvar__7__req__32650)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__32629,Vvar__1__rO__32630,Vvar__2__rI__32631,Vvar__3__radd__32632,Vvar__4__rmul__32637,Vvar__7__req__32650)
& ~ p(happ(happ(Vvar__7__req__32650,Vvar__2__rI__32631),Vvar__1__rO__32630))
& ! [Vvar__var__var__var__var__var__var__10__p__32685__32687__32694__32696__32698__32700__32702] :
( t(Vvar__var__var__var__var__var__var__10__p__32685__32687__32694__32696__32698__32700__32702,Vvar__0__R__32629)
=> ! [Vvar__var__var__var__var__var__var__11__q__32686__32688__32695__32697__32699__32701__32703] :
( t(Vvar__var__var__var__var__var__var__11__q__32686__32688__32695__32697__32699__32701__32703,Vvar__0__R__32629)
=> p(happ(happ(Vvar__7__req__32650,happ(happ(Vvar__5__rdiv__32642,Vvar__var__var__var__var__var__var__10__p__32685__32687__32694__32696__32698__32700__32702),Vvar__var__var__var__var__var__var__11__q__32686__32688__32695__32697__32699__32701__32703)),happ(happ(Vvar__4__rmul__32637,Vvar__var__var__var__var__var__var__10__p__32685__32687__32694__32696__32698__32700__32702),happ(Vvar__6__rinv__32647,Vvar__var__var__var__var__var__var__11__q__32686__32688__32695__32697__32699__32701__32703)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__32690__32692__32704__32706__32708__32710__32712__32714] :
( t(Vvar__var__var__var__var__var__var__var__11__p__32690__32692__32704__32706__32708__32710__32712__32714,Vvar__0__R__32629)
=> ( ~ p(happ(happ(Vvar__7__req__32650,Vvar__var__var__var__var__var__var__var__11__p__32690__32692__32704__32706__32708__32710__32712__32714),Vvar__1__rO__32630))
=> p(happ(happ(Vvar__7__req__32650,happ(happ(Vvar__4__rmul__32637,happ(Vvar__6__rinv__32647,Vvar__var__var__var__var__var__var__var__11__p__32690__32692__32704__32706__32708__32710__32712__32714)),Vvar__var__var__var__var__var__var__var__11__p__32690__32692__32704__32706__32708__32710__32712__32714)),Vvar__2__rI__32631)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
! [VX20797] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX20797)
=> ? [Vvar__0__hypo__type__20798] :
( cType___24t(Vvar__0__hypo__type__20798)
& ? [Vvar__1__hypo__proof__20799] :
( t(Vvar__1__hypo__proof__20799,Vvar__0__hypo__type__20798)
& VX20797 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__20798,Vvar__1__hypo__proof__20799) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX2096] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX2096)
=> ( VX2096 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__2097] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2097)
& ? [Vvar__1___24Anonymous__2098] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__2098)
& VX2096 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__2097,Vvar__1___24Anonymous__2098) ) )
| ? [Vvar__0___24Anonymous__2099] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2099)
& ? [Vvar__1___24Anonymous__2100] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__2100)
& VX2096 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__2099,Vvar__1___24Anonymous__2100) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__2117,VX2118] :
( cType___24t(Vvar__0__C__2117)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2117,VX2118)
=> ( VX2118 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2117)
| VX2118 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2117)
| ? [Vvar__1___24Anonymous__2122] :
( t(Vvar__1___24Anonymous__2122,Vvar__0__C__2117)
& VX2118 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2117,Vvar__1___24Anonymous__2122) )
| ? [Vvar__1___24Anonymous__2124] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2124)
& VX2118 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2117,Vvar__1___24Anonymous__2124) )
| ? [Vvar__1___24Anonymous__2126] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2117,Vvar__1___24Anonymous__2126)
& ? [Vvar__2___24Anonymous__2127] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2117,Vvar__2___24Anonymous__2127)
& VX2118 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2117,Vvar__1___24Anonymous__2126,Vvar__2___24Anonymous__2127) ) )
| ? [Vvar__1___24Anonymous__2129] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2117,Vvar__1___24Anonymous__2129)
& ? [Vvar__2___24Anonymous__2130] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2117,Vvar__2___24Anonymous__2130)
& VX2118 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2117,Vvar__1___24Anonymous__2129,Vvar__2___24Anonymous__2130) ) )
| ? [Vvar__1___24Anonymous__2132] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2117,Vvar__1___24Anonymous__2132)
& ? [Vvar__2___24Anonymous__2133] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2117,Vvar__2___24Anonymous__2133)
& VX2118 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2117,Vvar__1___24Anonymous__2132,Vvar__2___24Anonymous__2133) ) )
| ? [Vvar__1___24Anonymous__2135] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2117,Vvar__1___24Anonymous__2135)
& VX2118 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2117,Vvar__1___24Anonymous__2135) )
| ? [Vvar__1___24Anonymous__2137] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2117,Vvar__1___24Anonymous__2137)
& ? [Vvar__2___24Anonymous__2138] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2138)
& VX2118 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2117,Vvar__1___24Anonymous__2137,Vvar__2___24Anonymous__2138) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__1915,VX1916] :
( cType___24t(Vvar__0__C__1915)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1915,VX1916)
=> ( ? [Vvar__1___24Anonymous__1918] :
( t(Vvar__1___24Anonymous__1918,Vvar__0__C__1915)
& VX1916 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1915,Vvar__1___24Anonymous__1918) )
| ? [Vvar__1___24Anonymous__1920] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1920)
& ? [Vvar__2___24Anonymous__1921] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1915,Vvar__2___24Anonymous__1921)
& VX1916 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1915,Vvar__1___24Anonymous__1920,Vvar__2___24Anonymous__1921) ) )
| ? [Vvar__1___24Anonymous__1923] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1915,Vvar__1___24Anonymous__1923)
& ? [Vvar__2___24Anonymous__1924] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1924)
& ? [Vvar__3___24Anonymous__1925] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1915,Vvar__3___24Anonymous__1925)
& VX1916 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1915,Vvar__1___24Anonymous__1923,Vvar__2___24Anonymous__1924,Vvar__3___24Anonymous__1925) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__22934,Vvar__1__rO__22935,Vvar__2__rI__22936,Vvar__3__radd__22937,Vvar__4__rmul__22942,Vvar__5__rsub__22947,Vvar__6__ropp__22952,Vvar__7__req__22955] :
( cType___24t(Vvar__0__R__22934)
=> ( t(Vvar__1__rO__22935,Vvar__0__R__22934)
=> ( t(Vvar__2__rI__22936,Vvar__0__R__22934)
=> ( c_24__type__23183___24t(Vvar__0__R__22934,Vvar__1__rO__22935,Vvar__2__rI__22936,Vvar__3__radd__22937,Vvar__4__rmul__22942,Vvar__5__rsub__22947,Vvar__6__ropp__22952,Vvar__7__req__22955,Vvar__3__radd__22937)
=> ( c_24__type__23246___24t(Vvar__0__R__22934,Vvar__1__rO__22935,Vvar__2__rI__22936,Vvar__3__radd__22937,Vvar__4__rmul__22942,Vvar__5__rsub__22947,Vvar__6__ropp__22952,Vvar__7__req__22955,Vvar__4__rmul__22942)
=> ( c_24__type__23309___24t(Vvar__0__R__22934,Vvar__1__rO__22935,Vvar__2__rI__22936,Vvar__3__radd__22937,Vvar__4__rmul__22942,Vvar__5__rsub__22947,Vvar__6__ropp__22952,Vvar__7__req__22955,Vvar__5__rsub__22947)
=> ( c_24__type__23363___24t(Vvar__0__R__22934,Vvar__1__rO__22935,Vvar__2__rI__22936,Vvar__3__radd__22937,Vvar__4__rmul__22942,Vvar__5__rsub__22947,Vvar__6__ropp__22952,Vvar__7__req__22955,Vvar__6__ropp__22952)
=> ( c_24__type__23426___24t(Vvar__0__R__22934,Vvar__1__rO__22935,Vvar__2__rI__22936,Vvar__3__radd__22937,Vvar__4__rmul__22942,Vvar__5__rsub__22947,Vvar__6__ropp__22952,Vvar__7__req__22955,Vvar__7__req__22955)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__22934,Vvar__1__rO__22935,Vvar__2__rI__22936,Vvar__3__radd__22937,Vvar__4__rmul__22942,Vvar__5__rsub__22947,Vvar__6__ropp__22952,Vvar__7__req__22955)
=> ( ! [Vvar__var__var__var__var__var__8__x__22988__22989__23042__23043__23044__23045] :
( t(Vvar__var__var__var__var__var__8__x__22988__22989__23042__23043__23044__23045,Vvar__0__R__22934)
=> p(happ(happ(Vvar__7__req__22955,happ(happ(Vvar__3__radd__22937,Vvar__1__rO__22935),Vvar__var__var__var__var__var__8__x__22988__22989__23042__23043__23044__23045)),Vvar__var__var__var__var__var__8__x__22988__22989__23042__23043__23044__23045)) )
& ! [Vvar__var__var__var__var__9__x__22991__22993__23046__23048__23050] :
( t(Vvar__var__var__var__var__9__x__22991__22993__23046__23048__23050,Vvar__0__R__22934)
=> ! [Vvar__var__var__var__var__10__y__22992__22994__23047__23049__23051] :
( t(Vvar__var__var__var__var__10__y__22992__22994__23047__23049__23051,Vvar__0__R__22934)
=> p(happ(happ(Vvar__7__req__22955,happ(happ(Vvar__3__radd__22937,Vvar__var__var__var__var__9__x__22991__22993__23046__23048__23050),Vvar__var__var__var__var__10__y__22992__22994__23047__23049__23051)),happ(happ(Vvar__3__radd__22937,Vvar__var__var__var__var__10__y__22992__22994__23047__23049__23051),Vvar__var__var__var__var__9__x__22991__22993__23046__23048__23050))) ) )
& ! [Vvar__var__var__var__var__10__x__22996__22999__23052__23055__23058] :
( t(Vvar__var__var__var__var__10__x__22996__22999__23052__23055__23058,Vvar__0__R__22934)
=> ! [Vvar__var__var__var__var__11__y__22997__23000__23053__23056__23059] :
( t(Vvar__var__var__var__var__11__y__22997__23000__23053__23056__23059,Vvar__0__R__22934)
=> ! [Vvar__var__var__var__var__12__z__22998__23001__23054__23057__23060] :
( t(Vvar__var__var__var__var__12__z__22998__23001__23054__23057__23060,Vvar__0__R__22934)
=> p(happ(happ(Vvar__7__req__22955,happ(happ(Vvar__3__radd__22937,Vvar__var__var__var__var__10__x__22996__22999__23052__23055__23058),happ(happ(Vvar__3__radd__22937,Vvar__var__var__var__var__11__y__22997__23000__23053__23056__23059),Vvar__var__var__var__var__12__z__22998__23001__23054__23057__23060))),happ(happ(Vvar__3__radd__22937,happ(happ(Vvar__3__radd__22937,Vvar__var__var__var__var__10__x__22996__22999__23052__23055__23058),Vvar__var__var__var__var__11__y__22997__23000__23053__23056__23059)),Vvar__var__var__var__var__12__z__22998__23001__23054__23057__23060))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__23003__23004__23061__23062__23063__23064] :
( t(Vvar__var__var__var__var__var__11__x__23003__23004__23061__23062__23063__23064,Vvar__0__R__22934)
=> p(happ(happ(Vvar__7__req__22955,happ(happ(Vvar__4__rmul__22942,Vvar__2__rI__22936),Vvar__var__var__var__var__var__11__x__23003__23004__23061__23062__23063__23064)),Vvar__var__var__var__var__var__11__x__23003__23004__23061__23062__23063__23064)) )
& ! [Vvar__var__var__var__var__var__12__x__23006__23007__23065__23066__23067__23068] :
( t(Vvar__var__var__var__var__var__12__x__23006__23007__23065__23066__23067__23068,Vvar__0__R__22934)
=> p(happ(happ(Vvar__7__req__22955,happ(happ(Vvar__4__rmul__22942,Vvar__1__rO__22935),Vvar__var__var__var__var__var__12__x__23006__23007__23065__23066__23067__23068)),Vvar__1__rO__22935)) )
& ! [Vvar__var__var__var__var__13__x__23009__23011__23069__23071__23073] :
( t(Vvar__var__var__var__var__13__x__23009__23011__23069__23071__23073,Vvar__0__R__22934)
=> ! [Vvar__var__var__var__var__14__y__23010__23012__23070__23072__23074] :
( t(Vvar__var__var__var__var__14__y__23010__23012__23070__23072__23074,Vvar__0__R__22934)
=> p(happ(happ(Vvar__7__req__22955,happ(happ(Vvar__4__rmul__22942,Vvar__var__var__var__var__13__x__23009__23011__23069__23071__23073),Vvar__var__var__var__var__14__y__23010__23012__23070__23072__23074)),happ(happ(Vvar__4__rmul__22942,Vvar__var__var__var__var__14__y__23010__23012__23070__23072__23074),Vvar__var__var__var__var__13__x__23009__23011__23069__23071__23073))) ) )
& ! [Vvar__var__var__var__var__14__x__23014__23017__23075__23078__23081] :
( t(Vvar__var__var__var__var__14__x__23014__23017__23075__23078__23081,Vvar__0__R__22934)
=> ! [Vvar__var__var__var__var__15__y__23015__23018__23076__23079__23082] :
( t(Vvar__var__var__var__var__15__y__23015__23018__23076__23079__23082,Vvar__0__R__22934)
=> ! [Vvar__var__var__var__var__16__z__23016__23019__23077__23080__23083] :
( t(Vvar__var__var__var__var__16__z__23016__23019__23077__23080__23083,Vvar__0__R__22934)
=> p(happ(happ(Vvar__7__req__22955,happ(happ(Vvar__4__rmul__22942,Vvar__var__var__var__var__14__x__23014__23017__23075__23078__23081),happ(happ(Vvar__4__rmul__22942,Vvar__var__var__var__var__15__y__23015__23018__23076__23079__23082),Vvar__var__var__var__var__16__z__23016__23019__23077__23080__23083))),happ(happ(Vvar__4__rmul__22942,happ(happ(Vvar__4__rmul__22942,Vvar__var__var__var__var__14__x__23014__23017__23075__23078__23081),Vvar__var__var__var__var__15__y__23015__23018__23076__23079__23082)),Vvar__var__var__var__var__16__z__23016__23019__23077__23080__23083))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__23021__23024__23084__23087__23090__23093] :
( t(Vvar__var__var__var__var__var__15__x__23021__23024__23084__23087__23090__23093,Vvar__0__R__22934)
=> ! [Vvar__var__var__var__var__var__16__y__23022__23025__23085__23088__23091__23094] :
( t(Vvar__var__var__var__var__var__16__y__23022__23025__23085__23088__23091__23094,Vvar__0__R__22934)
=> ! [Vvar__var__var__var__var__var__17__z__23023__23026__23086__23089__23092__23095] :
( t(Vvar__var__var__var__var__var__17__z__23023__23026__23086__23089__23092__23095,Vvar__0__R__22934)
=> p(happ(happ(Vvar__7__req__22955,happ(happ(Vvar__4__rmul__22942,happ(happ(Vvar__3__radd__22937,Vvar__var__var__var__var__var__15__x__23021__23024__23084__23087__23090__23093),Vvar__var__var__var__var__var__16__y__23022__23025__23085__23088__23091__23094)),Vvar__var__var__var__var__var__17__z__23023__23026__23086__23089__23092__23095)),happ(happ(Vvar__3__radd__22937,happ(happ(Vvar__4__rmul__22942,Vvar__var__var__var__var__var__15__x__23021__23024__23084__23087__23090__23093),Vvar__var__var__var__var__var__17__z__23023__23026__23086__23089__23092__23095)),happ(happ(Vvar__4__rmul__22942,Vvar__var__var__var__var__var__16__y__23022__23025__23085__23088__23091__23094),Vvar__var__var__var__var__var__17__z__23023__23026__23086__23089__23092__23095)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__23028__23030__23096__23098__23100__23102] :
( t(Vvar__var__var__var__var__var__16__x__23028__23030__23096__23098__23100__23102,Vvar__0__R__22934)
=> ! [Vvar__var__var__var__var__var__17__y__23029__23031__23097__23099__23101__23103] :
( t(Vvar__var__var__var__var__var__17__y__23029__23031__23097__23099__23101__23103,Vvar__0__R__22934)
=> p(happ(happ(Vvar__7__req__22955,happ(Vvar__6__ropp__22952,happ(happ(Vvar__4__rmul__22942,Vvar__var__var__var__var__var__16__x__23028__23030__23096__23098__23100__23102),Vvar__var__var__var__var__var__17__y__23029__23031__23097__23099__23101__23103))),happ(happ(Vvar__4__rmul__22942,happ(Vvar__6__ropp__22952,Vvar__var__var__var__var__var__16__x__23028__23030__23096__23098__23100__23102)),Vvar__var__var__var__var__var__17__y__23029__23031__23097__23099__23101__23103))) ) )
& ! [Vvar__var__var__var__var__var__17__x__23033__23035__23104__23106__23108__23110] :
( t(Vvar__var__var__var__var__var__17__x__23033__23035__23104__23106__23108__23110,Vvar__0__R__22934)
=> ! [Vvar__var__var__var__var__var__18__y__23034__23036__23105__23107__23109__23111] :
( t(Vvar__var__var__var__var__var__18__y__23034__23036__23105__23107__23109__23111,Vvar__0__R__22934)
=> p(happ(happ(Vvar__7__req__22955,happ(Vvar__6__ropp__22952,happ(happ(Vvar__3__radd__22937,Vvar__var__var__var__var__var__17__x__23033__23035__23104__23106__23108__23110),Vvar__var__var__var__var__var__18__y__23034__23036__23105__23107__23109__23111))),happ(happ(Vvar__3__radd__22937,happ(Vvar__6__ropp__22952,Vvar__var__var__var__var__var__17__x__23033__23035__23104__23106__23108__23110)),happ(Vvar__6__ropp__22952,Vvar__var__var__var__var__var__18__y__23034__23036__23105__23107__23109__23111)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__23038__23040__23112__23114__23116__23118__23120] :
( t(Vvar__var__var__var__var__var__var__18__x__23038__23040__23112__23114__23116__23118__23120,Vvar__0__R__22934)
=> ! [Vvar__var__var__var__var__var__var__19__y__23039__23041__23113__23115__23117__23119__23121] :
( t(Vvar__var__var__var__var__var__var__19__y__23039__23041__23113__23115__23117__23119__23121,Vvar__0__R__22934)
=> p(happ(happ(Vvar__7__req__22955,happ(happ(Vvar__5__rsub__22947,Vvar__var__var__var__var__var__var__18__x__23038__23040__23112__23114__23116__23118__23120),Vvar__var__var__var__var__var__var__19__y__23039__23041__23113__23115__23117__23119__23121)),happ(happ(Vvar__3__radd__22937,Vvar__var__var__var__var__var__var__18__x__23038__23040__23112__23114__23116__23118__23120),happ(Vvar__6__ropp__22952,Vvar__var__var__var__var__var__var__19__y__23039__23041__23113__23115__23117__23119__23121)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__27613,Vvar__1__req__27614,Vvar__2__C__27619,Vvar__3__cadd__27620,Vvar__4__cmul__27625,Vvar__5__phi__27630,Vvar__6__cdiv__27633] :
( cType___24t(Vvar__0__R__27613)
=> ( c_24__type__27753___24t(Vvar__0__R__27613,Vvar__1__req__27614,Vvar__2__C__27619,Vvar__3__cadd__27620,Vvar__4__cmul__27625,Vvar__5__phi__27630,Vvar__6__cdiv__27633,Vvar__1__req__27614)
=> ( cType___24t(Vvar__2__C__27619)
=> ( c_24__type__27803___24t(Vvar__0__R__27613,Vvar__1__req__27614,Vvar__2__C__27619,Vvar__3__cadd__27620,Vvar__4__cmul__27625,Vvar__5__phi__27630,Vvar__6__cdiv__27633,Vvar__3__cadd__27620)
=> ( c_24__type__27853___24t(Vvar__0__R__27613,Vvar__1__req__27614,Vvar__2__C__27619,Vvar__3__cadd__27620,Vvar__4__cmul__27625,Vvar__5__phi__27630,Vvar__6__cdiv__27633,Vvar__4__cmul__27625)
=> ( c_24__type__27895___24t(Vvar__0__R__27613,Vvar__1__req__27614,Vvar__2__C__27619,Vvar__3__cadd__27620,Vvar__4__cmul__27625,Vvar__5__phi__27630,Vvar__6__cdiv__27633,Vvar__5__phi__27630)
=> ( c_24__type__27945___24t(Vvar__0__R__27613,Vvar__1__req__27614,Vvar__2__C__27619,Vvar__3__cadd__27620,Vvar__4__cmul__27625,Vvar__5__phi__27630,Vvar__6__cdiv__27633,Vvar__6__cdiv__27633)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__27613,Vvar__1__req__27614,Vvar__2__C__27619,Vvar__3__cadd__27620,Vvar__4__cmul__27625,Vvar__5__phi__27630,Vvar__6__cdiv__27633)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__27665__27670__27675__27680__27685__27690__27695__27700] :
( t(Vvar__var__var__var__var__var__var__var__7__a__27665__27670__27675__27680__27685__27690__27695__27700,Vvar__2__C__27619)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__27666__27671__27676__27681__27686__27691__27696__27701] :
( t(Vvar__var__var__var__var__var__var__var__8__b__27666__27671__27676__27681__27686__27691__27696__27701,Vvar__2__C__27619)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2428008___24a9(Vvar__0__R__27613,Vvar__1__req__27614,Vvar__2__C__27619,Vvar__3__cadd__27620,Vvar__4__cmul__27625,Vvar__5__phi__27630,Vvar__6__cdiv__27633,Vvar__var__var__var__var__var__var__var__7__a__27665__27670__27675__27680__27685__27690__27695__27700,Vvar__var__var__var__var__var__var__var__8__b__27666__27671__27676__27681__27686__27691__27696__27701) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__34517,Vvar__1__rI__34518,Vvar__2__rmul__34519,Vvar__3__req__34524,Vvar__4__Cpow__34529,Vvar__5__Cp__phi__34530,Vvar__6__rpow__34533] :
( cType___24t(Vvar__0__R__34517)
=> ( t(Vvar__1__rI__34518,Vvar__0__R__34517)
=> ( c_24__type__34619___24t(Vvar__0__R__34517,Vvar__1__rI__34518,Vvar__2__rmul__34519,Vvar__3__req__34524,Vvar__4__Cpow__34529,Vvar__5__Cp__phi__34530,Vvar__6__rpow__34533,Vvar__2__rmul__34519)
=> ( c_24__type__34663___24t(Vvar__0__R__34517,Vvar__1__rI__34518,Vvar__2__rmul__34519,Vvar__3__req__34524,Vvar__4__Cpow__34529,Vvar__5__Cp__phi__34530,Vvar__6__rpow__34533,Vvar__3__req__34524)
=> ( cType___24t(Vvar__4__Cpow__34529)
=> ( c_24__type__34699___24t(Vvar__0__R__34517,Vvar__1__rI__34518,Vvar__2__rmul__34519,Vvar__3__req__34524,Vvar__4__Cpow__34529,Vvar__5__Cp__phi__34530,Vvar__6__rpow__34533,Vvar__5__Cp__phi__34530)
=> ( c_24__type__34743___24t(Vvar__0__R__34517,Vvar__1__rI__34518,Vvar__2__rmul__34519,Vvar__3__req__34524,Vvar__4__Cpow__34529,Vvar__5__Cp__phi__34530,Vvar__6__rpow__34533,Vvar__6__rpow__34533)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__34517,Vvar__1__rI__34518,Vvar__2__rmul__34519,Vvar__3__req__34524,Vvar__4__Cpow__34529,Vvar__5__Cp__phi__34530,Vvar__6__rpow__34533)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__34561__34563__34565__34567__34569__34571__34573__34575] :
( t(Vvar__var__var__var__var__var__var__var__7__r__34561__34563__34565__34567__34569__34571__34573__34575,Vvar__0__R__34517)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__34562__34564__34566__34568__34570__34572__34574__34576] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__34562__34564__34566__34568__34570__34572__34574__34576)
=> p(happ(happ(Vvar__3__req__34524,happ(happ(Vvar__6__rpow__34533,Vvar__var__var__var__var__var__var__var__7__r__34561__34563__34565__34567__34569__34571__34573__34575),happ(Vvar__5__Cp__phi__34530,Vvar__var__var__var__var__var__var__var__8__n__34562__34564__34566__34568__34570__34572__34574__34576))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__34517,Vvar__1__rI__34518,Vvar__2__rmul__34519,Vvar__var__var__var__var__var__var__var__7__r__34561__34563__34565__34567__34569__34571__34573__34575,Vvar__var__var__var__var__var__var__var__8__n__34562__34564__34566__34568__34570__34572__34574__34576))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__23698,Vvar__1__radd__23699,Vvar__2__rmul__23704,Vvar__3__ropp__23709,Vvar__4__req__23712] :
( cType___24t(Vvar__0__R__23698)
=> ( c_24__type__23803___24t(Vvar__0__R__23698,Vvar__1__radd__23699,Vvar__2__rmul__23704,Vvar__3__ropp__23709,Vvar__4__req__23712,Vvar__1__radd__23699)
=> ( c_24__type__23833___24t(Vvar__0__R__23698,Vvar__1__radd__23699,Vvar__2__rmul__23704,Vvar__3__ropp__23709,Vvar__4__req__23712,Vvar__2__rmul__23704)
=> ( c_24__type__23857___24t(Vvar__0__R__23698,Vvar__1__radd__23699,Vvar__2__rmul__23704,Vvar__3__ropp__23709,Vvar__4__req__23712,Vvar__3__ropp__23709)
=> ( c_24__type__23887___24t(Vvar__0__R__23698,Vvar__1__radd__23699,Vvar__2__rmul__23704,Vvar__3__ropp__23709,Vvar__4__req__23712,Vvar__4__req__23712)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__23698,Vvar__1__radd__23699,Vvar__2__rmul__23704,Vvar__3__ropp__23709,Vvar__4__req__23712)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__23917___24a5(Vvar__0__R__23698,Vvar__1__radd__23699,Vvar__2__rmul__23704,Vvar__3__ropp__23709,Vvar__4__req__23712),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23698,c_24__type__23941___24a5(Vvar__0__R__23698,Vvar__1__radd__23699,Vvar__2__rmul__23704,Vvar__3__ropp__23709,Vvar__4__req__23712),Vvar__4__req__23712,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23698,Vvar__0__R__23698,Vvar__4__req__23712,Vvar__4__req__23712)),Vvar__1__radd__23699)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__23974___24a5(Vvar__0__R__23698,Vvar__1__radd__23699,Vvar__2__rmul__23704,Vvar__3__ropp__23709,Vvar__4__req__23712),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23698,c_24__type__23998___24a5(Vvar__0__R__23698,Vvar__1__radd__23699,Vvar__2__rmul__23704,Vvar__3__ropp__23709,Vvar__4__req__23712),Vvar__4__req__23712,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23698,Vvar__0__R__23698,Vvar__4__req__23712,Vvar__4__req__23712)),Vvar__2__rmul__23704)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__24025___24a5(Vvar__0__R__23698,Vvar__1__radd__23699,Vvar__2__rmul__23704,Vvar__3__ropp__23709,Vvar__4__req__23712),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23698,Vvar__0__R__23698,Vvar__4__req__23712,Vvar__4__req__23712),Vvar__3__ropp__23709)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX34747] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX34747)
=> ( VX34747 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__34748] :
( cType___24t(Vvar__0__R__34748)
& ? [Vvar__1__req__34749] :
( c_24__type__1199___24t(Vvar__0__R__34748,Vvar__1__req__34749)
& ? [Vvar__2__reqb__34754] :
( c_24__type__2080___24t(Vvar__0__R__34748,Vvar__2__reqb__34754)
& ! [Vvar__var__3__x__34760__34763] :
( t(Vvar__var__3__x__34760__34763,Vvar__0__R__34748)
=> ! [Vvar__var__4__y__34761__34764] :
( t(Vvar__var__4__y__34761__34764,Vvar__0__R__34748)
=> ( happ(happ(Vvar__2__reqb__34754,Vvar__var__3__x__34760__34763),Vvar__var__4__y__34761__34764) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__34749,Vvar__var__3__x__34760__34763),Vvar__var__4__y__34761__34764)) ) ) )
& VX34747 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__34748,Vvar__1__req__34749,Vvar__2__reqb__34754) ) ) )
| ? [Vvar__0__R__34766] :
( cType___24t(Vvar__0__R__34766)
& ? [Vvar__1__rO__34767] :
( t(Vvar__1__rO__34767,Vvar__0__R__34766)
& ? [Vvar__2__rI__34768] :
( t(Vvar__2__rI__34768,Vvar__0__R__34766)
& ? [Vvar__3__radd__34769] :
( c_24__type__1185___24t(Vvar__0__R__34766,Vvar__3__radd__34769)
& ? [Vvar__4__rmul__34774] :
( c_24__type__1185___24t(Vvar__0__R__34766,Vvar__4__rmul__34774)
& ? [Vvar__5__rsub__34779] :
( c_24__type__1185___24t(Vvar__0__R__34766,Vvar__5__rsub__34779)
& ? [Vvar__6__ropp__34784] :
( c_24__type__1194___24t(Vvar__0__R__34766,Vvar__6__ropp__34784)
& ? [Vvar__7__req__34787] :
( c_24__type__1199___24t(Vvar__0__R__34766,Vvar__7__req__34787)
& ? [Vvar__8__C__34792] :
( cType___24t(Vvar__8__C__34792)
& ? [Vvar__9__cO__34793] :
( t(Vvar__9__cO__34793,Vvar__8__C__34792)
& ? [Vvar__10__cI__34794] :
( t(Vvar__10__cI__34794,Vvar__8__C__34792)
& ? [Vvar__11__cadd__34795] :
( c_24__type__21408___24t(Vvar__0__R__34766,Vvar__8__C__34792,Vvar__11__cadd__34795)
& ? [Vvar__12__cmul__34800] :
( c_24__type__21408___24t(Vvar__0__R__34766,Vvar__8__C__34792,Vvar__12__cmul__34800)
& ? [Vvar__13__csub__34805] :
( c_24__type__21408___24t(Vvar__0__R__34766,Vvar__8__C__34792,Vvar__13__csub__34805)
& ? [Vvar__14__copp__34810] :
( c_24__type__21422___24t(Vvar__0__R__34766,Vvar__8__C__34792,Vvar__14__copp__34810)
& ? [Vvar__15__ceqb__34813] :
( c_24__type__21429___24t(Vvar__0__R__34766,Vvar__8__C__34792,Vvar__15__ceqb__34813)
& ? [Vvar__16__phi__34818] :
( c_24__type__6713___24t(Vvar__0__R__34766,Vvar__8__C__34792,Vvar__16__phi__34818)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__34766,Vvar__1__rO__34767,Vvar__2__rI__34768,Vvar__3__radd__34769,Vvar__4__rmul__34774,Vvar__5__rsub__34779,Vvar__6__ropp__34784,Vvar__7__req__34787,Vvar__8__C__34792,Vvar__9__cO__34793,Vvar__10__cI__34794,Vvar__11__cadd__34795,Vvar__12__cmul__34800,Vvar__13__csub__34805,Vvar__14__copp__34810,Vvar__15__ceqb__34813,Vvar__16__phi__34818)
& VX34747 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__34766,Vvar__1__rO__34767,Vvar__2__rI__34768,Vvar__3__radd__34769,Vvar__4__rmul__34774,Vvar__5__rsub__34779,Vvar__6__ropp__34784,Vvar__7__req__34787,Vvar__8__C__34792,Vvar__9__cO__34793,Vvar__10__cI__34794,Vvar__11__cadd__34795,Vvar__12__cmul__34800,Vvar__13__csub__34805,Vvar__14__copp__34810,Vvar__15__ceqb__34813,Vvar__16__phi__34818) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144] :
( cType___24t(Vvar__0__R__25092)
=> ( t(Vvar__1__rO__25093,Vvar__0__R__25092)
=> ( t(Vvar__2__rI__25094,Vvar__0__R__25092)
=> ( c_24__type__25488___24t(Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144,Vvar__3__radd__25095)
=> ( c_24__type__25701___24t(Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144,Vvar__4__rmul__25100)
=> ( c_24__type__25914___24t(Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144,Vvar__5__rsub__25105)
=> ( c_24__type__26109___24t(Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144,Vvar__6__ropp__25110)
=> ( c_24__type__26322___24t(Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144,Vvar__7__req__25113)
=> ( cType___24t(Vvar__8__C__25118)
=> ( t(Vvar__9__cO__25119,Vvar__8__C__25118)
=> ( t(Vvar__10__cI__25120,Vvar__8__C__25118)
=> ( c_24__type__26535___24t(Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144,Vvar__11__cadd__25121)
=> ( c_24__type__26748___24t(Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144,Vvar__12__cmul__25126)
=> ( c_24__type__26961___24t(Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144,Vvar__13__csub__25131)
=> ( c_24__type__27156___24t(Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144,Vvar__14__copp__25136)
=> ( c_24__type__27369___24t(Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144,Vvar__15__ceqb__25139)
=> ( c_24__type__27564___24t(Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144,Vvar__16__phi__25144)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__25092,Vvar__1__rO__25093,Vvar__2__rI__25094,Vvar__3__radd__25095,Vvar__4__rmul__25100,Vvar__5__rsub__25105,Vvar__6__ropp__25110,Vvar__7__req__25113,Vvar__8__C__25118,Vvar__9__cO__25119,Vvar__10__cI__25120,Vvar__11__cadd__25121,Vvar__12__cmul__25126,Vvar__13__csub__25131,Vvar__14__copp__25136,Vvar__15__ceqb__25139,Vvar__16__phi__25144)
=> ( p(happ(happ(Vvar__7__req__25113,happ(Vvar__16__phi__25144,Vvar__9__cO__25119)),Vvar__1__rO__25093))
& p(happ(happ(Vvar__7__req__25113,happ(Vvar__16__phi__25144,Vvar__10__cI__25120)),Vvar__2__rI__25094))
& ! [Vvar__var__var__var__var__var__var__19__x__25206__25208__25230__25232__25234__25236__25238] :
( t(Vvar__var__var__var__var__var__var__19__x__25206__25208__25230__25232__25234__25236__25238,Vvar__8__C__25118)
=> ! [Vvar__var__var__var__var__var__var__20__y__25207__25209__25231__25233__25235__25237__25239] :
( t(Vvar__var__var__var__var__var__var__20__y__25207__25209__25231__25233__25235__25237__25239,Vvar__8__C__25118)
=> p(happ(happ(Vvar__7__req__25113,happ(Vvar__16__phi__25144,happ(happ(Vvar__11__cadd__25121,Vvar__var__var__var__var__var__var__19__x__25206__25208__25230__25232__25234__25236__25238),Vvar__var__var__var__var__var__var__20__y__25207__25209__25231__25233__25235__25237__25239))),happ(happ(Vvar__3__radd__25095,happ(Vvar__16__phi__25144,Vvar__var__var__var__var__var__var__19__x__25206__25208__25230__25232__25234__25236__25238)),happ(Vvar__16__phi__25144,Vvar__var__var__var__var__var__var__20__y__25207__25209__25231__25233__25235__25237__25239)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__25211__25213__25240__25242__25244__25246__25248] :
( t(Vvar__var__var__var__var__var__var__20__x__25211__25213__25240__25242__25244__25246__25248,Vvar__8__C__25118)
=> ! [Vvar__var__var__var__var__var__var__21__y__25212__25214__25241__25243__25245__25247__25249] :
( t(Vvar__var__var__var__var__var__var__21__y__25212__25214__25241__25243__25245__25247__25249,Vvar__8__C__25118)
=> p(happ(happ(Vvar__7__req__25113,happ(Vvar__16__phi__25144,happ(happ(Vvar__13__csub__25131,Vvar__var__var__var__var__var__var__20__x__25211__25213__25240__25242__25244__25246__25248),Vvar__var__var__var__var__var__var__21__y__25212__25214__25241__25243__25245__25247__25249))),happ(happ(Vvar__5__rsub__25105,happ(Vvar__16__phi__25144,Vvar__var__var__var__var__var__var__20__x__25211__25213__25240__25242__25244__25246__25248)),happ(Vvar__16__phi__25144,Vvar__var__var__var__var__var__var__21__y__25212__25214__25241__25243__25245__25247__25249)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__25216__25218__25250__25252__25254__25256__25258] :
( t(Vvar__var__var__var__var__var__var__21__x__25216__25218__25250__25252__25254__25256__25258,Vvar__8__C__25118)
=> ! [Vvar__var__var__var__var__var__var__22__y__25217__25219__25251__25253__25255__25257__25259] :
( t(Vvar__var__var__var__var__var__var__22__y__25217__25219__25251__25253__25255__25257__25259,Vvar__8__C__25118)
=> p(happ(happ(Vvar__7__req__25113,happ(Vvar__16__phi__25144,happ(happ(Vvar__12__cmul__25126,Vvar__var__var__var__var__var__var__21__x__25216__25218__25250__25252__25254__25256__25258),Vvar__var__var__var__var__var__var__22__y__25217__25219__25251__25253__25255__25257__25259))),happ(happ(Vvar__4__rmul__25100,happ(Vvar__16__phi__25144,Vvar__var__var__var__var__var__var__21__x__25216__25218__25250__25252__25254__25256__25258)),happ(Vvar__16__phi__25144,Vvar__var__var__var__var__var__var__22__y__25217__25219__25251__25253__25255__25257__25259)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__25221__25222__25260__25261__25262__25263__25264] :
( t(Vvar__var__var__var__var__var__var__22__x__25221__25222__25260__25261__25262__25263__25264,Vvar__8__C__25118)
=> p(happ(happ(Vvar__7__req__25113,happ(Vvar__16__phi__25144,happ(Vvar__14__copp__25136,Vvar__var__var__var__var__var__var__22__x__25221__25222__25260__25261__25262__25263__25264))),happ(Vvar__6__ropp__25110,happ(Vvar__16__phi__25144,Vvar__var__var__var__var__var__var__22__x__25221__25222__25260__25261__25262__25263__25264)))) )
& ! [Vvar__var__var__var__var__var__23__x__25224__25227__25265__25268__25271__25274] :
( t(Vvar__var__var__var__var__var__23__x__25224__25227__25265__25268__25271__25274,Vvar__8__C__25118)
=> ! [Vvar__var__var__var__var__var__24__y__25225__25228__25266__25269__25272__25275] :
( t(Vvar__var__var__var__var__var__24__y__25225__25228__25266__25269__25272__25275,Vvar__8__C__25118)
=> ( happ(happ(Vvar__15__ceqb__25139,Vvar__var__var__var__var__var__23__x__25224__25227__25265__25268__25271__25274),Vvar__var__var__var__var__var__24__y__25225__25228__25266__25269__25272__25275) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__25113,happ(Vvar__16__phi__25144,Vvar__var__var__var__var__var__23__x__25224__25227__25265__25268__25271__25274)),happ(Vvar__16__phi__25144,Vvar__var__var__var__var__var__24__y__25225__25228__25266__25269__25272__25275))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__1255,Vvar__1__rO__1256,Vvar__2__rI__1257,Vvar__3__radd__1258,Vvar__4__rmul__1263,Vvar__5__rsub__1268,Vvar__6__ropp__1273,Vvar__7__req__1276] :
( cType___24t(Vvar__0__R__1255)
=> ( t(Vvar__1__rO__1256,Vvar__0__R__1255)
=> ( t(Vvar__2__rI__1257,Vvar__0__R__1255)
=> ( c_24__type__1479___24t(Vvar__0__R__1255,Vvar__1__rO__1256,Vvar__2__rI__1257,Vvar__3__radd__1258,Vvar__4__rmul__1263,Vvar__5__rsub__1268,Vvar__6__ropp__1273,Vvar__7__req__1276,Vvar__3__radd__1258)
=> ( c_24__type__1542___24t(Vvar__0__R__1255,Vvar__1__rO__1256,Vvar__2__rI__1257,Vvar__3__radd__1258,Vvar__4__rmul__1263,Vvar__5__rsub__1268,Vvar__6__ropp__1273,Vvar__7__req__1276,Vvar__4__rmul__1263)
=> ( c_24__type__1605___24t(Vvar__0__R__1255,Vvar__1__rO__1256,Vvar__2__rI__1257,Vvar__3__radd__1258,Vvar__4__rmul__1263,Vvar__5__rsub__1268,Vvar__6__ropp__1273,Vvar__7__req__1276,Vvar__5__rsub__1268)
=> ( c_24__type__1659___24t(Vvar__0__R__1255,Vvar__1__rO__1256,Vvar__2__rI__1257,Vvar__3__radd__1258,Vvar__4__rmul__1263,Vvar__5__rsub__1268,Vvar__6__ropp__1273,Vvar__7__req__1276,Vvar__6__ropp__1273)
=> ( c_24__type__1722___24t(Vvar__0__R__1255,Vvar__1__rO__1256,Vvar__2__rI__1257,Vvar__3__radd__1258,Vvar__4__rmul__1263,Vvar__5__rsub__1268,Vvar__6__ropp__1273,Vvar__7__req__1276,Vvar__7__req__1276)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__1255,Vvar__1__rO__1256,Vvar__2__rI__1257,Vvar__3__radd__1258,Vvar__4__rmul__1263,Vvar__5__rsub__1268,Vvar__6__ropp__1273,Vvar__7__req__1276)
=> ( ! [Vvar__var__var__var__var__var__8__x__1309__1310__1353__1354__1355__1356] :
( t(Vvar__var__var__var__var__var__8__x__1309__1310__1353__1354__1355__1356,Vvar__0__R__1255)
=> p(happ(happ(Vvar__7__req__1276,happ(happ(Vvar__3__radd__1258,Vvar__1__rO__1256),Vvar__var__var__var__var__var__8__x__1309__1310__1353__1354__1355__1356)),Vvar__var__var__var__var__var__8__x__1309__1310__1353__1354__1355__1356)) )
& ! [Vvar__var__var__var__var__9__x__1312__1314__1357__1359__1361] :
( t(Vvar__var__var__var__var__9__x__1312__1314__1357__1359__1361,Vvar__0__R__1255)
=> ! [Vvar__var__var__var__var__10__y__1313__1315__1358__1360__1362] :
( t(Vvar__var__var__var__var__10__y__1313__1315__1358__1360__1362,Vvar__0__R__1255)
=> p(happ(happ(Vvar__7__req__1276,happ(happ(Vvar__3__radd__1258,Vvar__var__var__var__var__9__x__1312__1314__1357__1359__1361),Vvar__var__var__var__var__10__y__1313__1315__1358__1360__1362)),happ(happ(Vvar__3__radd__1258,Vvar__var__var__var__var__10__y__1313__1315__1358__1360__1362),Vvar__var__var__var__var__9__x__1312__1314__1357__1359__1361))) ) )
& ! [Vvar__var__var__var__var__10__x__1317__1320__1363__1366__1369] :
( t(Vvar__var__var__var__var__10__x__1317__1320__1363__1366__1369,Vvar__0__R__1255)
=> ! [Vvar__var__var__var__var__11__y__1318__1321__1364__1367__1370] :
( t(Vvar__var__var__var__var__11__y__1318__1321__1364__1367__1370,Vvar__0__R__1255)
=> ! [Vvar__var__var__var__var__12__z__1319__1322__1365__1368__1371] :
( t(Vvar__var__var__var__var__12__z__1319__1322__1365__1368__1371,Vvar__0__R__1255)
=> p(happ(happ(Vvar__7__req__1276,happ(happ(Vvar__3__radd__1258,Vvar__var__var__var__var__10__x__1317__1320__1363__1366__1369),happ(happ(Vvar__3__radd__1258,Vvar__var__var__var__var__11__y__1318__1321__1364__1367__1370),Vvar__var__var__var__var__12__z__1319__1322__1365__1368__1371))),happ(happ(Vvar__3__radd__1258,happ(happ(Vvar__3__radd__1258,Vvar__var__var__var__var__10__x__1317__1320__1363__1366__1369),Vvar__var__var__var__var__11__y__1318__1321__1364__1367__1370)),Vvar__var__var__var__var__12__z__1319__1322__1365__1368__1371))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__1324__1325__1372__1373__1374__1375] :
( t(Vvar__var__var__var__var__var__11__x__1324__1325__1372__1373__1374__1375,Vvar__0__R__1255)
=> p(happ(happ(Vvar__7__req__1276,happ(happ(Vvar__4__rmul__1263,Vvar__2__rI__1257),Vvar__var__var__var__var__var__11__x__1324__1325__1372__1373__1374__1375)),Vvar__var__var__var__var__var__11__x__1324__1325__1372__1373__1374__1375)) )
& ! [Vvar__var__var__var__var__12__x__1327__1329__1376__1378__1380] :
( t(Vvar__var__var__var__var__12__x__1327__1329__1376__1378__1380,Vvar__0__R__1255)
=> ! [Vvar__var__var__var__var__13__y__1328__1330__1377__1379__1381] :
( t(Vvar__var__var__var__var__13__y__1328__1330__1377__1379__1381,Vvar__0__R__1255)
=> p(happ(happ(Vvar__7__req__1276,happ(happ(Vvar__4__rmul__1263,Vvar__var__var__var__var__12__x__1327__1329__1376__1378__1380),Vvar__var__var__var__var__13__y__1328__1330__1377__1379__1381)),happ(happ(Vvar__4__rmul__1263,Vvar__var__var__var__var__13__y__1328__1330__1377__1379__1381),Vvar__var__var__var__var__12__x__1327__1329__1376__1378__1380))) ) )
& ! [Vvar__var__var__var__var__13__x__1332__1335__1382__1385__1388] :
( t(Vvar__var__var__var__var__13__x__1332__1335__1382__1385__1388,Vvar__0__R__1255)
=> ! [Vvar__var__var__var__var__14__y__1333__1336__1383__1386__1389] :
( t(Vvar__var__var__var__var__14__y__1333__1336__1383__1386__1389,Vvar__0__R__1255)
=> ! [Vvar__var__var__var__var__15__z__1334__1337__1384__1387__1390] :
( t(Vvar__var__var__var__var__15__z__1334__1337__1384__1387__1390,Vvar__0__R__1255)
=> p(happ(happ(Vvar__7__req__1276,happ(happ(Vvar__4__rmul__1263,Vvar__var__var__var__var__13__x__1332__1335__1382__1385__1388),happ(happ(Vvar__4__rmul__1263,Vvar__var__var__var__var__14__y__1333__1336__1383__1386__1389),Vvar__var__var__var__var__15__z__1334__1337__1384__1387__1390))),happ(happ(Vvar__4__rmul__1263,happ(happ(Vvar__4__rmul__1263,Vvar__var__var__var__var__13__x__1332__1335__1382__1385__1388),Vvar__var__var__var__var__14__y__1333__1336__1383__1386__1389)),Vvar__var__var__var__var__15__z__1334__1337__1384__1387__1390))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__1339__1342__1391__1394__1397__1400] :
( t(Vvar__var__var__var__var__var__14__x__1339__1342__1391__1394__1397__1400,Vvar__0__R__1255)
=> ! [Vvar__var__var__var__var__var__15__y__1340__1343__1392__1395__1398__1401] :
( t(Vvar__var__var__var__var__var__15__y__1340__1343__1392__1395__1398__1401,Vvar__0__R__1255)
=> ! [Vvar__var__var__var__var__var__16__z__1341__1344__1393__1396__1399__1402] :
( t(Vvar__var__var__var__var__var__16__z__1341__1344__1393__1396__1399__1402,Vvar__0__R__1255)
=> p(happ(happ(Vvar__7__req__1276,happ(happ(Vvar__4__rmul__1263,happ(happ(Vvar__3__radd__1258,Vvar__var__var__var__var__var__14__x__1339__1342__1391__1394__1397__1400),Vvar__var__var__var__var__var__15__y__1340__1343__1392__1395__1398__1401)),Vvar__var__var__var__var__var__16__z__1341__1344__1393__1396__1399__1402)),happ(happ(Vvar__3__radd__1258,happ(happ(Vvar__4__rmul__1263,Vvar__var__var__var__var__var__14__x__1339__1342__1391__1394__1397__1400),Vvar__var__var__var__var__var__16__z__1341__1344__1393__1396__1399__1402)),happ(happ(Vvar__4__rmul__1263,Vvar__var__var__var__var__var__15__y__1340__1343__1392__1395__1398__1401),Vvar__var__var__var__var__var__16__z__1341__1344__1393__1396__1399__1402)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__1346__1348__1403__1405__1407__1409__1411] :
( t(Vvar__var__var__var__var__var__var__15__x__1346__1348__1403__1405__1407__1409__1411,Vvar__0__R__1255)
=> ! [Vvar__var__var__var__var__var__var__16__y__1347__1349__1404__1406__1408__1410__1412] :
( t(Vvar__var__var__var__var__var__var__16__y__1347__1349__1404__1406__1408__1410__1412,Vvar__0__R__1255)
=> p(happ(happ(Vvar__7__req__1276,happ(happ(Vvar__5__rsub__1268,Vvar__var__var__var__var__var__var__15__x__1346__1348__1403__1405__1407__1409__1411),Vvar__var__var__var__var__var__var__16__y__1347__1349__1404__1406__1408__1410__1412)),happ(happ(Vvar__3__radd__1258,Vvar__var__var__var__var__var__var__15__x__1346__1348__1403__1405__1407__1409__1411),happ(Vvar__6__ropp__1273,Vvar__var__var__var__var__var__var__16__y__1347__1349__1404__1406__1408__1410__1412)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__1351__1352__1413__1414__1415__1416__1417] :
( t(Vvar__var__var__var__var__var__var__16__x__1351__1352__1413__1414__1415__1416__1417,Vvar__0__R__1255)
=> p(happ(happ(Vvar__7__req__1276,happ(happ(Vvar__3__radd__1258,Vvar__var__var__var__var__var__var__16__x__1351__1352__1413__1414__1415__1416__1417),happ(Vvar__6__ropp__1273,Vvar__var__var__var__var__var__var__16__x__1351__1352__1413__1414__1415__1416__1417))),Vvar__1__rO__1256)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__24068,Vvar__1__rO__24069,Vvar__2__rI__24070,Vvar__3__radd__24071,Vvar__4__rmul__24076,Vvar__5__req__24081,Vvar__6__C__24086,Vvar__7__cO__24087,Vvar__8__cI__24088,Vvar__9__cadd__24089,Vvar__10__cmul__24094,Vvar__11__ceqb__24099,Vvar__12__phi__24104] :
( cType___24t(Vvar__0__R__24068)
=> ( t(Vvar__1__rO__24069,Vvar__0__R__24068)
=> ( t(Vvar__2__rI__24070,Vvar__0__R__24068)
=> ( c_24__type__24321___24t(Vvar__0__R__24068,Vvar__1__rO__24069,Vvar__2__rI__24070,Vvar__3__radd__24071,Vvar__4__rmul__24076,Vvar__5__req__24081,Vvar__6__C__24086,Vvar__7__cO__24087,Vvar__8__cI__24088,Vvar__9__cadd__24089,Vvar__10__cmul__24094,Vvar__11__ceqb__24099,Vvar__12__phi__24104,Vvar__3__radd__24071)
=> ( c_24__type__24446___24t(Vvar__0__R__24068,Vvar__1__rO__24069,Vvar__2__rI__24070,Vvar__3__radd__24071,Vvar__4__rmul__24076,Vvar__5__req__24081,Vvar__6__C__24086,Vvar__7__cO__24087,Vvar__8__cI__24088,Vvar__9__cadd__24089,Vvar__10__cmul__24094,Vvar__11__ceqb__24099,Vvar__12__phi__24104,Vvar__4__rmul__24076)
=> ( c_24__type__24571___24t(Vvar__0__R__24068,Vvar__1__rO__24069,Vvar__2__rI__24070,Vvar__3__radd__24071,Vvar__4__rmul__24076,Vvar__5__req__24081,Vvar__6__C__24086,Vvar__7__cO__24087,Vvar__8__cI__24088,Vvar__9__cadd__24089,Vvar__10__cmul__24094,Vvar__11__ceqb__24099,Vvar__12__phi__24104,Vvar__5__req__24081)
=> ( cType___24t(Vvar__6__C__24086)
=> ( t(Vvar__7__cO__24087,Vvar__6__C__24086)
=> ( t(Vvar__8__cI__24088,Vvar__6__C__24086)
=> ( c_24__type__24696___24t(Vvar__0__R__24068,Vvar__1__rO__24069,Vvar__2__rI__24070,Vvar__3__radd__24071,Vvar__4__rmul__24076,Vvar__5__req__24081,Vvar__6__C__24086,Vvar__7__cO__24087,Vvar__8__cI__24088,Vvar__9__cadd__24089,Vvar__10__cmul__24094,Vvar__11__ceqb__24099,Vvar__12__phi__24104,Vvar__9__cadd__24089)
=> ( c_24__type__24821___24t(Vvar__0__R__24068,Vvar__1__rO__24069,Vvar__2__rI__24070,Vvar__3__radd__24071,Vvar__4__rmul__24076,Vvar__5__req__24081,Vvar__6__C__24086,Vvar__7__cO__24087,Vvar__8__cI__24088,Vvar__9__cadd__24089,Vvar__10__cmul__24094,Vvar__11__ceqb__24099,Vvar__12__phi__24104,Vvar__10__cmul__24094)
=> ( c_24__type__24946___24t(Vvar__0__R__24068,Vvar__1__rO__24069,Vvar__2__rI__24070,Vvar__3__radd__24071,Vvar__4__rmul__24076,Vvar__5__req__24081,Vvar__6__C__24086,Vvar__7__cO__24087,Vvar__8__cI__24088,Vvar__9__cadd__24089,Vvar__10__cmul__24094,Vvar__11__ceqb__24099,Vvar__12__phi__24104,Vvar__11__ceqb__24099)
=> ( c_24__type__25057___24t(Vvar__0__R__24068,Vvar__1__rO__24069,Vvar__2__rI__24070,Vvar__3__radd__24071,Vvar__4__rmul__24076,Vvar__5__req__24081,Vvar__6__C__24086,Vvar__7__cO__24087,Vvar__8__cI__24088,Vvar__9__cadd__24089,Vvar__10__cmul__24094,Vvar__11__ceqb__24099,Vvar__12__phi__24104,Vvar__12__phi__24104)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__24068,Vvar__1__rO__24069,Vvar__2__rI__24070,Vvar__3__radd__24071,Vvar__4__rmul__24076,Vvar__5__req__24081,Vvar__6__C__24086,Vvar__7__cO__24087,Vvar__8__cI__24088,Vvar__9__cadd__24089,Vvar__10__cmul__24094,Vvar__11__ceqb__24099,Vvar__12__phi__24104)
=> ( p(happ(happ(Vvar__5__req__24081,happ(Vvar__12__phi__24104,Vvar__7__cO__24087)),Vvar__1__rO__24069))
& p(happ(happ(Vvar__5__req__24081,happ(Vvar__12__phi__24104,Vvar__8__cI__24088)),Vvar__2__rI__24070))
& ! [Vvar__var__var__var__var__var__var__15__x__24150__24152__24166__24168__24170__24172__24174] :
( t(Vvar__var__var__var__var__var__var__15__x__24150__24152__24166__24168__24170__24172__24174,Vvar__6__C__24086)
=> ! [Vvar__var__var__var__var__var__var__16__y__24151__24153__24167__24169__24171__24173__24175] :
( t(Vvar__var__var__var__var__var__var__16__y__24151__24153__24167__24169__24171__24173__24175,Vvar__6__C__24086)
=> p(happ(happ(Vvar__5__req__24081,happ(Vvar__12__phi__24104,happ(happ(Vvar__9__cadd__24089,Vvar__var__var__var__var__var__var__15__x__24150__24152__24166__24168__24170__24172__24174),Vvar__var__var__var__var__var__var__16__y__24151__24153__24167__24169__24171__24173__24175))),happ(happ(Vvar__3__radd__24071,happ(Vvar__12__phi__24104,Vvar__var__var__var__var__var__var__15__x__24150__24152__24166__24168__24170__24172__24174)),happ(Vvar__12__phi__24104,Vvar__var__var__var__var__var__var__16__y__24151__24153__24167__24169__24171__24173__24175)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__24155__24157__24176__24178__24180__24182__24184] :
( t(Vvar__var__var__var__var__var__var__16__x__24155__24157__24176__24178__24180__24182__24184,Vvar__6__C__24086)
=> ! [Vvar__var__var__var__var__var__var__17__y__24156__24158__24177__24179__24181__24183__24185] :
( t(Vvar__var__var__var__var__var__var__17__y__24156__24158__24177__24179__24181__24183__24185,Vvar__6__C__24086)
=> p(happ(happ(Vvar__5__req__24081,happ(Vvar__12__phi__24104,happ(happ(Vvar__10__cmul__24094,Vvar__var__var__var__var__var__var__16__x__24155__24157__24176__24178__24180__24182__24184),Vvar__var__var__var__var__var__var__17__y__24156__24158__24177__24179__24181__24183__24185))),happ(happ(Vvar__4__rmul__24076,happ(Vvar__12__phi__24104,Vvar__var__var__var__var__var__var__16__x__24155__24157__24176__24178__24180__24182__24184)),happ(Vvar__12__phi__24104,Vvar__var__var__var__var__var__var__17__y__24156__24158__24177__24179__24181__24183__24185)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__24160__24163__24186__24189__24192__24195] :
( t(Vvar__var__var__var__var__var__17__x__24160__24163__24186__24189__24192__24195,Vvar__6__C__24086)
=> ! [Vvar__var__var__var__var__var__18__y__24161__24164__24187__24190__24193__24196] :
( t(Vvar__var__var__var__var__var__18__y__24161__24164__24187__24190__24193__24196,Vvar__6__C__24086)
=> ( happ(happ(Vvar__11__ceqb__24099,Vvar__var__var__var__var__var__17__x__24160__24163__24186__24189__24192__24195),Vvar__var__var__var__var__var__18__y__24161__24164__24187__24190__24193__24196) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__24081,happ(Vvar__12__phi__24104,Vvar__var__var__var__var__var__17__x__24160__24163__24186__24189__24192__24195)),happ(Vvar__12__phi__24104,Vvar__var__var__var__var__var__18__y__24161__24164__24187__24190__24193__24196))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__34239,Vvar__1__rO__34240,Vvar__2__rI__34241,Vvar__3__radd__34242,Vvar__4__rmul__34247,Vvar__5__req__34252] :
( cType___24t(Vvar__0__R__34239)
=> ( t(Vvar__1__rO__34240,Vvar__0__R__34239)
=> ( t(Vvar__2__rI__34241,Vvar__0__R__34239)
=> ( c_24__type__34407___24t(Vvar__0__R__34239,Vvar__1__rO__34240,Vvar__2__rI__34241,Vvar__3__radd__34242,Vvar__4__rmul__34247,Vvar__5__req__34252,Vvar__3__radd__34242)
=> ( c_24__type__34446___24t(Vvar__0__R__34239,Vvar__1__rO__34240,Vvar__2__rI__34241,Vvar__3__radd__34242,Vvar__4__rmul__34247,Vvar__5__req__34252,Vvar__4__rmul__34247)
=> ( c_24__type__34485___24t(Vvar__0__R__34239,Vvar__1__rO__34240,Vvar__2__rI__34241,Vvar__3__radd__34242,Vvar__4__rmul__34247,Vvar__5__req__34252,Vvar__5__req__34252)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__34239,Vvar__1__rO__34240,Vvar__2__rI__34241,Vvar__3__radd__34242,Vvar__4__rmul__34247,Vvar__5__req__34252)
=> ( ! [Vvar__var__var__var__var__var__6__n__34277__34278__34316__34317__34318__34319] :
( t(Vvar__var__var__var__var__var__6__n__34277__34278__34316__34317__34318__34319,Vvar__0__R__34239)
=> p(happ(happ(Vvar__5__req__34252,happ(happ(Vvar__3__radd__34242,Vvar__1__rO__34240),Vvar__var__var__var__var__var__6__n__34277__34278__34316__34317__34318__34319)),Vvar__var__var__var__var__var__6__n__34277__34278__34316__34317__34318__34319)) )
& ! [Vvar__var__var__var__var__7__n__34280__34282__34320__34322__34324] :
( t(Vvar__var__var__var__var__7__n__34280__34282__34320__34322__34324,Vvar__0__R__34239)
=> ! [Vvar__var__var__var__var__8__m__34281__34283__34321__34323__34325] :
( t(Vvar__var__var__var__var__8__m__34281__34283__34321__34323__34325,Vvar__0__R__34239)
=> p(happ(happ(Vvar__5__req__34252,happ(happ(Vvar__3__radd__34242,Vvar__var__var__var__var__7__n__34280__34282__34320__34322__34324),Vvar__var__var__var__var__8__m__34281__34283__34321__34323__34325)),happ(happ(Vvar__3__radd__34242,Vvar__var__var__var__var__8__m__34281__34283__34321__34323__34325),Vvar__var__var__var__var__7__n__34280__34282__34320__34322__34324))) ) )
& ! [Vvar__var__var__var__var__8__n__34285__34288__34326__34329__34332] :
( t(Vvar__var__var__var__var__8__n__34285__34288__34326__34329__34332,Vvar__0__R__34239)
=> ! [Vvar__var__var__var__var__9__m__34286__34289__34327__34330__34333] :
( t(Vvar__var__var__var__var__9__m__34286__34289__34327__34330__34333,Vvar__0__R__34239)
=> ! [Vvar__var__var__var__var__10__p__34287__34290__34328__34331__34334] :
( t(Vvar__var__var__var__var__10__p__34287__34290__34328__34331__34334,Vvar__0__R__34239)
=> p(happ(happ(Vvar__5__req__34252,happ(happ(Vvar__3__radd__34242,Vvar__var__var__var__var__8__n__34285__34288__34326__34329__34332),happ(happ(Vvar__3__radd__34242,Vvar__var__var__var__var__9__m__34286__34289__34327__34330__34333),Vvar__var__var__var__var__10__p__34287__34290__34328__34331__34334))),happ(happ(Vvar__3__radd__34242,happ(happ(Vvar__3__radd__34242,Vvar__var__var__var__var__8__n__34285__34288__34326__34329__34332),Vvar__var__var__var__var__9__m__34286__34289__34327__34330__34333)),Vvar__var__var__var__var__10__p__34287__34290__34328__34331__34334))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__34292__34293__34335__34336__34337__34338] :
( t(Vvar__var__var__var__var__var__9__n__34292__34293__34335__34336__34337__34338,Vvar__0__R__34239)
=> p(happ(happ(Vvar__5__req__34252,happ(happ(Vvar__4__rmul__34247,Vvar__2__rI__34241),Vvar__var__var__var__var__var__9__n__34292__34293__34335__34336__34337__34338)),Vvar__var__var__var__var__var__9__n__34292__34293__34335__34336__34337__34338)) )
& ! [Vvar__var__var__var__var__var__10__n__34295__34296__34339__34340__34341__34342] :
( t(Vvar__var__var__var__var__var__10__n__34295__34296__34339__34340__34341__34342,Vvar__0__R__34239)
=> p(happ(happ(Vvar__5__req__34252,happ(happ(Vvar__4__rmul__34247,Vvar__1__rO__34240),Vvar__var__var__var__var__var__10__n__34295__34296__34339__34340__34341__34342)),Vvar__1__rO__34240)) )
& ! [Vvar__var__var__var__var__11__n__34298__34300__34343__34345__34347] :
( t(Vvar__var__var__var__var__11__n__34298__34300__34343__34345__34347,Vvar__0__R__34239)
=> ! [Vvar__var__var__var__var__12__m__34299__34301__34344__34346__34348] :
( t(Vvar__var__var__var__var__12__m__34299__34301__34344__34346__34348,Vvar__0__R__34239)
=> p(happ(happ(Vvar__5__req__34252,happ(happ(Vvar__4__rmul__34247,Vvar__var__var__var__var__11__n__34298__34300__34343__34345__34347),Vvar__var__var__var__var__12__m__34299__34301__34344__34346__34348)),happ(happ(Vvar__4__rmul__34247,Vvar__var__var__var__var__12__m__34299__34301__34344__34346__34348),Vvar__var__var__var__var__11__n__34298__34300__34343__34345__34347))) ) )
& ! [Vvar__var__var__var__var__12__n__34303__34306__34349__34352__34355] :
( t(Vvar__var__var__var__var__12__n__34303__34306__34349__34352__34355,Vvar__0__R__34239)
=> ! [Vvar__var__var__var__var__13__m__34304__34307__34350__34353__34356] :
( t(Vvar__var__var__var__var__13__m__34304__34307__34350__34353__34356,Vvar__0__R__34239)
=> ! [Vvar__var__var__var__var__14__p__34305__34308__34351__34354__34357] :
( t(Vvar__var__var__var__var__14__p__34305__34308__34351__34354__34357,Vvar__0__R__34239)
=> p(happ(happ(Vvar__5__req__34252,happ(happ(Vvar__4__rmul__34247,Vvar__var__var__var__var__12__n__34303__34306__34349__34352__34355),happ(happ(Vvar__4__rmul__34247,Vvar__var__var__var__var__13__m__34304__34307__34350__34353__34356),Vvar__var__var__var__var__14__p__34305__34308__34351__34354__34357))),happ(happ(Vvar__4__rmul__34247,happ(happ(Vvar__4__rmul__34247,Vvar__var__var__var__var__12__n__34303__34306__34349__34352__34355),Vvar__var__var__var__var__13__m__34304__34307__34350__34353__34356)),Vvar__var__var__var__var__14__p__34305__34308__34351__34354__34357))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__34310__34313__34358__34361__34364__34367] :
( t(Vvar__var__var__var__var__var__13__n__34310__34313__34358__34361__34364__34367,Vvar__0__R__34239)
=> ! [Vvar__var__var__var__var__var__14__m__34311__34314__34359__34362__34365__34368] :
( t(Vvar__var__var__var__var__var__14__m__34311__34314__34359__34362__34365__34368,Vvar__0__R__34239)
=> ! [Vvar__var__var__var__var__var__15__p__34312__34315__34360__34363__34366__34369] :
( t(Vvar__var__var__var__var__var__15__p__34312__34315__34360__34363__34366__34369,Vvar__0__R__34239)
=> p(happ(happ(Vvar__5__req__34252,happ(happ(Vvar__4__rmul__34247,happ(happ(Vvar__3__radd__34242,Vvar__var__var__var__var__var__13__n__34310__34313__34358__34361__34364__34367),Vvar__var__var__var__var__var__14__m__34311__34314__34359__34362__34365__34368)),Vvar__var__var__var__var__var__15__p__34312__34315__34360__34363__34366__34369)),happ(happ(Vvar__3__radd__34242,happ(happ(Vvar__4__rmul__34247,Vvar__var__var__var__var__var__13__n__34310__34313__34358__34361__34364__34367),Vvar__var__var__var__var__var__15__p__34312__34315__34360__34363__34366__34369)),happ(happ(Vvar__4__rmul__34247,Vvar__var__var__var__var__var__14__m__34311__34314__34359__34362__34365__34368),Vvar__var__var__var__var__var__15__p__34312__34315__34360__34363__34366__34369)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__23476,Vvar__1__radd__23477,Vvar__2__rmul__23482,Vvar__3__req__23487] :
( cType___24t(Vvar__0__R__23476)
=> ( c_24__type__23562___24t(Vvar__0__R__23476,Vvar__1__radd__23477,Vvar__2__rmul__23482,Vvar__3__req__23487,Vvar__1__radd__23477)
=> ( c_24__type__23585___24t(Vvar__0__R__23476,Vvar__1__radd__23477,Vvar__2__rmul__23482,Vvar__3__req__23487,Vvar__2__rmul__23482)
=> ( c_24__type__23608___24t(Vvar__0__R__23476,Vvar__1__radd__23477,Vvar__2__rmul__23482,Vvar__3__req__23487,Vvar__3__req__23487)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__23476,Vvar__1__radd__23477,Vvar__2__rmul__23482,Vvar__3__req__23487)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__23631___24a4(Vvar__0__R__23476,Vvar__1__radd__23477,Vvar__2__rmul__23482,Vvar__3__req__23487),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23476,c_24__type__23649___24a4(Vvar__0__R__23476,Vvar__1__radd__23477,Vvar__2__rmul__23482,Vvar__3__req__23487),Vvar__3__req__23487,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23476,Vvar__0__R__23476,Vvar__3__req__23487,Vvar__3__req__23487)),Vvar__1__radd__23477)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__23675___24a4(Vvar__0__R__23476,Vvar__1__radd__23477,Vvar__2__rmul__23482,Vvar__3__req__23487),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23476,c_24__type__23693___24a4(Vvar__0__R__23476,Vvar__1__radd__23477,Vvar__2__rmul__23482,Vvar__3__req__23487),Vvar__3__req__23487,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23476,Vvar__0__R__23476,Vvar__3__req__23487,Vvar__3__req__23487)),Vvar__2__rmul__23482)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [VX33472] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX33472)
=> ( VX33472 = cHammer_2eTactics_2eReconstr_2eEmpty
| VX33472 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).
fof('$_inversion_hahn.HahnBase.Equality.mixin_of',axiom,
! [Vvar__0__T__35298,VX35299] :
( cType___24t(Vvar__0__T__35298)
=> ( chahn_2eHahnBase_2eEquality_2emixin__of___24t(Vvar__0__T__35298,VX35299)
=> ? [Vvar__1__op__35301] :
( c_24__type__2080___24t(Vvar__0__T__35298,Vvar__1__op__35301)
& ? [Vvar__2___24Anonymous__35306] :
( chahn_2eHahnBase_2eEquality_2eaxiom___24t(Vvar__0__T__35298,Vvar__1__op__35301,Vvar__2___24Anonymous__35306)
& VX35299 = chahn_2eHahnBase_2eEquality_2eMixin___24a3(Vvar__0__T__35298,Vvar__1__op__35301,Vvar__2___24Anonymous__35306) ) ) ) ) ).
fof('$_inversion_hahn.HahnBase.Equality.type',axiom,
! [VX35318] :
( chahn_2eHahnBase_2eEquality_2etype___24t(VX35318)
=> ? [Vvar__0__sort__35319] :
( cType___24t(Vvar__0__sort__35319)
& ? [Vvar__1___24Anonymous__35320] :
( chahn_2eHahnBase_2eEquality_2emixin__of___24t(Vvar__0__sort__35319,Vvar__1___24Anonymous__35320)
& ? [Vvar__2___24Anonymous__35321] :
( cType___24t(Vvar__2___24Anonymous__35321)
& VX35318 = chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__35319,Vvar__1___24Anonymous__35320,Vvar__2___24Anonymous__35321) ) ) ) ) ).
fof('$_lam_10990',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__10990___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_30631',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__30631___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_33077',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__33077___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_33085',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__33085___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_35673',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__35673___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(c_24False) ) ).
fof('$_lam_3955',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__3955___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(c_24True) ) ).
fof('$_lam_40479',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__40479___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_40489',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__40489___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__4),Vv__CANONICAL__3) ).
fof('$_lam_40507',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__40507___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(c_24False) ) ).
fof('$_lam_40532',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__40532___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ).
fof('$_lam_45572',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__45572___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2einter__rel___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__2) ).
fof('$_lam_45583',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__45583___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2einter__rel___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_45594',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__45594___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2eminus__rel___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__2) ).
fof('$_lam_45609',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__45609___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__4),happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_45623',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__45623___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(c_24False) ) ).
fof('$_lam_61939',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__61939___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(c_24True) ) ).
fof('$_lam_61963',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__61963___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = chahn_2eHahnRelationsBasic_2epow__rel___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2)) ).
fof('$_lam_61967',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__61967___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = chahn_2eHahnRelationsBasic_2epow__rel___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ).
fof('$_lam_65591',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__65591___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) ).
fof('$_lam_65593',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__65593___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_65610',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__65610___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(Vv__CANONICAL__1,Vv__CANONICAL__3)) ).
fof('$_lam_65746',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__65746___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
& p(happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ).
fof('$_lam_65766',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__65766___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ).
fof('$_lam_65796',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__65796___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__4))
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5))
& p(happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ) ) ).
fof('$_lam_73829',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__73829___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_73839',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__73839___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2erestr__rel___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_73855',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__73855___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2erestr__rel___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_73861',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__73861___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_73888',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__73888___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(Vv__CANONICAL__2,Vv__CANONICAL__4) ).
fof('$_lam_73900',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__73900___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ).
fof('$_lam_75262',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__75262___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(c_24False) ) ).
fof('$_lam_75299',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__75299___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(c_24False) ) ).
fof('$_lam_75315',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__75315___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4))) ) ).
fof('$_lam_75325',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__75325___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4))) ) ).
fof('$_lam_76083',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__76083___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4))) ) ).
fof('$_prop_35352',axiom,
! [Vvar__0___24Anonymous__35328,Vvar__0__S__35330,Vvar__1__x__35331,Vvar__2__y__35332] :
( p(c_24__prop__35352___24a4(Vvar__0___24Anonymous__35328,Vvar__0__S__35330,Vvar__1__x__35331,Vvar__2__y__35332))
<=> Vvar__1__x__35331 = Vvar__2__y__35332 ) ).
fof('$_prop_35353',axiom,
! [Vvar__0___24Anonymous__35328,Vvar__0__x__35333,Vvar__1__y__35334] :
( p(c_24__prop__35353___24a3(Vvar__0___24Anonymous__35328,Vvar__0__x__35333,Vvar__1__y__35334))
<=> Vvar__0__x__35333 = Vvar__1__y__35334 ) ).
fof('$_prop_35354',axiom,
! [Vvar__0___24Anonymous__35328,Vvar__0__x__35335,Vvar__1__s__35336] :
( p(c_24__prop__35354___24a3(Vvar__0___24Anonymous__35328,Vvar__0__x__35335,Vvar__1__s__35336))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__35335,Vvar__1__s__35336) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_35355',axiom,
! [Vvar__0___24Anonymous__35328,Vvar__0__P__35337,Vvar__1__Q__35338] :
( p(c_24__prop__35355___24a3(Vvar__0___24Anonymous__35328,Vvar__0__P__35337,Vvar__1__Q__35338))
<=> ( p(Vvar__0__P__35337)
& p(Vvar__1__Q__35338) ) ) ).
fof('$_prop_35356',axiom,
! [Vvar__0___24Anonymous__35328,Vvar__0__P__35341,Vvar__1__Q__35342] :
( p(c_24__prop__35356___24a3(Vvar__0___24Anonymous__35328,Vvar__0__P__35341,Vvar__1__Q__35342))
<=> ( p(Vvar__0__P__35341)
| p(Vvar__1__Q__35342) ) ) ).
fof('$_prop_35357',axiom,
! [Vvar__0___24Anonymous__35328,Vvar__0__P__35345,Vvar__1__Q__35346] :
( p(c_24__prop__35357___24a3(Vvar__0___24Anonymous__35328,Vvar__0__P__35345,Vvar__1__Q__35346))
<=> ( p(Vvar__0__P__35345)
=> p(Vvar__1__Q__35346) ) ) ).
fof('$_prop_35358',axiom,
! [Vvar__0___24Anonymous__35328,Vvar__0__P__35350] :
( p(c_24__prop__35358___24a2(Vvar__0___24Anonymous__35328,Vvar__0__P__35350))
<=> ~ p(Vvar__0__P__35350) ) ).
fof('$_prop_35372',axiom,
! [Vvar__0___24Anonymous__35359,Vvar__0__s__35363] :
( p(c_24__prop__35372___24a2(Vvar__0___24Anonymous__35359,Vvar__0__s__35363))
<=> ! [Vvar__1__a__35364] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__35364)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__35364,Vvar__0__s__35363) ) ) ).
fof('$_prop_35373',axiom,
! [Vvar__0___24Anonymous__35359,Vvar__0__s1__35365,Vvar__1__s2__35366] :
( p(c_24__prop__35373___24a3(Vvar__0___24Anonymous__35359,Vvar__0__s1__35365,Vvar__1__s2__35366))
<=> ! [Vvar__2__a__35367] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__35367)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__35367,Vvar__0__s1__35365)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__35367,Vvar__1__s2__35366) ) ) ) ).
fof('$_prop_35374',axiom,
! [Vvar__0___24Anonymous__35359,Vvar__0__s1__35369,Vvar__1__s2__35370] :
( p(c_24__prop__35374___24a3(Vvar__0___24Anonymous__35359,Vvar__0__s1__35369,Vvar__1__s2__35370))
<=> ! [Vvar__2__a__35371] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__35371)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__35371,Vvar__0__s1__35369)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__35371,Vvar__1__s2__35370) ) ) ) ).
fof('$_type_10127',axiom,
! [Vvar__10128] :
( c_24__type__10127___24t(Vvar__10128)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__10128,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10150',axiom,
! [Vvar__10151] :
( c_24__type__10150___24t(Vvar__10151)
<=> ! [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__10151,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_10155',axiom,
! [Vvar__10156] :
( c_24__type__10155___24t(Vvar__10156)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__10156,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_10166',axiom,
! [Vvar__10167] :
( c_24__type__10166___24t(Vvar__10167)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__10167,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1030',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1031] :
( c_24__type__1030___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1031)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1031,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_10727',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10728] :
( c_24__type__10727___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10728)
<=> ! [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__10728,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_10755',axiom,
! [Vvar__10756] :
( c_24__type__10755___24t(Vvar__10756)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1199___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__10756,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10826',axiom,
! [Vvar__10827] :
( c_24__type__10826___24t(Vvar__10827)
<=> ! [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__10827,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10842',axiom,
! [Vvar__10843] :
( c_24__type__10842___24t(Vvar__10843)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__10843,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10852',axiom,
! [Vvar__10853] :
( c_24__type__10852___24t(Vvar__10853)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__10853,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10867',axiom,
! [Vvar__10868] :
( c_24__type__10867___24t(Vvar__10868)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__10868,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11002',axiom,
! [Vvar__11003] :
( c_24__type__11002___24t(Vvar__11003)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__11007___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__11003,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_11007',axiom,
! [Vv__CANONICAL__0,Vvar__11008] :
( c_24__type__11007___24t(Vv__CANONICAL__0,Vvar__11008)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11008,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11040',axiom,
! [Vv__CANONICAL__0,Vvar__11041] :
( c_24__type__11040___24t(Vv__CANONICAL__0,Vvar__11041)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__11041,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_11119',axiom,
! [Vvar__11120] :
( c_24__type__11119___24t(Vvar__11120)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__11120,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11127',axiom,
! [Vvar__11128] :
( c_24__type__11127___24t(Vvar__11128)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__11128,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11164',axiom,
! [Vvar__11165] :
( c_24__type__11164___24t(Vvar__11165)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__11165,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11167',axiom,
! [Vvar__11168] :
( c_24__type__11167___24t(Vvar__11168)
<=> ! [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__11168,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11170',axiom,
! [Vvar__11171] :
( c_24__type__11170___24t(Vvar__11171)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__11171,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11209',axiom,
! [Vvar__11210] :
( c_24__type__11209___24t(Vvar__11210)
<=> ! [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__11210,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1131',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1132] :
( c_24__type__1131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1132)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1132,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_11343',axiom,
! [Vvar__11344] :
( c_24__type__11343___24t(Vvar__11344)
<=> ! [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__11344,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11598',axiom,
! [Vvar__11599] :
( c_24__type__11598___24t(Vvar__11599)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__11599,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11601',axiom,
! [Vvar__11602] :
( c_24__type__11601___24t(Vvar__11602)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__11602,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11631',axiom,
! [Vvar__11632] :
( c_24__type__11631___24t(Vvar__11632)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__11632,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11691',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11692] :
( c_24__type__11691___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11692)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__21___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(Vvar__11692,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_11699',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11700] :
( c_24__type__11699___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11700)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(Vvar__11700,Vv__CANONICAL__2)) ) ) ).
fof('$_type_11719',axiom,
! [Vv__CANONICAL__0,Vvar__11720] :
( c_24__type__11719___24t(Vv__CANONICAL__0,Vvar__11720)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__11720,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_11726',axiom,
! [Vv__CANONICAL__0,Vvar__11727] :
( c_24__type__11726___24t(Vv__CANONICAL__0,Vvar__11727)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__11727,Vv__CANONICAL__1)) ) ) ).
fof('$_type_11731',axiom,
! [Vv__CANONICAL__0,Vvar__11732] :
( c_24__type__11731___24t(Vv__CANONICAL__0,Vvar__11732)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__11732,Vv__CANONICAL__1)) ) ) ).
fof('$_type_11736',axiom,
! [Vv__CANONICAL__0,Vvar__11737] :
( c_24__type__11736___24t(Vv__CANONICAL__0,Vvar__11737)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__11737,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_11739',axiom,
! [Vv__CANONICAL__0,Vvar__11740] :
( c_24__type__11739___24t(Vv__CANONICAL__0,Vvar__11740)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__11740,Vv__CANONICAL__1)) ) ) ).
fof('$_type_11748',axiom,
! [Vv__CANONICAL__0,Vvar__11749] :
( c_24__type__11748___24t(Vv__CANONICAL__0,Vvar__11749)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__11749,Vv__CANONICAL__1)) ) ) ).
fof('$_type_11760',axiom,
! [Vv__CANONICAL__0,Vvar__11761] :
( c_24__type__11760___24t(Vv__CANONICAL__0,Vvar__11761)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__11761,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_11779',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11780] :
( c_24__type__11779___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11780)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__11780,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_11787',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11788] :
( c_24__type__11787___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11788)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__11788,Vv__CANONICAL__2)) ) ) ).
fof('$_type_11802',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11803] :
( c_24__type__11802___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11803)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__11803,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_11817',axiom,
! [Vv__CANONICAL__0,Vvar__11818] :
( c_24__type__11817___24t(Vv__CANONICAL__0,Vvar__11818)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__11818,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_11829',axiom,
! [Vv__CANONICAL__0,Vvar__11830] :
( c_24__type__11829___24t(Vv__CANONICAL__0,Vvar__11830)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__11830,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_11847',axiom,
! [Vv__CANONICAL__0,Vvar__11848] :
( c_24__type__11847___24t(Vv__CANONICAL__0,Vvar__11848)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__11848,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_1185',axiom,
! [Vv__CANONICAL__0,Vvar__1186] :
( c_24__type__1185___24t(Vv__CANONICAL__0,Vvar__1186)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1186,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11851',axiom,
! [Vvar__11852] :
( c_24__type__11851___24t(Vvar__11852)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__11852,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11857',axiom,
! [Vvar__11858] :
( c_24__type__11857___24t(Vvar__11858)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__11858,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11872',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11873] :
( c_24__type__11872___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11873)
<=> ! [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__11873,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_11939',axiom,
! [Vvar__11940] :
( c_24__type__11939___24t(Vvar__11940)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__11940,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_1194',axiom,
! [Vv__CANONICAL__0,Vvar__1195] :
( c_24__type__1194___24t(Vv__CANONICAL__0,Vvar__1195)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__1195,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_11951',axiom,
! [Vvar__11952] :
( c_24__type__11951___24t(Vvar__11952)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__11952,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1199',axiom,
! [Vv__CANONICAL__0,Vvar__1200] :
( c_24__type__1199___24t(Vv__CANONICAL__0,Vvar__1200)
<=> ! [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__1200,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_12172',axiom,
! [Vvar__12173] :
( c_24__type__12172___24t(Vvar__12173)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__12173,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12203',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__12204] :
( c_24__type__12203___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__12204)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__12204,Vv__CANONICAL__6)) ) ) ).
fof('$_type_12227',axiom,
! [Vvar__12228] :
( c_24__type__12227___24t(Vvar__12228)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__12228,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_12273',axiom,
! [Vvar__12274] :
( c_24__type__12273___24t(Vvar__12274)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__6___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__12274,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_12313',axiom,
! [Vvar__12314] :
( c_24__type__12313___24t(Vvar__12314)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__12314,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_1233',axiom,
! [Vvar__1234] :
( c_24__type__1233___24t(Vvar__1234)
<=> ! [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__1234,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12337',axiom,
! [Vvar__12338] :
( c_24__type__12337___24t(Vvar__12338)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__12344___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__12338,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_12344',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12345] :
( c_24__type__12344___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12345)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12345,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12398',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12399] :
( c_24__type__12398___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12399)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__12399,Vv__CANONICAL__3)) ) ) ).
fof('$_type_12422',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12423] :
( c_24__type__12422___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12423)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__12423,Vv__CANONICAL__3)) ) ) ).
fof('$_type_12470',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12471] :
( c_24__type__12470___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12471)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__12471,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_12505',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12506] :
( c_24__type__12505___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12506)
<=> ! [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__12506,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_12549',axiom,
! [Vvar__12550] :
( c_24__type__12549___24t(Vvar__12550)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__7438___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7438___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__12550,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12720',axiom,
! [Vvar__12721] :
( c_24__type__12720___24t(Vvar__12721)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__12721,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12752',axiom,
! [Vvar__12753] :
( c_24__type__12752___24t(Vvar__12753)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__12753,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_13288',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13289] :
( c_24__type__13288___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13289)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13289,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13634',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__13635] :
( c_24__type__13634___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__13635)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13635,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13980',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13981] :
( c_24__type__13980___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13981)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13981,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_14303',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__14304] :
( c_24__type__14303___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__14304)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__14304,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_14649',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14650] :
( c_24__type__14649___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14650)
<=> ! [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__14650,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_1479',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1480] :
( c_24__type__1479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1480)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1480,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_14995',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14996] :
( c_24__type__14995___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14996)
<=> ! [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__14996,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_15341',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__15342] :
( c_24__type__15341___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__15342)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__15342,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_1542',axiom,
! [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__1543] :
( c_24__type__1542___24t(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__1543)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1543,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15687',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__15688] :
( c_24__type__15687___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__15688)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__15688,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_16033',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__16034] :
( c_24__type__16033___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__16034)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__16034,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_1605',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1606] :
( c_24__type__1605___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1606)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1606,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16356',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__16357] :
( c_24__type__16356___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__16357)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__16357,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_1659',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1660] :
( c_24__type__1659___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1660)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__1660,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_16702',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__16703] :
( c_24__type__16702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__16703)
<=> ! [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__16703,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_17048',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__17049] :
( c_24__type__17048___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__17049)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__17049,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_1722',axiom,
! [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__1723] :
( c_24__type__1722___24t(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__1723)
<=> ! [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__1723,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_17371',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__17372] :
( c_24__type__17371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__17372)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__17372,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_1754',axiom,
! [Vvar__1755] :
( c_24__type__1754___24t(Vvar__1755)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__1755,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1767',axiom,
! [Vvar__1768] :
( c_24__type__1767___24t(Vvar__1768)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__1768,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17694',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__17695] :
( c_24__type__17694___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__17695)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__17695,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_1777',axiom,
! [Vvar__1778] :
( c_24__type__1777___24t(Vvar__1778)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__1778,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18040',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__18041] :
( c_24__type__18040___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__18041)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__18041,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18159',axiom,
! [Vvar__18160] :
( c_24__type__18159___24t(Vvar__18160)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1185___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__18160,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_18200',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18201] :
( c_24__type__18200___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18201)
<=> ! [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__18201,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_18254',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__18255] :
( c_24__type__18254___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__18255)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__18255,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_18297',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18298] :
( c_24__type__18297___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18298)
<=> ! [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__18298,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_18336',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__18337] :
( c_24__type__18336___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__18337)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__18337,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_18371',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18372] :
( c_24__type__18371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18372)
<=> ! [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__18372,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_18397',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18398] :
( c_24__type__18397___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18398)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__18398,Vv__CANONICAL__3)) ) ) ).
fof('$_type_18405',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18406] :
( c_24__type__18405___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18406)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__18406,Vv__CANONICAL__3)) ) ) ).
fof('$_type_18413',axiom,
! [Vvar__18414] :
( c_24__type__18413___24t(Vvar__18414)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6460___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6460___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__18414,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_18604',axiom,
! [Vvar__18605] :
( c_24__type__18604___24t(Vvar__18605)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__18605,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18611',axiom,
! [Vvar__18612] :
( c_24__type__18611___24t(Vvar__18612)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__10852___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10852___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__18612,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18707',axiom,
! [Vvar__18708] :
( c_24__type__18707___24t(Vvar__18708)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__18708,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18715',axiom,
! [Vvar__18716] :
( c_24__type__18715___24t(Vvar__18716)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__18716,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1892',axiom,
! [Vv__CANONICAL__0,Vvar__1893] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vvar__1893)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1893,Vv__CANONICAL__1)) ) ) ).
fof('$_type_19670',axiom,
! [Vv__CANONICAL__0,Vvar__19671] :
( c_24__type__19670___24t(Vv__CANONICAL__0,Vvar__19671)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__19671,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_20702',axiom,
! [Vvar__20703] :
( c_24__type__20702___24t(Vvar__20703)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1185___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1185___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__20703,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_2080',axiom,
! [Vv__CANONICAL__0,Vvar__2081] :
( c_24__type__2080___24t(Vv__CANONICAL__0,Vvar__2081)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__2081,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_20818',axiom,
! [Vvar__20819] :
( c_24__type__20818___24t(Vvar__20819)
<=> ! [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__20819,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_21',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__22,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_21408',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21409] :
( c_24__type__21408___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21409)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__21409,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_21422',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21423] :
( c_24__type__21422___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21423)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__21423,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_21429',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21430] :
( c_24__type__21429___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21430)
<=> ! [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__21430,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_21477',axiom,
! [Vvar__21478] :
( c_24__type__21477___24t(Vvar__21478)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__21478,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22688',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22689] :
( c_24__type__22688___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22689)
<=> ! [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__22689,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_22885',axiom,
! [Vvar__22886] :
( c_24__type__22885___24t(Vvar__22886)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1185___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__22886,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_22929',axiom,
! [Vvar__22930] :
( c_24__type__22929___24t(Vvar__22930)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1185___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__22930,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_23183',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__23184] :
( c_24__type__23183___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__23184)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23184,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23246',axiom,
! [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__23247] :
( c_24__type__23246___24t(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__23247)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23247,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23309',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__23310] :
( c_24__type__23309___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__23310)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23310,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23363',axiom,
! [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__23364] :
( c_24__type__23363___24t(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__23364)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__23364,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_2340',axiom,
! [Vvar__2341] :
( c_24__type__2340___24t(Vvar__2341)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__2341,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23426',axiom,
! [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__23427] :
( c_24__type__23426___24t(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__23427)
<=> ! [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__23427,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_2345',axiom,
! [Vvar__2346] :
( c_24__type__2345___24t(Vvar__2346)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2346,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2348',axiom,
! [Vvar__2349] :
( c_24__type__2348___24t(Vvar__2349)
<=> ! [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__2349,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23562',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23563] :
( c_24__type__23562___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23563)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23563,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23585',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23586] :
( c_24__type__23585___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23586)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23586,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23608',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23609] :
( c_24__type__23608___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23609)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23609,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_23631',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23632] :
( c_24__type__23631___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23632)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23632,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23649',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23650] :
( c_24__type__23649___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23650)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__23650,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_23675',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23676] :
( c_24__type__23675___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23676)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23676,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23693',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23694] :
( c_24__type__23693___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23694)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__23694,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_23803',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23804] :
( c_24__type__23803___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23804)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23804,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23833',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23834] :
( c_24__type__23833___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23834)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23834,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23857',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23858] :
( c_24__type__23857___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23858)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__23858,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_23887',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23888] :
( c_24__type__23887___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23888)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23888,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_23917',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23918] :
( c_24__type__23917___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23918)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23918,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23941',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23942] :
( c_24__type__23941___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23942)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__23942,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_23974',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23975] :
( c_24__type__23974___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23975)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23975,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23998',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23999] :
( c_24__type__23998___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23999)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__23999,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_24025',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__24026] :
( c_24__type__24025___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__24026)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__24026,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_24321',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__24322] :
( c_24__type__24321___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__24322)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24322,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24446',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__24447] :
( c_24__type__24446___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__24447)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24447,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24571',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__24572] :
( c_24__type__24571___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__24572)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24572,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_24696',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__24697] :
( c_24__type__24696___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__24697)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__24697,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_24821',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__24822] :
( c_24__type__24821___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__24822)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__24822,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_24946',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__24947] :
( c_24__type__24946___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__24947)
<=> ! [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__24947,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_25057',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__25058] :
( c_24__type__25057___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__25058)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__25058,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_25488',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__25489] :
( c_24__type__25488___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__25489)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25489,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25701',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__25702] :
( c_24__type__25701___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__25702)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25702,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25914',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__25915] :
( c_24__type__25914___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__25915)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25915,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26109',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__26110] :
( c_24__type__26109___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__26110)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__26110,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_26322',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26323] :
( c_24__type__26322___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26323)
<=> ! [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__26323,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_26535',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__26536] :
( c_24__type__26535___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__26536)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__26536,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_26748',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26749] :
( c_24__type__26748___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26749)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__26749,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_26961',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__26962] :
( c_24__type__26961___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__26962)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__26962,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_27156',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__27157] :
( c_24__type__27156___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__27157)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__27157,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_27369',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__27370] :
( c_24__type__27369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__27370)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__27370,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_2753',axiom,
! [Vvar__2754] :
( c_24__type__2753___24t(Vvar__2754)
<=> ! [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__2754,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27564',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__27565] :
( c_24__type__27564___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__27565)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__27565,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_2768',axiom,
! [Vvar__2769] :
( c_24__type__2768___24t(Vvar__2769)
<=> ! [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__2769,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2772',axiom,
! [Vvar__2773] :
( c_24__type__2772___24t(Vvar__2773)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__2773,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27753',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27754] :
( c_24__type__27753___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27754)
<=> ! [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__27754,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_27803',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27804] :
( c_24__type__27803___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27804)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__27804,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_27853',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27854] :
( c_24__type__27853___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27854)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__27854,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_27895',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27896] :
( c_24__type__27895___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27896)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__27896,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_27945',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27946] :
( c_24__type__27945___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27946)
<=> ! [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__27946,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_28',axiom,
! [Vvar__29] :
( c_24__type__28___24t(Vvar__29)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__29,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28027',axiom,
! [Vvar__28028] :
( c_24__type__28027___24t(Vvar__28028)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28028,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28130',axiom,
! [Vvar__28131] :
( c_24__type__28130___24t(Vvar__28131)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1199___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__28140___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__28131,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_28140',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28141] :
( c_24__type__28140___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28141)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__28141,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_28181',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28182] :
( c_24__type__28181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28182)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28182,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_29266',axiom,
! [Vvar__29267] :
( c_24__type__29266___24t(Vvar__29267)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__29269___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__29267,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_29269',axiom,
! [Vv__CANONICAL__0,Vvar__29270] :
( c_24__type__29269___24t(Vv__CANONICAL__0,Vvar__29270)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__29270,Vv__CANONICAL__1)) ) ) ).
fof('$_type_2947',axiom,
! [Vvar__2948] :
( c_24__type__2947___24t(Vvar__2948)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2948,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2953',axiom,
! [Vvar__2954] :
( c_24__type__2953___24t(Vvar__2954)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2954,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29851',axiom,
! [Vvar__29852] :
( c_24__type__29851___24t(Vvar__29852)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__29852,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3019',axiom,
! [Vvar__3020] :
( c_24__type__3019___24t(Vvar__3020)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3020,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30476',axiom,
! [Vvar__30477] :
( c_24__type__30476___24t(Vvar__30477)
<=> ! [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__30477,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('$_type_30495',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30496] :
( c_24__type__30495___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30496)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__30496,Vv__CANONICAL__3)) ) ) ).
fof('$_type_30516',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30517] :
( c_24__type__30516___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30517)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__30517,Vv__CANONICAL__3)) ) ) ).
fof('$_type_30551',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30552] :
( c_24__type__30551___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30552)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__30552,Vv__CANONICAL__5)) ) ) ).
fof('$_type_30559',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30560] :
( c_24__type__30559___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30560)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__30560,Vv__CANONICAL__5)) ) ) ).
fof('$_type_30564',axiom,
! [Vvar__30565] :
( c_24__type__30564___24t(Vvar__30565)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__30565,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30566',axiom,
! [Vvar__30567] :
( c_24__type__30566___24t(Vvar__30567)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eByte_2ebyte___24t(happ(Vvar__30567,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30580',axiom,
! [Vvar__30581] :
( c_24__type__30580___24t(Vvar__30581)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__30581,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30593',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30594] :
( c_24__type__30593___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30594)
<=> ! [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__30594,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_30600',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30601] :
( c_24__type__30600___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30601)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__30601,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_30604',axiom,
! [Vvar__30605] :
( c_24__type__30604___24t(Vvar__30605)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6460___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__30605,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30610',axiom,
! [Vv__CANONICAL__0,Vvar__30611] :
( c_24__type__30610___24t(Vv__CANONICAL__0,Vvar__30611)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30611,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_30624',axiom,
! [Vv__CANONICAL__0,Vvar__30625] :
( c_24__type__30624___24t(Vv__CANONICAL__0,Vvar__30625)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___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__30631___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(Vvar__30625,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30686',axiom,
! [Vvar__30687] :
( c_24__type__30686___24t(Vvar__30687)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__3867___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__30687,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30717',axiom,
! [Vvar__30718] :
( c_24__type__30717___24t(Vvar__30718)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2euint___24t(happ(Vvar__30718,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30797',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__30798] :
( c_24__type__30797___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__30798)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__30798,Vv__CANONICAL__6)) ) ) ).
fof('$_type_30993',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__30994] :
( c_24__type__30993___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__30994)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30994,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31086',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31087] :
( c_24__type__31086___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31087)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31087,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31179',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__31180] :
( c_24__type__31179___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__31180)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31180,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31261',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31262] :
( c_24__type__31261___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31262)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__31262,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_31354',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__31355] :
( c_24__type__31354___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__31355)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31355,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31436',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31437] :
( c_24__type__31436___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31437)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__31437,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_31529',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__31530] :
( c_24__type__31529___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__31530)
<=> ! [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__31530,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_31863',axiom,
! [Vvar__31864] :
( c_24__type__31863___24t(Vvar__31864)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__31864,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32087',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__32088] :
( c_24__type__32087___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__32088)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32088,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32180',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__32181] :
( c_24__type__32180___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__32181)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32181,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32273',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__32274] :
( c_24__type__32273___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__32274)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32274,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32355',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__32356] :
( c_24__type__32355___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__32356)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__32356,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_32448',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__32449] :
( c_24__type__32448___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__32449)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32449,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32530',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__32531] :
( c_24__type__32530___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__32531)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__32531,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_32623',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__32624] :
( c_24__type__32623___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__32624)
<=> ! [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__32624,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_32777',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32778] :
( c_24__type__32777___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32778)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32778,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32840',axiom,
! [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__32841] :
( c_24__type__32840___24t(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__32841)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32841,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32903',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32904] :
( c_24__type__32903___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32904)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32904,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32957',axiom,
! [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__32958] :
( c_24__type__32957___24t(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__32958)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__32958,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_33020',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__33021] :
( c_24__type__33020___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__33021)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__33021,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_33041',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33042] :
( c_24__type__33041___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33042)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__33042,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_33046',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33047] :
( c_24__type__33046___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33047)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__33047,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_33052',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33053] :
( c_24__type__33052___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33053)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__33053,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_33057',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33058] :
( c_24__type__33057___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33058)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__33058,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_33069',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33070] :
( c_24__type__33069___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33070)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__33070,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_33089',axiom,
! [Vv__CANONICAL__0,Vvar__33090] :
( c_24__type__33089___24t(Vv__CANONICAL__0,Vvar__33090)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__33090,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_33100',axiom,
! [Vvar__33101] :
( c_24__type__33100___24t(Vvar__33101)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__33089___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__33101,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_33121',axiom,
! [Vvar__33122] :
( c_24__type__33121___24t(Vvar__33122)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__33122,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_33139',axiom,
! [Vvar__33140] :
( c_24__type__33139___24t(Vvar__33140)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__5348___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__33140,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_33160',axiom,
! [Vvar__33161] :
( c_24__type__33160___24t(Vvar__33161)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__7327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__33161,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_33224',axiom,
! [Vvar__33225] :
( c_24__type__33224___24t(Vvar__33225)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__33231___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__33225,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_33231',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33232] :
( c_24__type__33231___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33232)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__33232,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_33310',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__33311] :
( c_24__type__33310___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__33311)
<=> ! [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__33311,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_33329',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__33330] :
( c_24__type__33329___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__33330)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__33330,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_33349',axiom,
! [Vvar__33350] :
( c_24__type__33349___24t(Vvar__33350)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1199___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1199___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__33350,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_33468',axiom,
! [Vvar__33469] :
( c_24__type__33468___24t(Vvar__33469)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__33469,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33470',axiom,
! [Vvar__33471] :
( c_24__type__33470___24t(Vvar__33471)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__33471,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33544',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__33545] :
( c_24__type__33544___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__33545)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__33545,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_33569',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__33570] :
( c_24__type__33569___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__33570)
<=> ! [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__33570,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_33620',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33621] :
( c_24__type__33620___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33621)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__33621,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_33718',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33719] :
( c_24__type__33718___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33719)
<=> ! [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__33719,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_34199',axiom,
! [Vvar__34200] :
( c_24__type__34199___24t(Vvar__34200)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__34200,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34234',axiom,
! [Vvar__34235] :
( c_24__type__34234___24t(Vvar__34235)
<=> ! [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__34235,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34407',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34408] :
( c_24__type__34407___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34408)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34408,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34446',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34447] :
( c_24__type__34446___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34447)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34447,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34485',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34486] :
( c_24__type__34485___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34486)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34486,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_34619',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34620] :
( c_24__type__34619___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34620)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34620,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34663',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34664] :
( c_24__type__34663___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34664)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34664,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_34699',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34700] :
( c_24__type__34699___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34700)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__34700,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_34743',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34744] :
( c_24__type__34743___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34744)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__34744,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35005',axiom,
! [Vvar__35006] :
( c_24__type__35005___24t(Vvar__35006)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1199___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__35015___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__28140___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__35006,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_35015',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35016] :
( c_24__type__35015___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35016)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__35016,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_35063',axiom,
! [Vvar__35064] :
( c_24__type__35063___24t(Vvar__35064)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__35064,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35084',axiom,
! [Vvar__35085] :
( c_24__type__35084___24t(Vvar__35085)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ( p(c_24False)
=> t(happ(Vvar__35085,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35195',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__35196] :
( c_24__type__35195___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__35196)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__35196,Vv__CANONICAL__4)) ) ) ).
fof('$_type_35204',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__35205] :
( c_24__type__35204___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__35205)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__35205,Vv__CANONICAL__4)) ) ) ).
fof('$_type_35264',axiom,
! [Vvar__35265] :
( c_24__type__35264___24t(Vvar__35265)
<=> ! [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__35265,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35397',axiom,
! [Vvar__35398] :
( c_24__type__35397___24t(Vvar__35398)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1194___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__35398,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_35414',axiom,
! [Vvar__35415] :
( c_24__type__35414___24t(Vvar__35415)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1185___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__35415,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_35652',axiom,
! [Vv__CANONICAL__0,Vvar__35653] :
( c_24__type__35652___24t(Vv__CANONICAL__0,Vvar__35653)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__35653,Vv__CANONICAL__1)) ) ) ).
fof('$_type_35669',axiom,
! [Vv__CANONICAL__0,Vvar__35670] :
( c_24__type__35669___24t(Vv__CANONICAL__0,Vvar__35670)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__35670,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_3622',axiom,
! [Vvar__3623] :
( c_24__type__3622___24t(Vvar__3623)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__3623,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3641',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3642] :
( c_24__type__3641___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3642)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3642,Vv__CANONICAL__2)) ) ) ).
fof('$_type_3645',axiom,
! [Vvar__3646] :
( c_24__type__3645___24t(Vvar__3646)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__3646,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3663',axiom,
! [Vvar__3664] :
( c_24__type__3663___24t(Vvar__3664)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___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__3664,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_3865',axiom,
! [Vvar__3866] :
( c_24__type__3865___24t(Vvar__3866)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__3866,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3867',axiom,
! [Vvar__3868] :
( c_24__type__3867___24t(Vvar__3868)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3868,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3877',axiom,
! [Vvar__3878] :
( c_24__type__3877___24t(Vvar__3878)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__3878,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3895',axiom,
! [Vvar__3896] :
( c_24__type__3895___24t(Vvar__3896)
<=> ! [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__3896,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_3898',axiom,
! [Vv__CANONICAL__0,Vvar__3899] :
( c_24__type__3898___24t(Vv__CANONICAL__0,Vvar__3899)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__3899,Vv__CANONICAL__1)) ) ) ).
fof('$_type_3905',axiom,
! [Vvar__3906] :
( c_24__type__3905___24t(Vvar__3906)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__3906,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3916',axiom,
! [Vvar__3917] :
( c_24__type__3916___24t(Vvar__3917)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__3917,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3942',axiom,
! [Vvar__3943] :
( c_24__type__3942___24t(Vvar__3943)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3947___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__3943,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_3947',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3948] :
( c_24__type__3947___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3948)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(Vvar__3948,Vv__CANONICAL__2)) ) ) ).
fof('$_type_3978',axiom,
! [Vvar__3979] :
( c_24__type__3978___24t(Vvar__3979)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__3979,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_40',axiom,
! [Vvar__41] :
( c_24__type__40___24t(Vvar__41)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__41,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42',axiom,
! [Vvar__43] :
( c_24__type__42___24t(Vvar__43)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__43,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4399',axiom,
! [Vvar__4400] :
( c_24__type__4399___24t(Vvar__4400)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__4400,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4572',axiom,
! [Vvar__4573] :
( c_24__type__4572___24t(Vvar__4573)
<=> ! [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__4573,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4584',axiom,
! [Vvar__4585] :
( c_24__type__4584___24t(Vvar__4585)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__4585,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_4668',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__4669] :
( c_24__type__4668___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__4669)
<=> ! [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__4669,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_4733',axiom,
! [Vvar__4734] :
( c_24__type__4733___24t(Vvar__4734)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__4734,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_52',axiom,
! [Vvar__53] :
( c_24__type__52___24t(Vvar__53)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__53,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5348',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5349] :
( c_24__type__5348___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5349)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5349,Vv__CANONICAL__2)) ) ) ).
fof('$_type_5357',axiom,
! [Vvar__5358] :
( c_24__type__5357___24t(Vvar__5358)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__5358,Vv__CANONICAL__0)) ) ) ).
fof('$_type_536',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__537] :
( c_24__type__536___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__537)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__537,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5429',axiom,
! [Vvar__5430] :
( c_24__type__5429___24t(Vvar__5430)
<=> ! [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__5430,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5431',axiom,
! [Vvar__5432] :
( c_24__type__5431___24t(Vvar__5432)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5432,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5451',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5452] :
( c_24__type__5451___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5452)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3947___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(happ(Vvar__5452,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_5461',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5462] :
( c_24__type__5461___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5462)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__3947___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(Vvar__5462,Vv__CANONICAL__2)) ) ) ).
fof('$_type_6',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7] :
( c_24__type__6___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7)
<=> ! [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__7,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_6211',axiom,
! [Vvar__6212] :
( c_24__type__6211___24t(Vvar__6212)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__6212,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6241',axiom,
! [Vvar__6242] :
( c_24__type__6241___24t(Vvar__6242)
<=> ! [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__6242,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6244',axiom,
! [Vvar__6245] :
( c_24__type__6244___24t(Vvar__6245)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__6245,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6282',axiom,
! [Vvar__6283] :
( c_24__type__6282___24t(Vvar__6283)
<=> ! [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__6283,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_637',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__638] :
( c_24__type__637___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__638)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__638,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6460',axiom,
! [Vv__CANONICAL__0,Vvar__6461] :
( c_24__type__6460___24t(Vv__CANONICAL__0,Vvar__6461)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__6461,Vv__CANONICAL__1)) ) ) ).
fof('$_type_6713',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6714] :
( c_24__type__6713___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6714)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__6714,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_6759',axiom,
! [Vvar__6760] :
( c_24__type__6759___24t(Vvar__6760)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__6760,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7110',axiom,
! [Vvar__7111] :
( c_24__type__7110___24t(Vvar__7111)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__7111,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7207',axiom,
! [Vvar__7208] :
( c_24__type__7207___24t(Vvar__7208)
<=> ! [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__7208,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7213',axiom,
! [Vvar__7214] :
( c_24__type__7213___24t(Vvar__7214)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__7214,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7224',axiom,
! [Vvar__7225] :
( c_24__type__7224___24t(Vvar__7225)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__21___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__7225,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_7246',axiom,
! [Vvar__7247] :
( c_24__type__7246___24t(Vvar__7247)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__7247,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_7254',axiom,
! [Vvar__7255] :
( c_24__type__7254___24t(Vvar__7255)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___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__7255,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7286',axiom,
! [Vvar__7287] :
( c_24__type__7286___24t(Vvar__7287)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__7287,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7302',axiom,
! [Vvar__7303] :
( c_24__type__7302___24t(Vvar__7303)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1892___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__7303,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_7327',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7328] :
( c_24__type__7327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7328)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__7328,Vv__CANONICAL__2)) ) ) ).
fof('$_type_7331',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7332] :
( c_24__type__7331___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7332)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__7332,Vv__CANONICAL__2)) ) ) ).
fof('$_type_7354',axiom,
! [Vvar__7355] :
( c_24__type__7354___24t(Vvar__7355)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__7355,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_738',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__739] :
( c_24__type__738___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__739)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__739,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_73865',axiom,
! [Vvar__73866] :
( c_24__type__73865___24t(Vvar__73866)
<=> ! [Vv__CANONICAL__0] :
( cA___24t(Vv__CANONICAL__0)
=> cB___24t(happ(Vvar__73866,Vv__CANONICAL__0)) ) ) ).
fof('$_type_73880',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73881] :
( c_24__type__73880___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73881)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__73881,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_7394',axiom,
! [Vvar__7395] :
( c_24__type__7394___24t(Vvar__7395)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__7395,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7411',axiom,
! [Vvar__7412] :
( c_24__type__7411___24t(Vvar__7412)
<=> ! [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__7412,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7422',axiom,
! [Vvar__7423] :
( c_24__type__7422___24t(Vvar__7423)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__7423,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7438',axiom,
! [Vvar__7439] :
( c_24__type__7438___24t(Vvar__7439)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__7439,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7473',axiom,
! [Vvar__7474] :
( c_24__type__7473___24t(Vvar__7474)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__7474,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7484',axiom,
! [Vvar__7485] :
( c_24__type__7484___24t(Vvar__7485)
<=> ! [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__7485,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7489',axiom,
! [Vvar__7490] :
( c_24__type__7489___24t(Vvar__7490)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__7490,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7494',axiom,
! [Vvar__7495] :
( c_24__type__7494___24t(Vvar__7495)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__7495,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7544',axiom,
! [Vvar__7545] :
( c_24__type__7544___24t(Vvar__7545)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__7545,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7547',axiom,
! [Vvar__7548] :
( c_24__type__7547___24t(Vvar__7548)
<=> ! [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__7548,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_80',axiom,
! [Vvar__81] :
( c_24__type__80___24t(Vvar__81)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__81,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8060',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8061] :
( c_24__type__8060___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8061)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__8061,Vv__CANONICAL__3)) ) ) ).
fof('$_type_8068',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8069] :
( c_24__type__8068___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8069)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__8069,Vv__CANONICAL__3)) ) ) ).
fof('$_type_8076',axiom,
! [Vvar__8077] :
( c_24__type__8076___24t(Vvar__8077)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1892___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__8077,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8128',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8129] :
( c_24__type__8128___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8129)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__8129,Vv__CANONICAL__2)) ) ) ).
fof('$_type_8132',axiom,
! [Vvar__8133] :
( c_24__type__8132___24t(Vvar__8133)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6460___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__8133,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8150',axiom,
! [Vvar__8151] :
( c_24__type__8150___24t(Vvar__8151)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6460___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__8151,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_828',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__829] :
( c_24__type__828___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__829)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__829,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_85',axiom,
! [Vvar__86] :
( c_24__type__85___24t(Vvar__86)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__86,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_90',axiom,
! [Vvar__91] :
( c_24__type__90___24t(Vvar__91)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__91,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_929',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__930] :
( c_24__type__929___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__930)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__930,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_96',axiom,
! [Vvar__97] :
( c_24__type__96___24t(Vvar__97)
<=> ! [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__97,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_99',axiom,
! [Vvar__100] :
( c_24__type__99___24t(Vvar__100)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__100,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_typeof_A',axiom,
cType___24t(cA) ).
fof('$_typeof_B',axiom,
cType___24t(cB) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__7473___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
c_24__type__7473___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__12549___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
c_24__type__7473___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
c_24__type__7473___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__11002___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
c_24__type__7411___24t(cCoq_2eArith_2ePlus_2etail__plus) ).
fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
c_24__type__29266___24t(cCoq_2eArith_2eWf__nat_2eltof) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__11857___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__6241___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
c_24__type__30564___24t(cCoq_2eBool_2eBool_2eifb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__1777___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
c_24__type__11209___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_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__11343___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__30566___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('$_typeof_Coq.Init.Byte.xae',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exae) ).
fof('$_typeof_Coq.Init.Byte.xaf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exaf) ).
fof('$_typeof_Coq.Init.Byte.xb0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb0) ).
fof('$_typeof_Coq.Init.Byte.xb1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb1) ).
fof('$_typeof_Coq.Init.Byte.xb2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb2) ).
fof('$_typeof_Coq.Init.Byte.xb3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb3) ).
fof('$_typeof_Coq.Init.Byte.xb4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb4) ).
fof('$_typeof_Coq.Init.Byte.xb5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb5) ).
fof('$_typeof_Coq.Init.Byte.xb6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb6) ).
fof('$_typeof_Coq.Init.Byte.xb7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb7) ).
fof('$_typeof_Coq.Init.Byte.xb8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb8) ).
fof('$_typeof_Coq.Init.Byte.xb9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb9) ).
fof('$_typeof_Coq.Init.Byte.xba',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exba) ).
fof('$_typeof_Coq.Init.Byte.xbb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbb) ).
fof('$_typeof_Coq.Init.Byte.xbc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbc) ).
fof('$_typeof_Coq.Init.Byte.xbd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbd) ).
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('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__6282___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_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__42___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__3865___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__40___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__6241___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__11951___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_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__85___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__3895___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.implb',axiom,
c_24__type__6241___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__28___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__6244___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__80___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__28___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__6241___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__3877___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__52___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__11939___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__52___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.xorb',axiom,
c_24__type__6241___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Decimal.D0',axiom,
c_24__type__30717___24t(cCoq_2eInit_2eDecimal_2eD0) ).
fof('$_typeof_Coq.Init.Decimal.D1',axiom,
c_24__type__30717___24t(cCoq_2eInit_2eDecimal_2eD1) ).
fof('$_typeof_Coq.Init.Decimal.D2',axiom,
c_24__type__30717___24t(cCoq_2eInit_2eDecimal_2eD2) ).
fof('$_typeof_Coq.Init.Decimal.D3',axiom,
c_24__type__30717___24t(cCoq_2eInit_2eDecimal_2eD3) ).
fof('$_typeof_Coq.Init.Decimal.D4',axiom,
c_24__type__30717___24t(cCoq_2eInit_2eDecimal_2eD4) ).
fof('$_typeof_Coq.Init.Decimal.D5',axiom,
c_24__type__30717___24t(cCoq_2eInit_2eDecimal_2eD5) ).
fof('$_typeof_Coq.Init.Decimal.D6',axiom,
c_24__type__30717___24t(cCoq_2eInit_2eDecimal_2eD6) ).
fof('$_typeof_Coq.Init.Decimal.D7',axiom,
c_24__type__30717___24t(cCoq_2eInit_2eDecimal_2eD7) ).
fof('$_typeof_Coq.Init.Decimal.D8',axiom,
c_24__type__30717___24t(cCoq_2eInit_2eDecimal_2eD8) ).
fof('$_typeof_Coq.Init.Decimal.D9',axiom,
c_24__type__30717___24t(cCoq_2eInit_2eDecimal_2eD9) ).
fof('$_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('$_typeof_Coq.Init.Decimal.nzhead',axiom,
c_24__type__30717___24t(cCoq_2eInit_2eDecimal_2enzhead) ).
fof('$_typeof_Coq.Init.Decimal.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
c_24__type__2953___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__7411___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__3865___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__3865___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__7422___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__7438___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__7422___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__7411___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__7411___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__7411___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__7411___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__3865___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__7411___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.succ',axiom,
c_24__type__3865___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__7411___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__3867___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__7473___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__7473___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__7473___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.except',axiom,
c_24__type__35084___24t(cCoq_2eInit_2eSpecif_2eexcept) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__3663___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__8150___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__10150___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__10155___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__3645___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__8076___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__8132___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__18413___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__10127___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__35063___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__10755___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__7394___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__33224___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__12337___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__20818___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__12313___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__28130___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__28130___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__35005___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__35005___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ConstructiveIndefiniteDescription_on',axiom,
c_24__type__28___24t(cCoq_2eLogic_2eChoiceFacts_2eConstructiveIndefiniteDescription__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on',axiom,
c_24__type__30604___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__2947___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalChoice_on_rel',axiom,
c_24__type__30580___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on',axiom,
c_24__type__2953___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.GeneralizedSetoidFunctionalChoice_on',axiom,
c_24__type__2947___24t(cCoq_2eLogic_2eChoiceFacts_2eGeneralizedSetoidFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ProofIrrelevance',axiom,
cProp___24t(cCoq_2eLogic_2eChoiceFacts_2eProofIrrelevance) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.RepresentativeFunctionalChoice_on',axiom,
c_24__type__2953___24t(cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.SetoidFunctionalChoice_on',axiom,
c_24__type__2947___24t(cCoq_2eLogic_2eChoiceFacts_2eSetoidFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on',axiom,
c_24__type__2947___24t(cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on) ).
fof('$_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__30686___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('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__3019___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.FinFun.Bijective',axiom,
c_24__type__7110___24t(cCoq_2eLogic_2eFinFun_2eBijective) ).
fof('$_typeof_Coq.Logic.FinFun.Injective',axiom,
c_24__type__7110___24t(cCoq_2eLogic_2eFinFun_2eInjective) ).
fof('$_typeof_Coq.Logic.FinFun.Surjective',axiom,
c_24__type__7110___24t(cCoq_2eLogic_2eFinFun_2eSurjective) ).
fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
c_24__type__10867___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__18611___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__10867___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__10867___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__10826___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
c_24__type__10826___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__10826___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__10826___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__5357___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__5357___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__10842___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__18604___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ezero) ).
fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__6211___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__1767___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__1767___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__1754___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__1754___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
c_24__type__29851___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
c_24__type__11170___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).
fof('$_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__11127___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__11164___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
c_24__type__1754___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
c_24__type__11167___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__35397___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__35414___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
c_24__type__11119___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
c_24__type__11119___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__1754___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_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__7494___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__7484___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__7489___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__12720___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_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__7547___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__12720___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__7547___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__7547___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__7544___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__12720___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__7544___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__33470___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__34199___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.inclusion',axiom,
c_24__type__1233___24t(cCoq_2eRelations_2eRelation__Definitions_2einclusion) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__99___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__28___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.same_relation',axiom,
c_24__type__1233___24t(cCoq_2eRelations_2eRelation__Definitions_2esame__relation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.symmetric',axiom,
c_24__type__99___24t(cCoq_2eRelations_2eRelation__Definitions_2esymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__99___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Relations.Relation_Operators.transp',axiom,
c_24__type__4572___24t(cCoq_2eRelations_2eRelation__Operators_2etransp) ).
fof('$_typeof_Coq.Relations.Relation_Operators.union',axiom,
c_24__type__4584___24t(cCoq_2eRelations_2eRelation__Operators_2eunion) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__99___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__28___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
c_24__type__30476___24t(cCoq_2eStrings_2eAscii_2eAscii) ).
fof('$_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('$_typeof_Coq.Structures.GenericMinMax.gmax',axiom,
c_24__type__33100___24t(cCoq_2eStructures_2eGenericMinMax_2egmax) ).
fof('$_typeof_Coq.Structures.GenericMinMax.gmin',axiom,
c_24__type__33100___24t(cCoq_2eStructures_2eGenericMinMax_2egmin) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__33349___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__10867___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__10867___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__7473___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__7473___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__11170___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__11170___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
c_24__type__11170___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__11170___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
c_24__type__11170___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt) ).
fof('$_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__5429___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
c_24__type__5429___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt) ).
fof('$_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('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__6759___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__10166___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
c_24__type__2768___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
c_24__type__2768___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__5429___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
c_24__type__5429___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__5429___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__5429___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__5429___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__2772___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__2768___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__2768___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
c_24__type__11631___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__2768___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__2768___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__2768___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__2768___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__11631___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__11601___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__2772___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__2768___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__2772___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__18707___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__18715___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ezero) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__2753___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__5431___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__5431___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__11851___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__34199___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__35264___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__28___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__28___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__12172___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__28___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_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('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__33468___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__12752___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__4399___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__28___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('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__28___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__28___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__28___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__4733___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__28___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_nat\'',axiom,
c_24__type__11598___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zneg\'',axiom,
c_24__type__1767___24t(cCoq_2eomega_2ePreOmega_2eZneg_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zpos\'',axiom,
c_24__type__1767___24t(cCoq_2eomega_2ePreOmega_2eZpos_27) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__31863___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__28___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__28___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__28___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('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__20702___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__20702___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.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__3622___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__3622___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__2340___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__2345___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__34234___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__2345___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__2348___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__2345___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__28___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__21477___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__28___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__22885___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_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__28027___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__28027___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__5357___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__18159___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__22929___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_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('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
c_24__type__7354___24t(cHammer_2eTactics_2eReconstr_2erdone) ).
fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
c_24__type__7354___24t(cHammer_2eTactics_2eTactics_2erdone) ).
fof('$_typeof_f',axiom,
c_24__type__73865___24t(cf) ).
fof('$_typeof_hahn.HahnBase.Equality.mixin_of',axiom,
c_24__type__28___24t(chahn_2eHahnBase_2eEquality_2emixin__of) ).
fof('$_typeof_hahn.HahnBase.Equality.type',axiom,
cType___24t(chahn_2eHahnBase_2eEquality_2etype) ).
fof('$_typeof_hahn.HahnRelationsBasic.acyclic',axiom,
c_24__type__99___24t(chahn_2eHahnRelationsBasic_2eacyclic) ).
fof('$_typeof_hahn.HahnRelationsBasic.bunion',axiom,
c_24__type__3942___24t(chahn_2eHahnRelationsBasic_2ebunion) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_refl',axiom,
c_24__type__96___24t(chahn_2eHahnRelationsBasic_2eclos__refl) ).
fof('$_typeof_hahn.HahnRelationsBasic.collect_rel',axiom,
c_24__type__7246___24t(chahn_2eHahnRelationsBasic_2ecollect__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.cross_rel',axiom,
c_24__type__7302___24t(chahn_2eHahnRelationsBasic_2ecross__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eqv_dom_rel',axiom,
c_24__type__7207___24t(chahn_2eHahnRelationsBasic_2eeqv__dom__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eqv_rel',axiom,
c_24__type__3905___24t(chahn_2eHahnRelationsBasic_2eeqv__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.functional',axiom,
c_24__type__99___24t(chahn_2eHahnRelationsBasic_2efunctional) ).
fof('$_typeof_hahn.HahnRelationsBasic.immediate',axiom,
c_24__type__96___24t(chahn_2eHahnRelationsBasic_2eimmediate) ).
fof('$_typeof_hahn.HahnRelationsBasic.inter_rel',axiom,
c_24__type__90___24t(chahn_2eHahnRelationsBasic_2einter__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.irreflexive',axiom,
c_24__type__99___24t(chahn_2eHahnRelationsBasic_2eirreflexive) ).
fof('$_typeof_hahn.HahnRelationsBasic.is_total',axiom,
c_24__type__7254___24t(chahn_2eHahnRelationsBasic_2eis__total) ).
fof('$_typeof_hahn.HahnRelationsBasic.map_rel',axiom,
c_24__type__7224___24t(chahn_2eHahnRelationsBasic_2emap__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.minus_rel',axiom,
c_24__type__90___24t(chahn_2eHahnRelationsBasic_2eminus__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.pow_rel',axiom,
c_24__type__7286___24t(chahn_2eHahnRelationsBasic_2epow__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_eq_rel',axiom,
c_24__type__3916___24t(chahn_2eHahnRelationsBasic_2erestr__eq__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_rel',axiom,
c_24__type__7213___24t(chahn_2eHahnRelationsBasic_2erestr__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.seq',axiom,
c_24__type__90___24t(chahn_2eHahnRelationsBasic_2eseq) ).
fof('$_typeof_hahn.HahnSets.set_bunion',axiom,
c_24__type__12273___24t(chahn_2eHahnSets_2eset__bunion) ).
fof('$_typeof_hahn.HahnSets.set_collect',axiom,
c_24__type__33139___24t(chahn_2eHahnSets_2eset__collect) ).
fof('$_typeof_hahn.HahnSets.set_compl',axiom,
c_24__type__33121___24t(chahn_2eHahnSets_2eset__compl) ).
fof('$_typeof_hahn.HahnSets.set_disjoint',axiom,
c_24__type__3978___24t(chahn_2eHahnSets_2eset__disjoint) ).
fof('$_typeof_hahn.HahnSets.set_empty',axiom,
c_24__type__7354___24t(chahn_2eHahnSets_2eset__empty) ).
fof('$_typeof_hahn.HahnSets.set_equiv',axiom,
c_24__type__3978___24t(chahn_2eHahnSets_2eset__equiv) ).
fof('$_typeof_hahn.HahnSets.set_full',axiom,
c_24__type__7354___24t(chahn_2eHahnSets_2eset__full) ).
fof('$_typeof_hahn.HahnSets.set_inter',axiom,
c_24__type__12227___24t(chahn_2eHahnSets_2eset__inter) ).
fof('$_typeof_hahn.HahnSets.set_map',axiom,
c_24__type__33160___24t(chahn_2eHahnSets_2eset__map) ).
fof('$_typeof_hahn.HahnSets.set_minus',axiom,
c_24__type__12227___24t(chahn_2eHahnSets_2eset__minus) ).
fof('$_typeof_hahn.HahnSets.set_subset',axiom,
c_24__type__3978___24t(chahn_2eHahnSets_2eset__subset) ).
fof('$_typeof_hahn.HahnSets.set_union',axiom,
c_24__type__12227___24t(chahn_2eHahnSets_2eset__union) ).
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.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> 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_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.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.Wf_nat.lt_wf_ind',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__3867___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.Init.Datatypes.idProp',axiom,
p(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__3867___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.Init.Peano.plus_n_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Init.Peano.plus_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ).
fof('Coq.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.not_all_ex_not',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__1892___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__1892___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.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_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.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__21___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__21___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__6460___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__33041___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__33046___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__21___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__33085___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__6460___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__33069___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__33077___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__21___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__21___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__6460___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__33052___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__33057___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.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
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_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V0__n) ) ).
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__1892___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.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__1199___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_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__1199___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.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.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.Sorting.Permutation.Permutation_in\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__35669___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__3898___24a1(V0__A),c_3d___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cProp,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),c_3c_3d_3e)),cCoq_2eLists_2eList_2eIn___24a1(V0__A)) ) ).
fof('Coq.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.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_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.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__1185___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1185___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1185___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1194___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1199___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__1185___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1185___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1185___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1194___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1199___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__1185___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1185___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1185___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1194___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1199___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('HahnEquational.acyclic_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__x)
<=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V2__y) ) ) ) ) ) ).
fof('HahnEquational.acyclic_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11731___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),c_3c_3d_3e),chahn_2eHahnRelationsBasic_2eacyclic___24a1(V0__A)) ) ).
fof('HahnEquational.bunion_empty',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__rr] :
( c_24__type__3947___24t(V0__B,V1__A,V2__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,chahn_2eHahnSets_2eset__empty___24a1(V0__B),V2__rr),c_24__lam__45623___24a2(V0__B,V1__A)) ) ) ) ).
fof('HahnEquational.bunion_eq',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__a] :
( t(V2__a,V0__B)
=> ! [V3__rr] :
( c_24__type__3947___24t(V0__B,V1__A,V3__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,c_3d___24a2(V0__B,V2__a),V3__rr),happ(V3__rr,V2__a)) ) ) ) ) ).
fof('HahnEquational.bunion_inter_compat_l',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__1892___24t(V0__B,V2__s)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V3__r)
=> ! [V4__rr] :
( c_24__type__3947___24t(V0__B,V1__A,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,c_24__lam__45583___24a4(V0__B,V1__A,V3__r,V4__rr)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V1__A,V3__r,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,V4__rr))) ) ) ) ) ) ).
fof('HahnEquational.bunion_inter_compat_r',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__1892___24t(V0__B,V2__s)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V3__r)
=> ! [V4__rr] :
( c_24__type__3947___24t(V0__B,V1__A,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,c_24__lam__45572___24a4(V0__B,V1__A,V3__r,V4__rr)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,V4__rr),V3__r)) ) ) ) ) ) ).
fof('HahnEquational.bunion_minus_compat_r',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__1892___24t(V0__B,V2__s)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V3__r)
=> ! [V4__rr] :
( c_24__type__3947___24t(V0__B,V1__A,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,c_24__lam__45594___24a4(V0__B,V1__A,V3__r,V4__rr)),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,V4__rr),V3__r)) ) ) ) ) ) ).
fof('HahnEquational.bunion_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__x] :
( c_24__type__1892___24t(V0__A,V2__x)
=> ! [V3__y] :
( c_24__type__1892___24t(V0__A,V3__y)
=> ( chahn_2eHahnSets_2eset__equiv___24a3(V0__A,V2__x,V3__y)
=> ! [V5__x] :
( c_24__type__3947___24t(V0__A,V1__B,V5__x)
=> ! [V6__y] :
( c_24__type__3947___24t(V0__A,V1__B,V6__y)
=> ( V5__x = V6__y
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__B,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V2__x,V5__x),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V3__y,V6__y)) ) ) ) ) ) ) ) ) ).
fof('HahnEquational.bunion_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5451___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__1892___24a1(V0__A),c_24__type__5461___24a2(V0__A,V1__B),chahn_2eHahnSets_2eset__equiv___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__3947___24a2(V0__A,V1__B),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V1__B),c_3d___24a1(c_24__type__3947___24a2(V0__A,V1__B)),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V1__B))),chahn_2eHahnRelationsBasic_2ebunion___24a2(V0__A,V1__B)) ) ) ).
fof('HahnEquational.bunion_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__1892___24t(V1__B,V2__f)
=> ! [V3__s] :
( c_24__type__5348___24t(V0__A,V1__B,V3__s)
=> ! [V4__rr] :
( c_24__type__3947___24t(V0__A,V1__B,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__B,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V3__s,c_24__lam__73855___24a4(V0__A,V1__B,V2__f,V4__rr)),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V1__B,V2__f,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V3__s,c_24__lam__73861___24a3(V0__A,V1__B,V4__rr)))) ) ) ) ) ) ).
fof('HahnEquational.bunion_union_l',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__1892___24t(V0__B,V2__s)
=> ! [V3__s_27] :
( c_24__type__1892___24t(V0__B,V3__s_27)
=> ! [V4__rr] :
( c_24__type__3947___24t(V0__B,V1__A,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,chahn_2eHahnSets_2eset__union___24a3(V0__B,V2__s,V3__s_27),V4__rr),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,V4__rr),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V3__s_27,V4__rr))) ) ) ) ) ) ).
fof('HahnEquational.bunion_union_r',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__1892___24t(V0__B,V2__s)
=> ! [V3__rr] :
( c_24__type__3947___24t(V0__B,V1__A,V3__rr)
=> ! [V4__rr_27] :
( c_24__type__3947___24t(V0__B,V1__A,V4__rr_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,c_24__lam__45609___24a4(V0__B,V1__A,V3__rr,V4__rr_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,V3__rr),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,V4__rr_27))) ) ) ) ) ) ).
fof('HahnEquational.clos_refl_trans_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__x),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('HahnEquational.clos_refl_trans_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11748___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a1(V0__A)) ) ).
fof('HahnEquational.clos_relf_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('HahnEquational.clos_relf_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11748___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eclos__refl___24a1(V0__A)) ) ).
fof('HahnEquational.clos_trans_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__x),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('HahnEquational.clos_trans_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11748___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a1(V0__A)) ) ).
fof('HahnEquational.collect_rel_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__x] :
( c_24__type__21___24t(V0__A,V1__B,V2__x)
=> ! [V3__y] :
( c_24__type__21___24t(V0__A,V1__B,V3__y)
=> ( V2__x = V3__y
=> ! [V5__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__x)
=> ! [V6__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V5__x,V6__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__x,V5__x),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V3__y,V6__y)) ) ) ) ) ) ) ) ) ).
fof('HahnEquational.collect_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11691___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__21___24a2(V0__A,V1__B),c_24__type__11699___24a2(V0__A,V1__B),c_3d___24a1(c_24__type__21___24a2(V0__A,V1__B)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V1__B),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V1__B))),chahn_2eHahnRelationsBasic_2ecollect__rel___24a2(V0__A,V1__B)) ) ) ).
fof('HahnEquational.collect_rel_mori',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__x] :
( c_24__type__21___24t(V0__A,V1__B,V2__x)
=> ! [V3__y] :
( c_24__type__21___24t(V0__A,V1__B,V3__y)
=> ( V2__x = V3__y
=> ! [V5__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__x)
=> ! [V6__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V5__x,V6__y)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__x,V5__x),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V3__y,V6__y)) ) ) ) ) ) ) ) ) ).
fof('HahnEquational.collect_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11691___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__21___24a2(V0__A,V1__B),c_24__type__11699___24a2(V0__A,V1__B),c_3d___24a1(c_24__type__21___24a2(V0__A,V1__B)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V1__B),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V1__B))),chahn_2eHahnRelationsBasic_2ecollect__rel___24a2(V0__A,V1__B)) ) ) ).
fof('HahnEquational.crE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__3955___24a1(V0__A)),V1__r)) ) ) ).
fof('HahnEquational.cr_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.cr_of_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.cr_of_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.cr_of_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___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('HahnEquational.cr_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.cr_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27))) ) ) ) ).
fof('HahnEquational.cr_union_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),V2__r_27)) ) ) ) ).
fof('HahnEquational.cr_union_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27))) ) ) ) ).
fof('HahnEquational.cross_false_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__1892___24t(V0__A,V1__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,chahn_2eHahnSets_2eset__empty___24a1(V0__A),V1__s),c_24__lam__40507___24a1(V0__A)) ) ) ).
fof('HahnEquational.cross_false_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__1892___24t(V0__A,V1__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V1__s,chahn_2eHahnSets_2eset__empty___24a1(V0__A)),c_24__lam__40507___24a1(V0__A)) ) ) ).
fof('HahnEquational.cross_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( c_24__type__1892___24t(V0__A,V1__x)
=> ! [V2__y] :
( c_24__type__1892___24t(V0__A,V2__y)
=> ( chahn_2eHahnSets_2eset__equiv___24a3(V0__A,V1__x,V2__y)
=> ! [V4__x] :
( c_24__type__1892___24t(V0__A,V4__x)
=> ! [V5__y] :
( c_24__type__1892___24t(V0__A,V5__y)
=> ( chahn_2eHahnSets_2eset__equiv___24a3(V0__A,V4__x,V5__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V1__x,V4__x),chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('HahnEquational.cross_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11719___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__1892___24a1(V0__A),c_24__type__11726___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__1892___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),chahn_2eHahnRelationsBasic_2ecross__rel___24a1(V0__A)) ) ).
fof('HahnEquational.crt_double',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r)))) ) ) ).
fof('HahnEquational.ctEE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2ebunion___24a4(cCoq_2eInit_2eDatatypes_2enat,V0__A,c_24__lam__61939___24a1(V0__A),c_24__lam__61963___24a2(V0__A,V1__r))) ) ) ).
fof('HahnEquational.ct_begin',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r))) ) ) ).
fof('HahnEquational.ct_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.ct_end',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V1__r)) ) ) ).
fof('HahnEquational.ct_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__11748___24t(V0__A,V1__P)
=> ( cHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V3__r),V4__r_27)
=> ( ! [V6__k] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__k)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V6__k),V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V6__k)),V4__r_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r)),V4__r_27) ) ) ) ) ) ) ) ).
fof('HahnEquational.ct_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__11748___24t(V0__A,V1__P)
=> ( cHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V3__r),V4__r_27)
=> ( ! [V6__k] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__k)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V6__k),V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__k,V3__r)),V4__r_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r)),V4__r_27) ) ) ) ) ) ) ) ).
fof('HahnEquational.ct_of_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.ct_of_cross',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__1892___24t(V0__A,V1__s)
=> ! [V2__s_27] :
( c_24__type__1892___24t(V0__A,V2__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V1__s,V2__s_27)),chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V1__s,V2__s_27)) ) ) ) ).
fof('HahnEquational.ct_of_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.ct_of_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.ct_of_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V1__r) ) ) ) ).
fof('HahnEquational.ct_of_union_ct_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27))) ) ) ) ).
fof('HahnEquational.ct_of_union_ct_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27))),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27))) ) ) ) ).
fof('HahnEquational.ct_rotl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)),V2__r_27))) ) ) ) ).
fof('HahnEquational.ct_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.ct_seq_swap',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)))) ) ) ) ).
fof('HahnEquational.eqv_dom_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__35652___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a1(V0__A)) ) ).
fof('HahnEquational.eqv_empty',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnSets_2eset__empty___24a1(V0__A)),c_24__lam__40507___24a1(V0__A)) ) ).
fof('HahnEquational.eqv_rel_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( c_24__type__1892___24t(V0__A,V1__x)
=> ! [V2__y] :
( c_24__type__1892___24t(V0__A,V2__y)
=> ( chahn_2eHahnSets_2eset__equiv___24a3(V0__A,V1__x,V2__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('HahnEquational.eqv_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11726___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__1892___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a1(V0__A)) ) ).
fof('HahnEquational.functional_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> cCoq_2eProgram_2eBasics_2eimpl___24a2(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('HahnEquational.functional_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11731___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eProgram_2eBasics_2eimpl),chahn_2eHahnRelationsBasic_2efunctional___24a1(V0__A)) ) ).
fof('HahnEquational.good_ctx_id',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__65593___24a1(V0__A)) ) ).
fof('HahnEquational.good_ctx_seq_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__11748___24t(V0__A,V1__P)
=> ( cHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__65591___24a3(V0__A,V1__P,V3__r)) ) ) ) ) ).
fof('HahnEquational.good_ctx_seq_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__11748___24t(V0__A,V1__P)
=> ( cHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__65610___24a3(V0__A,V1__P,V3__r)) ) ) ) ) ).
fof('HahnEquational.id_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__1892___24t(V0__A,V1__s)
=> ! [V2__s_27] :
( c_24__type__1892___24t(V0__A,V2__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnSets_2eset__inter___24a3(V0__A,V1__s,V2__s_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__s_27))) ) ) ) ).
fof('HahnEquational.id_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__1892___24t(V0__A,V1__s)
=> ! [V2__s_27] :
( c_24__type__1892___24t(V0__A,V2__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnSets_2eset__union___24a3(V0__A,V1__s,V2__s_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__s_27))) ) ) ) ).
fof('HahnEquational.immediate_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('HahnEquational.immediate_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11748___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eimmediate___24a1(V0__A)) ) ).
fof('HahnEquational.inclusion_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> ! [V4__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__x)
=> ! [V5__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V4__x,V5__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__x,V4__x)
<=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__y,V5__y) ) ) ) ) ) ) ) ) ).
fof('HahnEquational.inclusion_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11847___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__11731___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),c_3c_3d_3e)),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('HahnEquational.inclusion_rel_Reflexive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('HahnEquational.inclusion_rel_Transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('HahnEquational.interA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r1,V2__r2),V3__r3),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r2,V3__r3))) ) ) ) ) ).
fof('HahnEquational.interAC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V3__r_27_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V3__r_27_27))) ) ) ) ) ).
fof('HahnEquational.interC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r1,V2__r2),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r2,V1__r1)) ) ) ) ).
fof('HahnEquational.interK',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V1__r),V1__r) ) ) ).
fof('HahnEquational.inter_absorb_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V1__r),V1__r) ) ) ) ) ).
fof('HahnEquational.inter_absorb_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V1__r) ) ) ) ) ).
fof('HahnEquational.inter_false_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,c_24__lam__40507___24a1(V0__A),V1__r),c_24__lam__40507___24a1(V0__A)) ) ) ).
fof('HahnEquational.inter_false_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,c_24__lam__40507___24a1(V0__A)),c_24__lam__40507___24a1(V0__A)) ) ) ).
fof('HahnEquational.inter_rel_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> ! [V4__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__x)
=> ! [V5__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V4__x,V5__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__x,V4__x),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('HahnEquational.inter_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11829___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__11748___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),chahn_2eHahnRelationsBasic_2einter__rel___24a1(V0__A)) ) ).
fof('HahnEquational.inter_union_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r1)
=> ! [V3__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r1,V3__r2),V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r1,V1__r),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V3__r2,V1__r))) ) ) ) ) ).
fof('HahnEquational.inter_union_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r1)
=> ! [V3__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r1,V3__r2)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r1),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V3__r2))) ) ) ) ) ).
fof('HahnEquational.irreflexive_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__x)
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__y) ) ) ) ) ) ).
fof('HahnEquational.irreflexive_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11731___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),c_3c_3d_3e),chahn_2eHahnRelationsBasic_2eirreflexive___24a1(V0__A)) ) ).
fof('HahnEquational.is_total_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11760___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__1892___24a1(V0__A),c_24__type__11731___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),c_3c_3d_3e)),chahn_2eHahnRelationsBasic_2eis__total___24a1(V0__A)) ) ).
fof('HahnEquational.map_rel_cross',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__21___24t(V0__A,V1__B,V2__f)
=> ! [V3__s] :
( c_24__type__7327___24t(V0__A,V1__B,V3__s)
=> ! [V4__s_27] :
( c_24__type__7327___24t(V0__A,V1__B,V4__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V1__B,V3__s,V4__s_27)),chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,c_24__lam__75315___24a4(V0__A,V1__B,V2__f,V3__s),c_24__lam__75325___24a4(V0__A,V1__B,V2__f,V4__s_27))) ) ) ) ) ) ).
fof('HahnEquational.map_rel_false',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__21___24t(V0__A,V1__B,V2__f)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,c_24__lam__45623___24a2(V0__A,V1__B)),c_24__lam__75299___24a2(V0__A,V1__B)) ) ) ) ).
fof('HahnEquational.map_rel_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__21___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V1__B,V3__r,V4__r_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r),chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V4__r_27))) ) ) ) ) ) ).
fof('HahnEquational.map_rel_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__21___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V1__B,V3__r,V4__r_27)),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r),chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V4__r_27))) ) ) ) ) ) ).
fof('HahnEquational.map_rel_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__x] :
( c_24__type__21___24t(V0__A,V1__B,V2__x)
=> ! [V3__y] :
( c_24__type__21___24t(V0__A,V1__B,V3__y)
=> ( V2__x = V3__y
=> ! [V5__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V5__x)
=> ! [V6__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V6__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__B,V5__x,V6__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__x,V5__x),chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V3__y,V6__y)) ) ) ) ) ) ) ) ) ).
fof('HahnEquational.map_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11779___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__21___24a2(V0__A,V1__B),c_24__type__11787___24a2(V0__A,V1__B),c_3d___24a1(c_24__type__21___24a2(V0__A,V1__B)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V1__B),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V1__B),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),chahn_2eHahnRelationsBasic_2emap__rel___24a2(V0__A,V1__B)) ) ) ).
fof('HahnEquational.map_rel_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__21___24t(V0__A,V1__B,V2__f)
=> ! [V3__d] :
( c_24__type__7327___24t(V0__A,V1__B,V3__d)
=> ! [V4__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V4__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V1__B,V3__d,V4__r)),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,c_24__lam__76083___24a4(V0__A,V1__B,V2__f,V3__d),chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V4__r))) ) ) ) ) ) ).
fof('HahnEquational.map_rel_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__21___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V1__B,V3__r,V4__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r),chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V4__r_27))) ) ) ) ) ) ).
fof('HahnEquational.minusK',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V1__r),c_24__lam__40507___24a1(V0__A)) ) ) ).
fof('HahnEquational.minus_absorb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),c_24__lam__40507___24a1(V0__A)) ) ) ) ) ).
fof('HahnEquational.minus_false_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,c_24__lam__40507___24a1(V0__A),V1__r),c_24__lam__40507___24a1(V0__A)) ) ) ).
fof('HahnEquational.minus_false_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,c_24__lam__40507___24a1(V0__A)),V1__r) ) ) ).
fof('HahnEquational.minus_rel_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> ! [V4__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__x)
=> ! [V5__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V4__x,V5__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__x,V4__x),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('HahnEquational.minus_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11829___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__11748___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),chahn_2eHahnRelationsBasic_2eminus__rel___24a1(V0__A)) ) ).
fof('HahnEquational.minus_union_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,V2__r2),V3__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r1,V3__r),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r2,V3__r))) ) ) ) ) ).
fof('HahnEquational.pow_inclusion',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V3__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,V2__r,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V0__n),chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V3__r_27,V0__n)) ) ) ) ) ) ).
fof('HahnEquational.pow_nm',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V3__r,V1__n),chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V3__r,V2__m)),chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V3__r,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m))) ) ) ) ) ).
fof('HahnEquational.pow_rel_more',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__X,V1__x,V2__y)
=> ! [V4__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__x)
=> ! [V5__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__y)
=> ( V4__x = V5__y
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__X,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__X,V1__x,V4__x),chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__X,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('HahnEquational.pow_rel_more_Proper',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11736___24a1(V0__X),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__X),c_24__type__11739___24a1(V0__X),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__X),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__X),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__X))),chahn_2eHahnRelationsBasic_2epow__rel___24a1(V0__X)) ) ).
fof('HahnEquational.pow_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V2__r,V1__n),V2__r),chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V2__r,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n))) ) ) ) ).
fof('HahnEquational.pow_unit',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V1__r,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__r) ) ) ).
fof('HahnEquational.restrC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__1892___24t(V0__A,V1__d)
=> ! [V2__d_27] :
( c_24__type__1892___24t(V0__A,V2__d_27)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__d,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V2__d_27,V3__r)),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V2__d_27,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__d,V3__r))) ) ) ) ) ).
fof('HahnEquational.restr_bunion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__1892___24t(V1__B,V2__f)
=> ! [V3__s] :
( c_24__type__5348___24t(V0__A,V1__B,V3__s)
=> ! [V4__rr] :
( c_24__type__3947___24t(V0__A,V1__B,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__B,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V1__B,V2__f,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V3__s,c_24__lam__73829___24a3(V0__A,V1__B,V4__rr))),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V3__s,c_24__lam__73839___24a4(V0__A,V1__B,V2__f,V4__rr))) ) ) ) ) ) ).
fof('HahnEquational.restr_eq_bunion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__1892___24t(V0__A,V1__s)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__rr] :
( c_24__type__3947___24t(V0__A,V2__B,V3__rr)
=> ! [V4__C] :
( cType___24t(V4__C)
=> ! [V5__f] :
( c_24__type__73880___24t(V0__A,V2__B,V4__C,V5__f)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V2__B,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V2__B,V4__C,V5__f,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V2__B,V1__s,c_24__lam__73888___24a4(V0__A,V2__B,V3__rr,V4__C))),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V2__B,V1__s,c_24__lam__73900___24a5(V0__A,V2__B,V3__rr,V4__C,V5__f))) ) ) ) ) ) ) ).
fof('HahnEquational.restr_eq_elim',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__f] :
( c_24__type__21___24t(V0__A,V2__B,V3__f)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__r,V4__x),V5__y))
=> happ(V3__f,V4__x) = happ(V3__f,V5__y) ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V2__B,V3__f,V1__r),V1__r) ) ) ) ) ) ).
fof('HahnEquational.restr_eq_rel_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__x] :
( c_24__type__21___24t(V0__A,V1__B,V2__x)
=> ! [V3__y] :
( c_24__type__21___24t(V0__A,V1__B,V3__y)
=> ( V2__x = V3__y
=> ! [V5__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__x)
=> ! [V6__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V5__x,V6__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__x,V5__x),chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V3__y,V6__y)) ) ) ) ) ) ) ) ) ).
fof('HahnEquational.restr_eq_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11802___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__21___24a2(V0__A,V1__B),c_24__type__11748___24a1(V0__A),c_3d___24a1(c_24__type__21___24a2(V0__A,V1__B)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a2(V0__A,V1__B)) ) ) ).
fof('HahnEquational.restr_eq_seq_eqv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__f] :
( c_24__type__21___24t(V0__A,V2__B,V3__f)
=> ! [V4__dom] :
( c_24__type__5348___24t(V0__A,V2__B,V4__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V2__B,V3__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__dom),V1__r)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__dom),chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V2__B,V3__f,V1__r))) ) ) ) ) ) ).
fof('HahnEquational.restr_eq_seq_eqv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__f] :
( c_24__type__21___24t(V0__A,V2__B,V3__f)
=> ! [V4__dom] :
( c_24__type__5348___24t(V0__A,V2__B,V4__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V2__B,V3__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__dom))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V2__B,V3__f,V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__dom))) ) ) ) ) ) ).
fof('HahnEquational.restr_eq_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__f] :
( c_24__type__21___24t(V0__A,V3__B,V4__f)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V3__B,V4__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V3__B,V4__f,V1__r),chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V3__B,V4__f,V2__r_27))) ) ) ) ) ) ).
fof('HahnEquational.restr_full',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,c_24__lam__3955___24a1(V0__A),V1__r),V1__r) ) ) ).
fof('HahnEquational.restr_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1892___24t(V0__A,V1__f)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r,V3__r_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V3__r_27))) ) ) ) ) ).
fof('HahnEquational.restr_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1892___24t(V0__A,V1__f)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r,V3__r_27)),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V3__r_27))) ) ) ) ) ).
fof('HahnEquational.restr_minus_alt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1892___24t(V0__A,V1__f)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r,V3__r_27)),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),V3__r_27)) ) ) ) ) ).
fof('HahnEquational.restr_relE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__1892___24t(V0__A,V1__d)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__d,V2__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__d),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__d)))) ) ) ) ).
fof('HahnEquational.restr_rel_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( c_24__type__1892___24t(V0__A,V1__x)
=> ! [V2__y] :
( c_24__type__1892___24t(V0__A,V2__y)
=> ( chahn_2eHahnSets_2eset__equiv___24a3(V0__A,V1__x,V2__y)
=> ! [V4__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__x)
=> ! [V5__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V4__x,V5__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__x,V4__x),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('HahnEquational.restr_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11817___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__1892___24a1(V0__A),c_24__type__11748___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),chahn_2eHahnRelationsBasic_2erestr__rel___24a1(V0__A)) ) ).
fof('HahnEquational.restr_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__1892___24t(V0__A,V1__d)
=> ! [V2__d_27] :
( c_24__type__1892___24t(V0__A,V2__d_27)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__d,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V2__d_27,V3__r)),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,chahn_2eHahnSets_2eset__inter___24a3(V0__A,V2__d_27,V1__d),V3__r)) ) ) ) ) ).
fof('HahnEquational.restr_seq_eqv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1892___24t(V0__A,V1__f)
=> ! [V2__d] :
( c_24__type__1892___24t(V0__A,V2__d)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),V3__r)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V3__r))) ) ) ) ) ).
fof('HahnEquational.restr_seq_eqv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1892___24t(V0__A,V1__f)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__d] :
( c_24__type__1892___24t(V0__A,V3__d)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d))) ) ) ) ) ).
fof('HahnEquational.restr_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1892___24t(V0__A,V1__f)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r,V3__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V3__r_27))) ) ) ) ) ).
fof('HahnEquational.rtE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__3955___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r))) ) ) ).
fof('HahnEquational.rtEE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2ebunion___24a4(cCoq_2eInit_2eDatatypes_2enat,V0__A,c_24__lam__61939___24a1(V0__A),c_24__lam__61967___24a2(V0__A,V1__r))) ) ) ).
fof('HahnEquational.rt_begin',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__3955___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)))) ) ) ).
fof('HahnEquational.rt_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.rt_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.rt_end',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__3955___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V1__r))) ) ) ).
fof('HahnEquational.rt_of_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.rt_of_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.rt_of_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.rt_of_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ) ).
fof('HahnEquational.rt_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('HahnEquational.rt_seq_swap',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)))) ) ) ) ).
fof('HahnEquational.same_rel',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('HahnEquational.same_rel_Reflexive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('HahnEquational.same_rel_Symmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('HahnEquational.same_rel_Transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('HahnEquational.same_rel_relation',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eRewriteRelation___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('HahnEquational.same_relation_exp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__r,V4__x),V5__y))
<=> p(happ(happ(V2__r_27,V4__x),V5__y)) ) ) ) ) ) ) ) ).
fof('HahnEquational.same_relation_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('HahnEquational.same_relation_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1892___24t(V0__A,V1__f)
=> ! [V2__r] :
( c_24__type__1199___24t(V0__A,V2__r)
=> ! [V3__r_27] :
( c_24__type__1199___24t(V0__A,V3__r_27)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(happ(V1__f,V4__x))
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(V1__f,V6__y))
=> ( p(happ(happ(V2__r,V4__x),V6__y))
<=> p(happ(happ(V3__r_27,V4__x),V6__y)) ) ) ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V3__r_27)) ) ) ) ) ) ).
fof('HahnEquational.same_relation_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('HahnEquational.same_relation_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('HahnEquational.same_relation_transpE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r_27))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27) ) ) ) ) ).
fof('HahnEquational.seqA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,V2__r2),V3__r3),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V3__r3))) ) ) ) ) ).
fof('HahnEquational.seq_bunion_l',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__P] :
( c_24__type__1892___24t(V0__B,V2__P)
=> ! [V3__rr] :
( c_24__type__3947___24t(V0__B,V1__A,V3__rr)
=> ! [V4__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V4__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__P,V3__rr),V4__r),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__P,c_24__lam__40489___24a4(V0__B,V1__A,V3__rr,V4__r))) ) ) ) ) ) ).
fof('HahnEquational.seq_bunion_r',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V2__r)
=> ! [V3__P] :
( c_24__type__5348___24t(V0__B,V1__A,V3__P)
=> ! [V4__rr] :
( c_24__type__3947___24t(V0__B,V1__A,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V1__A,V2__r,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V3__P,V4__rr)),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V3__P,c_24__lam__40479___24a4(V0__B,V1__A,V2__r,V4__rr))) ) ) ) ) ) ).
fof('HahnEquational.seq_eqv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__doma] :
( c_24__type__1892___24t(V0__A,V1__doma)
=> ! [V2__domb] :
( c_24__type__1892___24t(V0__A,V2__domb)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__doma),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__domb)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__40532___24a3(V0__A,V1__doma,V2__domb))) ) ) ) ).
fof('HahnEquational.seq_eqvC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__doma] :
( c_24__type__1892___24t(V0__A,V1__doma)
=> ! [V2__domb] :
( c_24__type__1892___24t(V0__A,V2__domb)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__doma),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__domb)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__domb),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__doma))) ) ) ) ).
fof('HahnEquational.seq_eqvK',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__1892___24t(V0__A,V1__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom)) ) ) ).
fof('HahnEquational.seq_eqvK_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom1] :
( c_24__type__1892___24t(V0__A,V1__dom1)
=> ! [V2__dom2] :
( c_24__type__1892___24t(V0__A,V2__dom2)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V2__dom2,V3__x))
=> p(happ(V1__dom1,V3__x)) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom1),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom2)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom2)) ) ) ) ) ).
fof('HahnEquational.seq_eqvK_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom1] :
( c_24__type__1892___24t(V0__A,V1__dom1)
=> ! [V2__dom2] :
( c_24__type__1892___24t(V0__A,V2__dom2)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__dom1,V3__x))
=> p(happ(V2__dom2,V3__x)) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom1),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom2)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom1)) ) ) ) ) ).
fof('HahnEquational.seq_eqv_inter_ll',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__S] :
( c_24__type__1892___24t(V0__A,V1__S)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__S),V2__r),V3__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__S),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r,V3__r_27))) ) ) ) ) ).
fof('HahnEquational.seq_eqv_inter_lr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__S] :
( c_24__type__1892___24t(V0__A,V1__S)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__S)),V3__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r,V3__r_27),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__S))) ) ) ) ) ).
fof('HahnEquational.seq_eqv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__1892___24t(V0__A,V2__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom),V1__r),c_24__lam__65766___24a3(V0__A,V1__r,V2__dom)) ) ) ) ).
fof('HahnEquational.seq_eqv_lr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom1] :
( c_24__type__1892___24t(V0__A,V2__dom1)
=> ! [V3__dom2] :
( c_24__type__1892___24t(V0__A,V3__dom2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom1),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__dom2))),c_24__lam__65796___24a4(V0__A,V1__r,V2__dom1,V3__dom2)) ) ) ) ) ).
fof('HahnEquational.seq_eqv_minus_ll',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__1892___24t(V0__A,V1__s)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s),V2__r),V3__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r,V3__r_27))) ) ) ) ) ).
fof('HahnEquational.seq_eqv_minus_lr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__1892___24t(V0__A,V1__s)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s)),V3__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r,V3__r_27),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s))) ) ) ) ) ).
fof('HahnEquational.seq_eqv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__1892___24t(V0__A,V2__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom)),c_24__lam__65746___24a3(V0__A,V1__r,V2__dom)) ) ) ) ).
fof('HahnEquational.seq_false_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,c_24__lam__40507___24a1(V0__A),V1__r),c_24__lam__40507___24a1(V0__A)) ) ) ).
fof('HahnEquational.seq_false_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,c_24__lam__40507___24a1(V0__A)),c_24__lam__40507___24a1(V0__A)) ) ) ).
fof('HahnEquational.seq_id_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__3955___24a1(V0__A)),V1__r),V1__r) ) ) ).
fof('HahnEquational.seq_id_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__3955___24a1(V0__A))),V1__r) ) ) ).
fof('HahnEquational.seq_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> ! [V4__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__x)
=> ! [V5__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V4__x,V5__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__x,V4__x),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('HahnEquational.seq_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11829___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__11748___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),chahn_2eHahnRelationsBasic_2eseq___24a1(V0__A)) ) ).
fof('HahnEquational.seq_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11829___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__11748___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A))),chahn_2eHahnRelationsBasic_2eseq___24a1(V0__A)) ) ).
fof('HahnEquational.seq_pow_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V1__r,V2__n),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V1__r,V2__n))) ) ) ) ).
fof('HahnEquational.seq_rtE_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27),V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)))) ) ) ) ).
fof('HahnEquational.seq_rtE_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)))) ) ) ) ).
fof('HahnEquational.seq_union_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,V2__r2),V3__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,V3__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V3__r))) ) ) ) ) ).
fof('HahnEquational.seq_union_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r1)
=> ! [V3__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r1,V3__r2)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r1),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V3__r2))) ) ) ) ) ).
fof('HahnEquational.transitive_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__x)
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__y) ) ) ) ) ) ).
fof('HahnEquational.transitive_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11731___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),c_3c_3d_3e),cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a1(V0__A)) ) ).
fof('HahnEquational.transp_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r))) ) ) ).
fof('HahnEquational.transp_cross',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__1892___24t(V0__A,V1__d)
=> ! [V2__d_27] :
( c_24__type__1892___24t(V0__A,V2__d_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V1__d,V2__d_27)),chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V2__d_27,V1__d)) ) ) ) ).
fof('HahnEquational.transp_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r))) ) ) ).
fof('HahnEquational.transp_eqv_rel',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__1892___24t(V0__A,V1__d)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__d)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__d)) ) ) ).
fof('HahnEquational.transp_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r1,V2__r2)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r1),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r2))) ) ) ) ).
fof('HahnEquational.transp_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r)),V1__r) ) ) ).
fof('HahnEquational.transp_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r1,V2__r2)),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r1),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r2))) ) ) ) ).
fof('HahnEquational.transp_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__x),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('HahnEquational.transp_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11748___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2etransp___24a1(V0__A)) ) ).
fof('HahnEquational.transp_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___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,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r))) ) ) ).
fof('HahnEquational.transp_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,V2__r2)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r2),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r1))) ) ) ) ).
fof('HahnEquational.transp_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,V2__r2)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r1),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r2))) ) ) ) ).
fof('HahnEquational.unionA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,V2__r2),V3__r3),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r2,V3__r3))) ) ) ) ) ).
fof('HahnEquational.unionAC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__r_27_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V3__r_27_27))) ) ) ) ) ).
fof('HahnEquational.unionC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,V2__r2),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r2,V1__r1)) ) ) ) ).
fof('HahnEquational.unionK',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V1__r),V1__r) ) ) ).
fof('HahnEquational.union_absorb_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V2__r_27) ) ) ) ) ).
fof('HahnEquational.union_absorb_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V1__r),V2__r_27) ) ) ) ) ).
fof('HahnEquational.union_false_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,c_24__lam__40507___24a1(V0__A),V1__r),V1__r) ) ) ).
fof('HahnEquational.union_false_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,c_24__lam__40507___24a1(V0__A)),V1__r) ) ) ).
fof('HahnEquational.union_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> ! [V4__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__x)
=> ! [V5__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V4__x,V5__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__x,V4__x),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('HahnEquational.union_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11829___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__11748___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),cCoq_2eRelations_2eRelation__Operators_2eunion___24a1(V0__A)) ) ).
fof('HahnEquational.union_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__1892___24t(V0__A,V1__f)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V3__r_27)),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r,V3__r_27))) ) ) ) ) ).
fof('HahnEquational.well_founded_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> ( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__x)
<=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V2__y) ) ) ) ) ) ).
fof('HahnEquational.well_founded_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11731___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),c_3c_3d_3e),cCoq_2eInit_2eWf_2ewell__founded___24a1(V0__A)) ) ).
fof('hahn.HahnRelationsBasic.clos_refl_transE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V2__a,V3__b)
<=> ( V2__a = V3__b
| cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V3__b) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_refl_trans_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V3__a,V4__b)
=> ( ! [V6__a] :
( t(V6__a,V0__A)
=> ! [V7__b] :
( t(V7__b,V0__A)
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> p(happ(happ(V2__r_27,V6__a),V7__b)) ) ) )
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V2__r_27,V3__a,V4__b) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V3__a,V4__b)
=> ( ! [V6__a] :
( t(V6__a,V0__A)
=> ! [V7__b] :
( t(V7__b,V0__A)
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> p(happ(happ(V2__r_27,V6__a),V7__b)) ) ) )
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V2__r_27,V3__a,V4__b) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.eq_in_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.eq_in_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V1__r) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.immediateE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r))) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_bunion_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__P] :
( c_24__type__7327___24t(V0__A,V1__B,V3__P)
=> ! [V4__rr] :
( c_24__type__7331___24t(V0__A,V1__B,V4__rr)
=> ( ! [V5__x] :
( t(V5__x,V1__B)
=> ( p(happ(V3__P,V5__x))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V4__rr,V5__x),V2__r_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V1__B,V0__A,V3__P,V4__rr),V2__r_27) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_r_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_refl2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V1__r) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_rt_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_rt_rt2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__s)
=> ! [V4__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__s,V4__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V3__s),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V4__s_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__t)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V3__t)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__t)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__t)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__t) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_step_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_step_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V3__r_27_27) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r1_search',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r2_search',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.rt_t_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__c] :
( t(V4__c,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V2__a,V3__b)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V3__b,V4__c)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V4__c) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.same_relation_refl2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V1__r) ) ) ).
fof('hahn.HahnRelationsBasic.t_rt_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ? [V4__z] :
( t(V4__z,V0__A)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V2__x,V4__z)
& p(happ(happ(V1__r,V4__z),V3__y)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.t_rt_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__c] :
( t(V4__c,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V3__b)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V3__b,V4__c)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V4__c) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.t_step_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ? [V4__z] :
( t(V4__z,V0__A)
& p(happ(happ(V1__r,V2__x),V4__z))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V4__z,V3__y) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.transitive_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.transitive_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('$adef_hahn.HahnSets.set_equiv_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnSets_2eset__equiv,V_24X1) = chahn_2eHahnSets_2eset__equiv___24a1(V_24X1) ).
fof('$adef_$_lam_3955_$a1',axiom,
! [V_24X1] : happ(c_24__lam__3955,V_24X1) = c_24__lam__3955___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.GenericMinMax.gmin_$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('$adef_Coq.Logic.ChoiceFacts.FunctionalChoice_on_$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('$adef_Coq.Init.Nat.mul_$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('$adef_Coq.Arith.PeanoNat.Nat.eqf_$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('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$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('$adef_Coq.Logic.FinFun.Injective_$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('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$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('$adef_$_lam_65593_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__65593,V_24X1),V_24X2) = c_24__lam__65593___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_75262_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__75262,V_24X1),V_24X2))
<=> c_24__lam__75262___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnSets.set_full_$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('$adef_Coq.NArith.BinNatDef.N.testbit_$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('$adef_$_lam_40507_$a1',axiom,
! [V_24X1] : happ(c_24__lam__40507,V_24X1) = c_24__lam__40507___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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.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.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_$_lam_65593_$a1',axiom,
! [V_24X1] : happ(c_24__lam__65593,V_24X1) = c_24__lam__65593___24a1(V_24X1) ).
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('$adef_$_lam_45583_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__45583,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__45583___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_65766_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__65766,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__65766___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_Coq.Init.Datatypes.CompLtT_$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('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.nzhead_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2enzhead,V_24X1) = cCoq_2eInit_2eDecimal_2enzhead___24a1(V_24X1) ).
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('$adef_Coq.Lists.List.Exists_$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('$adef_$_lam_65796_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__65796,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__65796___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_76083_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__76083,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__76083___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_40532_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__40532,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__40532___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_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.Init.Wf.well_founded_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1) = cCoq_2eInit_2eWf_2ewell__founded___24a1(V_24X1) ).
fof('$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.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.Reals.RIneq.mkposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).
fof('$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.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.acyclic_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnRelationsBasic_2eacyclic,V_24X1),V_24X2))
<=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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_$_let_var_6_p_22917_22919_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__22917__22919,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__22917__22919___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnRelationsBasic.restr_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2erestr__rel,V_24X1) = chahn_2eHahnRelationsBasic_2erestr__rel___24a1(V_24X1) ).
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('$adef_hahn.HahnRelationsBasic.restr_eq_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2erestr__eq__rel,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_HahnEquational.good_ctx_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHahnEquational_2egood__ctx,V_24X1),V_24X2))
<=> cHahnEquational_2egood__ctx___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnRelationsBasic.immediate_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eimmediate,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eimmediate___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.EnvRing.Pol_$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('$adef_hahn.HahnRelationsBasic.is_total_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eis__total,V_24X1) = chahn_2eHahnRelationsBasic_2eis__total___24a1(V_24X1) ).
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('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$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('$adef_Coq.micromega.RMicromega.CMult_$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('$adef_Coq.Relations.Relation_Definitions.symmetric_$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('$adef_Coq.Sorting.Sorted.LocallySorted_$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('$adef_$_lam_73829_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__73829,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__73829___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_lam_73888_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__73888,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__73888___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Definitions.inclusion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2einclusion,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V_24X1) ).
fof('$adef_$_lam_73855_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__73855,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__73855___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_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.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.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.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.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_$_lam_40479_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__40479,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__40479___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$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('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on_$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('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.eqv_dom_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eeqv__dom__rel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Peano.IsSucc_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2ePeano_2eIsSucc,V_24X1))
<=> cCoq_2eInit_2ePeano_2eIsSucc___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.eq_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eDatatypes_2eeq__true,V_24X1))
<=> cCoq_2eInit_2eDatatypes_2eeq__true___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Specif.existT_$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('$adef_Coq.micromega.VarMap.Elt_$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('$adef_Coq.Relations.Relation_Operators.union_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Operators_2eunion,V_24X1) = cCoq_2eRelations_2eRelation__Operators_2eunion___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_65766_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__65766,V_24X1),V_24X2),V_24X3) = c_24__lam__65766___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_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.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_$_lam_61939_$a1',axiom,
! [V_24X1] : happ(c_24__lam__61939,V_24X1) = c_24__lam__61939___24a1(V_24X1) ).
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('$adef_$_case_Coq.Init.Datatypes.prod$28008_$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_2428008,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_2428008___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_$_lam_61939_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__61939,V_24X1),V_24X2))
<=> c_24__lam__61939___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_lam_33085_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__33085,V_24X1),V_24X2),V_24X3) = c_24__lam__33085___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_75325_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__75325,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__75325___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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.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.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_$_lam_76083_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__76083,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__76083___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_45609_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__45609,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__45609___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.Init.Decimal.D4_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_pow_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_3955_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__3955,V_24X1),V_24X2))
<=> c_24__lam__3955___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eclos__refl,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$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('$adef_Coq.Relations.Relation_Definitions.transitive_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a1(V_24X1) ).
fof('$adef_hahn.HahnSets.set_union_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnSets_2eset__union,V_24X1),V_24X2),V_24X3) = chahn_2eHahnSets_2eset__union___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on_$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('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnRelationsBasic.seq_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2eseq,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2eseq___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.cross_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2ecross__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_40489_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__40489,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__40489___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_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.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.Lists.SetoidList.transpose_restr2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_hahn.HahnRelationsBasic.minus_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eminus__rel,V_24X1) = chahn_2eHahnRelationsBasic_2eminus__rel___24a1(V_24X1) ).
fof('$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_$_lam_35673_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__35673,V_24X1),V_24X2))
<=> c_24__lam__35673___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('$adef_$_lam_65746_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__65746,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__65746___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_hahn.HahnSets.set_inter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnSets_2eset__inter,V_24X1),V_24X2),V_24X3) = chahn_2eHahnSets_2eset__inter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.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_hahn.HahnRelationsBasic.minus_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eminus__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2eminus__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.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_$_lam_40479_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__40479,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__40479___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('$adef_Coq.Structures.OrderedTypeEx.Z_as_OT.lt_$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('$adef_Coq.Arith.Between.between_$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('$adef_Coq.micromega.RingMicromega.PsatzIn_$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('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$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_45572_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__45572,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__45572___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_hahn.HahnRelationsBasic.restr_eq_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2erestr__eq__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a2(V_24X1,V_24X2) ).
fof('$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_hahn.HahnRelationsBasic.restr_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2erestr__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_hahn.HahnRelationsBasic.irreflexive_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eirreflexive,V_24X1) = chahn_2eHahnRelationsBasic_2eirreflexive___24a1(V_24X1) ).
fof('$adef_$_lam_45609_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__45609,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__45609___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('$adef_Coq.Arith.Plus.tail_plus_$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('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.eqlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$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('$adef_Coq.Init.Specif.exist2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.irreflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnRelationsBasic_2eirreflexive,V_24X1),V_24X2))
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.In_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLists_2eList_2eIn,V_24X1) = cCoq_2eLists_2eList_2eIn___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.ZArith.Zpower.two_power_pos_$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('$adef_Coq.Strings.String.String_$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('$adef_hahn.HahnRelationsBasic.bunion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ebunion,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnRelationsBasic_2ebunion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$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('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Refl.make_impl_$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('$adef_hahn.HahnSets.set_union_$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('$adef_hahn.HahnSets.set_compl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnSets_2eset__compl,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnSets_2eset__compl___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.identity_$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('$adef_Coq.Init.Nat.leb_$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('$adef_$_lam_75299_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__75299,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__75299___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_hahn.HahnRelationsBasic.bunion_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2ebunion,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2ebunion___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_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_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_$_lam_45594_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__45594,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__45594___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_lam_75315_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__75315,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__75315___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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.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.micromega.EnvRing.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_lam_10990_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__10990,V_24X1),V_24X2) = c_24__lam__10990___24a2(V_24X1,V_24X2) ).
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('$adef_hahn.HahnRelationsBasic.map_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2emap__rel,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnRelationsBasic_2emap__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.eqb_$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('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.restr_eq_rel_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2erestr__eq__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1) = cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.minus_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2eminus__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Hammer.Tactics.Reconstr.rdone_$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('$adef_Coq.Classes.RelationClasses.RewriteRelation_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eRewriteRelation,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eRewriteRelation___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnRelationsBasic.acyclic_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eacyclic,V_24X1) = chahn_2eHahnRelationsBasic_2eacyclic___24a1(V_24X1) ).
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('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_1n_$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('$adef_$_lam_73900_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__73900,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__73900___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.transpose2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose2,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_73861_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__73861,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__73861___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('$adef_$_lam_40489_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__40489,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__40489___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$33916_$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_2433916,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2433916___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D9_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).
fof('$adef_$_lam_45594_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__45594,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__45594___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_61967_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__61967,V_24X1),V_24X2),V_24X3) = c_24__lam__61967___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_35353_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__35353,V_24X1),V_24X2),V_24X3) = c_24__prop__35353___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.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_$_fix_35474_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__35474__v__CANONICAL__0,V_24X1) = c_24__fix__35474__v__CANONICAL__0___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('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_hahn.HahnSets.set_empty_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnSets_2eset__empty,V_24X1) = chahn_2eHahnSets_2eset__empty___24a1(V_24X1) ).
fof('$adef_$_lam_75325_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__75325,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__75325___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.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.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.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.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_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_$_lam_73888_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__73888,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__73888___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_40507_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__40507,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__40507___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Arith.Wf_nat.ltof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2eltof,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eArith_2eWf__nat_2eltof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.immediate_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eimmediate,V_24X1) = chahn_2eHahnRelationsBasic_2eimmediate___24a1(V_24X1) ).
fof('$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.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_hahn.HahnRelationsBasic.eqv_dom_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eeqv__dom__rel,V_24X1) = chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_61963_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__61963,V_24X1),V_24X2),V_24X3) = c_24__lam__61963___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_35356_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__35356,V_24X1),V_24X2),V_24X3) = c_24__prop__35356___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_$_case_Coq.Numbers.BinNums.Z$34187_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2434187,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2434187___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_hahn.HahnRelationsBasic.inter_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2einter__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2einter__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$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('$adef_$_prop_35358_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35358,V_24X1),V_24X2) = c_24__prop__35358___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.is_total_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnRelationsBasic_2eis__total,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnRelationsBasic_2eis__total___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_35374_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__35374,V_24X1),V_24X2),V_24X3) = c_24__prop__35374___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.map_rel_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2emap__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> chahn_2eHahnRelationsBasic_2emap__rel___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$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('$adef_$_lam_45572_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__45572,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__45572___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_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_$_lam_75315_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__75315,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__75315___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_let_var_6_p_22915_22918_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__22915__22918,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__22915__22918___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Numbers.BinNums.positive$35458_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435458,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435458___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33085_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33085,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33085___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_75299_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__75299,V_24X1),V_24X2) = c_24__lam__75299___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_$_lam_45623_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__45623,V_24X1),V_24X2) = c_24__lam__45623___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnSets.set_empty_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnSets_2eset__empty,V_24X1),V_24X2))
<=> chahn_2eHahnSets_2eset__empty___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnRelationsBasic.collect_rel_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ecollect__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> chahn_2eHahnRelationsBasic_2ecollect__rel___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.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.ZArith.Zeven.Zodd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).
fof('$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_hahn.HahnRelationsBasic.eqv_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eeqv__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_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.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_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.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.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_$_lam_33077_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__33077,V_24X1),V_24X2),V_24X3) = c_24__lam__33077___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.Computational_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eComputational,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).
fof('$adef_$_lam_45583_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__45583,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__45583___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_65610_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__65610,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__65610___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ChoiceFacts.RepresentativeFunctionalChoice_on_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on,V_24X1))
<=> cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.transp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Operators_2etransp,V_24X1) = cCoq_2eRelations_2eRelation__Operators_2etransp___24a1(V_24X1) ).
fof('$adef_$_lam_30631_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__30631,V_24X1),V_24X2) = c_24__lam__30631___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.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_hahn.HahnRelationsBasic.inter_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2einter__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2einter__rel___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_$_prop_35373_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__35373,V_24X1),V_24X2),V_24X3) = c_24__prop__35373___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_35354_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__35354,V_24X1),V_24X2),V_24X3) = c_24__prop__35354___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_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_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_$_lam_73839_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__73839,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__73839___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnRelationsBasic.immediate_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eimmediate,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eimmediate___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Even.odd_$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('$adef_$_lam_65796_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__65796,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__65796___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$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_$_prop_35372_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35372,V_24X1),V_24X2) = c_24__prop__35372___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_$_lam_73829_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__73829,V_24X1),V_24X2),V_24X3) = c_24__lam__73829___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.map_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2emap__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2emap__rel___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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.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_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_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.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.setoid_ring.Field_theory.FEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_Coq.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_$_lam_65591_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__65591,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__65591___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_hahn.HahnRelationsBasic.restr_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2erestr__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2erestr__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_Coq.Program.Basics.impl_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eProgram_2eBasics_2eimpl,V_24X1),V_24X2))
<=> cCoq_2eProgram_2eBasics_2eimpl___24a2(V_24X1,V_24X2) ) ).
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('$adef_hahn.HahnSets.set_inter_$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('$adef_hahn.HahnRelationsBasic.collect_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2ecollect__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2ecollect__rel___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_73855_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__73855,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__73855___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_hahn.HahnRelationsBasic.cross_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ecross__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2ecross__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.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_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_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_hahn.HahnRelationsBasic.functional_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2efunctional,V_24X1) = chahn_2eHahnRelationsBasic_2efunctional___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.eqv_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eeqv__rel,V_24X1) = chahn_2eHahnRelationsBasic_2eeqv__rel___24a1(V_24X1) ).
fof('$adef_$_lam_73861_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__73861,V_24X1),V_24X2),V_24X3) = c_24__lam__73861___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Permutation.Permutation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1) = cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$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('$adef_$_lam_30631_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__30631,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__30631___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.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.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.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.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.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_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_hahn.HahnRelationsBasic.pow_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2epow__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2epow__rel___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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.Relations.Relation_Definitions.same_relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2esame__relation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V_24X1) ).
fof('$adef_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.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_hahn.HahnRelationsBasic.eqv_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eeqv__rel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eeqv__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.nat$34192_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2434192,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2434192___24a1(V_24X1) ).
fof('$adef_$_lam_61967_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__61967,V_24X1),V_24X2) = c_24__lam__61967___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$34003_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2434003,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2434003___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_65591_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__65591,V_24X1),V_24X2),V_24X3) = c_24__lam__65591___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.seq_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eseq,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2eseq___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_hahn.HahnRelationsBasic.pow_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2epow__rel,V_24X1) = chahn_2eHahnRelationsBasic_2epow__rel___24a1(V_24X1) ).
fof('$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_hahn.HahnRelationsBasic.bunion_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ebunion,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> chahn_2eHahnRelationsBasic_2ebunion___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_Coq.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_$_lam_65746_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__65746,V_24X1),V_24X2),V_24X3) = c_24__lam__65746___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Relations.Relation_Operators.union_$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('$adef_Coq.micromega.RingMicromega.PsatzC_$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('$adef_Coq.Lists.SetoidList.InA_$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('$adef_Coq.setoid_ring.InitialRing.mkhypo_$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('$adef_Coq.Reals.Rdefinitions.Rlt_$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('$adef_hahn.HahnRelationsBasic.clos_refl_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eclos__refl,V_24X1) = chahn_2eHahnRelationsBasic_2eclos__refl___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$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('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$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('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
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('$adef_$_case_Coq.Init.Datatypes.nat$34170_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2434170,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2434170___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.fold_right_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Operators.Ltl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eLtl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.cross_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2ecross__rel,V_24X1) = chahn_2eHahnRelationsBasic_2ecross__rel___24a1(V_24X1) ).
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('$adef_$_lam_73839_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__73839,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__73839___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_hahn.HahnRelationsBasic.inter_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2einter__rel,V_24X1) = chahn_2eHahnRelationsBasic_2einter__rel___24a1(V_24X1) ).
fof('$adef_Coq.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_$_prop_35355_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__35355,V_24X1),V_24X2),V_24X3) = c_24__prop__35355___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_$_prop_35357_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__35357,V_24X1),V_24X2),V_24X3) = c_24__prop__35357___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_61963_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__61963,V_24X1),V_24X2) = c_24__lam__61963___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
<=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_33077_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33077,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33077___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_hahn.HahnSets.set_equiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnSets_2eset__equiv,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnSets_2eset__equiv___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_73900_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__73900,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__73900___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Specif.left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_65610_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__65610,V_24X1),V_24X2),V_24X3) = c_24__lam__65610___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Init.Specif.sigT_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_fix_34048_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__34048__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__34048__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Decimal.D3_$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('$adef_Coq.Init.Decimal.D8_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$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('$adef_$_prop_35352_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__35352,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__35352___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.Relations.Relation_Operators.clos_refl_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_hahn.HahnRelationsBasic.seq_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eseq,V_24X1) = chahn_2eHahnRelationsBasic_2eseq___24a1(V_24X1) ).
fof('$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.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.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.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_$_lam_10990_$a1',axiom,
! [V_24X1] : happ(c_24__lam__10990,V_24X1) = c_24__lam__10990___24a1(V_24X1) ).
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('$adef_hahn.HahnRelationsBasic.collect_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ecollect__rel,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNat.N.eqf_$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('$adef_Coq.Relations.Relation_Operators.clos_trans_$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('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$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('$adef_Coq.Vectors.Fin.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).
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('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_$_lam_45623_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__45623,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__45623___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_40532_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__40532,V_24X1),V_24X2),V_24X3) = c_24__lam__40532___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$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('$adef_hahn.HahnRelationsBasic.functional_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2efunctional,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2efunctional___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.gt_$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('$adef_Coq.Init.Peano.lt_$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('$tdef_$_type_33046',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33046___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33046___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_10727',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__10727___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__10727___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_21',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28027',axiom,
! [V_24Y] :
( c_24__type__28027___24t(V_24Y)
<=> t(V_24Y,c_24__type__28027) ) ).
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_28181',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__28181___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__28181___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_30797',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__30797___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__30797___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_11739',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11739___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11739___24a1(V_24X1)) ) ).
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_$_type_33468',axiom,
! [V_24Y] :
( c_24__type__33468___24t(V_24Y)
<=> t(V_24Y,c_24__type__33468) ) ).
fof('$tdef_$_type_828',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__828___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__828___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_33057',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33057___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33057___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34663',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34663___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34663___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_30624',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30624___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30624___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35015',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35015___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35015___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11631',axiom,
! [V_24Y] :
( c_24__type__11631___24t(V_24Y)
<=> t(V_24Y,c_24__type__11631) ) ).
fof('$tdef_$_type_30593',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30593___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30593___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35669',axiom,
! [V_24X1,V_24Y] :
( c_24__type__35669___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__35669___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35204',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__35204___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__35204___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_6211',axiom,
! [V_24Y] :
( c_24__type__6211___24t(V_24Y)
<=> t(V_24Y,c_24__type__6211) ) ).
fof('$tdef_$_type_4733',axiom,
! [V_24Y] :
( c_24__type__4733___24t(V_24Y)
<=> t(V_24Y,c_24__type__4733) ) ).
fof('$tdef_$_type_25057',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__25057___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__25057___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('$tdef_Coq.micromega.VarMap.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).
fof('$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_11802',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__11802___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__11802___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_24446',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__24446___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__24446___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_32623',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__32623___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__32623___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Specif.sigT2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_8060',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__8060___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__8060___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_7473',axiom,
! [V_24Y] :
( c_24__type__7473___24t(V_24Y)
<=> t(V_24Y,c_24__type__7473) ) ).
fof('$tdef_$_type_3905',axiom,
! [V_24Y] :
( c_24__type__3905___24t(V_24Y)
<=> t(V_24Y,c_24__type__3905) ) ).
fof('$tdef_$_type_28130',axiom,
! [V_24Y] :
( c_24__type__28130___24t(V_24Y)
<=> t(V_24Y,c_24__type__28130) ) ).
fof('$tdef_$_type_11343',axiom,
! [V_24Y] :
( c_24__type__11343___24t(V_24Y)
<=> t(V_24Y,c_24__type__11343) ) ).
fof('$tdef_$_type_11164',axiom,
! [V_24Y] :
( c_24__type__11164___24t(V_24Y)
<=> t(V_24Y,c_24__type__11164) ) ).
fof('$tdef_$_type_7331',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__7331___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__7331___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5451',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5451___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5451___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23309',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__23309___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__23309___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_12172',axiom,
! [V_24Y] :
( c_24__type__12172___24t(V_24Y)
<=> t(V_24Y,c_24__type__12172) ) ).
fof('$tdef_$_type_1722',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__1722___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__1722___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_11119',axiom,
! [V_24Y] :
( c_24__type__11119___24t(V_24Y)
<=> t(V_24Y,c_24__type__11119) ) ).
fof('$tdef_$_type_738',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__738___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__738___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_33041',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33041___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33041___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_21477',axiom,
! [V_24Y] :
( c_24__type__21477___24t(V_24Y)
<=> t(V_24Y,c_24__type__21477) ) ).
fof('$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_34619',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34619___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34619___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_$_type_12505',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__12505___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__12505___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_18397',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__18397___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__18397___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_10127',axiom,
! [V_24Y] :
( c_24__type__10127___24t(V_24Y)
<=> t(V_24Y,c_24__type__10127) ) ).
fof('$tdef_$_type_23585',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23585___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23585___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_35397',axiom,
! [V_24Y] :
( c_24__type__35397___24t(V_24Y)
<=> t(V_24Y,c_24__type__35397) ) ).
fof('$tdef_$_type_23246',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__23246___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__23246___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_12344',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__12344___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__12344___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_24321',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__24321___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__24321___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_13634',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__13634___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__13634___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_7110',axiom,
! [V_24Y] :
( c_24__type__7110___24t(V_24Y)
<=> t(V_24Y,c_24__type__7110) ) ).
fof('$tdef_$_type_12313',axiom,
! [V_24Y] :
( c_24__type__12313___24t(V_24Y)
<=> t(V_24Y,c_24__type__12313) ) ).
fof('$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_$_type_3947',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3947___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3947___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12422',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__12422___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__12422___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_30516',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30516___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30516___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_11726',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11726___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11726___24a1(V_24X1)) ) ).
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_$_type_929',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__929___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__929___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ) ).
fof('$tdef_$_type_11817',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11817___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11817___24a1(V_24X1)) ) ).
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_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_7286',axiom,
! [V_24Y] :
( c_24__type__7286___24t(V_24Y)
<=> t(V_24Y,c_24__type__7286) ) ).
fof('$tdef_$_type_31863',axiom,
! [V_24Y] :
( c_24__type__31863___24t(V_24Y)
<=> t(V_24Y,c_24__type__31863) ) ).
fof('$tdef_$_type_12273',axiom,
! [V_24Y] :
( c_24__type__12273___24t(V_24Y)
<=> t(V_24Y,c_24__type__12273) ) ).
fof('$tdef_$_type_23693',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23693___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23693___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_10155',axiom,
! [V_24Y] :
( c_24__type__10155___24t(V_24Y)
<=> t(V_24Y,c_24__type__10155) ) ).
fof('$tdef_$_type_7547',axiom,
! [V_24Y] :
( c_24__type__7547___24t(V_24Y)
<=> t(V_24Y,c_24__type__7547) ) ).
fof('$tdef_$_type_7544',axiom,
! [V_24Y] :
( c_24__type__7544___24t(V_24Y)
<=> t(V_24Y,c_24__type__7544) ) ).
fof('$tdef_$_type_27564',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__27564___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__27564___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_10826',axiom,
! [V_24Y] :
( c_24__type__10826___24t(V_24Y)
<=> t(V_24Y,c_24__type__10826) ) ).
fof('$tdef_$_type_34485',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34485___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34485___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_7411',axiom,
! [V_24Y] :
( c_24__type__7411___24t(V_24Y)
<=> t(V_24Y,c_24__type__7411) ) ).
fof('$tdef_$_type_7207',axiom,
! [V_24Y] :
( c_24__type__7207___24t(V_24Y)
<=> t(V_24Y,c_24__type__7207) ) ).
fof('$tdef_$_type_23833',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23833___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23833___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_hahn.HahnBase.Equality.mixin_of',axiom,
! [V_24X1,V_24Y] :
( chahn_2eHahnBase_2eEquality_2emixin__of___24t(V_24X1,V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2emixin__of___24a1(V_24X1)) ) ).
fof('$tdef_$_type_24946',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__24946___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__24946___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_7213',axiom,
! [V_24Y] :
( c_24__type__7213___24t(V_24Y)
<=> t(V_24Y,c_24__type__7213) ) ).
fof('$tdef_$_type_23562',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23562___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23562___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_536',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__536___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__536___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_34743',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34743___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34743___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_30559',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__30559___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__30559___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_35264',axiom,
! [V_24Y] :
( c_24__type__35264___24t(V_24Y)
<=> t(V_24Y,c_24__type__35264) ) ).
fof('$tdef_$_type_11857',axiom,
! [V_24Y] :
( c_24__type__11857___24t(V_24Y)
<=> t(V_24Y,c_24__type__11857) ) ).
fof('$tdef_$_type_10150',axiom,
! [V_24Y] :
( c_24__type__10150___24t(V_24Y)
<=> t(V_24Y,c_24__type__10150) ) ).
fof('$tdef_$_type_33349',axiom,
! [V_24Y] :
( c_24__type__33349___24t(V_24Y)
<=> t(V_24Y,c_24__type__33349) ) ).
fof('$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_$_type_1754',axiom,
! [V_24Y] :
( c_24__type__1754___24t(V_24Y)
<=> t(V_24Y,c_24__type__1754) ) ).
fof('$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_$_type_8132',axiom,
! [V_24Y] :
( c_24__type__8132___24t(V_24Y)
<=> t(V_24Y,c_24__type__8132) ) ).
fof('$tdef_$_type_23998',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23998___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23998___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_11002',axiom,
! [V_24Y] :
( c_24__type__11002___24t(V_24Y)
<=> t(V_24Y,c_24__type__11002) ) ).
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_$_type_31436',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__31436___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__31436___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_18405',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__18405___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__18405___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_24025',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__24025___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__24025___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_6282',axiom,
! [V_24Y] :
( c_24__type__6282___24t(V_24Y)
<=> t(V_24Y,c_24__type__6282) ) ).
fof('$tdef_$_type_22929',axiom,
! [V_24Y] :
( c_24__type__22929___24t(V_24Y)
<=> t(V_24Y,c_24__type__22929) ) ).
fof('$tdef_$_type_24821',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__24821___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__24821___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZWitness) ) ).
fof('$tdef_$_type_11598',axiom,
! [V_24Y] :
( c_24__type__11598___24t(V_24Y)
<=> t(V_24Y,c_24__type__11598) ) ).
fof('$tdef_$_type_34407',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34407___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34407___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_18336',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__18336___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__18336___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_7438',axiom,
! [V_24Y] :
( c_24__type__7438___24t(V_24Y)
<=> t(V_24Y,c_24__type__7438) ) ).
fof('$tdef_$_type_32777',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__32777___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__32777___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_18707',axiom,
! [V_24Y] :
( c_24__type__18707___24t(V_24Y)
<=> t(V_24Y,c_24__type__18707) ) ).
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_$_type_12398',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__12398___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__12398___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_7494',axiom,
! [V_24Y] :
( c_24__type__7494___24t(V_24Y)
<=> t(V_24Y,c_24__type__7494) ) ).
fof('$tdef_$_type_5431',axiom,
! [V_24Y] :
( c_24__type__5431___24t(V_24Y)
<=> t(V_24Y,c_24__type__5431) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15687',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__15687___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__15687___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('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).
fof('$tdef_$_type_11872',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__11872___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__11872___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_40',axiom,
! [V_24Y] :
( c_24__type__40___24t(V_24Y)
<=> t(V_24Y,c_24__type__40) ) ).
fof('$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_1479',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__1479___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__1479___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_23675',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23675___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23675___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_33020',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__33020___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__33020___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_30564',axiom,
! [V_24Y] :
( c_24__type__30564___24t(V_24Y)
<=> t(V_24Y,c_24__type__30564) ) ).
fof('$tdef_$_type_7489',axiom,
! [V_24Y] :
( c_24__type__7489___24t(V_24Y)
<=> t(V_24Y,c_24__type__7489) ) ).
fof('$tdef_$_type_3019',axiom,
! [V_24Y] :
( c_24__type__3019___24t(V_24Y)
<=> t(V_24Y,c_24__type__3019) ) ).
fof('$tdef_$_type_2345',axiom,
! [V_24Y] :
( c_24__type__2345___24t(V_24Y)
<=> t(V_24Y,c_24__type__2345) ) ).
fof('$tdef_$_type_5429',axiom,
! [V_24Y] :
( c_24__type__5429___24t(V_24Y)
<=> t(V_24Y,c_24__type__5429) ) ).
fof('$tdef_$_type_13288',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__13288___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__13288___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('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_25488',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__25488___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__25488___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.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_1542',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__1542___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__1542___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_17371',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__17371___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__17371___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_42',axiom,
! [V_24Y] :
( c_24__type__42___24t(V_24Y)
<=> t(V_24Y,c_24__type__42) ) ).
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_$_type_1892',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1892___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1892___24a1(V_24X1)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).
fof('$tdef_Coq.Relations.Relation_Definitions.relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12470',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__12470___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__12470___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_10166',axiom,
! [V_24Y] :
( c_24__type__10166___24t(V_24Y)
<=> t(V_24Y,c_24__type__10166) ) ).
fof('$tdef_$_type_2753',axiom,
! [V_24Y] :
( c_24__type__2753___24t(V_24Y)
<=> t(V_24Y,c_24__type__2753) ) ).
fof('$tdef_$_type_11691',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__11691___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__11691___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23857',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23857___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23857___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_32355',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__32355___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__32355___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_11851',axiom,
! [V_24Y] :
( c_24__type__11851___24t(V_24Y)
<=> t(V_24Y,c_24__type__11851) ) ).
fof('$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_27156',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__27156___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__27156___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_27803',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27803___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27803___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_32180',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__32180___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__32180___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_33121',axiom,
! [V_24Y] :
( c_24__type__33121___24t(V_24Y)
<=> t(V_24Y,c_24__type__33121) ) ).
fof('$tdef_$_type_33718',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__33718___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__33718___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_30686',axiom,
! [V_24Y] :
( c_24__type__30686___24t(V_24Y)
<=> t(V_24Y,c_24__type__30686) ) ).
fof('$tdef_$_type_11736',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11736___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11736___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13980',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__13980___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__13980___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('$tdef_Coq.setoid_ring.Field_theory.linear',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22688',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22688___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22688___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2340',axiom,
! [V_24Y] :
( c_24__type__2340___24t(V_24Y)
<=> t(V_24Y,c_24__type__2340) ) ).
fof('$tdef_$_type_90',axiom,
! [V_24Y] :
( c_24__type__90___24t(V_24Y)
<=> t(V_24Y,c_24__type__90) ) ).
fof('$tdef_$_type_33139',axiom,
! [V_24Y] :
( c_24__type__33139___24t(V_24Y)
<=> t(V_24Y,c_24__type__33139) ) ).
fof('$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_$_type_35005',axiom,
! [V_24Y] :
( c_24__type__35005___24t(V_24Y)
<=> t(V_24Y,c_24__type__35005) ) ).
fof('$tdef_$_type_31354',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__31354___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__31354___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3865',axiom,
! [V_24Y] :
( c_24__type__3865___24t(V_24Y)
<=> t(V_24Y,c_24__type__3865) ) ).
fof('$tdef_$_type_19670',axiom,
! [V_24X1,V_24Y] :
( c_24__type__19670___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__19670___24a1(V_24X1)) ) ).
fof('$tdef_$_type_29266',axiom,
! [V_24Y] :
( c_24__type__29266___24t(V_24Y)
<=> t(V_24Y,c_24__type__29266) ) ).
fof('$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_30566',axiom,
! [V_24Y] :
( c_24__type__30566___24t(V_24Y)
<=> t(V_24Y,c_24__type__30566) ) ).
fof('$tdef_$_type_18413',axiom,
! [V_24Y] :
( c_24__type__18413___24t(V_24Y)
<=> t(V_24Y,c_24__type__18413) ) ).
fof('$tdef_$_type_12752',axiom,
! [V_24Y] :
( c_24__type__12752___24t(V_24Y)
<=> t(V_24Y,c_24__type__12752) ) ).
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_$_type_33089',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33089___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33089___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1194',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1194___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1194___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33470',axiom,
! [V_24Y] :
( c_24__type__33470___24t(V_24Y)
<=> t(V_24Y,c_24__type__33470) ) ).
fof('$tdef_$_type_33100',axiom,
! [V_24Y] :
( c_24__type__33100___24t(V_24Y)
<=> t(V_24Y,c_24__type__33100) ) ).
fof('$tdef_$_type_18254',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__18254___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__18254___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_B',axiom,
! [V_24Y] :
( cB___24t(V_24Y)
<=> t(V_24Y,cB) ) ).
fof('$tdef_$_type_1030',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__1030___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__1030___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Byte.byte',axiom,
! [V_24Y] :
( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).
fof('$tdef_$_type_34699',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34699___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34699___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_2947',axiom,
! [V_24Y] :
( c_24__type__2947___24t(V_24Y)
<=> t(V_24Y,c_24__type__2947) ) ).
fof('$tdef_$_type_18715',axiom,
! [V_24Y] :
( c_24__type__18715___24t(V_24Y)
<=> t(V_24Y,c_24__type__18715) ) ).
fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23917',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23917___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23917___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
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_$_type_24571',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__24571___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__24571___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_11731',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11731___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11731___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21422',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21422___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21422___24a2(V_24X1,V_24X2)) ) ).
fof('$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_$_type_11787',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__11787___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__11787___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11209',axiom,
! [V_24Y] :
( c_24__type__11209___24t(V_24Y)
<=> t(V_24Y,c_24__type__11209) ) ).
fof('$tdef_$_type_6241',axiom,
! [V_24Y] :
( c_24__type__6241___24t(V_24Y)
<=> t(V_24Y,c_24__type__6241) ) ).
fof('$tdef_$_type_7327',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__7327___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__7327___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30604',axiom,
! [V_24Y] :
( c_24__type__30604___24t(V_24Y)
<=> t(V_24Y,c_24__type__30604) ) ).
fof('$tdef_$_type_32840',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__32840___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__32840___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_10867',axiom,
! [V_24Y] :
( c_24__type__10867___24t(V_24Y)
<=> t(V_24Y,c_24__type__10867) ) ).
fof('$tdef_$_type_11719',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11719___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11719___24a1(V_24X1)) ) ).
fof('$tdef_$_type_30551',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__30551___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__30551___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_5348',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5348___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5348___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11601',axiom,
! [V_24Y] :
( c_24__type__11601___24t(V_24Y)
<=> t(V_24Y,c_24__type__11601) ) ).
fof('$tdef_$_type_7394',axiom,
! [V_24Y] :
( c_24__type__7394___24t(V_24Y)
<=> t(V_24Y,c_24__type__7394) ) ).
fof('$tdef_$_type_30717',axiom,
! [V_24Y] :
( c_24__type__30717___24t(V_24Y)
<=> t(V_24Y,c_24__type__30717) ) ).
fof('$tdef_$_type_23941',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23941___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23941___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_22885',axiom,
! [V_24Y] :
( c_24__type__22885___24t(V_24Y)
<=> t(V_24Y,c_24__type__22885) ) ).
fof('$tdef_$_type_11760',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11760___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11760___24a1(V_24X1)) ) ).
fof('$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_$_type_80',axiom,
! [V_24Y] :
( c_24__type__80___24t(V_24Y)
<=> t(V_24Y,c_24__type__80) ) ).
fof('$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_$_type_33224',axiom,
! [V_24Y] :
( c_24__type__33224___24t(V_24Y)
<=> t(V_24Y,c_24__type__33224) ) ).
fof('$tdef_$_type_16033',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__16033___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__16033___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_3641',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3641___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3641___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3622',axiom,
! [V_24Y] :
( c_24__type__3622___24t(V_24Y)
<=> t(V_24Y,c_24__type__3622) ) ).
fof('$tdef_$_type_2768',axiom,
! [V_24Y] :
( c_24__type__2768___24t(V_24Y)
<=> t(V_24Y,c_24__type__2768) ) ).
fof('$tdef_$_type_2080',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2080___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2080___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8150',axiom,
! [V_24Y] :
( c_24__type__8150___24t(V_24Y)
<=> t(V_24Y,c_24__type__8150) ) ).
fof('$tdef_A',axiom,
! [V_24Y] :
( cA___24t(V_24Y)
<=> t(V_24Y,cA) ) ).
fof('$tdef_$_type_11170',axiom,
! [V_24Y] :
( c_24__type__11170___24t(V_24Y)
<=> t(V_24Y,c_24__type__11170) ) ).
fof('$tdef_$_type_32448',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__32448___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__32448___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_34446',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34446___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34446___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_31086',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__31086___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__31086___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4572',axiom,
! [V_24Y] :
( c_24__type__4572___24t(V_24Y)
<=> t(V_24Y,c_24__type__4572) ) ).
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_$_type_35063',axiom,
! [V_24Y] :
( c_24__type__35063___24t(V_24Y)
<=> t(V_24Y,c_24__type__35063) ) ).
fof('$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_18297',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__18297___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__18297___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_12337',axiom,
! [V_24Y] :
( c_24__type__12337___24t(V_24Y)
<=> t(V_24Y,c_24__type__12337) ) ).
fof('$tdef_$_type_11847',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11847___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11847___24a1(V_24X1)) ) ).
fof('$tdef_$_type_11127',axiom,
! [V_24Y] :
( c_24__type__11127___24t(V_24Y)
<=> t(V_24Y,c_24__type__11127) ) ).
fof('$tdef_$_type_23631',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23631___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23631___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_2348',axiom,
! [V_24Y] :
( c_24__type__2348___24t(V_24Y)
<=> t(V_24Y,c_24__type__2348) ) ).
fof('$tdef_$_type_12227',axiom,
! [V_24Y] :
( c_24__type__12227___24t(V_24Y)
<=> t(V_24Y,c_24__type__12227) ) ).
fof('$tdef_$_type_7224',axiom,
! [V_24Y] :
( c_24__type__7224___24t(V_24Y)
<=> t(V_24Y,c_24__type__7224) ) ).
fof('$tdef_$_type_2953',axiom,
! [V_24Y] :
( c_24__type__2953___24t(V_24Y)
<=> t(V_24Y,c_24__type__2953) ) ).
fof('$tdef_$_type_3978',axiom,
! [V_24Y] :
( c_24__type__3978___24t(V_24Y)
<=> t(V_24Y,c_24__type__3978) ) ).
fof('$tdef_$_type_12549',axiom,
! [V_24Y] :
( c_24__type__12549___24t(V_24Y)
<=> t(V_24Y,c_24__type__12549) ) ).
fof('$tdef_$_type_26322',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__26322___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__26322___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_32530',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__32530___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__32530___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_33052',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33052___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33052___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11951',axiom,
! [V_24Y] :
( c_24__type__11951___24t(V_24Y)
<=> t(V_24Y,c_24__type__11951) ) ).
fof('$tdef_$_type_21408',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21408___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21408___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11939',axiom,
! [V_24Y] :
( c_24__type__11939___24t(V_24Y)
<=> t(V_24Y,c_24__type__11939) ) ).
fof('$tdef_$_type_27369',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__27369___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__27369___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_27895',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27895___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27895___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_7246',axiom,
! [V_24Y] :
( c_24__type__7246___24t(V_24Y)
<=> t(V_24Y,c_24__type__7246) ) ).
fof('$tdef_$_type_3916',axiom,
! [V_24Y] :
( c_24__type__3916___24t(V_24Y)
<=> t(V_24Y,c_24__type__3916) ) ).
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_8068',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__8068___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__8068___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_31261',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__31261___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__31261___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_85',axiom,
! [V_24Y] :
( c_24__type__85___24t(V_24Y)
<=> t(V_24Y,c_24__type__85) ) ).
fof('$tdef_$_type_11007',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11007___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11007___24a1(V_24X1)) ) ).
fof('$tdef_$_type_16702',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__16702___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__16702___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_18371',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__18371___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__18371___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_99',axiom,
! [V_24Y] :
( c_24__type__99___24t(V_24Y)
<=> t(V_24Y,c_24__type__99) ) ).
fof('$tdef_$_type_2772',axiom,
! [V_24Y] :
( c_24__type__2772___24t(V_24Y)
<=> t(V_24Y,c_24__type__2772) ) ).
fof('$tdef_$_type_7484',axiom,
! [V_24Y] :
( c_24__type__7484___24t(V_24Y)
<=> t(V_24Y,c_24__type__7484) ) ).
fof('$tdef_$_type_8128',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__8128___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__8128___24a2(V_24X1,V_24X2)) ) ).
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_$_type_30993',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__30993___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__30993___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_27945',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27945___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27945___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_1777',axiom,
! [V_24Y] :
( c_24__type__1777___24t(V_24Y)
<=> t(V_24Y,c_24__type__1777) ) ).
fof('$tdef_$_type_35652',axiom,
! [V_24X1,V_24Y] :
( c_24__type__35652___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__35652___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33069',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33069___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33069___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_24696',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__24696___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__24696___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_1605',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__1605___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__1605___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_1131',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__1131___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__1131___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_7354',axiom,
! [V_24Y] :
( c_24__type__7354___24t(V_24Y)
<=> t(V_24Y,c_24__type__7354) ) ).
fof('$tdef_$_type_4668',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__4668___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__4668___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Bool.Bool.reflect',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23803',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23803___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23803___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3663',axiom,
! [V_24Y] :
( c_24__type__3663___24t(V_24Y)
<=> t(V_24Y,c_24__type__3663) ) ).
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_$_type_33544',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__33544___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__33544___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_30495',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30495___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30495___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_6713',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__6713___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__6713___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__6___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__6___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5357',axiom,
! [V_24Y] :
( c_24__type__5357___24t(V_24Y)
<=> t(V_24Y,c_24__type__5357) ) ).
fof('$tdef_$_type_1767',axiom,
! [V_24Y] :
( c_24__type__1767___24t(V_24Y)
<=> t(V_24Y,c_24__type__1767) ) ).
fof('$tdef_$_type_8076',axiom,
! [V_24Y] :
( c_24__type__8076___24t(V_24Y)
<=> t(V_24Y,c_24__type__8076) ) ).
fof('$tdef_$_type_73880',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__73880___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__73880___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1659',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__1659___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__1659___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_14303',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__14303___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__14303___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Numbers.BinNums.Z',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eZ) ) ).
fof('$tdef_$_type_23608',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23608___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23608___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_30600',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30600___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30600___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27753',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27753___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27753___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_23426',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__23426___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__23426___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_31179',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__31179___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__31179___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
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_$_type_11699',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__11699___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__11699___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_hahn.HahnBase.Equality.type',axiom,
! [V_24Y] :
( chahn_2eHahnBase_2eEquality_2etype___24t(V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2etype) ) ).
fof('$tdef_$_type_15341',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__15341___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__15341___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_33329',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__33329___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__33329___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
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('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_4584',axiom,
! [V_24Y] :
( c_24__type__4584___24t(V_24Y)
<=> t(V_24Y,c_24__type__4584) ) ).
fof('$tdef_$_type_26535',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__26535___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__26535___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_11829',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11829___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11829___24a1(V_24X1)) ) ).
fof('$tdef_$_type_18611',axiom,
! [V_24Y] :
( c_24__type__18611___24t(V_24Y)
<=> t(V_24Y,c_24__type__18611) ) ).
fof('$tdef_$_type_35084',axiom,
! [V_24Y] :
( c_24__type__35084___24t(V_24Y)
<=> t(V_24Y,c_24__type__35084) ) ).
fof('$tdef_$_type_33231',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33231___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33231___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3867',axiom,
! [V_24Y] :
( c_24__type__3867___24t(V_24Y)
<=> t(V_24Y,c_24__type__3867) ) ).
fof('$tdef_$_type_14995',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__14995___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__14995___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.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_25914',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__25914___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__25914___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('$tdef_Coq.Init.Datatypes.prod',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30476',axiom,
! [V_24Y] :
( c_24__type__30476___24t(V_24Y)
<=> t(V_24Y,c_24__type__30476) ) ).
fof('$tdef_$_type_29851',axiom,
! [V_24Y] :
( c_24__type__29851___24t(V_24Y)
<=> t(V_24Y,c_24__type__29851) ) ).
fof('$tdef_$_type_23649',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23649___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23649___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_12720',axiom,
! [V_24Y] :
( c_24__type__12720___24t(V_24Y)
<=> t(V_24Y,c_24__type__12720) ) ).
fof('$tdef_$_type_7422',axiom,
! [V_24Y] :
( c_24__type__7422___24t(V_24Y)
<=> t(V_24Y,c_24__type__7422) ) ).
fof('$tdef_$_type_23974',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23974___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23974___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_26748',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__26748___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__26748___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_637',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__637___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__637___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_7254',axiom,
! [V_24Y] :
( c_24__type__7254___24t(V_24Y)
<=> t(V_24Y,c_24__type__7254) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Formula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_52',axiom,
! [V_24Y] :
( c_24__type__52___24t(V_24Y)
<=> t(V_24Y,c_24__type__52) ) ).
fof('$tdef_$_type_18040',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__18040___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__18040___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('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$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_3898',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3898___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3898___24a1(V_24X1)) ) ).
fof('$tdef_$_type_30610',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30610___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30610___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6460',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6460___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6460___24a1(V_24X1)) ) ).
fof('$tdef_$_type_17048',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__17048___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__17048___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('$tdef_Coq.NArith.BinNatDef.N.t',axiom,
! [V_24Y] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNArith_2eBinNatDef_2eN_2et) ) ).
fof('$tdef_Coq.Init.Datatypes.ID',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).
fof('$tdef_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [V_24Y] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(V_24Y)
<=> t(V_24Y,cHammer_2eTactics_2eReconstr_2eReconstrT) ) ).
fof('$tdef_$_type_33310',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__33310___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__33310___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_6244',axiom,
! [V_24Y] :
( c_24__type__6244___24t(V_24Y)
<=> t(V_24Y,c_24__type__6244) ) ).
fof('$tdef_$_type_32087',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__32087___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__32087___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_21429',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21429___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21429___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_29269',axiom,
! [V_24X1,V_24Y] :
( c_24__type__29269___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__29269___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32903',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__32903___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__32903___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_33569',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__33569___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__33569___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$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_34234',axiom,
! [V_24Y] :
( c_24__type__34234___24t(V_24Y)
<=> t(V_24Y,c_24__type__34234) ) ).
fof('$tdef_$_type_30580',axiom,
! [V_24Y] :
( c_24__type__30580___24t(V_24Y)
<=> t(V_24Y,c_24__type__30580) ) ).
fof('$tdef_$_type_20818',axiom,
! [V_24Y] :
( c_24__type__20818___24t(V_24Y)
<=> t(V_24Y,c_24__type__20818) ) ).
fof('$tdef_$_type_18604',axiom,
! [V_24Y] :
( c_24__type__18604___24t(V_24Y)
<=> t(V_24Y,c_24__type__18604) ) ).
fof('$tdef_$_type_35414',axiom,
! [V_24Y] :
( c_24__type__35414___24t(V_24Y)
<=> t(V_24Y,c_24__type__35414) ) ).
fof('$tdef_$_type_33160',axiom,
! [V_24Y] :
( c_24__type__33160___24t(V_24Y)
<=> t(V_24Y,c_24__type__33160) ) ).
fof('$tdef_$_type_96',axiom,
! [V_24Y] :
( c_24__type__96___24t(V_24Y)
<=> t(V_24Y,c_24__type__96) ) ).
fof('$tdef_$_type_1185',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1185___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1185___24a1(V_24X1)) ) ).
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_$_type_18200',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__18200___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__18200___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_11748',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11748___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11748___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28',axiom,
! [V_24Y] :
( c_24__type__28___24t(V_24Y)
<=> t(V_24Y,c_24__type__28) ) ).
fof('$tdef_$_type_35195',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__35195___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__35195___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_7302',axiom,
! [V_24Y] :
( c_24__type__7302___24t(V_24Y)
<=> t(V_24Y,c_24__type__7302) ) ).
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_$_type_1233',axiom,
! [V_24Y] :
( c_24__type__1233___24t(V_24Y)
<=> t(V_24Y,c_24__type__1233) ) ).
fof('$tdef_$_type_3877',axiom,
! [V_24Y] :
( c_24__type__3877___24t(V_24Y)
<=> t(V_24Y,c_24__type__3877) ) ).
fof('$tdef_$_type_31529',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__31529___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__31529___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_10852',axiom,
! [V_24Y] :
( c_24__type__10852___24t(V_24Y)
<=> t(V_24Y,c_24__type__10852) ) ).
fof('$tdef_$_type_26109',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__26109___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__26109___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_17694',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__17694___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__17694___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_26961',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__26961___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__26961___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_25701',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__25701___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__25701___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_33620',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__33620___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__33620___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_23887',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23887___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23887___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_23183',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__23183___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__23183___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_1199',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1199___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1199___24a1(V_24X1)) ) ).
fof('$tdef_$_type_10842',axiom,
! [V_24Y] :
( c_24__type__10842___24t(V_24Y)
<=> t(V_24Y,c_24__type__10842) ) ).
fof('$tdef_$_type_11040',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11040___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11040___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3942',axiom,
! [V_24Y] :
( c_24__type__3942___24t(V_24Y)
<=> t(V_24Y,c_24__type__3942) ) ).
fof('$tdef_$_type_28140',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__28140___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__28140___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_18159',axiom,
! [V_24Y] :
( c_24__type__18159___24t(V_24Y)
<=> t(V_24Y,c_24__type__18159) ) ).
fof('$tdef_$_type_10755',axiom,
! [V_24Y] :
( c_24__type__10755___24t(V_24Y)
<=> t(V_24Y,c_24__type__10755) ) ).
fof('$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_$_type_5461',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5461___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5461___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11167',axiom,
! [V_24Y] :
( c_24__type__11167___24t(V_24Y)
<=> t(V_24Y,c_24__type__11167) ) ).
fof('$tdef_$_type_32957',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__32957___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__32957___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_11779',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__11779___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__11779___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3645',axiom,
! [V_24Y] :
( c_24__type__3645___24t(V_24Y)
<=> t(V_24Y,c_24__type__3645) ) ).
fof('$tdef_$_type_34199',axiom,
! [V_24Y] :
( c_24__type__34199___24t(V_24Y)
<=> t(V_24Y,c_24__type__34199) ) ).
fof('$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_6759',axiom,
! [V_24Y] :
( c_24__type__6759___24t(V_24Y)
<=> t(V_24Y,c_24__type__6759) ) ).
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_$_type_3895',axiom,
! [V_24Y] :
( c_24__type__3895___24t(V_24Y)
<=> t(V_24Y,c_24__type__3895) ) ).
fof('$tdef_$_type_14649',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__14649___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__14649___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_27853',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27853___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27853___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_32273',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__32273___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__32273___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_23363',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__23363___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__23363___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_12203',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__12203___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__12203___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_73865',axiom,
! [V_24Y] :
( c_24__type__73865___24t(V_24Y)
<=> t(V_24Y,c_24__type__73865) ) ).
fof('$tdef_$_type_4399',axiom,
! [V_24Y] :
( c_24__type__4399___24t(V_24Y)
<=> t(V_24Y,c_24__type__4399) ) ).
fof('$tdef_$_type_20702',axiom,
! [V_24Y] :
( c_24__type__20702___24t(V_24Y)
<=> t(V_24Y,c_24__type__20702) ) ).
fof('$tdef_$_type_16356',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__16356___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__16356___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('_HAMMER_GOAL',conjecture,
cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(cB,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(cA,cB,cf,c_24__lam__35673),c_24__lam__75262) ).
%------------------------------------------------------------------------------