TPTP Problem File: SEV622+1.p
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%------------------------------------------------------------------------------
% File : SEV622+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - HahnMinElt min elt t
% 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 : HahnMinElt.min.elt.t.p [Kal26]
% Status : Theorem
% Rating : 0.91 v9.3.0
% Syntax : Number of formulae : 2762 ( 841 unt; 0 def)
% Number of atoms : 9891 (1958 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 7208 ( 79 ~; 564 |;1195 &)
% (1064 <=>;4306 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 7 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 566 ( 565 usr; 0 prp; 1-23 aty)
% Number of functors : 1551 (1551 usr; 966 con; 0-22 aty)
% Number of variables : 10176 (9704 !; 472 ?)
% 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$23942',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2424029___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2423942___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__23946] :
( t(Vvar__1___24Anonymous__23946,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__23947] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__23947)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2424029___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__23946,Vvar__2___24Anonymous__23947)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2423942___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__23946,c_24__fix__24074__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__23947,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$24029',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2424029___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__24033] :
( t(Vvar__1___24Anonymous__24033,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__24034] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__24034)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__24033,Vvar__2___24Anonymous__24034)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2424029___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__24033,c_24__fix__24074__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__24034,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$9184',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_249184___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__9185] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9185)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9185)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_249184___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__9185)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$9206',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_249206___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__9207] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9207)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9207)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_249206___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__9207)) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.N$4971',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__type__4974___24t(Vv__CANONICAL__0,Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
& c_24__case__Coq_2eNumbers_2eBinNums_2eN_244971___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 )
| ? [Vvar__0___24Anonymous__4972] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4972)
& Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4972)
& c_24__case__Coq_2eNumbers_2eBinNums_2eN_244971___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect___24a4(c_24__let__4__P_27__4957___24a1(Vv__CANONICAL__0),happ(happ(Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0),Vv__CANONICAL__1),c_24__let__5__f_27__4958___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vvar__0___24Anonymous__4972) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$9201',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_249206___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_249201___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__9202] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9202)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_249206___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__9202)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_249201___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__9202) )
| ? [Vvar__0___24Anonymous__9203] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9203)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_249206___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__9203)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_249201___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__9203) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.positive$16576',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__16577] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16577)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16577)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2416576___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__16592__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__16577)) )
| ? [Vvar__0___24Anonymous__16584] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16584)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16584)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2416576___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16584) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2416576___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_$_let_4_P\'_4957',axiom,
! [V0__P,V4__p] : c_24__let__4__P_27__4957___24a2(V0__P,V4__p) = happ(V0__P,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V4__p)) ).
fof('$_def_$_let_5_f\'_4958',axiom,
! [V0__P,V2__f,V5__p] : c_24__let__5__f_27__4958___24a3(V0__P,V2__f,V5__p) = happ(V2__f,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V5__p)) ).
fof('$_def_$_let_var_6_p_9707_9710',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__9706] : c_24__let__var__6__p__9707__9710___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__9706) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__9706) ).
fof('$_def_$_let_var_6_p_9709_9711',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__9708] : c_24__let__var__6__p__9709__9711___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__9708) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__9708) ).
fof('$_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__5779] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5779)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5779)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__5780] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5780)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5780)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__5783] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5783)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5783)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__5780,Vvar__0___24Anonymous__5783) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.Arith.PeanoNat.Nat.recursion',axiom,
! [V0__A] : cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(c_24__lam__5105___24a1(V0__A)) ).
fof('$_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('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__16603] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__16603)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__16603) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__16617] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__16617)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__16617) ) ).
fof('$_def_Coq.Init.Datatypes.ID',axiom,
! [Vvar__5533] :
( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__5533)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> t(happ(happ(Vvar__5533,V0__A),V1___24Anonymous),V0__A) ) ) ) ).
fof('$_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__1479] :
( t(Vvar__1___24Anonymous__1479,V0__A)
& ? [Vvar__2___24Anonymous__1480] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1480)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1479,Vvar__2___24Anonymous__1480)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1479,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__1480,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__1469] :
( t(Vvar__1___24Anonymous__1469,V0__A)
& ? [Vvar__2___24Anonymous__1470] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1470)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1469,Vvar__2___24Anonymous__1470)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__1470)) ) ) ) ) ) ).
fof('$_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.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('$_def_Coq.Init.Logic_Type.notT',axiom,
! [V0__A] :
( cCoq_2eInit_2eLogic__Type_2enotT___24a1(V0__A)
<=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> p(c_24False) ) ) ).
fof('$_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__2757] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2757)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2757)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__2757,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__17070] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17070)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17070)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__17073] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17073)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17073)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__17070,Vvar__0___24Anonymous__17073)) ) ) ) ) ) ) ) ).
fof('$_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__17076] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17076)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17076)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__17079] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17079)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17079)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__17076,Vvar__0___24Anonymous__17079)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__7838] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7838)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7838)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__7838,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__7836] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7836)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7836)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__7836 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__2762] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2762)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2762)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__2765] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2765)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2765)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__2762,Vvar__0___24Anonymous__2765) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.t',axiom,
! [Vvar__7835] :
( cCoq_2eInit_2eNat_2et___24t(Vvar__7835)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__7835) ) ).
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__17697] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17697)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17697)
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24True) ) ) ) ) ).
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('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__1338] :
( t(Vvar__1___24Anonymous__1338,V0__A)
& ? [Vvar__2___24Anonymous__1339] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1339)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1338,Vvar__2___24Anonymous__1339)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> ( Vvar__1___24Anonymous__1338 = V2__a
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__1339)) ) ) ) ) ) ) ) ).
fof('$_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.DependentFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__5355___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__5362___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('$_def_Coq.Logic.ChoiceFacts.FunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__702___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,V1__B)
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__163___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ).
fof('$_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__163___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('$_def_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on',axiom,
! [V0__A] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on___24a1(V0__A)
<=> ! [V1__R] :
( c_24__type__5374___24t(V0__A,V1__R)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ? [V3__y] :
( t(V3__y,V0__A)
& p(happ(happ(V1__R,V2__n),V3__y)) ) )
=> ? [V3__f] :
( c_24__type__5155___24t(V0__A,V3__f)
& ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(happ(happ(V1__R,V4__n),happ(V3__f,V4__n))) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.ProofIrrelevance',axiom,
( p(cCoq_2eLogic_2eChoiceFacts_2eProofIrrelevance)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> ( p(V0__A)
=> c_24Proof = c_24Proof ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.BoolP',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eBoolP)
<=> ! [V0__C] :
( cProp___24t(V0__C)
=> ( p(V0__C)
=> ( p(V0__C)
=> p(V0__C) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.DrinkerParadox',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eDrinkerParadox)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__21___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__21___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('$_def_Coq.Logic.ClassicalFacts.RightDistributivityImplicationOverDisjunction',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eRightDistributivityImplicationOverDisjunction)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__C] :
( cProp___24t(V2__C)
=> ( ( p(V2__C)
=> ( p(V0__A)
| p(V1__B) ) )
=> ( ( p(V2__C)
=> p(V0__A) )
| ( p(V2__C)
=> p(V1__B) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Logic.ClassicalFacts.weak_generalized_excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eweak__generalized__excluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
=> p(V1__B) )
=> p(V1__B) )
| ( p(V0__A)
=> p(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.Logic.FinFun.Bijective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eBijective___24a3(V0__A,V1__B,V2__f)
<=> ? [V3__g] :
( c_24__type__3419___24t(V0__A,V1__B,V3__g)
& ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V3__g,happ(V2__f,V4__x)) = V4__x )
& ! [V4__y] :
( t(V4__y,V1__B)
=> happ(V2__f,happ(V3__g,V4__y)) = V4__y ) ) ) ).
fof('$_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.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNat.N.peano_rect',axiom,
! [V0__P,V1__f0,V2__f,V3__n] : cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V0__P,V1__f0,V2__f,V3__n) = c_24__case__Coq_2eNumbers_2eBinNums_2eN_244971___24a4(V0__P,V1__f0,V2__f,V3__n) ).
fof('$_def_Coq.NArith.BinNat.N.recursion',axiom,
! [V0__A] : cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(c_24__lam__5004___24a1(V0__A)) ).
fof('$_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__4924] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4924)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4924)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__4924)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
! [Vvar__16515] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__16515)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__16515) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.div2',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__24420] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24420)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24420)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__24420 )
| ? [Vvar__0___24Anonymous__24421] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24421)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24421)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__24421 )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__16526] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16526)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16526)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__16526),Vvar__0___24Anonymous__16526)) )
| ? [Vvar__0___24Anonymous__16527] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16527)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16527)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__16527),Vvar__0___24Anonymous__16527) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_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__23161] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23161)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23161)
& 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__23161,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__23162] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23162)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23162)
& 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__23162,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('$_def_Coq.PArith.BinPosDef.Pos.t',axiom,
! [Vvar__16518] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__16518)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__16518) ) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__23566] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__23566)
& ? [Vvar__1__Qden__23567] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__23567)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__23566,Vvar__1__Qden__23567)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__23567 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__23561] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__23561)
& ? [Vvar__1__Qden__23562] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__23562)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__23561,Vvar__1__Qden__23562)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__23561 ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V2__x))
=> V2__x = V3__y ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.commut',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2ecommut___24a3(V0__A,V1__R1,V2__R2)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R1,V4__y),V3__x))
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V2__R2,V6__z),V4__y))
=> cCoq_2eInit_2eLogic_2eex2___24a3(V0__A,c_24__lam__3062___24a3(V0__A,V2__R2,V3__x),c_24__lam__3066___24a3(V0__A,V1__R1,V6__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.equiv',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2(V0__A,V1__R)
<=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.inclusion',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__R1,V2__R2)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R1,V3__x),V4__y))
=> p(happ(happ(V2__R2,V3__x),V4__y)) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.reflexive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__90___24a1(V0__A) ).
fof('$_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__90___24a1(V0__U) ).
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__16516] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__16516)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__16516) ) ).
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('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__16517] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__16517)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__16517) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__23142] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23142)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23142)
& ( ? [Vvar__0___24Anonymous__23146] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23146)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23146)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__23142,Vvar__0___24Anonymous__23146) ) )
| ? [Vvar__0___24Anonymous__23147] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23147)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23147)
& ( 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__23148] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23148)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23148)
& ( ? [Vvar__0___24Anonymous__23152] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23152)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23152)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__23153] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23153)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23153)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__23148,Vvar__0___24Anonymous__23153) ) )
| ( 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__23154] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23154)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23154)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__23155] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23155)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23155)
& ( 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.t',axiom,
! [Vvar__16437] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__16437)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__16437) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__16618] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__16618)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__16618) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__23186] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__23186)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__23186) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__16620] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__16620)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__16620) ) ).
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.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__5204] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5204)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5204)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__5208] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5208)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5208)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__5204,Vvar__0___24Anonymous__5208)) )
| ? [Vvar__0___24Anonymous__5209] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5209)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5209)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__5204,Vvar__0___24Anonymous__5209) ) ) ) ) )
| ? [Vvar__0___24Anonymous__5210] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5210)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5210)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__5214] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5214)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5214)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__5214,Vvar__0___24Anonymous__5210) )
| ? [Vvar__0___24Anonymous__5215] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5215)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5215)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__5210,Vvar__0___24Anonymous__5215)) ) ) ) ) ) ) ) ).
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__5223] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5223)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5223)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__5227] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5227)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5227)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5223,Vvar__0___24Anonymous__5227)) )
| ? [Vvar__0___24Anonymous__5228] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5228)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5228)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5223,Vvar__0___24Anonymous__5228)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__5229] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5229)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5229)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__5233] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5233)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5233)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5229,Vvar__0___24Anonymous__5233)) )
| ? [Vvar__0___24Anonymous__5234] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5234)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5234)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5229,Vvar__0___24Anonymous__5234)) ) ) ) ) ) ) ) ).
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__5219] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5219)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5219)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5219) )
| ? [Vvar__0___24Anonymous__5220] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5220)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5220)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5220) ) ) ) ).
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('$_def_Coq.ZArith.BinIntDef.Z.t',axiom,
! [Vvar__16619] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__16619)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__16619) ) ).
fof('$_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__23187] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23187)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23187)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__23187 )
| ? [Vvar__0___24Anonymous__23188] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23188)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23188)
& 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.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__23074] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23074)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23074)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23074)
& ( ? [Vvar__0___24Anonymous__23078] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23078)
& Vvar__0___24Anonymous__23074 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23078)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__23079] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23079)
& Vvar__0___24Anonymous__23074 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23079)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__23074 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23080] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23080)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23080)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23080)
& ( ? [Vvar__0___24Anonymous__23084] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23084)
& Vvar__0___24Anonymous__23080 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23084)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__23085] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23085)
& Vvar__0___24Anonymous__23080 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23085)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__23080 = 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__23086] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23086)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23086)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23086)
& ( ? [Vvar__0___24Anonymous__23090] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23090)
& Vvar__0___24Anonymous__23086 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23090)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__23091] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23091)
& Vvar__0___24Anonymous__23086 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23091)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__23086 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23092] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23092)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23092)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23092)
& ( ? [Vvar__0___24Anonymous__23096] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23096)
& Vvar__0___24Anonymous__23092 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23096)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__23097] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23097)
& Vvar__0___24Anonymous__23092 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23097)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__23092 = 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__23099] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23099)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23099)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__23100] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23100)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23100)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__23100) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__5708___24a1(V0__D) ).
fof('$_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__23575] :
( t(Vvar__1___24Anonymous__23575,V1__A)
& ? [Vvar__2___24Anonymous__23576] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__23576)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__23576)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__23575,Vvar__2___24Anonymous__23576)
& ( ( Vvar__2___24Anonymous__23576 = 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__23575)) ) )
| ? [Vvar__1___24Anonymous__23587] :
( t(Vvar__1___24Anonymous__23587,V1__A)
& ? [Vvar__2___24Anonymous__23588] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__23588)
& Vvar__2___24Anonymous__23576 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__23587,Vvar__2___24Anonymous__23588)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__23575))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__23576) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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.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__7794] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7794)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7794)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7794)
& ( ? [Vvar__0___24Anonymous__7798] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7798)
& Vvar__0___24Anonymous__7794 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7798)
& 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__7794))) )
| ? [Vvar__0___24Anonymous__7799] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7799)
& Vvar__0___24Anonymous__7794 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7799)
& 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__7794))) )
| ( Vvar__0___24Anonymous__7794 = 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__7800] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7800)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7800)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7800)
& ( ? [Vvar__0___24Anonymous__7804] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7804)
& Vvar__0___24Anonymous__7800 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7804)
& 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__7800)) )
| ? [Vvar__0___24Anonymous__7805] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7805)
& Vvar__0___24Anonymous__7800 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7805)
& 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__7800)) )
| ( Vvar__0___24Anonymous__7800 = 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__7761] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7761)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7761)
& 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__7761))) )
| ? [Vvar__0___24Anonymous__7762] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7762)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7762)
& 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__7762)) )
| ( 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('$_def_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__9685] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9685)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__9685)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(happ(V1__rmul,V3__r),V4__x),V4__x,Vvar__0___24Anonymous__9685),V4__x,Vvar__0___24Anonymous__9685) )
| ? [Vvar__0___24Anonymous__9686] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9686)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__9686)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,Vvar__0___24Anonymous__9686),V4__x,Vvar__0___24Anonymous__9686) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_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('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__9706] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9706)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__9706)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__9707__9710___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__9706)),c_24__let__var__6__p__9707__9710___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__9706))) )
| ? [Vvar__0___24Anonymous__9708] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9708)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__9708)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__9709__9711___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__9708)),c_24__let__var__6__p__9709__9711___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__9708)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_HahnMinElt.min_elt',axiom,
! [V0__A,V1__r,V2__a] :
( cHahnMinElt_2emin__elt___24a3(V0__A,V1__r,V2__a)
<=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(happ(happ(V1__r,V3__b),V2__a))
=> p(c_24False) ) ) ) ).
fof('$_def_HahnMinElt.wmin_elt',axiom,
! [V0__A,V1__r,V2__a] :
( cHahnMinElt_2ewmin__elt___24a3(V0__A,V1__r,V2__a)
<=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(happ(happ(V1__r,V3__b),V2__a))
=> V2__a = V3__b ) ) ) ).
fof('$_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.HahnBase.NW',axiom,
! [V0__P] :
( chahn_2eHahnBase_2eNW___24a1(V0__P)
<=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2ett)) ) ).
fof('$_def_hahn.HahnEquational.good_ctx',axiom,
! [V0__A,V1__P] :
( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
<=> ( chahn_2eHahnBase_2eNW___24a1(c_24__lam__2067___24a2(V0__A,V1__P))
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__2094___24a2(V0__A,V1__P)) ) ) ).
fof('$_def_hahn.HahnFuneq.funeq',axiom,
! [V0__A,V1__B,V2__f,V3__r] :
( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
<=> ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(happ(V3__r,V4__a),V5__b))
=> happ(V2__f,V4__a) = happ(V2__f,V5__b) ) ) ) ) ).
fof('$_def_hahn.HahnList.undup',axiom,
! [V1__A,V2__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& chahn_2eHahnList_2eundup___24a2(V1__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A) )
| ? [Vvar__1___24Anonymous__2456] :
( t(Vvar__1___24Anonymous__2456,V1__A)
& ? [Vvar__2___24Anonymous__2457] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__2457)
& ( cType___24t(V1__A)
=> ( t(Vvar__1___24Anonymous__2456,V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__2457)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457)
& ( ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457))
& cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457)) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457),c_24__prop__2473___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457))
& chahn_2eHahnList_2eundup___24a2(V1__A,V2__l) = chahn_2eHahnList_2eundup___24a2(V1__A,Vvar__2___24Anonymous__2457) )
| ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457))
& cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457)) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457),c_24__prop__2485___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457))
& chahn_2eHahnList_2eundup___24a2(V1__A,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__2456,chahn_2eHahnList_2eundup___24a2(V1__A,Vvar__2___24Anonymous__2457)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_hahn.HahnMaxElt.max_elt',axiom,
! [V0__A,V1__r,V2__a] :
( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a)
<=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(happ(happ(V1__r,V2__a),V3__b))
=> p(c_24False) ) ) ) ).
fof('$_def_hahn.HahnMaxElt.wmax_elt',axiom,
! [V0__A,V1__r,V2__a] :
( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
<=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(happ(happ(V1__r,V2__a),V3__b))
=> V2__a = V3__b ) ) ) ).
fof('$_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('$_def_hahn.HahnRelationsBasic.clos_refl_sym',axiom,
! [V0__A,V1__r,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ( V2__x = V3__y
| p(happ(happ(V1__r,V2__x),V3__y))
| p(happ(happ(V1__r,V3__y),V2__x)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.clos_sym',axiom,
! [V0__A,V1__r,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eclos__sym___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ( p(happ(happ(V1__r,V2__x),V3__y))
| p(happ(happ(V1__r,V3__y),V2__x)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.codom_rel',axiom,
! [V0__A,V1__r,V2__y] :
( chahn_2eHahnRelationsBasic_2ecodom__rel___24a3(V0__A,V1__r,V2__y)
<=> ? [V3__x] :
( t(V3__x,V0__A)
& p(happ(happ(V1__r,V3__x),V2__y)) ) ) ).
fof('$_def_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.dom_rel',axiom,
! [V0__A,V1__r,V2__x] :
( chahn_2eHahnRelationsBasic_2edom__rel___24a3(V0__A,V1__r,V2__x)
<=> ? [V3__y] :
( t(V3__y,V0__A)
& p(happ(happ(V1__r,V2__x),V3__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.eq_rel',axiom,
! [V0__A,V1__B,V2__f,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2eeq__rel___24a5(V0__A,V1__B,V2__f,V3__x,V4__y)
<=> happ(V2__f,V3__x) = happ(V2__f,V4__y) ) ).
fof('$_def_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
& p(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] :
( 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('$_def_hahn.HahnRelationsBasic.pow_rel',axiom,
! [V1__A,V2__r,V3__n] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V3__n) = chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V1__A,c_24__lam__14___24a1(V1__A)) )
| ? [Vvar__0___24Anonymous__2552] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2552)
& V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2552)
& chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V3__n) = chahn_2eHahnRelationsBasic_2eseq___24a3(V1__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,Vvar__0___24Anonymous__2552),V2__r) ) ) ) ) ).
fof('$_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.restr_subset',axiom,
! [V0__A,V1__cond,V2__r,V3__r_27] :
( chahn_2eHahnRelationsBasic_2erestr__subset___24a4(V0__A,V1__cond,V2__r,V3__r_27)
<=> ! [V4__a] :
( t(V4__a,V0__A)
=> ( p(happ(V1__cond,V4__a))
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ( p(happ(V1__cond,V6__b))
=> ( p(happ(happ(V2__r,V4__a),V6__b))
=> p(happ(happ(V3__r_27,V4__a),V6__b)) ) ) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.seq',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2eseq___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ? [V5__z] :
( t(V5__z,V0__A)
& p(happ(happ(V1__r,V3__x),V5__z))
& p(happ(happ(V2__r_27,V5__z),V4__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.singl_rel',axiom,
! [V0__A,V1__a,V2__b,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2esingl__rel___24a5(V0__A,V1__a,V2__b,V3__x,V4__y)
<=> ( V3__x = V1__a
& V4__y = V2__b ) ) ).
fof('$_def_hahn.HahnRelationsBasic.strict_partial_order',axiom,
! [V0__A,V1__r] :
( chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V0__A,V1__r)
<=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.strict_total_order',axiom,
! [V0__A,V1__cond,V2__r] :
( chahn_2eHahnRelationsBasic_2estrict__total__order___24a3(V0__A,V1__cond,V2__r)
<=> ( chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V0__A,V2__r)
& chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__cond,V2__r) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.upward_closed',axiom,
! [V0__A,V1__r,V2__P] :
( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V1__r,V2__P)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__r,V3__x),V4__y))
=> ( p(happ(V2__P,V4__y))
=> p(happ(V2__P,V3__x)) ) ) ) ) ) ).
fof('$_def_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$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__5305,Vvar__1___24Anonymous__5306,Vvar__0__P__5307,Vvar__1___24Anonymous__5308] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5305) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5307) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__16608,Vvar__1___24Anonymous__16609,Vvar__2___24Anonymous__16610] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__16608,Vvar__1___24Anonymous__16609,Vvar__2___24Anonymous__16610) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__17298,Vvar__1__Plt__17299,Vvar__2__Pgt__17300,Vvar__3___24Anonymous__17301,Vvar__0__Peq__17302,Vvar__1__Plt__17303,Vvar__2__Pgt__17304,Vvar__3___24Anonymous__17305] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__17298,Vvar__1__Plt__17299,Vvar__2__Pgt__17300) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__17302,Vvar__1__Plt__17303,Vvar__2__Pgt__17304) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__1424] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1424) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__1438,Vvar__1___24Anonymous__1439,Vvar__0__A__1440] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1438,Vvar__1___24Anonymous__1439) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1440) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__5476,Vvar__1__B__5477,Vvar__2___24Anonymous__5478,Vvar__0__A__5479,Vvar__1__B__5480,Vvar__2___24Anonymous__5481] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__5476,Vvar__1__B__5477,Vvar__2___24Anonymous__5478) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__5479,Vvar__1__B__5480,Vvar__2___24Anonymous__5481) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__413,Vvar__0__A__414,Vvar__1___24Anonymous__415,Vvar__2___24Anonymous__416] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__413) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__414,Vvar__1___24Anonymous__415,Vvar__2___24Anonymous__416) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Decimal.Decimal$Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__5682,Vvar__1__f__5683,Vvar__0__i__5684,Vvar__1__f__5685,Vvar__2__e__5686] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__5682,Vvar__1__f__5683) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__5684,Vvar__1__f__5685,Vvar__2__e__5686) ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__5646] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__5646) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__5670,Vvar__0__d__5671] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__5670) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__5671) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__15781,Vvar__1__B__15782,Vvar__2___24Anonymous__15783,Vvar__0__A__15784,Vvar__1__B__15785,Vvar__2___24Anonymous__15786] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__15781,Vvar__1__B__15782,Vvar__2___24Anonymous__15783) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__15784,Vvar__1__B__15785) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__4346,Vvar__1__B__4347,Vvar__2___24Anonymous__4348,Vvar__0__A__4349,Vvar__1__B__4350,Vvar__2___24Anonymous__4351] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__4346,Vvar__1__B__4347) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__4349,Vvar__1__B__4350) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__1383] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1383) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1392] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1392) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1375,Vvar__0___24Anonymous__1376] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1375) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1376) ).
fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__16597,Vvar__1___24Anonymous__16598] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__16597,Vvar__1___24Anonymous__16598) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__16522] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__16522) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__9226,Vvar__1___24Anonymous__9227,Vvar__0__x__9228,Vvar__1__n__9229,Vvar__2___24Anonymous__9230] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__9226) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__9228,Vvar__1__n__9229) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__15805,Vvar__1___24Anonymous__15806] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__15805,Vvar__1___24Anonymous__15806) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__9062,Vvar__1__lt__9063,Vvar__2__eq__9064,Vvar__3__x__9065,Vvar__4__y__9066,Vvar__5___24Anonymous__9067,Vvar__0__X__9068,Vvar__1__lt__9069,Vvar__2__eq__9070,Vvar__3__x__9071,Vvar__4__y__9072,Vvar__5___24Anonymous__9073] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__9062,Vvar__1__lt__9063,Vvar__2__eq__9064,Vvar__3__x__9065,Vvar__4__y__9066) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__9068,Vvar__1__lt__9069,Vvar__2__eq__9070,Vvar__3__x__9071,Vvar__4__y__9072) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__7735,Vvar__0__n__7736,Vvar__1___24Anonymous__7737] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__7735) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__7736,Vvar__1___24Anonymous__7737) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__16303,Vvar__0__A__16304,Vvar__1__h__16305,Vvar__2__n__16306,Vvar__3___24Anonymous__16307] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__16303) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__16304,Vvar__1__h__16305,Vvar__2__n__16306,Vvar__3___24Anonymous__16307) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__1614,Vvar__1___24Anonymous__1615,Vvar__0__C__1616,Vvar__1___24Anonymous__1617] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__1614,Vvar__1___24Anonymous__1615) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__1616,Vvar__1___24Anonymous__1617) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__5734,Vvar__1___24Anonymous__5735,Vvar__0__C__5736,Vvar__1___24Anonymous__5737,Vvar__2___24Anonymous__5738] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__5734,Vvar__1___24Anonymous__5735) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__5736,Vvar__1___24Anonymous__5737,Vvar__2___24Anonymous__5738) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__5768,Vvar__1___24Anonymous__5769] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__5768,Vvar__1___24Anonymous__5769) ).
fof('$_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$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__9357,Vvar__1___24Anonymous__9358,Vvar__0__C__9359,Vvar__1___24Anonymous__9360] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__9357,Vvar__1___24Anonymous__9358) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__9359,Vvar__1___24Anonymous__9360) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__16161,Vvar__1__TX__16162,Vvar__2__AA__16163,Vvar__3__AF__16164,Vvar__0__TA__16165,Vvar__1__TX__16166,Vvar__2__AA__16167,Vvar__3__AF__16168] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__16161,Vvar__1__TX__16162,Vvar__2__AA__16163,Vvar__3__AF__16164) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__16165,Vvar__1__TX__16166,Vvar__2__AA__16167,Vvar__3__AF__16168) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__16275,Vvar__0__A__16276,Vvar__1___24Anonymous__16277] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__16275) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__16276,Vvar__1___24Anonymous__16277) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__16345,Vvar__1___24Anonymous__16346] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__16345,Vvar__1___24Anonymous__16346) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__17605,Vvar__0__C__17606] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__17605) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__17606) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__9642,Vvar__0__C__9643] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__9642) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__9643) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__9418,Vvar__1___24Anonymous__9419,Vvar__0__C__9420,Vvar__1___24Anonymous__9421,Vvar__2___24Anonymous__9422] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__9418,Vvar__1___24Anonymous__9419) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__9420,Vvar__1___24Anonymous__9421,Vvar__2___24Anonymous__9422) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__9452,Vvar__1___24Anonymous__9453] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__9452,Vvar__1___24Anonymous__9453) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__15424,Vvar__1__req__15425,Vvar__2__reqb__15426,Vvar__3___24Anonymous__15427] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__15424,Vvar__1__req__15425,Vvar__2__reqb__15426) ).
fof('$_discrim_Hammer.Tactics.Reconstr.Empty$Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eEmpty != cHammer_2eTactics_2eReconstr_2eAllHyps ).
fof('$_fix_16592_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__16593] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16593)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16593)
& c_24__fix__16592__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__16592__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__16593)) )
| ? [Vvar__0___24Anonymous__16594] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16594)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16594)
& c_24__fix__16592__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16594) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__16592__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_fix_24074_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__24074__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__24078] :
( t(Vvar__1___24Anonymous__24078,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__24079] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__24079)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__24078,Vvar__2___24Anonymous__24079)
& c_24__fix__24074__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__24078,c_24__fix__24074__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__24079,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__5313,Vvar__0__P__5314,Vvar__1___24Anonymous__5315,Vvar__1___24Anonymous__5316] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5313) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5314)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__5313 = Vvar__0__P__5314 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__5309,Vvar__0__P__5310,Vvar__1___24Anonymous__5311,Vvar__1___24Anonymous__5312] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5309) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5310)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__5309 = Vvar__0__P__5310 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__16611,Vvar__0___24Anonymous__16612,Vvar__1___24Anonymous__16613,Vvar__1___24Anonymous__16614,Vvar__2___24Anonymous__16615,Vvar__2___24Anonymous__16616] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__16611,Vvar__1___24Anonymous__16613,Vvar__2___24Anonymous__16615) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__16612,Vvar__1___24Anonymous__16614,Vvar__2___24Anonymous__16616)
=> ( Vvar__2___24Anonymous__16615 = Vvar__2___24Anonymous__16616
& Vvar__1___24Anonymous__16613 = Vvar__1___24Anonymous__16614
& Vvar__0___24Anonymous__16611 = Vvar__0___24Anonymous__16612 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__17306,Vvar__0__Peq__17307,Vvar__1__Plt__17308,Vvar__1__Plt__17309,Vvar__2__Pgt__17310,Vvar__2__Pgt__17311,Vvar__3___24Anonymous__17312,Vvar__3___24Anonymous__17313] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__17306,Vvar__1__Plt__17308,Vvar__2__Pgt__17310) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__17307,Vvar__1__Plt__17309,Vvar__2__Pgt__17311)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__17310 = Vvar__2__Pgt__17311
& Vvar__1__Plt__17308 = Vvar__1__Plt__17309
& Vvar__0__Peq__17306 = Vvar__0__Peq__17307 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__17322,Vvar__0__Peq__17323,Vvar__1__Plt__17324,Vvar__1__Plt__17325,Vvar__2__Pgt__17326,Vvar__2__Pgt__17327,Vvar__3___24Anonymous__17328,Vvar__3___24Anonymous__17329] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__17322,Vvar__1__Plt__17324,Vvar__2__Pgt__17326) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__17323,Vvar__1__Plt__17325,Vvar__2__Pgt__17327)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__17326 = Vvar__2__Pgt__17327
& Vvar__1__Plt__17324 = Vvar__1__Plt__17325
& Vvar__0__Peq__17322 = Vvar__0__Peq__17323 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__17314,Vvar__0__Peq__17315,Vvar__1__Plt__17316,Vvar__1__Plt__17317,Vvar__2__Pgt__17318,Vvar__2__Pgt__17319,Vvar__3___24Anonymous__17320,Vvar__3___24Anonymous__17321] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__17314,Vvar__1__Plt__17316,Vvar__2__Pgt__17318) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__17315,Vvar__1__Plt__17317,Vvar__2__Pgt__17319)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__17318 = Vvar__2__Pgt__17319
& Vvar__1__Plt__17316 = Vvar__1__Plt__17317
& Vvar__0__Peq__17314 = Vvar__0__Peq__17315 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__1445,Vvar__0__A__1446] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1445) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1446)
=> Vvar__0__A__1445 = Vvar__0__A__1446 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__1425,Vvar__0___24Anonymous__1426] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1425) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1426)
=> Vvar__0___24Anonymous__1425 = Vvar__0___24Anonymous__1426 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__1441,Vvar__0__A__1442,Vvar__1___24Anonymous__1443,Vvar__1___24Anonymous__1444] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1441,Vvar__1___24Anonymous__1443) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1442,Vvar__1___24Anonymous__1444)
=> ( Vvar__1___24Anonymous__1443 = Vvar__1___24Anonymous__1444
& Vvar__0__A__1441 = Vvar__0__A__1442 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__419,Vvar__0__A__420,Vvar__1___24Anonymous__421,Vvar__1___24Anonymous__422,Vvar__2___24Anonymous__423,Vvar__2___24Anonymous__424] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__419,Vvar__1___24Anonymous__421,Vvar__2___24Anonymous__423) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__420,Vvar__1___24Anonymous__422,Vvar__2___24Anonymous__424)
=> ( Vvar__2___24Anonymous__423 = Vvar__2___24Anonymous__424
& Vvar__1___24Anonymous__421 = Vvar__1___24Anonymous__422
& Vvar__0__A__419 = Vvar__0__A__420 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__5482,Vvar__0__A__5483,Vvar__1__B__5484,Vvar__1__B__5485,Vvar__2___24Anonymous__5486,Vvar__2___24Anonymous__5487] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__5482,Vvar__1__B__5484,Vvar__2___24Anonymous__5486) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__5483,Vvar__1__B__5485,Vvar__2___24Anonymous__5487)
=> ( Vvar__2___24Anonymous__5486 = Vvar__2___24Anonymous__5487
& Vvar__1__B__5484 = Vvar__1__B__5485
& Vvar__0__A__5482 = Vvar__0__A__5483 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__5488,Vvar__0__A__5489,Vvar__1__B__5490,Vvar__1__B__5491,Vvar__2___24Anonymous__5492,Vvar__2___24Anonymous__5493] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__5488,Vvar__1__B__5490,Vvar__2___24Anonymous__5492) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__5489,Vvar__1__B__5491,Vvar__2___24Anonymous__5493)
=> ( Vvar__2___24Anonymous__5492 = Vvar__2___24Anonymous__5493
& Vvar__1__B__5490 = Vvar__1__B__5491
& Vvar__0__A__5488 = Vvar__0__A__5489 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__417,Vvar__0__A__418] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__417) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__418)
=> Vvar__0__A__417 = Vvar__0__A__418 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__5502,Vvar__0__A__5503,Vvar__1__B__5504,Vvar__1__B__5505,Vvar__2___24Anonymous__5506,Vvar__2___24Anonymous__5507,Vvar__3___24Anonymous__5508,Vvar__3___24Anonymous__5509] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__5502,Vvar__1__B__5504,Vvar__2___24Anonymous__5506,Vvar__3___24Anonymous__5508) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__5503,Vvar__1__B__5505,Vvar__2___24Anonymous__5507,Vvar__3___24Anonymous__5509)
=> ( Vvar__3___24Anonymous__5508 = Vvar__3___24Anonymous__5509
& Vvar__2___24Anonymous__5506 = Vvar__2___24Anonymous__5507
& Vvar__1__B__5504 = Vvar__1__B__5505
& Vvar__0__A__5502 = Vvar__0__A__5503 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__5647,Vvar__0___24Anonymous__5648] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__5647) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__5648)
=> Vvar__0___24Anonymous__5647 = Vvar__0___24Anonymous__5648 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__5649,Vvar__0___24Anonymous__5650] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__5649) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__5650)
=> Vvar__0___24Anonymous__5649 = Vvar__0___24Anonymous__5650 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__5651,Vvar__0___24Anonymous__5652] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__5651) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__5652)
=> Vvar__0___24Anonymous__5651 = Vvar__0___24Anonymous__5652 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__5653,Vvar__0___24Anonymous__5654] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__5653) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__5654)
=> Vvar__0___24Anonymous__5653 = Vvar__0___24Anonymous__5654 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__5655,Vvar__0___24Anonymous__5656] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__5655) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__5656)
=> Vvar__0___24Anonymous__5655 = Vvar__0___24Anonymous__5656 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__5657,Vvar__0___24Anonymous__5658] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__5657) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__5658)
=> Vvar__0___24Anonymous__5657 = Vvar__0___24Anonymous__5658 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__5659,Vvar__0___24Anonymous__5660] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__5659) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__5660)
=> Vvar__0___24Anonymous__5659 = Vvar__0___24Anonymous__5660 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__5661,Vvar__0___24Anonymous__5662] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__5661) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__5662)
=> Vvar__0___24Anonymous__5661 = Vvar__0___24Anonymous__5662 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__5663,Vvar__0___24Anonymous__5664] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__5663) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__5664)
=> Vvar__0___24Anonymous__5663 = Vvar__0___24Anonymous__5664 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__5665,Vvar__0___24Anonymous__5666] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__5665) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__5666)
=> Vvar__0___24Anonymous__5665 = Vvar__0___24Anonymous__5666 ) ).
fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
! [Vvar__0__i__5687,Vvar__0__i__5688,Vvar__1__f__5689,Vvar__1__f__5690] :
( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__5687,Vvar__1__f__5689) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__5688,Vvar__1__f__5690)
=> ( Vvar__1__f__5689 = Vvar__1__f__5690
& Vvar__0__i__5687 = Vvar__0__i__5688 ) ) ).
fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__5691,Vvar__0__i__5692,Vvar__1__f__5693,Vvar__1__f__5694,Vvar__2__e__5695,Vvar__2__e__5696] :
( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__5691,Vvar__1__f__5693,Vvar__2__e__5695) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__5692,Vvar__1__f__5694,Vvar__2__e__5696)
=> ( Vvar__2__e__5695 = Vvar__2__e__5696
& Vvar__1__f__5693 = Vvar__1__f__5694
& Vvar__0__i__5691 = Vvar__0__i__5692 ) ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__5674,Vvar__0__d__5675] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__5674) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__5675)
=> Vvar__0__d__5674 = Vvar__0__d__5675 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__5672,Vvar__0__d__5673] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__5672) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__5673)
=> Vvar__0__d__5672 = Vvar__0__d__5673 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__15620,Vvar__0__A__15621,Vvar__1__P__15622,Vvar__1__P__15623,Vvar__2__x__15624,Vvar__2__x__15625,Vvar__3___24Anonymous__15626,Vvar__3___24Anonymous__15627] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__15620,Vvar__1__P__15622,Vvar__2__x__15624) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__15621,Vvar__1__P__15623,Vvar__2__x__15625)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__15624 = Vvar__2__x__15625
& Vvar__1__P__15622 = Vvar__1__P__15623
& Vvar__0__A__15620 = Vvar__0__A__15621 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__15672,Vvar__0__A__15673,Vvar__1__P__15674,Vvar__1__P__15675,Vvar__2__Q__15676,Vvar__2__Q__15677,Vvar__3__x__15678,Vvar__3__x__15679,Vvar__4___24Anonymous__15680,Vvar__4___24Anonymous__15681,Vvar__5___24Anonymous__15682,Vvar__5___24Anonymous__15683] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__15672,Vvar__1__P__15674,Vvar__2__Q__15676,Vvar__3__x__15678) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__15673,Vvar__1__P__15675,Vvar__2__Q__15677,Vvar__3__x__15679)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__15678 = Vvar__3__x__15679
& Vvar__2__Q__15676 = Vvar__2__Q__15677
& Vvar__1__P__15674 = Vvar__1__P__15675
& Vvar__0__A__15672 = Vvar__0__A__15673 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__15705,Vvar__0__A__15706,Vvar__1__P__15707,Vvar__1__P__15708,Vvar__2__x__15709,Vvar__2__x__15710,Vvar__3___24Anonymous__15711,Vvar__3___24Anonymous__15712] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__15705,Vvar__1__P__15707,Vvar__2__x__15709,Vvar__3___24Anonymous__15711) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__15706,Vvar__1__P__15708,Vvar__2__x__15710,Vvar__3___24Anonymous__15712)
=> ( Vvar__3___24Anonymous__15711 = Vvar__3___24Anonymous__15712
& Vvar__2__x__15709 = Vvar__2__x__15710
& Vvar__1__P__15707 = Vvar__1__P__15708
& Vvar__0__A__15705 = Vvar__0__A__15706 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__15757,Vvar__0__A__15758,Vvar__1__P__15759,Vvar__1__P__15760,Vvar__2__Q__15761,Vvar__2__Q__15762,Vvar__3__x__15763,Vvar__3__x__15764,Vvar__4___24Anonymous__15765,Vvar__4___24Anonymous__15766,Vvar__5___24Anonymous__15767,Vvar__5___24Anonymous__15768] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__15757,Vvar__1__P__15759,Vvar__2__Q__15761,Vvar__3__x__15763,Vvar__4___24Anonymous__15765,Vvar__5___24Anonymous__15767) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__15758,Vvar__1__P__15760,Vvar__2__Q__15762,Vvar__3__x__15764,Vvar__4___24Anonymous__15766,Vvar__5___24Anonymous__15768)
=> ( Vvar__5___24Anonymous__15767 = Vvar__5___24Anonymous__15768
& Vvar__4___24Anonymous__15765 = Vvar__4___24Anonymous__15766
& Vvar__3__x__15763 = Vvar__3__x__15764
& Vvar__2__Q__15761 = Vvar__2__Q__15762
& Vvar__1__P__15759 = Vvar__1__P__15760
& Vvar__0__A__15757 = Vvar__0__A__15758 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__15787,Vvar__0__A__15788,Vvar__1__B__15789,Vvar__1__B__15790,Vvar__2___24Anonymous__15791,Vvar__2___24Anonymous__15792] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__15787,Vvar__1__B__15789,Vvar__2___24Anonymous__15791) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__15788,Vvar__1__B__15790,Vvar__2___24Anonymous__15792)
=> ( Vvar__2___24Anonymous__15791 = Vvar__2___24Anonymous__15792
& Vvar__1__B__15789 = Vvar__1__B__15790
& Vvar__0__A__15787 = Vvar__0__A__15788 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__15793,Vvar__0__A__15794,Vvar__1__B__15795,Vvar__1__B__15796,Vvar__2___24Anonymous__15797,Vvar__2___24Anonymous__15798] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__15793,Vvar__1__B__15795) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__15794,Vvar__1__B__15796)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__15795 = Vvar__1__B__15796
& Vvar__0__A__15793 = Vvar__0__A__15794 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__4352,Vvar__0__A__4353,Vvar__1__B__4354,Vvar__1__B__4355,Vvar__2___24Anonymous__4356,Vvar__2___24Anonymous__4357] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__4352,Vvar__1__B__4354) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__4353,Vvar__1__B__4355)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__4354 = Vvar__1__B__4355
& Vvar__0__A__4352 = Vvar__0__A__4353 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__4358,Vvar__0__A__4359,Vvar__1__B__4360,Vvar__1__B__4361,Vvar__2___24Anonymous__4362,Vvar__2___24Anonymous__4363] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__4358,Vvar__1__B__4360) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__4359,Vvar__1__B__4361)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__4360 = Vvar__1__B__4361
& Vvar__0__A__4358 = Vvar__0__A__4359 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__1384,Vvar__0___24Anonymous__1385] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1384) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1385)
=> Vvar__0___24Anonymous__1384 = Vvar__0___24Anonymous__1385 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__1395,Vvar__0___24Anonymous__1396] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1395) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1396)
=> Vvar__0___24Anonymous__1395 = Vvar__0___24Anonymous__1396 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1393,Vvar__0___24Anonymous__1394] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1393) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1394)
=> Vvar__0___24Anonymous__1393 = Vvar__0___24Anonymous__1394 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__1377,Vvar__0___24Anonymous__1378] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1377) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1378)
=> Vvar__0___24Anonymous__1377 = Vvar__0___24Anonymous__1378 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1379,Vvar__0___24Anonymous__1380] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1379) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1380)
=> Vvar__0___24Anonymous__1379 = Vvar__0___24Anonymous__1380 ) ).
fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__16599,Vvar__0__p__16600,Vvar__1___24Anonymous__16601,Vvar__1___24Anonymous__16602] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__16599,Vvar__1___24Anonymous__16601) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__16600,Vvar__1___24Anonymous__16602)
=> ( Vvar__1___24Anonymous__16601 = Vvar__1___24Anonymous__16602
& Vvar__0__p__16599 = Vvar__0__p__16600 ) ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__16523,Vvar__0___24Anonymous__16524] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__16523) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__16524)
=> Vvar__0___24Anonymous__16523 = Vvar__0___24Anonymous__16524 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__9114,Vvar__0__Qnum__9115,Vvar__1__Qden__9116,Vvar__1__Qden__9117] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9114,Vvar__1__Qden__9116) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9115,Vvar__1__Qden__9117)
=> ( Vvar__1__Qden__9116 = Vvar__1__Qden__9117
& Vvar__0__Qnum__9114 = Vvar__0__Qnum__9115 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
! [Vvar__0__neg__9142,Vvar__0__neg__9143,Vvar__1__cond__neg__9144,Vvar__1__cond__neg__9145] :
( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__9142) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__9143)
=> ( c_24Proof = c_24Proof
& Vvar__0__neg__9142 = Vvar__0__neg__9143 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__9121,Vvar__0__nonneg__9122,Vvar__1__cond__nonneg__9123,Vvar__1__cond__nonneg__9124] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__9121) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__9122)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__9121 = Vvar__0__nonneg__9122 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
! [Vvar__0__nonpos__9135,Vvar__0__nonpos__9136,Vvar__1__cond__nonpos__9137,Vvar__1__cond__nonpos__9138] :
( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__9135) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__9136)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonpos__9135 = Vvar__0__nonpos__9136 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__9149,Vvar__0__nonzero__9150,Vvar__1__cond__nonzero__9151,Vvar__1__cond__nonzero__9152] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__9149) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__9150)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__9149 = Vvar__0__nonzero__9150 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__9128,Vvar__0__pos__9129,Vvar__1__cond__pos__9130,Vvar__1__cond__pos__9131] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__9128) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__9129)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__9128 = Vvar__0__pos__9129 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__9241,Vvar__0__x__9242,Vvar__1__n__9243,Vvar__1__n__9244,Vvar__2___24Anonymous__9245,Vvar__2___24Anonymous__9246] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__9241,Vvar__1__n__9243) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__9242,Vvar__1__n__9244)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__9243 = Vvar__1__n__9244
& Vvar__0__x__9241 = Vvar__0__x__9242 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__9231,Vvar__0__x__9232,Vvar__1___24Anonymous__9233,Vvar__1___24Anonymous__9234] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__9231) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__9232)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__9231 = Vvar__0__x__9232 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__9235,Vvar__0__x__9236,Vvar__1__n__9237,Vvar__1__n__9238,Vvar__2___24Anonymous__9239,Vvar__2___24Anonymous__9240] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__9235,Vvar__1__n__9237) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__9236,Vvar__1__n__9238)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__9237 = Vvar__1__n__9238
& Vvar__0__x__9235 = Vvar__0__x__9236 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__5275,Vvar__0___24Anonymous__5276,Vvar__1___24Anonymous__5277,Vvar__1___24Anonymous__5278,Vvar__2___24Anonymous__5279,Vvar__2___24Anonymous__5280,Vvar__3___24Anonymous__5281,Vvar__3___24Anonymous__5282,Vvar__4___24Anonymous__5283,Vvar__4___24Anonymous__5284,Vvar__5___24Anonymous__5285,Vvar__5___24Anonymous__5286,Vvar__6___24Anonymous__5287,Vvar__6___24Anonymous__5288,Vvar__7___24Anonymous__5289,Vvar__7___24Anonymous__5290] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__5275,Vvar__1___24Anonymous__5277,Vvar__2___24Anonymous__5279,Vvar__3___24Anonymous__5281,Vvar__4___24Anonymous__5283,Vvar__5___24Anonymous__5285,Vvar__6___24Anonymous__5287,Vvar__7___24Anonymous__5289) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__5276,Vvar__1___24Anonymous__5278,Vvar__2___24Anonymous__5280,Vvar__3___24Anonymous__5282,Vvar__4___24Anonymous__5284,Vvar__5___24Anonymous__5286,Vvar__6___24Anonymous__5288,Vvar__7___24Anonymous__5290)
=> ( Vvar__7___24Anonymous__5289 = Vvar__7___24Anonymous__5290
& Vvar__6___24Anonymous__5287 = Vvar__6___24Anonymous__5288
& Vvar__5___24Anonymous__5285 = Vvar__5___24Anonymous__5286
& Vvar__4___24Anonymous__5283 = Vvar__4___24Anonymous__5284
& Vvar__3___24Anonymous__5281 = Vvar__3___24Anonymous__5282
& Vvar__2___24Anonymous__5279 = Vvar__2___24Anonymous__5280
& Vvar__1___24Anonymous__5277 = Vvar__1___24Anonymous__5278
& Vvar__0___24Anonymous__5275 = Vvar__0___24Anonymous__5276 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__15807,Vvar__0___24Anonymous__15808,Vvar__1___24Anonymous__15809,Vvar__1___24Anonymous__15810] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__15807,Vvar__1___24Anonymous__15809) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__15808,Vvar__1___24Anonymous__15810)
=> ( Vvar__1___24Anonymous__15809 = Vvar__1___24Anonymous__15810
& Vvar__0___24Anonymous__15807 = Vvar__0___24Anonymous__15808 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__9086,Vvar__0__X__9087,Vvar__1__lt__9088,Vvar__1__lt__9089,Vvar__2__eq__9090,Vvar__2__eq__9091,Vvar__3__x__9092,Vvar__3__x__9093,Vvar__4__y__9094,Vvar__4__y__9095,Vvar__5___24Anonymous__9096,Vvar__5___24Anonymous__9097] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__9086,Vvar__1__lt__9088,Vvar__2__eq__9090,Vvar__3__x__9092,Vvar__4__y__9094) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__9087,Vvar__1__lt__9089,Vvar__2__eq__9091,Vvar__3__x__9093,Vvar__4__y__9095)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__9094 = Vvar__4__y__9095
& Vvar__3__x__9092 = Vvar__3__x__9093
& Vvar__2__eq__9090 = Vvar__2__eq__9091
& Vvar__1__lt__9088 = Vvar__1__lt__9089
& Vvar__0__X__9086 = Vvar__0__X__9087 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__9098,Vvar__0__X__9099,Vvar__1__lt__9100,Vvar__1__lt__9101,Vvar__2__eq__9102,Vvar__2__eq__9103,Vvar__3__x__9104,Vvar__3__x__9105,Vvar__4__y__9106,Vvar__4__y__9107,Vvar__5___24Anonymous__9108,Vvar__5___24Anonymous__9109] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__9098,Vvar__1__lt__9100,Vvar__2__eq__9102,Vvar__3__x__9104,Vvar__4__y__9106) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__9099,Vvar__1__lt__9101,Vvar__2__eq__9103,Vvar__3__x__9105,Vvar__4__y__9107)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__9106 = Vvar__4__y__9107
& Vvar__3__x__9104 = Vvar__3__x__9105
& Vvar__2__eq__9102 = Vvar__2__eq__9103
& Vvar__1__lt__9100 = Vvar__1__lt__9101
& Vvar__0__X__9098 = Vvar__0__X__9099 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__9074,Vvar__0__X__9075,Vvar__1__lt__9076,Vvar__1__lt__9077,Vvar__2__eq__9078,Vvar__2__eq__9079,Vvar__3__x__9080,Vvar__3__x__9081,Vvar__4__y__9082,Vvar__4__y__9083,Vvar__5___24Anonymous__9084,Vvar__5___24Anonymous__9085] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__9074,Vvar__1__lt__9076,Vvar__2__eq__9078,Vvar__3__x__9080,Vvar__4__y__9082) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__9075,Vvar__1__lt__9077,Vvar__2__eq__9079,Vvar__3__x__9081,Vvar__4__y__9083)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__9082 = Vvar__4__y__9083
& Vvar__3__x__9080 = Vvar__3__x__9081
& Vvar__2__eq__9078 = Vvar__2__eq__9079
& Vvar__1__lt__9076 = Vvar__1__lt__9077
& Vvar__0__X__9074 = Vvar__0__X__9075 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__7738,Vvar__0__n__7739] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__7738) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__7739)
=> Vvar__0__n__7738 = Vvar__0__n__7739 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__7740,Vvar__0__n__7741,Vvar__1___24Anonymous__7742,Vvar__1___24Anonymous__7743] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__7740,Vvar__1___24Anonymous__7742) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__7741,Vvar__1___24Anonymous__7743)
=> ( Vvar__1___24Anonymous__7742 = Vvar__1___24Anonymous__7743
& Vvar__0__n__7740 = Vvar__0__n__7741 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__16310,Vvar__0__A__16311,Vvar__1__h__16312,Vvar__1__h__16313,Vvar__2__n__16314,Vvar__2__n__16315,Vvar__3___24Anonymous__16316,Vvar__3___24Anonymous__16317] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__16310,Vvar__1__h__16312,Vvar__2__n__16314,Vvar__3___24Anonymous__16316) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__16311,Vvar__1__h__16313,Vvar__2__n__16315,Vvar__3___24Anonymous__16317)
=> ( Vvar__3___24Anonymous__16316 = Vvar__3___24Anonymous__16317
& Vvar__2__n__16314 = Vvar__2__n__16315
& Vvar__1__h__16312 = Vvar__1__h__16313
& Vvar__0__A__16310 = Vvar__0__A__16311 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__16308,Vvar__0__A__16309] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__16308) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__16309)
=> Vvar__0__A__16308 = Vvar__0__A__16309 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__16400,Vvar__0__a__16401,Vvar__1__b__16402,Vvar__1__b__16403,Vvar__2__u__16404,Vvar__2__u__16405,Vvar__3__v__16406,Vvar__3__v__16407,Vvar__4__d__16408,Vvar__4__d__16409,Vvar__5___24Anonymous__16410,Vvar__5___24Anonymous__16411,Vvar__6___24Anonymous__16412,Vvar__6___24Anonymous__16413] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__16400,Vvar__1__b__16402,Vvar__2__u__16404,Vvar__3__v__16406,Vvar__4__d__16408) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__16401,Vvar__1__b__16403,Vvar__2__u__16405,Vvar__3__v__16407,Vvar__4__d__16409)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__16408 = Vvar__4__d__16409
& Vvar__3__v__16406 = Vvar__3__v__16407
& Vvar__2__u__16404 = Vvar__2__u__16405
& Vvar__1__b__16402 = Vvar__1__b__16403
& Vvar__0__a__16400 = Vvar__0__a__16401 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__23127,Vvar__0__x__23128,Vvar__1__p__23129,Vvar__1__p__23130,Vvar__2__q__23131,Vvar__2__q__23132,Vvar__3__r__23133,Vvar__3__r__23134,Vvar__4___24Anonymous__23135,Vvar__4___24Anonymous__23136,Vvar__5___24Anonymous__23137,Vvar__5___24Anonymous__23138,Vvar__6___24Anonymous__23139,Vvar__6___24Anonymous__23140] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__23127,Vvar__1__p__23129,Vvar__2__q__23131,Vvar__3__r__23133) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__23128,Vvar__1__p__23130,Vvar__2__q__23132,Vvar__3__r__23134)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__23133 = Vvar__3__r__23134
& Vvar__2__q__23131 = Vvar__2__q__23132
& Vvar__1__p__23129 = Vvar__1__p__23130
& Vvar__0__x__23127 = Vvar__0__x__23128 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__1622,Vvar__0__C__1623,Vvar__1___24Anonymous__1624,Vvar__1___24Anonymous__1625] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__1622,Vvar__1___24Anonymous__1624) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__1623,Vvar__1___24Anonymous__1625)
=> ( Vvar__1___24Anonymous__1624 = Vvar__1___24Anonymous__1625
& Vvar__0__C__1622 = Vvar__0__C__1623 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__1626,Vvar__0__C__1627,Vvar__1___24Anonymous__1628,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1630,Vvar__2___24Anonymous__1631] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__1626,Vvar__1___24Anonymous__1628,Vvar__2___24Anonymous__1630) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__1627,Vvar__1___24Anonymous__1629,Vvar__2___24Anonymous__1631)
=> ( Vvar__2___24Anonymous__1630 = Vvar__2___24Anonymous__1631
& Vvar__1___24Anonymous__1628 = Vvar__1___24Anonymous__1629
& Vvar__0__C__1626 = Vvar__0__C__1627 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__1618,Vvar__0__C__1619,Vvar__1___24Anonymous__1620,Vvar__1___24Anonymous__1621] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__1618,Vvar__1___24Anonymous__1620) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__1619,Vvar__1___24Anonymous__1621)
=> ( Vvar__1___24Anonymous__1620 = Vvar__1___24Anonymous__1621
& Vvar__0__C__1618 = Vvar__0__C__1619 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__1638,Vvar__0__C__1639,Vvar__1___24Anonymous__1640,Vvar__1___24Anonymous__1641,Vvar__2___24Anonymous__1642,Vvar__2___24Anonymous__1643] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__1638,Vvar__1___24Anonymous__1640,Vvar__2___24Anonymous__1642) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__1639,Vvar__1___24Anonymous__1641,Vvar__2___24Anonymous__1643)
=> ( Vvar__2___24Anonymous__1642 = Vvar__2___24Anonymous__1643
& Vvar__1___24Anonymous__1640 = Vvar__1___24Anonymous__1641
& Vvar__0__C__1638 = Vvar__0__C__1639 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__1644,Vvar__0__C__1645,Vvar__1___24Anonymous__1646,Vvar__1___24Anonymous__1647] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__1644,Vvar__1___24Anonymous__1646) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__1645,Vvar__1___24Anonymous__1647)
=> ( Vvar__1___24Anonymous__1646 = Vvar__1___24Anonymous__1647
& Vvar__0__C__1644 = Vvar__0__C__1645 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__1648,Vvar__0__C__1649,Vvar__1___24Anonymous__1650,Vvar__1___24Anonymous__1651,Vvar__2___24Anonymous__1652,Vvar__2___24Anonymous__1653] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__1648,Vvar__1___24Anonymous__1650,Vvar__2___24Anonymous__1652) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__1649,Vvar__1___24Anonymous__1651,Vvar__2___24Anonymous__1653)
=> ( Vvar__2___24Anonymous__1652 = Vvar__2___24Anonymous__1653
& Vvar__1___24Anonymous__1650 = Vvar__1___24Anonymous__1651
& Vvar__0__C__1648 = Vvar__0__C__1649 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__1632,Vvar__0__C__1633,Vvar__1___24Anonymous__1634,Vvar__1___24Anonymous__1635,Vvar__2___24Anonymous__1636,Vvar__2___24Anonymous__1637] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__1632,Vvar__1___24Anonymous__1634,Vvar__2___24Anonymous__1636) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__1633,Vvar__1___24Anonymous__1635,Vvar__2___24Anonymous__1637)
=> ( Vvar__2___24Anonymous__1636 = Vvar__2___24Anonymous__1637
& Vvar__1___24Anonymous__1634 = Vvar__1___24Anonymous__1635
& Vvar__0__C__1632 = Vvar__0__C__1633 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__5749,Vvar__0__C__5750,Vvar__1___24Anonymous__5751,Vvar__1___24Anonymous__5752,Vvar__2___24Anonymous__5753,Vvar__2___24Anonymous__5754,Vvar__3___24Anonymous__5755,Vvar__3___24Anonymous__5756] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__5749,Vvar__1___24Anonymous__5751,Vvar__2___24Anonymous__5753,Vvar__3___24Anonymous__5755) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__5750,Vvar__1___24Anonymous__5752,Vvar__2___24Anonymous__5754,Vvar__3___24Anonymous__5756)
=> ( Vvar__3___24Anonymous__5755 = Vvar__3___24Anonymous__5756
& Vvar__2___24Anonymous__5753 = Vvar__2___24Anonymous__5754
& Vvar__1___24Anonymous__5751 = Vvar__1___24Anonymous__5752
& Vvar__0__C__5749 = Vvar__0__C__5750 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__5739,Vvar__0__C__5740,Vvar__1___24Anonymous__5741,Vvar__1___24Anonymous__5742] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__5739,Vvar__1___24Anonymous__5741) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__5740,Vvar__1___24Anonymous__5742)
=> ( Vvar__1___24Anonymous__5741 = Vvar__1___24Anonymous__5742
& Vvar__0__C__5739 = Vvar__0__C__5740 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__5743,Vvar__0__C__5744,Vvar__1___24Anonymous__5745,Vvar__1___24Anonymous__5746,Vvar__2___24Anonymous__5747,Vvar__2___24Anonymous__5748] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__5743,Vvar__1___24Anonymous__5745,Vvar__2___24Anonymous__5747) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__5744,Vvar__1___24Anonymous__5746,Vvar__2___24Anonymous__5748)
=> ( Vvar__2___24Anonymous__5747 = Vvar__2___24Anonymous__5748
& Vvar__1___24Anonymous__5745 = Vvar__1___24Anonymous__5746
& Vvar__0__C__5743 = Vvar__0__C__5744 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__5774,Vvar__0___24Anonymous__5775,Vvar__1___24Anonymous__5776,Vvar__1___24Anonymous__5777] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__5774,Vvar__1___24Anonymous__5776) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__5775,Vvar__1___24Anonymous__5777)
=> ( Vvar__1___24Anonymous__5776 = Vvar__1___24Anonymous__5777
& Vvar__0___24Anonymous__5774 = Vvar__0___24Anonymous__5775 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__5770,Vvar__0___24Anonymous__5771,Vvar__1___24Anonymous__5772,Vvar__1___24Anonymous__5773] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__5770,Vvar__1___24Anonymous__5772) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__5771,Vvar__1___24Anonymous__5773)
=> ( Vvar__1___24Anonymous__5772 = Vvar__1___24Anonymous__5773
& Vvar__0___24Anonymous__5770 = Vvar__0___24Anonymous__5771 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__2947,Vvar__0__r__2948] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__2947) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__2948)
=> Vvar__0__r__2947 = Vvar__0__r__2948 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__2935,Vvar__0__r1__2936,Vvar__1__r2__2937,Vvar__1__r2__2938] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__2935,Vvar__1__r2__2937) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__2936,Vvar__1__r2__2938)
=> ( Vvar__1__r2__2937 = Vvar__1__r2__2938
& Vvar__0__r1__2935 = Vvar__0__r1__2936 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__2939,Vvar__0__r1__2940,Vvar__1__r2__2941,Vvar__1__r2__2942] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__2939,Vvar__1__r2__2941) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__2940,Vvar__1__r2__2942)
=> ( Vvar__1__r2__2941 = Vvar__1__r2__2942
& Vvar__0__r1__2939 = Vvar__0__r1__2940 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__2949,Vvar__0__r__2950] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__2949) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__2950)
=> Vvar__0__r__2949 = Vvar__0__r__2950 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__2931,Vvar__0__r1__2932,Vvar__1__r2__2933,Vvar__1__r2__2934] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__2931,Vvar__1__r2__2933) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__2932,Vvar__1__r2__2934)
=> ( Vvar__1__r2__2933 = Vvar__1__r2__2934
& Vvar__0__r1__2931 = Vvar__0__r1__2932 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__2943,Vvar__0__r1__2944,Vvar__1__z__2945,Vvar__1__z__2946] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__2943,Vvar__1__z__2945) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__2944,Vvar__1__z__2946)
=> ( Vvar__1__z__2945 = Vvar__1__z__2946
& Vvar__0__r1__2943 = Vvar__0__r1__2944 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__2927,Vvar__0__r__2928] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__2927) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__2928)
=> Vvar__0__r__2927 = Vvar__0__r__2928 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__2929,Vvar__0__r__2930] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__2929) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__2930)
=> Vvar__0__r__2929 = Vvar__0__r__2930 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__3641,Vvar__0__T__3642,Vvar__1__Flhs__3643,Vvar__1__Flhs__3644,Vvar__2__Fop__3645,Vvar__2__Fop__3646,Vvar__3__Frhs__3647,Vvar__3__Frhs__3648] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__3641,Vvar__1__Flhs__3643,Vvar__2__Fop__3645,Vvar__3__Frhs__3647) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__3642,Vvar__1__Flhs__3644,Vvar__2__Fop__3646,Vvar__3__Frhs__3648)
=> ( Vvar__3__Frhs__3647 = Vvar__3__Frhs__3648
& Vvar__2__Fop__3645 = Vvar__2__Fop__3646
& Vvar__1__Flhs__3643 = Vvar__1__Flhs__3644
& Vvar__0__T__3641 = Vvar__0__T__3642 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__9381,Vvar__0__C__9382,Vvar__1___24Anonymous__9383,Vvar__1___24Anonymous__9384,Vvar__2___24Anonymous__9385,Vvar__2___24Anonymous__9386] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__9381,Vvar__1___24Anonymous__9383,Vvar__2___24Anonymous__9385) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__9382,Vvar__1___24Anonymous__9384,Vvar__2___24Anonymous__9386)
=> ( Vvar__2___24Anonymous__9385 = Vvar__2___24Anonymous__9386
& Vvar__1___24Anonymous__9383 = Vvar__1___24Anonymous__9384
& Vvar__0__C__9381 = Vvar__0__C__9382 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__9387,Vvar__0__C__9388,Vvar__1___24Anonymous__9389,Vvar__1___24Anonymous__9390] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__9387,Vvar__1___24Anonymous__9389) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__9388,Vvar__1___24Anonymous__9390)
=> ( Vvar__1___24Anonymous__9389 = Vvar__1___24Anonymous__9390
& Vvar__0__C__9387 = Vvar__0__C__9388 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__9361,Vvar__0__C__9362,Vvar__1___24Anonymous__9363,Vvar__1___24Anonymous__9364] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__9361,Vvar__1___24Anonymous__9363) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__9362,Vvar__1___24Anonymous__9364)
=> ( Vvar__1___24Anonymous__9363 = Vvar__1___24Anonymous__9364
& Vvar__0__C__9361 = Vvar__0__C__9362 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__9369,Vvar__0__C__9370,Vvar__1___24Anonymous__9371,Vvar__1___24Anonymous__9372,Vvar__2___24Anonymous__9373,Vvar__2___24Anonymous__9374] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__9369,Vvar__1___24Anonymous__9371,Vvar__2___24Anonymous__9373) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__9370,Vvar__1___24Anonymous__9372,Vvar__2___24Anonymous__9374)
=> ( Vvar__2___24Anonymous__9373 = Vvar__2___24Anonymous__9374
& Vvar__1___24Anonymous__9371 = Vvar__1___24Anonymous__9372
& Vvar__0__C__9369 = Vvar__0__C__9370 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__9375,Vvar__0__C__9376,Vvar__1___24Anonymous__9377,Vvar__1___24Anonymous__9378,Vvar__2___24Anonymous__9379,Vvar__2___24Anonymous__9380] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__9375,Vvar__1___24Anonymous__9377,Vvar__2___24Anonymous__9379) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__9376,Vvar__1___24Anonymous__9378,Vvar__2___24Anonymous__9380)
=> ( Vvar__2___24Anonymous__9379 = Vvar__2___24Anonymous__9380
& Vvar__1___24Anonymous__9377 = Vvar__1___24Anonymous__9378
& Vvar__0__C__9375 = Vvar__0__C__9376 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__9365,Vvar__0__C__9366,Vvar__1___24Anonymous__9367,Vvar__1___24Anonymous__9368] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__9365,Vvar__1___24Anonymous__9367) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__9366,Vvar__1___24Anonymous__9368)
=> ( Vvar__1___24Anonymous__9367 = Vvar__1___24Anonymous__9368
& Vvar__0__C__9365 = Vvar__0__C__9366 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__9391,Vvar__0__C__9392] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__9391) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__9392)
=> Vvar__0__C__9391 = Vvar__0__C__9392 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__16195,Vvar__0__TA__16196,Vvar__1__TX__16197,Vvar__1__TX__16198,Vvar__2__AA__16199,Vvar__2__AA__16200,Vvar__3__AF__16201,Vvar__3__AF__16202,Vvar__4___24Anonymous__16203,Vvar__4___24Anonymous__16204,Vvar__5___24Anonymous__16205,Vvar__5___24Anonymous__16206] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__16195,Vvar__1__TX__16197,Vvar__2__AA__16199,Vvar__3__AF__16201,Vvar__4___24Anonymous__16203,Vvar__5___24Anonymous__16205) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__16196,Vvar__1__TX__16198,Vvar__2__AA__16200,Vvar__3__AF__16202,Vvar__4___24Anonymous__16204,Vvar__5___24Anonymous__16206)
=> ( Vvar__5___24Anonymous__16205 = Vvar__5___24Anonymous__16206
& Vvar__4___24Anonymous__16203 = Vvar__4___24Anonymous__16204
& Vvar__3__AF__16201 = Vvar__3__AF__16202
& Vvar__2__AA__16199 = Vvar__2__AA__16200
& Vvar__1__TX__16197 = Vvar__1__TX__16198
& Vvar__0__TA__16195 = Vvar__0__TA__16196 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__16207,Vvar__0__TA__16208,Vvar__1__TX__16209,Vvar__1__TX__16210,Vvar__2__AA__16211,Vvar__2__AA__16212,Vvar__3__AF__16213,Vvar__3__AF__16214,Vvar__4___24Anonymous__16215,Vvar__4___24Anonymous__16216,Vvar__5___24Anonymous__16217,Vvar__5___24Anonymous__16218] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__16207,Vvar__1__TX__16209,Vvar__2__AA__16211,Vvar__3__AF__16213,Vvar__4___24Anonymous__16215,Vvar__5___24Anonymous__16217) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__16208,Vvar__1__TX__16210,Vvar__2__AA__16212,Vvar__3__AF__16214,Vvar__4___24Anonymous__16216,Vvar__5___24Anonymous__16218)
=> ( Vvar__5___24Anonymous__16217 = Vvar__5___24Anonymous__16218
& Vvar__4___24Anonymous__16215 = Vvar__4___24Anonymous__16216
& Vvar__3__AF__16213 = Vvar__3__AF__16214
& Vvar__2__AA__16211 = Vvar__2__AA__16212
& Vvar__1__TX__16209 = Vvar__1__TX__16210
& Vvar__0__TA__16207 = Vvar__0__TA__16208 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__16219,Vvar__0__TA__16220,Vvar__1__TX__16221,Vvar__1__TX__16222,Vvar__2__AA__16223,Vvar__2__AA__16224,Vvar__3__AF__16225,Vvar__3__AF__16226,Vvar__4___24Anonymous__16227,Vvar__4___24Anonymous__16228,Vvar__5___24Anonymous__16229,Vvar__5___24Anonymous__16230] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__16219,Vvar__1__TX__16221,Vvar__2__AA__16223,Vvar__3__AF__16225,Vvar__4___24Anonymous__16227,Vvar__5___24Anonymous__16229) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__16220,Vvar__1__TX__16222,Vvar__2__AA__16224,Vvar__3__AF__16226,Vvar__4___24Anonymous__16228,Vvar__5___24Anonymous__16230)
=> ( Vvar__5___24Anonymous__16229 = Vvar__5___24Anonymous__16230
& Vvar__4___24Anonymous__16227 = Vvar__4___24Anonymous__16228
& Vvar__3__AF__16225 = Vvar__3__AF__16226
& Vvar__2__AA__16223 = Vvar__2__AA__16224
& Vvar__1__TX__16221 = Vvar__1__TX__16222
& Vvar__0__TA__16219 = Vvar__0__TA__16220 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__16177,Vvar__0__TA__16178,Vvar__1__TX__16179,Vvar__1__TX__16180,Vvar__2__AA__16181,Vvar__2__AA__16182,Vvar__3__AF__16183,Vvar__3__AF__16184] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__16177,Vvar__1__TX__16179,Vvar__2__AA__16181,Vvar__3__AF__16183) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__16178,Vvar__1__TX__16180,Vvar__2__AA__16182,Vvar__3__AF__16184)
=> ( Vvar__3__AF__16183 = Vvar__3__AF__16184
& Vvar__2__AA__16181 = Vvar__2__AA__16182
& Vvar__1__TX__16179 = Vvar__1__TX__16180
& Vvar__0__TA__16177 = Vvar__0__TA__16178 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__16241,Vvar__0__TA__16242,Vvar__1__TX__16243,Vvar__1__TX__16244,Vvar__2__AA__16245,Vvar__2__AA__16246,Vvar__3__AF__16247,Vvar__3__AF__16248,Vvar__4___24Anonymous__16249,Vvar__4___24Anonymous__16250,Vvar__5___24Anonymous__16251,Vvar__5___24Anonymous__16252,Vvar__6___24Anonymous__16253,Vvar__6___24Anonymous__16254] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__16241,Vvar__1__TX__16243,Vvar__2__AA__16245,Vvar__3__AF__16247,Vvar__4___24Anonymous__16249,Vvar__5___24Anonymous__16251,Vvar__6___24Anonymous__16253) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__16242,Vvar__1__TX__16244,Vvar__2__AA__16246,Vvar__3__AF__16248,Vvar__4___24Anonymous__16250,Vvar__5___24Anonymous__16252,Vvar__6___24Anonymous__16254)
=> ( Vvar__6___24Anonymous__16253 = Vvar__6___24Anonymous__16254
& Vvar__5___24Anonymous__16251 = Vvar__5___24Anonymous__16252
& Vvar__4___24Anonymous__16249 = Vvar__4___24Anonymous__16250
& Vvar__3__AF__16247 = Vvar__3__AF__16248
& Vvar__2__AA__16245 = Vvar__2__AA__16246
& Vvar__1__TX__16243 = Vvar__1__TX__16244
& Vvar__0__TA__16241 = Vvar__0__TA__16242 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__16231,Vvar__0__TA__16232,Vvar__1__TX__16233,Vvar__1__TX__16234,Vvar__2__AA__16235,Vvar__2__AA__16236,Vvar__3__AF__16237,Vvar__3__AF__16238,Vvar__4___24Anonymous__16239,Vvar__4___24Anonymous__16240] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__16231,Vvar__1__TX__16233,Vvar__2__AA__16235,Vvar__3__AF__16237,Vvar__4___24Anonymous__16239) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__16232,Vvar__1__TX__16234,Vvar__2__AA__16236,Vvar__3__AF__16238,Vvar__4___24Anonymous__16240)
=> ( Vvar__4___24Anonymous__16239 = Vvar__4___24Anonymous__16240
& Vvar__3__AF__16237 = Vvar__3__AF__16238
& Vvar__2__AA__16235 = Vvar__2__AA__16236
& Vvar__1__TX__16233 = Vvar__1__TX__16234
& Vvar__0__TA__16231 = Vvar__0__TA__16232 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__16169,Vvar__0__TA__16170,Vvar__1__TX__16171,Vvar__1__TX__16172,Vvar__2__AA__16173,Vvar__2__AA__16174,Vvar__3__AF__16175,Vvar__3__AF__16176] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__16169,Vvar__1__TX__16171,Vvar__2__AA__16173,Vvar__3__AF__16175) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__16170,Vvar__1__TX__16172,Vvar__2__AA__16174,Vvar__3__AF__16176)
=> ( Vvar__3__AF__16175 = Vvar__3__AF__16176
& Vvar__2__AA__16173 = Vvar__2__AA__16174
& Vvar__1__TX__16171 = Vvar__1__TX__16172
& Vvar__0__TA__16169 = Vvar__0__TA__16170 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__16185,Vvar__0__TA__16186,Vvar__1__TX__16187,Vvar__1__TX__16188,Vvar__2__AA__16189,Vvar__2__AA__16190,Vvar__3__AF__16191,Vvar__3__AF__16192,Vvar__4___24Anonymous__16193,Vvar__4___24Anonymous__16194] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__16185,Vvar__1__TX__16187,Vvar__2__AA__16189,Vvar__3__AF__16191,Vvar__4___24Anonymous__16193) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__16186,Vvar__1__TX__16188,Vvar__2__AA__16190,Vvar__3__AF__16192,Vvar__4___24Anonymous__16194)
=> ( Vvar__4___24Anonymous__16193 = Vvar__4___24Anonymous__16194
& Vvar__3__AF__16191 = Vvar__3__AF__16192
& Vvar__2__AA__16189 = Vvar__2__AA__16190
& Vvar__1__TX__16187 = Vvar__1__TX__16188
& Vvar__0__TA__16185 = Vvar__0__TA__16186 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__16284,Vvar__0__A__16285,Vvar__1___24Anonymous__16286,Vvar__1___24Anonymous__16287,Vvar__2___24Anonymous__16288,Vvar__2___24Anonymous__16289,Vvar__3___24Anonymous__16290,Vvar__3___24Anonymous__16291] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__16284,Vvar__1___24Anonymous__16286,Vvar__2___24Anonymous__16288,Vvar__3___24Anonymous__16290) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__16285,Vvar__1___24Anonymous__16287,Vvar__2___24Anonymous__16289,Vvar__3___24Anonymous__16291)
=> ( Vvar__3___24Anonymous__16290 = Vvar__3___24Anonymous__16291
& Vvar__2___24Anonymous__16288 = Vvar__2___24Anonymous__16289
& Vvar__1___24Anonymous__16286 = Vvar__1___24Anonymous__16287
& Vvar__0__A__16284 = Vvar__0__A__16285 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__16280,Vvar__0__A__16281,Vvar__1___24Anonymous__16282,Vvar__1___24Anonymous__16283] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__16280,Vvar__1___24Anonymous__16282) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__16281,Vvar__1___24Anonymous__16283)
=> ( Vvar__1___24Anonymous__16282 = Vvar__1___24Anonymous__16283
& Vvar__0__A__16280 = Vvar__0__A__16281 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__16278,Vvar__0__A__16279] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__16278) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__16279)
=> Vvar__0__A__16278 = Vvar__0__A__16279 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__16351,Vvar__0___24Anonymous__16352,Vvar__1___24Anonymous__16353,Vvar__1___24Anonymous__16354] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__16351,Vvar__1___24Anonymous__16353) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__16352,Vvar__1___24Anonymous__16354)
=> ( Vvar__1___24Anonymous__16353 = Vvar__1___24Anonymous__16354
& Vvar__0___24Anonymous__16351 = Vvar__0___24Anonymous__16352 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__16355,Vvar__0___24Anonymous__16356,Vvar__1___24Anonymous__16357,Vvar__1___24Anonymous__16358,Vvar__2___24Anonymous__16359,Vvar__2___24Anonymous__16360] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__16355,Vvar__1___24Anonymous__16357,Vvar__2___24Anonymous__16359) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__16356,Vvar__1___24Anonymous__16358,Vvar__2___24Anonymous__16360)
=> ( Vvar__2___24Anonymous__16359 = Vvar__2___24Anonymous__16360
& Vvar__1___24Anonymous__16357 = Vvar__1___24Anonymous__16358
& Vvar__0___24Anonymous__16355 = Vvar__0___24Anonymous__16356 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__16347,Vvar__0___24Anonymous__16348,Vvar__1___24Anonymous__16349,Vvar__1___24Anonymous__16350] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__16347,Vvar__1___24Anonymous__16349) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__16348,Vvar__1___24Anonymous__16350)
=> ( Vvar__1___24Anonymous__16349 = Vvar__1___24Anonymous__16350
& Vvar__0___24Anonymous__16347 = Vvar__0___24Anonymous__16348 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__17609,Vvar__0__C__17610] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__17609) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__17610)
=> Vvar__0__C__17609 = Vvar__0__C__17610 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__17607,Vvar__0__C__17608] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__17607) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__17608)
=> Vvar__0__C__17607 = Vvar__0__C__17608 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__17615,Vvar__0__C__17616,Vvar__1___24Anonymous__17617,Vvar__1___24Anonymous__17618] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__17615,Vvar__1___24Anonymous__17617) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__17616,Vvar__1___24Anonymous__17618)
=> ( Vvar__1___24Anonymous__17617 = Vvar__1___24Anonymous__17618
& Vvar__0__C__17615 = Vvar__0__C__17616 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__17619,Vvar__0__C__17620,Vvar__1___24Anonymous__17621,Vvar__1___24Anonymous__17622,Vvar__2___24Anonymous__17623,Vvar__2___24Anonymous__17624] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__17619,Vvar__1___24Anonymous__17621,Vvar__2___24Anonymous__17623) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__17620,Vvar__1___24Anonymous__17622,Vvar__2___24Anonymous__17624)
=> ( Vvar__2___24Anonymous__17623 = Vvar__2___24Anonymous__17624
& Vvar__1___24Anonymous__17621 = Vvar__1___24Anonymous__17622
& Vvar__0__C__17619 = Vvar__0__C__17620 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__17611,Vvar__0__C__17612,Vvar__1___24Anonymous__17613,Vvar__1___24Anonymous__17614] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__17611,Vvar__1___24Anonymous__17613) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__17612,Vvar__1___24Anonymous__17614)
=> ( Vvar__1___24Anonymous__17613 = Vvar__1___24Anonymous__17614
& Vvar__0__C__17611 = Vvar__0__C__17612 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__17645,Vvar__0__C__17646,Vvar__1___24Anonymous__17647,Vvar__1___24Anonymous__17648,Vvar__2___24Anonymous__17649,Vvar__2___24Anonymous__17650] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__17645,Vvar__1___24Anonymous__17647,Vvar__2___24Anonymous__17649) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__17646,Vvar__1___24Anonymous__17648,Vvar__2___24Anonymous__17650)
=> ( Vvar__2___24Anonymous__17649 = Vvar__2___24Anonymous__17650
& Vvar__1___24Anonymous__17647 = Vvar__1___24Anonymous__17648
& Vvar__0__C__17645 = Vvar__0__C__17646 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__17641,Vvar__0__C__17642,Vvar__1___24Anonymous__17643,Vvar__1___24Anonymous__17644] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__17641,Vvar__1___24Anonymous__17643) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__17642,Vvar__1___24Anonymous__17644)
=> ( Vvar__1___24Anonymous__17643 = Vvar__1___24Anonymous__17644
& Vvar__0__C__17641 = Vvar__0__C__17642 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__17631,Vvar__0__C__17632,Vvar__1___24Anonymous__17633,Vvar__1___24Anonymous__17634,Vvar__2___24Anonymous__17635,Vvar__2___24Anonymous__17636] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__17631,Vvar__1___24Anonymous__17633,Vvar__2___24Anonymous__17635) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__17632,Vvar__1___24Anonymous__17634,Vvar__2___24Anonymous__17636)
=> ( Vvar__2___24Anonymous__17635 = Vvar__2___24Anonymous__17636
& Vvar__1___24Anonymous__17633 = Vvar__1___24Anonymous__17634
& Vvar__0__C__17631 = Vvar__0__C__17632 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__17637,Vvar__0__C__17638,Vvar__1___24Anonymous__17639,Vvar__1___24Anonymous__17640] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__17637,Vvar__1___24Anonymous__17639) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__17638,Vvar__1___24Anonymous__17640)
=> ( Vvar__1___24Anonymous__17639 = Vvar__1___24Anonymous__17640
& Vvar__0__C__17637 = Vvar__0__C__17638 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__17651,Vvar__0__C__17652,Vvar__1___24Anonymous__17653,Vvar__1___24Anonymous__17654,Vvar__2___24Anonymous__17655,Vvar__2___24Anonymous__17656] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__17651,Vvar__1___24Anonymous__17653,Vvar__2___24Anonymous__17655) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__17652,Vvar__1___24Anonymous__17654,Vvar__2___24Anonymous__17656)
=> ( Vvar__2___24Anonymous__17655 = Vvar__2___24Anonymous__17656
& Vvar__1___24Anonymous__17653 = Vvar__1___24Anonymous__17654
& Vvar__0__C__17651 = Vvar__0__C__17652 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__17625,Vvar__0__C__17626,Vvar__1___24Anonymous__17627,Vvar__1___24Anonymous__17628,Vvar__2___24Anonymous__17629,Vvar__2___24Anonymous__17630] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__17625,Vvar__1___24Anonymous__17627,Vvar__2___24Anonymous__17629) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__17626,Vvar__1___24Anonymous__17628,Vvar__2___24Anonymous__17630)
=> ( Vvar__2___24Anonymous__17629 = Vvar__2___24Anonymous__17630
& Vvar__1___24Anonymous__17627 = Vvar__1___24Anonymous__17628
& Vvar__0__C__17625 = Vvar__0__C__17626 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__17663,Vvar__0__C__17664,Vvar__1__num__17665,Vvar__1__num__17666,Vvar__2__denum__17667,Vvar__2__denum__17668,Vvar__3__condition__17669,Vvar__3__condition__17670] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__17663,Vvar__1__num__17665,Vvar__2__denum__17667,Vvar__3__condition__17669) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__17664,Vvar__1__num__17666,Vvar__2__denum__17668,Vvar__3__condition__17670)
=> ( Vvar__3__condition__17669 = Vvar__3__condition__17670
& Vvar__2__denum__17667 = Vvar__2__denum__17668
& Vvar__1__num__17665 = Vvar__1__num__17666
& Vvar__0__C__17663 = Vvar__0__C__17664 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__6587,Vvar__0__C__6588,Vvar__1__rsplit__left__6589,Vvar__1__rsplit__left__6590,Vvar__2__rsplit__common__6591,Vvar__2__rsplit__common__6592,Vvar__3__rsplit__right__6593,Vvar__3__rsplit__right__6594] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__6587,Vvar__1__rsplit__left__6589,Vvar__2__rsplit__common__6591,Vvar__3__rsplit__right__6593) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__6588,Vvar__1__rsplit__left__6590,Vvar__2__rsplit__common__6592,Vvar__3__rsplit__right__6594)
=> ( Vvar__3__rsplit__right__6593 = Vvar__3__rsplit__right__6594
& Vvar__2__rsplit__common__6591 = Vvar__2__rsplit__common__6592
& Vvar__1__rsplit__left__6589 = Vvar__1__rsplit__left__6590
& Vvar__0__C__6587 = Vvar__0__C__6588 ) ) ).
fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
! [Vvar__0__hypo__type__7831,Vvar__0__hypo__type__7832,Vvar__1__hypo__proof__7833,Vvar__1__hypo__proof__7834] :
( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__7831,Vvar__1__hypo__proof__7833) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__7832,Vvar__1__hypo__proof__7834)
=> ( Vvar__1__hypo__proof__7833 = Vvar__1__hypo__proof__7834
& Vvar__0__hypo__type__7831 = Vvar__0__hypo__type__7832 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__9646,Vvar__0__C__9647] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__9646) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__9647)
=> Vvar__0__C__9646 = Vvar__0__C__9647 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__9644,Vvar__0__C__9645] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__9644) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__9645)
=> Vvar__0__C__9644 = Vvar__0__C__9645 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__9652,Vvar__0__C__9653,Vvar__1___24Anonymous__9654,Vvar__1___24Anonymous__9655] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__9652,Vvar__1___24Anonymous__9654) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__9653,Vvar__1___24Anonymous__9655)
=> ( Vvar__1___24Anonymous__9654 = Vvar__1___24Anonymous__9655
& Vvar__0__C__9652 = Vvar__0__C__9653 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__9656,Vvar__0__C__9657,Vvar__1___24Anonymous__9658,Vvar__1___24Anonymous__9659,Vvar__2___24Anonymous__9660,Vvar__2___24Anonymous__9661] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__9656,Vvar__1___24Anonymous__9658,Vvar__2___24Anonymous__9660) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__9657,Vvar__1___24Anonymous__9659,Vvar__2___24Anonymous__9661)
=> ( Vvar__2___24Anonymous__9660 = Vvar__2___24Anonymous__9661
& Vvar__1___24Anonymous__9658 = Vvar__1___24Anonymous__9659
& Vvar__0__C__9656 = Vvar__0__C__9657 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__9648,Vvar__0__C__9649,Vvar__1___24Anonymous__9650,Vvar__1___24Anonymous__9651] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__9648,Vvar__1___24Anonymous__9650) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__9649,Vvar__1___24Anonymous__9651)
=> ( Vvar__1___24Anonymous__9650 = Vvar__1___24Anonymous__9651
& Vvar__0__C__9648 = Vvar__0__C__9649 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__9668,Vvar__0__C__9669,Vvar__1___24Anonymous__9670,Vvar__1___24Anonymous__9671,Vvar__2___24Anonymous__9672,Vvar__2___24Anonymous__9673] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__9668,Vvar__1___24Anonymous__9670,Vvar__2___24Anonymous__9672) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__9669,Vvar__1___24Anonymous__9671,Vvar__2___24Anonymous__9673)
=> ( Vvar__2___24Anonymous__9672 = Vvar__2___24Anonymous__9673
& Vvar__1___24Anonymous__9670 = Vvar__1___24Anonymous__9671
& Vvar__0__C__9668 = Vvar__0__C__9669 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__9674,Vvar__0__C__9675,Vvar__1___24Anonymous__9676,Vvar__1___24Anonymous__9677] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__9674,Vvar__1___24Anonymous__9676) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__9675,Vvar__1___24Anonymous__9677)
=> ( Vvar__1___24Anonymous__9676 = Vvar__1___24Anonymous__9677
& Vvar__0__C__9674 = Vvar__0__C__9675 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__9678,Vvar__0__C__9679,Vvar__1___24Anonymous__9680,Vvar__1___24Anonymous__9681,Vvar__2___24Anonymous__9682,Vvar__2___24Anonymous__9683] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__9678,Vvar__1___24Anonymous__9680,Vvar__2___24Anonymous__9682) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__9679,Vvar__1___24Anonymous__9681,Vvar__2___24Anonymous__9683)
=> ( Vvar__2___24Anonymous__9682 = Vvar__2___24Anonymous__9683
& Vvar__1___24Anonymous__9680 = Vvar__1___24Anonymous__9681
& Vvar__0__C__9678 = Vvar__0__C__9679 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__9662,Vvar__0__C__9663,Vvar__1___24Anonymous__9664,Vvar__1___24Anonymous__9665,Vvar__2___24Anonymous__9666,Vvar__2___24Anonymous__9667] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__9662,Vvar__1___24Anonymous__9664,Vvar__2___24Anonymous__9666) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__9663,Vvar__1___24Anonymous__9665,Vvar__2___24Anonymous__9667)
=> ( Vvar__2___24Anonymous__9666 = Vvar__2___24Anonymous__9667
& Vvar__1___24Anonymous__9664 = Vvar__1___24Anonymous__9665
& Vvar__0__C__9662 = Vvar__0__C__9663 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__9433,Vvar__0__C__9434,Vvar__1___24Anonymous__9435,Vvar__1___24Anonymous__9436,Vvar__2___24Anonymous__9437,Vvar__2___24Anonymous__9438,Vvar__3___24Anonymous__9439,Vvar__3___24Anonymous__9440] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__9433,Vvar__1___24Anonymous__9435,Vvar__2___24Anonymous__9437,Vvar__3___24Anonymous__9439) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__9434,Vvar__1___24Anonymous__9436,Vvar__2___24Anonymous__9438,Vvar__3___24Anonymous__9440)
=> ( Vvar__3___24Anonymous__9439 = Vvar__3___24Anonymous__9440
& Vvar__2___24Anonymous__9437 = Vvar__2___24Anonymous__9438
& Vvar__1___24Anonymous__9435 = Vvar__1___24Anonymous__9436
& Vvar__0__C__9433 = Vvar__0__C__9434 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__9423,Vvar__0__C__9424,Vvar__1___24Anonymous__9425,Vvar__1___24Anonymous__9426] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__9423,Vvar__1___24Anonymous__9425) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__9424,Vvar__1___24Anonymous__9426)
=> ( Vvar__1___24Anonymous__9425 = Vvar__1___24Anonymous__9426
& Vvar__0__C__9423 = Vvar__0__C__9424 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__9427,Vvar__0__C__9428,Vvar__1___24Anonymous__9429,Vvar__1___24Anonymous__9430,Vvar__2___24Anonymous__9431,Vvar__2___24Anonymous__9432] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__9427,Vvar__1___24Anonymous__9429,Vvar__2___24Anonymous__9431) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__9428,Vvar__1___24Anonymous__9430,Vvar__2___24Anonymous__9432)
=> ( Vvar__2___24Anonymous__9431 = Vvar__2___24Anonymous__9432
& Vvar__1___24Anonymous__9429 = Vvar__1___24Anonymous__9430
& Vvar__0__C__9427 = Vvar__0__C__9428 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__9458,Vvar__0___24Anonymous__9459,Vvar__1___24Anonymous__9460,Vvar__1___24Anonymous__9461] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__9458,Vvar__1___24Anonymous__9460) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__9459,Vvar__1___24Anonymous__9461)
=> ( Vvar__1___24Anonymous__9460 = Vvar__1___24Anonymous__9461
& Vvar__0___24Anonymous__9458 = Vvar__0___24Anonymous__9459 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__9454,Vvar__0___24Anonymous__9455,Vvar__1___24Anonymous__9456,Vvar__1___24Anonymous__9457] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__9454,Vvar__1___24Anonymous__9456) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__9455,Vvar__1___24Anonymous__9457)
=> ( Vvar__1___24Anonymous__9456 = Vvar__1___24Anonymous__9457
& Vvar__0___24Anonymous__9454 = Vvar__0___24Anonymous__9455 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__15428,Vvar__0__R__15429,Vvar__1__req__15430,Vvar__1__req__15431,Vvar__2__reqb__15432,Vvar__2__reqb__15433,Vvar__3___24Anonymous__15434,Vvar__3___24Anonymous__15435] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__15428,Vvar__1__req__15430,Vvar__2__reqb__15432) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__15429,Vvar__1__req__15431,Vvar__2__reqb__15433)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__15432 = Vvar__2__reqb__15433
& Vvar__1__req__15430 = Vvar__1__req__15431
& Vvar__0__R__15428 = Vvar__0__R__15429 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__15436,Vvar__0__R__15437,Vvar__1__rO__15438,Vvar__1__rO__15439,Vvar__2__rI__15440,Vvar__2__rI__15441,Vvar__3__radd__15442,Vvar__3__radd__15443,Vvar__4__rmul__15444,Vvar__4__rmul__15445,Vvar__5__rsub__15446,Vvar__5__rsub__15447,Vvar__6__ropp__15448,Vvar__6__ropp__15449,Vvar__7__req__15450,Vvar__7__req__15451,Vvar__8__C__15452,Vvar__8__C__15453,Vvar__9__cO__15454,Vvar__9__cO__15455,Vvar__10__cI__15456,Vvar__10__cI__15457,Vvar__11__cadd__15458,Vvar__11__cadd__15459,Vvar__12__cmul__15460,Vvar__12__cmul__15461,Vvar__13__csub__15462,Vvar__13__csub__15463,Vvar__14__copp__15464,Vvar__14__copp__15465,Vvar__15__ceqb__15466,Vvar__15__ceqb__15467,Vvar__16__phi__15468,Vvar__16__phi__15469,Vvar__17___24Anonymous__15470,Vvar__17___24Anonymous__15471] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__15436,Vvar__1__rO__15438,Vvar__2__rI__15440,Vvar__3__radd__15442,Vvar__4__rmul__15444,Vvar__5__rsub__15446,Vvar__6__ropp__15448,Vvar__7__req__15450,Vvar__8__C__15452,Vvar__9__cO__15454,Vvar__10__cI__15456,Vvar__11__cadd__15458,Vvar__12__cmul__15460,Vvar__13__csub__15462,Vvar__14__copp__15464,Vvar__15__ceqb__15466,Vvar__16__phi__15468) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__15437,Vvar__1__rO__15439,Vvar__2__rI__15441,Vvar__3__radd__15443,Vvar__4__rmul__15445,Vvar__5__rsub__15447,Vvar__6__ropp__15449,Vvar__7__req__15451,Vvar__8__C__15453,Vvar__9__cO__15455,Vvar__10__cI__15457,Vvar__11__cadd__15459,Vvar__12__cmul__15461,Vvar__13__csub__15463,Vvar__14__copp__15465,Vvar__15__ceqb__15467,Vvar__16__phi__15469)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__15468 = Vvar__16__phi__15469
& Vvar__15__ceqb__15466 = Vvar__15__ceqb__15467
& Vvar__14__copp__15464 = Vvar__14__copp__15465
& Vvar__13__csub__15462 = Vvar__13__csub__15463
& Vvar__12__cmul__15460 = Vvar__12__cmul__15461
& Vvar__11__cadd__15458 = Vvar__11__cadd__15459
& Vvar__10__cI__15456 = Vvar__10__cI__15457
& Vvar__9__cO__15454 = Vvar__9__cO__15455
& Vvar__8__C__15452 = Vvar__8__C__15453
& Vvar__7__req__15450 = Vvar__7__req__15451
& Vvar__6__ropp__15448 = Vvar__6__ropp__15449
& Vvar__5__rsub__15446 = Vvar__5__rsub__15447
& Vvar__4__rmul__15444 = Vvar__4__rmul__15445
& Vvar__3__radd__15442 = Vvar__3__radd__15443
& Vvar__2__rI__15440 = Vvar__2__rI__15441
& Vvar__1__rO__15438 = Vvar__1__rO__15439
& Vvar__0__R__15436 = Vvar__0__R__15437 ) ) ).
fof('$_inj_hahn.HahnBase.Equality.Mixin',axiom,
! [Vvar__0__T__16452,Vvar__0__T__16453,Vvar__1__op__16454,Vvar__1__op__16455,Vvar__2___24Anonymous__16456,Vvar__2___24Anonymous__16457] :
( chahn_2eHahnBase_2eEquality_2eMixin___24a3(Vvar__0__T__16452,Vvar__1__op__16454,Vvar__2___24Anonymous__16456) = chahn_2eHahnBase_2eEquality_2eMixin___24a3(Vvar__0__T__16453,Vvar__1__op__16455,Vvar__2___24Anonymous__16457)
=> ( Vvar__2___24Anonymous__16456 = Vvar__2___24Anonymous__16457
& Vvar__1__op__16454 = Vvar__1__op__16455
& Vvar__0__T__16452 = Vvar__0__T__16453 ) ) ).
fof('$_inj_hahn.HahnBase.Equality.Pack',axiom,
! [Vvar__0__sort__16462,Vvar__0__sort__16463,Vvar__1___24Anonymous__16464,Vvar__1___24Anonymous__16465,Vvar__2___24Anonymous__16466,Vvar__2___24Anonymous__16467] :
( chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__16462,Vvar__1___24Anonymous__16464,Vvar__2___24Anonymous__16466) = chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__16463,Vvar__1___24Anonymous__16465,Vvar__2___24Anonymous__16467)
=> ( Vvar__2___24Anonymous__16466 = Vvar__2___24Anonymous__16467
& Vvar__1___24Anonymous__16464 = Vvar__1___24Anonymous__16465
& Vvar__0__sort__16462 = Vvar__0__sort__16463 ) ) ).
fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
! [Vvar__0__P__17205,Vvar__1__Q__17207,Vvar__2__init__17210,Vvar__3___24Anonymous__17211,Vvar__4___24Anonymous__17212] :
( c_24__type__17238___24t(Vvar__0__P__17205,Vvar__1__Q__17207,Vvar__2__init__17210,Vvar__3___24Anonymous__17211,Vvar__4___24Anonymous__17212,Vvar__0__P__17205)
=> ( c_24__type__17246___24t(Vvar__0__P__17205,Vvar__1__Q__17207,Vvar__2__init__17210,Vvar__3___24Anonymous__17211,Vvar__4___24Anonymous__17212,Vvar__1__Q__17207)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__17210)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__17211)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__17212)
=> ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__17205,Vvar__1__Q__17207,Vvar__2__init__17210,Vvar__3___24Anonymous__17211,Vvar__4___24Anonymous__17212)
=> ( ( Vvar__4___24Anonymous__17212 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__3___24Anonymous__17211 = Vvar__2__init__17210 )
| ? [Vvar__3__k__17226] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__17226)
& ? [Vvar__4__l__17227] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__17227)
& ? [Vvar__5__n__17228] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__17228)
& cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__17205,Vvar__1__Q__17207,Vvar__2__init__17210,Vvar__3__k__17226,Vvar__5__n__17228)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__17205,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__17226),Vvar__4__l__17227)
& p(happ(Vvar__1__Q__17207,Vvar__4__l__17227))
& Vvar__4___24Anonymous__17212 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__17228)
& Vvar__3___24Anonymous__17211 = Vvar__4__l__17227 ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__17165,Vvar__1__k__17167,Vvar__2___24Anonymous__17168] :
( c_24__type__17182___24t(Vvar__0__P__17165,Vvar__1__k__17167,Vvar__2___24Anonymous__17168,Vvar__0__P__17165)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__17167)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__17168)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__17165,Vvar__1__k__17167,Vvar__2___24Anonymous__17168)
=> ( Vvar__2___24Anonymous__17168 = Vvar__1__k__17167
| ? [Vvar__2__l__17176] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__17176)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__17165,Vvar__1__k__17167,Vvar__2__l__17176)
& p(happ(Vvar__0__P__17165,Vvar__2__l__17176))
& Vvar__2___24Anonymous__17168 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__17176) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__17184,Vvar__1__k__17186,Vvar__2___24Anonymous__17187] :
( c_24__type__17203___24t(Vvar__0__Q__17184,Vvar__1__k__17186,Vvar__2___24Anonymous__17187,Vvar__0__Q__17184)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__17186)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__17187)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__17184,Vvar__1__k__17186,Vvar__2___24Anonymous__17187)
=> ( ? [Vvar__2__l__17192] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__17192)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__17184,Vvar__1__k__17186,Vvar__2__l__17192)
& Vvar__2___24Anonymous__17187 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__17192) )
| ? [Vvar__2__l__17197] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__17197)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__17186,Vvar__2__l__17197)
& p(happ(Vvar__0__Q__17184,Vvar__2__l__17197))
& Vvar__2___24Anonymous__17187 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__17197) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__5837] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5837)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__5837)
=> ( Vvar__0___24Anonymous__5837 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__5839] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__5839)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__5839)
& Vvar__0___24Anonymous__5837 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__5839) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__5841] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5841)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__5841)
=> ? [Vvar__0__n__5843] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__5843)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__5843)
& Vvar__0___24Anonymous__5841 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__5843) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__5295,Vvar__1___24Anonymous__5296,VX5297] :
( cProp___24t(Vvar__0__P__5295)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__5296)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__5295,Vvar__1___24Anonymous__5296,VX5297)
=> ( ( p(Vvar__0__P__5295)
& Vvar__1___24Anonymous__5296 = cCoq_2eInit_2eDatatypes_2etrue
& VX5297 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5295) )
| ( ~ p(Vvar__0__P__5295)
& Vvar__1___24Anonymous__5296 = cCoq_2eInit_2eDatatypes_2efalse
& VX5297 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5295) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
! [Vvar__0___24Anonymous__23177,Vvar__1___24Anonymous__23178,Vvar__2___24Anonymous__23179] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__23177)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__23178)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__23179)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__23177,Vvar__1___24Anonymous__23178,Vvar__2___24Anonymous__23179)
=> ( ? [Vvar__0__x__23181] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__23181)
& Vvar__2___24Anonymous__23179 = Vvar__0__x__23181
& Vvar__1___24Anonymous__23178 = Vvar__0__x__23181
& Vvar__0___24Anonymous__23177 = Vvar__0__x__23181 )
| ? [Vvar__0__x__23182] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__23182)
& Vvar__2___24Anonymous__23179 = Vvar__0__x__23182
& Vvar__1___24Anonymous__23178 = cCoq_2eInit_2eDatatypes_2eEq
& Vvar__0___24Anonymous__23177 = Vvar__0__x__23182 )
| ? [Vvar__0__x__23183] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__23183)
& Vvar__2___24Anonymous__23179 = Vvar__0__x__23183
& Vvar__1___24Anonymous__23178 = Vvar__0__x__23183
& Vvar__0___24Anonymous__23177 = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0__x__23184] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__23184)
& Vvar__2___24Anonymous__23179 = Vvar__0__x__23184
& Vvar__1___24Anonymous__23178 = cCoq_2eInit_2eDatatypes_2eLt
& Vvar__0___24Anonymous__23177 = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0__x__23185] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__23185)
& Vvar__2___24Anonymous__23179 = Vvar__0__x__23185
& Vvar__1___24Anonymous__23178 = cCoq_2eInit_2eDatatypes_2eGt
& Vvar__0___24Anonymous__23177 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX16604] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX16604)
=> ( VX16604 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__16605] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__16605)
& ? [Vvar__1___24Anonymous__16606] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__16606)
& ? [Vvar__2___24Anonymous__16607] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__16607)
& VX16604 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__16605,Vvar__1___24Anonymous__16606,Vvar__2___24Anonymous__16607) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX5317] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX5317)
=> ( VX5317 = cCoq_2eInit_2eByte_2ex00
| VX5317 = cCoq_2eInit_2eByte_2ex01
| VX5317 = cCoq_2eInit_2eByte_2ex02
| VX5317 = cCoq_2eInit_2eByte_2ex03
| VX5317 = cCoq_2eInit_2eByte_2ex04
| VX5317 = cCoq_2eInit_2eByte_2ex05
| VX5317 = cCoq_2eInit_2eByte_2ex06
| VX5317 = cCoq_2eInit_2eByte_2ex07
| VX5317 = cCoq_2eInit_2eByte_2ex08
| VX5317 = cCoq_2eInit_2eByte_2ex09
| VX5317 = cCoq_2eInit_2eByte_2ex0a
| VX5317 = cCoq_2eInit_2eByte_2ex0b
| VX5317 = cCoq_2eInit_2eByte_2ex0c
| VX5317 = cCoq_2eInit_2eByte_2ex0d
| VX5317 = cCoq_2eInit_2eByte_2ex0e
| VX5317 = cCoq_2eInit_2eByte_2ex0f
| VX5317 = cCoq_2eInit_2eByte_2ex10
| VX5317 = cCoq_2eInit_2eByte_2ex11
| VX5317 = cCoq_2eInit_2eByte_2ex12
| VX5317 = cCoq_2eInit_2eByte_2ex13
| VX5317 = cCoq_2eInit_2eByte_2ex14
| VX5317 = cCoq_2eInit_2eByte_2ex15
| VX5317 = cCoq_2eInit_2eByte_2ex16
| VX5317 = cCoq_2eInit_2eByte_2ex17
| VX5317 = cCoq_2eInit_2eByte_2ex18
| VX5317 = cCoq_2eInit_2eByte_2ex19
| VX5317 = cCoq_2eInit_2eByte_2ex1a
| VX5317 = cCoq_2eInit_2eByte_2ex1b
| VX5317 = cCoq_2eInit_2eByte_2ex1c
| VX5317 = cCoq_2eInit_2eByte_2ex1d
| VX5317 = cCoq_2eInit_2eByte_2ex1e
| VX5317 = cCoq_2eInit_2eByte_2ex1f
| VX5317 = cCoq_2eInit_2eByte_2ex20
| VX5317 = cCoq_2eInit_2eByte_2ex21
| VX5317 = cCoq_2eInit_2eByte_2ex22
| VX5317 = cCoq_2eInit_2eByte_2ex23
| VX5317 = cCoq_2eInit_2eByte_2ex24
| VX5317 = cCoq_2eInit_2eByte_2ex25
| VX5317 = cCoq_2eInit_2eByte_2ex26
| VX5317 = cCoq_2eInit_2eByte_2ex27
| VX5317 = cCoq_2eInit_2eByte_2ex28
| VX5317 = cCoq_2eInit_2eByte_2ex29
| VX5317 = cCoq_2eInit_2eByte_2ex2a
| VX5317 = cCoq_2eInit_2eByte_2ex2b
| VX5317 = cCoq_2eInit_2eByte_2ex2c
| VX5317 = cCoq_2eInit_2eByte_2ex2d
| VX5317 = cCoq_2eInit_2eByte_2ex2e
| VX5317 = cCoq_2eInit_2eByte_2ex2f
| VX5317 = cCoq_2eInit_2eByte_2ex30
| VX5317 = cCoq_2eInit_2eByte_2ex31
| VX5317 = cCoq_2eInit_2eByte_2ex32
| VX5317 = cCoq_2eInit_2eByte_2ex33
| VX5317 = cCoq_2eInit_2eByte_2ex34
| VX5317 = cCoq_2eInit_2eByte_2ex35
| VX5317 = cCoq_2eInit_2eByte_2ex36
| VX5317 = cCoq_2eInit_2eByte_2ex37
| VX5317 = cCoq_2eInit_2eByte_2ex38
| VX5317 = cCoq_2eInit_2eByte_2ex39
| VX5317 = cCoq_2eInit_2eByte_2ex3a
| VX5317 = cCoq_2eInit_2eByte_2ex3b
| VX5317 = cCoq_2eInit_2eByte_2ex3c
| VX5317 = cCoq_2eInit_2eByte_2ex3d
| VX5317 = cCoq_2eInit_2eByte_2ex3e
| VX5317 = cCoq_2eInit_2eByte_2ex3f
| VX5317 = cCoq_2eInit_2eByte_2ex40
| VX5317 = cCoq_2eInit_2eByte_2ex41
| VX5317 = cCoq_2eInit_2eByte_2ex42
| VX5317 = cCoq_2eInit_2eByte_2ex43
| VX5317 = cCoq_2eInit_2eByte_2ex44
| VX5317 = cCoq_2eInit_2eByte_2ex45
| VX5317 = cCoq_2eInit_2eByte_2ex46
| VX5317 = cCoq_2eInit_2eByte_2ex47
| VX5317 = cCoq_2eInit_2eByte_2ex48
| VX5317 = cCoq_2eInit_2eByte_2ex49
| VX5317 = cCoq_2eInit_2eByte_2ex4a
| VX5317 = cCoq_2eInit_2eByte_2ex4b
| VX5317 = cCoq_2eInit_2eByte_2ex4c
| VX5317 = cCoq_2eInit_2eByte_2ex4d
| VX5317 = cCoq_2eInit_2eByte_2ex4e
| VX5317 = cCoq_2eInit_2eByte_2ex4f
| VX5317 = cCoq_2eInit_2eByte_2ex50
| VX5317 = cCoq_2eInit_2eByte_2ex51
| VX5317 = cCoq_2eInit_2eByte_2ex52
| VX5317 = cCoq_2eInit_2eByte_2ex53
| VX5317 = cCoq_2eInit_2eByte_2ex54
| VX5317 = cCoq_2eInit_2eByte_2ex55
| VX5317 = cCoq_2eInit_2eByte_2ex56
| VX5317 = cCoq_2eInit_2eByte_2ex57
| VX5317 = cCoq_2eInit_2eByte_2ex58
| VX5317 = cCoq_2eInit_2eByte_2ex59
| VX5317 = cCoq_2eInit_2eByte_2ex5a
| VX5317 = cCoq_2eInit_2eByte_2ex5b
| VX5317 = cCoq_2eInit_2eByte_2ex5c
| VX5317 = cCoq_2eInit_2eByte_2ex5d
| VX5317 = cCoq_2eInit_2eByte_2ex5e
| VX5317 = cCoq_2eInit_2eByte_2ex5f
| VX5317 = cCoq_2eInit_2eByte_2ex60
| VX5317 = cCoq_2eInit_2eByte_2ex61
| VX5317 = cCoq_2eInit_2eByte_2ex62
| VX5317 = cCoq_2eInit_2eByte_2ex63
| VX5317 = cCoq_2eInit_2eByte_2ex64
| VX5317 = cCoq_2eInit_2eByte_2ex65
| VX5317 = cCoq_2eInit_2eByte_2ex66
| VX5317 = cCoq_2eInit_2eByte_2ex67
| VX5317 = cCoq_2eInit_2eByte_2ex68
| VX5317 = cCoq_2eInit_2eByte_2ex69
| VX5317 = cCoq_2eInit_2eByte_2ex6a
| VX5317 = cCoq_2eInit_2eByte_2ex6b
| VX5317 = cCoq_2eInit_2eByte_2ex6c
| VX5317 = cCoq_2eInit_2eByte_2ex6d
| VX5317 = cCoq_2eInit_2eByte_2ex6e
| VX5317 = cCoq_2eInit_2eByte_2ex6f
| VX5317 = cCoq_2eInit_2eByte_2ex70
| VX5317 = cCoq_2eInit_2eByte_2ex71
| VX5317 = cCoq_2eInit_2eByte_2ex72
| VX5317 = cCoq_2eInit_2eByte_2ex73
| VX5317 = cCoq_2eInit_2eByte_2ex74
| VX5317 = cCoq_2eInit_2eByte_2ex75
| VX5317 = cCoq_2eInit_2eByte_2ex76
| VX5317 = cCoq_2eInit_2eByte_2ex77
| VX5317 = cCoq_2eInit_2eByte_2ex78
| VX5317 = cCoq_2eInit_2eByte_2ex79
| VX5317 = cCoq_2eInit_2eByte_2ex7a
| VX5317 = cCoq_2eInit_2eByte_2ex7b
| VX5317 = cCoq_2eInit_2eByte_2ex7c
| VX5317 = cCoq_2eInit_2eByte_2ex7d
| VX5317 = cCoq_2eInit_2eByte_2ex7e
| VX5317 = cCoq_2eInit_2eByte_2ex7f
| VX5317 = cCoq_2eInit_2eByte_2ex80
| VX5317 = cCoq_2eInit_2eByte_2ex81
| VX5317 = cCoq_2eInit_2eByte_2ex82
| VX5317 = cCoq_2eInit_2eByte_2ex83
| VX5317 = cCoq_2eInit_2eByte_2ex84
| VX5317 = cCoq_2eInit_2eByte_2ex85
| VX5317 = cCoq_2eInit_2eByte_2ex86
| VX5317 = cCoq_2eInit_2eByte_2ex87
| VX5317 = cCoq_2eInit_2eByte_2ex88
| VX5317 = cCoq_2eInit_2eByte_2ex89
| VX5317 = cCoq_2eInit_2eByte_2ex8a
| VX5317 = cCoq_2eInit_2eByte_2ex8b
| VX5317 = cCoq_2eInit_2eByte_2ex8c
| VX5317 = cCoq_2eInit_2eByte_2ex8d
| VX5317 = cCoq_2eInit_2eByte_2ex8e
| VX5317 = cCoq_2eInit_2eByte_2ex8f
| VX5317 = cCoq_2eInit_2eByte_2ex90
| VX5317 = cCoq_2eInit_2eByte_2ex91
| VX5317 = cCoq_2eInit_2eByte_2ex92
| VX5317 = cCoq_2eInit_2eByte_2ex93
| VX5317 = cCoq_2eInit_2eByte_2ex94
| VX5317 = cCoq_2eInit_2eByte_2ex95
| VX5317 = cCoq_2eInit_2eByte_2ex96
| VX5317 = cCoq_2eInit_2eByte_2ex97
| VX5317 = cCoq_2eInit_2eByte_2ex98
| VX5317 = cCoq_2eInit_2eByte_2ex99
| VX5317 = cCoq_2eInit_2eByte_2ex9a
| VX5317 = cCoq_2eInit_2eByte_2ex9b
| VX5317 = cCoq_2eInit_2eByte_2ex9c
| VX5317 = cCoq_2eInit_2eByte_2ex9d
| VX5317 = cCoq_2eInit_2eByte_2ex9e
| VX5317 = cCoq_2eInit_2eByte_2ex9f
| VX5317 = cCoq_2eInit_2eByte_2exa0
| VX5317 = cCoq_2eInit_2eByte_2exa1
| VX5317 = cCoq_2eInit_2eByte_2exa2
| VX5317 = cCoq_2eInit_2eByte_2exa3
| VX5317 = cCoq_2eInit_2eByte_2exa4
| VX5317 = cCoq_2eInit_2eByte_2exa5
| VX5317 = cCoq_2eInit_2eByte_2exa6
| VX5317 = cCoq_2eInit_2eByte_2exa7
| VX5317 = cCoq_2eInit_2eByte_2exa8
| VX5317 = cCoq_2eInit_2eByte_2exa9
| VX5317 = cCoq_2eInit_2eByte_2exaa
| VX5317 = cCoq_2eInit_2eByte_2exab
| VX5317 = cCoq_2eInit_2eByte_2exac
| VX5317 = cCoq_2eInit_2eByte_2exad
| VX5317 = cCoq_2eInit_2eByte_2exae
| VX5317 = cCoq_2eInit_2eByte_2exaf
| VX5317 = cCoq_2eInit_2eByte_2exb0
| VX5317 = cCoq_2eInit_2eByte_2exb1
| VX5317 = cCoq_2eInit_2eByte_2exb2
| VX5317 = cCoq_2eInit_2eByte_2exb3
| VX5317 = cCoq_2eInit_2eByte_2exb4
| VX5317 = cCoq_2eInit_2eByte_2exb5
| VX5317 = cCoq_2eInit_2eByte_2exb6
| VX5317 = cCoq_2eInit_2eByte_2exb7
| VX5317 = cCoq_2eInit_2eByte_2exb8
| VX5317 = cCoq_2eInit_2eByte_2exb9
| VX5317 = cCoq_2eInit_2eByte_2exba
| VX5317 = cCoq_2eInit_2eByte_2exbb
| VX5317 = cCoq_2eInit_2eByte_2exbc
| VX5317 = cCoq_2eInit_2eByte_2exbd
| VX5317 = cCoq_2eInit_2eByte_2exbe
| VX5317 = cCoq_2eInit_2eByte_2exbf
| VX5317 = cCoq_2eInit_2eByte_2exc0
| VX5317 = cCoq_2eInit_2eByte_2exc1
| VX5317 = cCoq_2eInit_2eByte_2exc2
| VX5317 = cCoq_2eInit_2eByte_2exc3
| VX5317 = cCoq_2eInit_2eByte_2exc4
| VX5317 = cCoq_2eInit_2eByte_2exc5
| VX5317 = cCoq_2eInit_2eByte_2exc6
| VX5317 = cCoq_2eInit_2eByte_2exc7
| VX5317 = cCoq_2eInit_2eByte_2exc8
| VX5317 = cCoq_2eInit_2eByte_2exc9
| VX5317 = cCoq_2eInit_2eByte_2exca
| VX5317 = cCoq_2eInit_2eByte_2excb
| VX5317 = cCoq_2eInit_2eByte_2excc
| VX5317 = cCoq_2eInit_2eByte_2excd
| VX5317 = cCoq_2eInit_2eByte_2exce
| VX5317 = cCoq_2eInit_2eByte_2excf
| VX5317 = cCoq_2eInit_2eByte_2exd0
| VX5317 = cCoq_2eInit_2eByte_2exd1
| VX5317 = cCoq_2eInit_2eByte_2exd2
| VX5317 = cCoq_2eInit_2eByte_2exd3
| VX5317 = cCoq_2eInit_2eByte_2exd4
| VX5317 = cCoq_2eInit_2eByte_2exd5
| VX5317 = cCoq_2eInit_2eByte_2exd6
| VX5317 = cCoq_2eInit_2eByte_2exd7
| VX5317 = cCoq_2eInit_2eByte_2exd8
| VX5317 = cCoq_2eInit_2eByte_2exd9
| VX5317 = cCoq_2eInit_2eByte_2exda
| VX5317 = cCoq_2eInit_2eByte_2exdb
| VX5317 = cCoq_2eInit_2eByte_2exdc
| VX5317 = cCoq_2eInit_2eByte_2exdd
| VX5317 = cCoq_2eInit_2eByte_2exde
| VX5317 = cCoq_2eInit_2eByte_2exdf
| VX5317 = cCoq_2eInit_2eByte_2exe0
| VX5317 = cCoq_2eInit_2eByte_2exe1
| VX5317 = cCoq_2eInit_2eByte_2exe2
| VX5317 = cCoq_2eInit_2eByte_2exe3
| VX5317 = cCoq_2eInit_2eByte_2exe4
| VX5317 = cCoq_2eInit_2eByte_2exe5
| VX5317 = cCoq_2eInit_2eByte_2exe6
| VX5317 = cCoq_2eInit_2eByte_2exe7
| VX5317 = cCoq_2eInit_2eByte_2exe8
| VX5317 = cCoq_2eInit_2eByte_2exe9
| VX5317 = cCoq_2eInit_2eByte_2exea
| VX5317 = cCoq_2eInit_2eByte_2exeb
| VX5317 = cCoq_2eInit_2eByte_2exec
| VX5317 = cCoq_2eInit_2eByte_2exed
| VX5317 = cCoq_2eInit_2eByte_2exee
| VX5317 = cCoq_2eInit_2eByte_2exef
| VX5317 = cCoq_2eInit_2eByte_2exf0
| VX5317 = cCoq_2eInit_2eByte_2exf1
| VX5317 = cCoq_2eInit_2eByte_2exf2
| VX5317 = cCoq_2eInit_2eByte_2exf3
| VX5317 = cCoq_2eInit_2eByte_2exf4
| VX5317 = cCoq_2eInit_2eByte_2exf5
| VX5317 = cCoq_2eInit_2eByte_2exf6
| VX5317 = cCoq_2eInit_2eByte_2exf7
| VX5317 = cCoq_2eInit_2eByte_2exf8
| VX5317 = cCoq_2eInit_2eByte_2exf9
| VX5317 = cCoq_2eInit_2eByte_2exfa
| VX5317 = cCoq_2eInit_2eByte_2exfb
| VX5317 = cCoq_2eInit_2eByte_2exfc
| VX5317 = cCoq_2eInit_2eByte_2exfd
| VX5317 = cCoq_2eInit_2eByte_2exfe
| VX5317 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__5454,Vvar__1__Q__5455,Vvar__2___24Anonymous__5456] :
( cProp___24t(Vvar__0__P__5454)
=> ( cProp___24t(Vvar__1__Q__5455)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__5456)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__5454,Vvar__1__Q__5455,Vvar__2___24Anonymous__5456)
=> ( ( p(Vvar__0__P__5454)
& Vvar__2___24Anonymous__5456 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__5455)
& Vvar__2___24Anonymous__5456 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__5510,Vvar__1__Plt__5511,Vvar__2__Pgt__5512,Vvar__3___24Anonymous__5513] :
( cProp___24t(Vvar__0__Peq__5510)
=> ( cProp___24t(Vvar__1__Plt__5511)
=> ( cProp___24t(Vvar__2__Pgt__5512)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__5513)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__5510,Vvar__1__Plt__5511,Vvar__2__Pgt__5512,Vvar__3___24Anonymous__5513)
=> ( ( p(Vvar__0__Peq__5510)
& Vvar__3___24Anonymous__5513 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__5511)
& Vvar__3___24Anonymous__5513 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__5512)
& Vvar__3___24Anonymous__5513 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__17257,Vvar__1__Plt__17258,Vvar__2__Pgt__17259,Vvar__3___24Anonymous__17260,VX17261] :
( cProp___24t(Vvar__0__Peq__17257)
=> ( cProp___24t(Vvar__1__Plt__17258)
=> ( cProp___24t(Vvar__2__Pgt__17259)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__17260)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__17257,Vvar__1__Plt__17258,Vvar__2__Pgt__17259,Vvar__3___24Anonymous__17260,VX17261)
=> ( ( p(Vvar__0__Peq__17257)
& Vvar__3___24Anonymous__17260 = cCoq_2eInit_2eDatatypes_2eEq
& VX17261 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__17257,Vvar__1__Plt__17258,Vvar__2__Pgt__17259) )
| ( p(Vvar__1__Plt__17258)
& Vvar__3___24Anonymous__17260 = cCoq_2eInit_2eDatatypes_2eLt
& VX17261 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__17257,Vvar__1__Plt__17258,Vvar__2__Pgt__17259) )
| ( p(Vvar__2__Pgt__17259)
& Vvar__3___24Anonymous__17260 = cCoq_2eInit_2eDatatypes_2eGt
& VX17261 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__17257,Vvar__1__Plt__17258,Vvar__2__Pgt__17259) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX1421] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX1421)
=> ( VX1421 = cCoq_2eInit_2eDatatypes_2etrue
| VX1421 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX1487] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX1487)
=> ( VX1487 = cCoq_2eInit_2eDatatypes_2eEq
| VX1487 = cCoq_2eInit_2eDatatypes_2eLt
| VX1487 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
! [Vvar__0___24Anonymous__5452] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__5452)
=> ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__5452)
=> Vvar__0___24Anonymous__5452 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
! [Vvar__0__A__5527,Vvar__1__a__5528,Vvar__2___24Anonymous__5529] :
( cType___24t(Vvar__0__A__5527)
=> ( t(Vvar__1__a__5528,Vvar__0__A__5527)
=> ( t(Vvar__2___24Anonymous__5529,Vvar__0__A__5527)
=> ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__5527,Vvar__1__a__5528,Vvar__2___24Anonymous__5529)
=> Vvar__2___24Anonymous__5529 = Vvar__1__a__5528 ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__407,VX408] :
( cType___24t(Vvar__0__A__407)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__407,VX408)
=> ( VX408 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__407)
| ? [Vvar__1___24Anonymous__411] :
( t(Vvar__1___24Anonymous__411,Vvar__0__A__407)
& ? [Vvar__2___24Anonymous__412] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__407,Vvar__2___24Anonymous__412)
& VX408 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__407,Vvar__1___24Anonymous__411,Vvar__2___24Anonymous__412) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX1422] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX1422)
=> ( VX1422 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__1423] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1423)
& VX1422 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1423) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__1433,VX1434] :
( cType___24t(Vvar__0__A__1433)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__1433,VX1434)
=> ( ? [Vvar__1___24Anonymous__1436] :
( t(Vvar__1___24Anonymous__1436,Vvar__0__A__1433)
& VX1434 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1433,Vvar__1___24Anonymous__1436) )
| VX1434 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1433) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__5494,Vvar__1__B__5495,VX5496] :
( cType___24t(Vvar__0__A__5494)
=> ( cType___24t(Vvar__1__B__5495)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__5494,Vvar__1__B__5495,VX5496)
=> ? [Vvar__2___24Anonymous__5499] :
( t(Vvar__2___24Anonymous__5499,Vvar__0__A__5494)
& ? [Vvar__3___24Anonymous__5500] :
( t(Vvar__3___24Anonymous__5500,Vvar__1__B__5495)
& VX5496 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__5494,Vvar__1__B__5495,Vvar__2___24Anonymous__5499,Vvar__3___24Anonymous__5500) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__5464,Vvar__1__B__5465,VX5466] :
( cType___24t(Vvar__0__A__5464)
=> ( cType___24t(Vvar__1__B__5465)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__5464,Vvar__1__B__5465,VX5466)
=> ( ? [Vvar__2___24Anonymous__5469] :
( t(Vvar__2___24Anonymous__5469,Vvar__0__A__5464)
& VX5466 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__5464,Vvar__1__B__5465,Vvar__2___24Anonymous__5469) )
| ? [Vvar__2___24Anonymous__5472] :
( t(Vvar__2___24Anonymous__5472,Vvar__1__B__5465)
& VX5466 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__5464,Vvar__1__B__5465,Vvar__2___24Anonymous__5472) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX1420] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX1420)
=> VX1420 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
! [VX5676] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(VX5676)
=> ( ? [Vvar__0__i__5677] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__5677)
& ? [Vvar__1__f__5678] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__5678)
& VX5676 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__5677,Vvar__1__f__5678) ) )
| ? [Vvar__0__i__5679] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__5679)
& ? [Vvar__1__f__5680] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__5680)
& ? [Vvar__2__e__5681] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__5681)
& VX5676 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__5679,Vvar__1__f__5680,Vvar__2__e__5681) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX5667] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX5667)
=> ( ? [Vvar__0__d__5668] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__5668)
& VX5667 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__5668) )
| ? [Vvar__0__d__5669] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__5669)
& VX5667 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__5669) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX5536] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX5536)
=> ( VX5536 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__5537] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__5537)
& VX5536 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__5537) )
| ? [Vvar__0___24Anonymous__5538] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__5538)
& VX5536 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__5538) )
| ? [Vvar__0___24Anonymous__5539] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__5539)
& VX5536 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__5539) )
| ? [Vvar__0___24Anonymous__5540] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__5540)
& VX5536 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__5540) )
| ? [Vvar__0___24Anonymous__5541] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__5541)
& VX5536 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__5541) )
| ? [Vvar__0___24Anonymous__5542] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__5542)
& VX5536 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__5542) )
| ? [Vvar__0___24Anonymous__5543] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__5543)
& VX5536 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__5543) )
| ? [Vvar__0___24Anonymous__5544] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__5544)
& VX5536 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__5544) )
| ? [Vvar__0___24Anonymous__5545] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__5545)
& VX5536 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__5545) )
| ? [Vvar__0___24Anonymous__5546] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__5546)
& VX5536 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__5546) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__2787,Vvar__1___24Anonymous__2788] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__2787)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__2788)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__2787,Vvar__1___24Anonymous__2788)
=> ( Vvar__1___24Anonymous__2788 = Vvar__0__n__2787
| ? [Vvar__1__m__2792] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__2792)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__2787,Vvar__1__m__2792)
& Vvar__1___24Anonymous__2788 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__2792) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__15599,Vvar__1__P__15600,VX15603] :
( cType___24t(Vvar__0__A__15599)
=> ( c_24__type__15613___24t(Vvar__0__A__15599,Vvar__1__P__15600,Vvar__1__P__15600)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__15599,Vvar__1__P__15600,VX15603)
=> ? [Vvar__2__x__15608] :
( t(Vvar__2__x__15608,Vvar__0__A__15599)
& p(happ(Vvar__1__P__15600,Vvar__2__x__15608))
& VX15603 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__15599,Vvar__1__P__15600,Vvar__2__x__15608) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__15628,Vvar__1__P__15629,Vvar__2__Q__15632,VX15635] :
( cType___24t(Vvar__0__A__15628)
=> ( c_24__type__15652___24t(Vvar__0__A__15628,Vvar__1__P__15629,Vvar__2__Q__15632,Vvar__1__P__15629)
=> ( c_24__type__15660___24t(Vvar__0__A__15628,Vvar__1__P__15629,Vvar__2__Q__15632,Vvar__2__Q__15632)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__15628,Vvar__1__P__15629,Vvar__2__Q__15632,VX15635)
=> ? [Vvar__3__x__15643] :
( t(Vvar__3__x__15643,Vvar__0__A__15628)
& p(happ(Vvar__1__P__15629,Vvar__3__x__15643))
& p(happ(Vvar__2__Q__15632,Vvar__3__x__15643))
& VX15635 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__15628,Vvar__1__P__15629,Vvar__2__Q__15632,Vvar__3__x__15643) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__15684,Vvar__1__P__15685,VX15688] :
( cType___24t(Vvar__0__A__15684)
=> ( c_24__type__15698___24t(Vvar__0__A__15684,Vvar__1__P__15685,Vvar__1__P__15685)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__15684,Vvar__1__P__15685,VX15688)
=> ? [Vvar__2__x__15693] :
( t(Vvar__2__x__15693,Vvar__0__A__15684)
& ? [Vvar__3___24Anonymous__15694] :
( t(Vvar__3___24Anonymous__15694,happ(Vvar__1__P__15685,Vvar__2__x__15693))
& VX15688 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__15684,Vvar__1__P__15685,Vvar__2__x__15693,Vvar__3___24Anonymous__15694) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__15713,Vvar__1__P__15714,Vvar__2__Q__15717,VX15720] :
( cType___24t(Vvar__0__A__15713)
=> ( c_24__type__15737___24t(Vvar__0__A__15713,Vvar__1__P__15714,Vvar__2__Q__15717,Vvar__1__P__15714)
=> ( c_24__type__15745___24t(Vvar__0__A__15713,Vvar__1__P__15714,Vvar__2__Q__15717,Vvar__2__Q__15717)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__15713,Vvar__1__P__15714,Vvar__2__Q__15717,VX15720)
=> ? [Vvar__3__x__15728] :
( t(Vvar__3__x__15728,Vvar__0__A__15713)
& ? [Vvar__4___24Anonymous__15729] :
( t(Vvar__4___24Anonymous__15729,happ(Vvar__1__P__15714,Vvar__3__x__15728))
& ? [Vvar__5___24Anonymous__15730] :
( t(Vvar__5___24Anonymous__15730,happ(Vvar__2__Q__15717,Vvar__3__x__15728))
& VX15720 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__15713,Vvar__1__P__15714,Vvar__2__Q__15717,Vvar__3__x__15728,Vvar__4___24Anonymous__15729,Vvar__5___24Anonymous__15730) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__4334,Vvar__1__B__4335,VX4336] :
( cProp___24t(Vvar__0__A__4334)
=> ( cProp___24t(Vvar__1__B__4335)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__4334,Vvar__1__B__4335,VX4336)
=> ( ( p(Vvar__0__A__4334)
& VX4336 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__4334,Vvar__1__B__4335) )
| ( p(Vvar__1__B__4335)
& VX4336 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__4334,Vvar__1__B__4335) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__15769,Vvar__1__B__15770,VX15771] :
( cType___24t(Vvar__0__A__15769)
=> ( cProp___24t(Vvar__1__B__15770)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__15769,Vvar__1__B__15770,VX15771)
=> ( ? [Vvar__2___24Anonymous__15774] :
( t(Vvar__2___24Anonymous__15774,Vvar__0__A__15769)
& VX15771 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__15769,Vvar__1__B__15770,Vvar__2___24Anonymous__15774) )
| ( p(Vvar__1__B__15770)
& VX15771 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__15769,Vvar__1__B__15770) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__4856,Vvar__1__R__4857,Vvar__2__x__4862] :
( cType___24t(Vvar__0__A__4856)
=> ( c_24__type__4891___24t(Vvar__0__A__4856,Vvar__1__R__4857,Vvar__2__x__4862,Vvar__1__R__4857)
=> ( t(Vvar__2__x__4862,Vvar__0__A__4856)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__4856,Vvar__1__R__4857,Vvar__2__x__4862)
=> ( ! [Vvar__var__var__var__var__3__y__4872__4874__4876__4878__4880] :
( t(Vvar__var__var__var__var__3__y__4872__4874__4876__4878__4880,Vvar__0__A__4856)
=> ( p(happ(happ(Vvar__1__R__4857,Vvar__var__var__var__var__3__y__4872__4874__4876__4878__4880),Vvar__2__x__4862))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__4856,Vvar__1__R__4857,Vvar__var__var__var__var__3__y__4872__4874__4876__4878__4880) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__23429,Vvar__1__P__23430,Vvar__2___24Anonymous__23433] :
( cType___24t(Vvar__0__A__23429)
=> ( c_24__type__23453___24t(Vvar__0__A__23429,Vvar__1__P__23430,Vvar__2___24Anonymous__23433,Vvar__1__P__23430)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23429,Vvar__2___24Anonymous__23433)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__23429,Vvar__1__P__23430,Vvar__2___24Anonymous__23433)
=> ( ? [Vvar__2__x__23439] :
( t(Vvar__2__x__23439,Vvar__0__A__23429)
& ? [Vvar__3__l__23440] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23429,Vvar__3__l__23440)
& p(happ(Vvar__1__P__23430,Vvar__2__x__23439))
& Vvar__2___24Anonymous__23433 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23429,Vvar__2__x__23439,Vvar__3__l__23440) ) )
| ? [Vvar__2__x__23446] :
( t(Vvar__2__x__23446,Vvar__0__A__23429)
& ? [Vvar__3__l__23447] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23429,Vvar__3__l__23447)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__23429,Vvar__1__P__23430,Vvar__3__l__23447)
& Vvar__2___24Anonymous__23433 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23429,Vvar__2__x__23446,Vvar__3__l__23447) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__23455,Vvar__1__P__23456,Vvar__2___24Anonymous__23459] :
( cType___24t(Vvar__0__A__23455)
=> ( c_24__type__23477___24t(Vvar__0__A__23455,Vvar__1__P__23456,Vvar__2___24Anonymous__23459,Vvar__1__P__23456)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23455,Vvar__2___24Anonymous__23459)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__23455,Vvar__1__P__23456,Vvar__2___24Anonymous__23459)
=> ( Vvar__2___24Anonymous__23459 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23455)
| ? [Vvar__2__x__23469] :
( t(Vvar__2__x__23469,Vvar__0__A__23455)
& ? [Vvar__3__l__23470] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23455,Vvar__3__l__23470)
& p(happ(Vvar__1__P__23456,Vvar__2__x__23469))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__23455,Vvar__1__P__23456,Vvar__3__l__23470)
& Vvar__2___24Anonymous__23459 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23455,Vvar__2__x__23469,Vvar__3__l__23470) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__23479,Vvar__1__B__23480,Vvar__2__R__23481,Vvar__3___24Anonymous__23486,Vvar__4___24Anonymous__23487] :
( cType___24t(Vvar__0__A__23479)
=> ( cType___24t(Vvar__1__B__23480)
=> ( c_24__type__23524___24t(Vvar__0__A__23479,Vvar__1__B__23480,Vvar__2__R__23481,Vvar__3___24Anonymous__23486,Vvar__4___24Anonymous__23487,Vvar__2__R__23481)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23479,Vvar__3___24Anonymous__23486)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__23480,Vvar__4___24Anonymous__23487)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__23479,Vvar__1__B__23480,Vvar__2__R__23481,Vvar__3___24Anonymous__23486,Vvar__4___24Anonymous__23487)
=> ( ( Vvar__4___24Anonymous__23487 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__23480)
& Vvar__3___24Anonymous__23486 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23479) )
| ? [Vvar__3__x__23503] :
( t(Vvar__3__x__23503,Vvar__0__A__23479)
& ? [Vvar__4__y__23504] :
( t(Vvar__4__y__23504,Vvar__1__B__23480)
& ? [Vvar__5__l__23505] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23479,Vvar__5__l__23505)
& ? [Vvar__6__l_27__23506] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__23480,Vvar__6__l_27__23506)
& p(happ(happ(Vvar__2__R__23481,Vvar__3__x__23503),Vvar__4__y__23504))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__23479,Vvar__1__B__23480,Vvar__2__R__23481,Vvar__5__l__23505,Vvar__6__l_27__23506)
& Vvar__4___24Anonymous__23487 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__23480,Vvar__4__y__23504,Vvar__6__l_27__23506)
& Vvar__3___24Anonymous__23486 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23479,Vvar__3__x__23503,Vvar__5__l__23505) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__23526,Vvar__1__R__23527,Vvar__2___24Anonymous__23532] :
( cType___24t(Vvar__0__A__23526)
=> ( c_24__type__23559___24t(Vvar__0__A__23526,Vvar__1__R__23527,Vvar__2___24Anonymous__23532,Vvar__1__R__23527)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23526,Vvar__2___24Anonymous__23532)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__23526,Vvar__1__R__23527,Vvar__2___24Anonymous__23532)
=> ( Vvar__2___24Anonymous__23532 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23526)
| ? [Vvar__2__a__23546] :
( t(Vvar__2__a__23546,Vvar__0__A__23526)
& ? [Vvar__3__l__23547] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23526,Vvar__3__l__23547)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__23526,happ(Vvar__1__R__23527,Vvar__2__a__23546),Vvar__3__l__23547)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__23526,Vvar__1__R__23527,Vvar__3__l__23547)
& Vvar__2___24Anonymous__23532 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23526,Vvar__2__a__23546,Vvar__3__l__23547) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__2741,Vvar__1___24Anonymous__2742] :
( cType___24t(Vvar__0__A__2741)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2741,Vvar__1___24Anonymous__2742)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__2741,Vvar__1___24Anonymous__2742)
=> ( Vvar__1___24Anonymous__2742 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2741)
| ? [Vvar__1__x__2746] :
( t(Vvar__1__x__2746,Vvar__0__A__2741)
& ? [Vvar__2__l__2747] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2741,Vvar__2__l__2747)
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__2741,Vvar__1__x__2746,Vvar__2__l__2747))
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__2741,Vvar__2__l__2747)
& Vvar__1___24Anonymous__2742 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2741,Vvar__1__x__2746,Vvar__2__l__2747) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__22997,Vvar__1__eqA__22998,Vvar__2__x__23003,Vvar__3___24Anonymous__23004] :
( cType___24t(Vvar__0__A__22997)
=> ( c_24__type__23037___24t(Vvar__0__A__22997,Vvar__1__eqA__22998,Vvar__2__x__23003,Vvar__3___24Anonymous__23004,Vvar__1__eqA__22998)
=> ( t(Vvar__2__x__23003,Vvar__0__A__22997)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22997,Vvar__3___24Anonymous__23004)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__22997,Vvar__1__eqA__22998,Vvar__2__x__23003,Vvar__3___24Anonymous__23004)
=> ( ? [Vvar__3__y__23013] :
( t(Vvar__3__y__23013,Vvar__0__A__22997)
& ? [Vvar__4__l__23014] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22997,Vvar__4__l__23014)
& p(happ(happ(Vvar__1__eqA__22998,Vvar__2__x__23003),Vvar__3__y__23013))
& Vvar__3___24Anonymous__23004 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22997,Vvar__3__y__23013,Vvar__4__l__23014) ) )
| ? [Vvar__3__y__23023] :
( t(Vvar__3__y__23023,Vvar__0__A__22997)
& ? [Vvar__4__l__23024] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22997,Vvar__4__l__23024)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__22997,Vvar__1__eqA__22998,Vvar__2__x__23003,Vvar__4__l__23024)
& Vvar__3___24Anonymous__23004 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22997,Vvar__3__y__23023,Vvar__4__l__23024) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__23039,Vvar__1__eqA__23040,Vvar__2___24Anonymous__23045] :
( cType___24t(Vvar__0__A__23039)
=> ( c_24__type__23072___24t(Vvar__0__A__23039,Vvar__1__eqA__23040,Vvar__2___24Anonymous__23045,Vvar__1__eqA__23040)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23039,Vvar__2___24Anonymous__23045)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__23039,Vvar__1__eqA__23040,Vvar__2___24Anonymous__23045)
=> ( Vvar__2___24Anonymous__23045 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23039)
| ? [Vvar__2__x__23059] :
( t(Vvar__2__x__23059,Vvar__0__A__23039)
& ? [Vvar__3__l__23060] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23039,Vvar__3__l__23060)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__23039,Vvar__1__eqA__23040,Vvar__2__x__23059,Vvar__3__l__23060)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__23039,Vvar__1__eqA__23040,Vvar__3__l__23060)
& Vvar__2___24Anonymous__23045 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23039,Vvar__2__x__23059,Vvar__3__l__23060) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__24172,Vvar__1__eqA__24173,Vvar__2___24Anonymous__24178,Vvar__3___24Anonymous__24179] :
( cType___24t(Vvar__0__A__24172)
=> ( c_24__type__24210___24t(Vvar__0__A__24172,Vvar__1__eqA__24173,Vvar__2___24Anonymous__24178,Vvar__3___24Anonymous__24179,Vvar__1__eqA__24173)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24172,Vvar__2___24Anonymous__24178)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24172,Vvar__3___24Anonymous__24179)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__24172,Vvar__1__eqA__24173,Vvar__2___24Anonymous__24178,Vvar__3___24Anonymous__24179)
=> ( ( Vvar__3___24Anonymous__24179 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24172)
& Vvar__2___24Anonymous__24178 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24172) )
| ? [Vvar__2__x__24193] :
( t(Vvar__2__x__24193,Vvar__0__A__24172)
& ? [Vvar__3__x_27__24194] :
( t(Vvar__3__x_27__24194,Vvar__0__A__24172)
& ? [Vvar__4__l__24195] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24172,Vvar__4__l__24195)
& ? [Vvar__5__l_27__24196] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24172,Vvar__5__l_27__24196)
& p(happ(happ(Vvar__1__eqA__24173,Vvar__2__x__24193),Vvar__3__x_27__24194))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__24172,Vvar__1__eqA__24173,Vvar__4__l__24195,Vvar__5__l_27__24196)
& Vvar__3___24Anonymous__24179 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24172,Vvar__3__x_27__24194,Vvar__5__l_27__24196)
& Vvar__2___24Anonymous__24178 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24172,Vvar__2__x__24193,Vvar__4__l__24195) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.boolP',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eboolP)
=> p(c_24True) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.has_fixpoint',axiom,
! [Vvar__0__A__5405] :
( cProp___24t(Vvar__0__A__5405)
=> ( cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1(Vvar__0__A__5405)
=> ( ( ( p(Vvar__0__A__5405)
=> p(Vvar__0__A__5405) )
=> p(Vvar__0__A__5405) )
& ( ( p(Vvar__0__A__5405)
=> p(Vvar__0__A__5405) )
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.retract',axiom,
! [Vvar__0__A__5381,Vvar__1__B__5382] :
( cProp___24t(Vvar__0__A__5381)
=> ( cProp___24t(Vvar__1__B__5382)
=> ( cCoq_2eLogic_2eClassicalFacts_2eretract___24a2(Vvar__0__A__5381,Vvar__1__B__5382)
=> ( ( p(Vvar__0__A__5381)
=> p(Vvar__1__B__5382) )
& ( p(Vvar__1__B__5382)
=> p(Vvar__0__A__5381) )
& ( p(Vvar__1__B__5382)
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__5785,Vvar__1__P__5786,Vvar__2__p__5789,Vvar__3__x__5790,Vvar__4__q__5791,Vvar__5___24Anonymous__5792] :
( cType___24t(Vvar__0__U__5785)
=> ( c_24__type__5807___24t(Vvar__0__U__5785,Vvar__1__P__5786,Vvar__2__p__5789,Vvar__3__x__5790,Vvar__4__q__5791,Vvar__5___24Anonymous__5792,Vvar__1__P__5786)
=> ( t(Vvar__2__p__5789,Vvar__0__U__5785)
=> ( t(Vvar__3__x__5790,happ(Vvar__1__P__5786,Vvar__2__p__5789))
=> ( t(Vvar__4__q__5791,Vvar__0__U__5785)
=> ( t(Vvar__5___24Anonymous__5792,happ(Vvar__1__P__5786,Vvar__4__q__5791))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__5785,Vvar__1__P__5786,Vvar__2__p__5789,Vvar__3__x__5790,Vvar__4__q__5791,Vvar__5___24Anonymous__5792)
=> ( Vvar__5___24Anonymous__5792 = Vvar__3__x__5790
& Vvar__4__q__5791 = Vvar__2__p__5789 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__5809,Vvar__1__P__5810,Vvar__2__p__5813,Vvar__3__x__5814,Vvar__4__q__5815,Vvar__5__y__5816] :
( cType___24t(Vvar__0__U__5809)
=> ( c_24__type__5835___24t(Vvar__0__U__5809,Vvar__1__P__5810,Vvar__2__p__5813,Vvar__3__x__5814,Vvar__4__q__5815,Vvar__5__y__5816,Vvar__1__P__5810)
=> ( t(Vvar__2__p__5813,Vvar__0__U__5809)
=> ( t(Vvar__3__x__5814,happ(Vvar__1__P__5810,Vvar__2__p__5813))
=> ( t(Vvar__4__q__5815,Vvar__0__U__5809)
=> ( t(Vvar__5__y__5816,happ(Vvar__1__P__5810,Vvar__4__q__5815))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__5809,Vvar__1__P__5810,Vvar__2__p__5813,Vvar__3__x__5814,Vvar__4__q__5815,Vvar__5__y__5816)
=> ( Vvar__4__q__5815 = Vvar__2__p__5813
& Vvar__3__x__5814 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__5809,Vvar__4__q__5815,Vvar__1__P__5810,Vvar__5__y__5816,Vvar__2__p__5813)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX1381] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX1381)
=> ( VX1381 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__1382] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1382)
& VX1381 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1382) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX1386] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX1386)
=> ( VX1386 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__1387] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1387)
& VX1386 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1387) )
| ? [Vvar__0___24Anonymous__1388] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1388)
& VX1386 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1388) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX1370] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1370)
=> ( ? [Vvar__0___24Anonymous__1371] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1371)
& VX1370 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1371) )
| ? [Vvar__0___24Anonymous__1372] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1372)
& VX1370 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1372) )
| VX1370 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [Vvar__0___24Anonymous__16538,VX16539] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16538)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__16538,VX16539)
=> ( ( Vvar__0___24Anonymous__16538 = cCoq_2eNumbers_2eBinNums_2exH
& VX16539 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
| ? [Vvar__0__p__16540] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__16540)
& ? [Vvar__1___24Anonymous__16541] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__16540,Vvar__1___24Anonymous__16541)
& Vvar__0___24Anonymous__16538 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2416576___24a2(Vvar__0___24Anonymous__16538,Vvar__0__p__16540)
& VX16539 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__16540,Vvar__1___24Anonymous__16541) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX16519] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX16519)
=> ( VX16519 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__16520] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16520)
& VX16519 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__16520) )
| VX16519 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX9111] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX9111)
=> ? [Vvar__0__Qnum__9112] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__9112)
& ? [Vvar__1__Qden__9113] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__9113)
& VX9111 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9112,Vvar__1__Qden__9113) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
! [VX9139] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(VX9139)
=> ? [Vvar__0__neg__9140] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__9140)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__9140,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX9139 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__9140) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX9118] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX9118)
=> ? [Vvar__0__nonneg__9119] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__9119)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__9119)
& VX9118 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__9119) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
! [VX9132] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX9132)
=> ? [Vvar__0__nonpos__9133] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__9133)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__9133,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX9132 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__9133) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX9146] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX9146)
=> ? [Vvar__0__nonzero__9147] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__9147)
& Vvar__0__nonzero__9147 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX9146 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__9147) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX9125] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX9125)
=> ? [Vvar__0__pos__9126] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__9126)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__9126)
& VX9125 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__9126) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__9158,Vvar__1___24Anonymous__9159,VX9160] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__9158)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__9159)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__9158,Vvar__1___24Anonymous__9159,VX9160)
=> ( ( Vvar__0__x__9158 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__9159 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX9160 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__9158) )
| ? [Vvar__1__n__9164] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__9164)
& Vvar__0__x__9158 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__9164)
& Vvar__1___24Anonymous__9159 = c_24__case__Coq_2eInit_2eDatatypes_2enat_249184___24a3(Vvar__0__x__9158,Vvar__1___24Anonymous__9159,Vvar__1__n__9164)
& VX9160 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__9158,Vvar__1__n__9164) )
| ? [Vvar__1__n__9169] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__9169)
& Vvar__0__x__9158 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__9169))
& Vvar__1___24Anonymous__9159 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_249201___24a3(Vvar__0__x__9158,Vvar__1___24Anonymous__9159,Vvar__1__n__9169)
& VX9160 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__9158,Vvar__1__n__9169) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
! [Vvar__0__A__3052,Vvar__1__R__3053] :
( cType___24t(Vvar__0__A__3052)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3052,Vvar__1__R__3053)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__3052,Vvar__1__R__3053)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__3052,Vvar__1__R__3053)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__3052,Vvar__1__R__3053)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
! [Vvar__0__A__3044,Vvar__1__R__3045] :
( cType___24t(Vvar__0__A__3044)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3044,Vvar__1__R__3045)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__3044,Vvar__1__R__3045)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__3044,Vvar__1__R__3045)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__3044,Vvar__1__R__3045)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__3044,Vvar__1__R__3045)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
! [Vvar__0__A__3036,Vvar__1__R__3037] :
( cType___24t(Vvar__0__A__3036)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3036,Vvar__1__R__3037)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__3036,Vvar__1__R__3037)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__3036,Vvar__1__R__3037)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__3036,Vvar__1__R__3037)
& cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__3036,Vvar__1__R__3037)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__3029,Vvar__1__R__3030] :
( cType___24t(Vvar__0__A__3029)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3029,Vvar__1__R__3030)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__3029,Vvar__1__R__3030)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__3029,Vvar__1__R__3030)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__3029,Vvar__1__R__3030)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__23648,Vvar__1__leA__23649,Vvar__2___24Anonymous__23654] :
( cType___24t(Vvar__0__A__23648)
=> ( c_24__type__23744___24t(Vvar__0__A__23648,Vvar__1__leA__23649,Vvar__2___24Anonymous__23654,Vvar__1__leA__23649)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23648,Vvar__2___24Anonymous__23654)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__23648,Vvar__1__leA__23649,Vvar__2___24Anonymous__23654)
=> ( Vvar__2___24Anonymous__23654 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23648)
| ? [Vvar__2__x__23668] :
( t(Vvar__2__x__23668,Vvar__0__A__23648)
& Vvar__2___24Anonymous__23654 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23648,Vvar__2__x__23668,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23648)) )
| ? [Vvar__2__x__23675] :
( t(Vvar__2__x__23675,Vvar__0__A__23648)
& ? [Vvar__3__y__23676] :
( t(Vvar__3__y__23676,Vvar__0__A__23648)
& ? [Vvar__4__l__23677] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23648,Vvar__4__l__23677)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__23648,Vvar__1__leA__23649,Vvar__2__x__23675,Vvar__3__y__23676)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__23648,Vvar__1__leA__23649,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__23648,Vvar__4__l__23677,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23648,Vvar__3__y__23676,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23648))))
& Vvar__2___24Anonymous__23654 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2423942___24a6(Vvar__0__A__23648,Vvar__1__leA__23649,Vvar__2___24Anonymous__23654,Vvar__2__x__23675,Vvar__3__y__23676,Vvar__4__l__23677) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__23597,Vvar__1__leA__23598,Vvar__2___24Anonymous__23603,Vvar__3___24Anonymous__23604] :
( cType___24t(Vvar__0__A__23597)
=> ( c_24__type__23646___24t(Vvar__0__A__23597,Vvar__1__leA__23598,Vvar__2___24Anonymous__23603,Vvar__3___24Anonymous__23604,Vvar__1__leA__23598)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23597,Vvar__2___24Anonymous__23603)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23597,Vvar__3___24Anonymous__23604)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__23597,Vvar__1__leA__23598,Vvar__2___24Anonymous__23603,Vvar__3___24Anonymous__23604)
=> ( ? [Vvar__2__a__23612] :
( t(Vvar__2__a__23612,Vvar__0__A__23597)
& ? [Vvar__3__x__23613] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23597,Vvar__3__x__23613)
& Vvar__3___24Anonymous__23604 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23597,Vvar__2__a__23612,Vvar__3__x__23613)
& Vvar__2___24Anonymous__23603 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23597) ) )
| ? [Vvar__2__a__23620] :
( t(Vvar__2__a__23620,Vvar__0__A__23597)
& ? [Vvar__3__b__23621] :
( t(Vvar__3__b__23621,Vvar__0__A__23597)
& p(happ(happ(Vvar__1__leA__23598,Vvar__2__a__23620),Vvar__3__b__23621))
& ? [Vvar__5__x__23623] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23597,Vvar__5__x__23623)
& ? [Vvar__6__y__23624] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23597,Vvar__6__y__23624)
& Vvar__3___24Anonymous__23604 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23597,Vvar__3__b__23621,Vvar__6__y__23624)
& Vvar__2___24Anonymous__23603 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23597,Vvar__2__a__23620,Vvar__5__x__23623) ) ) ) )
| ? [Vvar__2__a__23631] :
( t(Vvar__2__a__23631,Vvar__0__A__23597)
& ? [Vvar__3__x__23632] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23597,Vvar__3__x__23632)
& ? [Vvar__4__y__23633] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23597,Vvar__4__y__23633)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__23597,Vvar__1__leA__23598,Vvar__3__x__23632,Vvar__4__y__23633)
& Vvar__3___24Anonymous__23604 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23597,Vvar__2__a__23631,Vvar__4__y__23633)
& Vvar__2___24Anonymous__23603 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23597,Vvar__2__a__23631,Vvar__3__x__23632) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__3128,Vvar__1__R__3129,Vvar__2__x__3130,Vvar__3___24Anonymous__3131] :
( cType___24t(Vvar__0__A__3128)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3128,Vvar__1__R__3129)
=> ( t(Vvar__2__x__3130,Vvar__0__A__3128)
=> ( t(Vvar__3___24Anonymous__3131,Vvar__0__A__3128)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__3128,Vvar__1__R__3129,Vvar__2__x__3130,Vvar__3___24Anonymous__3131)
=> ( ? [Vvar__3__y__3136] :
( t(Vvar__3__y__3136,Vvar__0__A__3128)
& p(happ(happ(Vvar__1__R__3129,Vvar__2__x__3130),Vvar__3__y__3136))
& Vvar__3___24Anonymous__3131 = Vvar__3__y__3136 )
| Vvar__3___24Anonymous__3131 = Vvar__2__x__3130 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans',axiom,
! [Vvar__0__A__3223,Vvar__1__R__3224,Vvar__1___24Anonymous__3225,Vvar__2___24Anonymous__3226] :
( cType___24t(Vvar__0__A__3223)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3223,Vvar__1__R__3224)
=> ( t(Vvar__1___24Anonymous__3225,Vvar__0__A__3223)
=> ( t(Vvar__2___24Anonymous__3226,Vvar__0__A__3223)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__3223,Vvar__1__R__3224,Vvar__1___24Anonymous__3225,Vvar__2___24Anonymous__3226)
=> ( ? [Vvar__2__x__3230] :
( t(Vvar__2__x__3230,Vvar__0__A__3223)
& ? [Vvar__3__y__3231] :
( t(Vvar__3__y__3231,Vvar__0__A__3223)
& p(happ(happ(Vvar__1__R__3224,Vvar__2__x__3230),Vvar__3__y__3231))
& Vvar__2___24Anonymous__3226 = Vvar__3__y__3231
& Vvar__1___24Anonymous__3225 = Vvar__2__x__3230 ) )
| ? [Vvar__2__x__3235] :
( t(Vvar__2__x__3235,Vvar__0__A__3223)
& Vvar__2___24Anonymous__3226 = Vvar__2__x__3235
& Vvar__1___24Anonymous__3225 = Vvar__2__x__3235 )
| ? [Vvar__2__x__3238] :
( t(Vvar__2__x__3238,Vvar__0__A__3223)
& ? [Vvar__3__y__3239] :
( t(Vvar__3__y__3239,Vvar__0__A__3223)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__3223,Vvar__1__R__3224,Vvar__2__x__3238,Vvar__3__y__3239)
& Vvar__2___24Anonymous__3226 = Vvar__2__x__3238
& Vvar__1___24Anonymous__3225 = Vvar__3__y__3239 ) )
| ? [Vvar__2__x__3243] :
( t(Vvar__2__x__3243,Vvar__0__A__3223)
& ? [Vvar__3__y__3244] :
( t(Vvar__3__y__3244,Vvar__0__A__3223)
& ? [Vvar__4__z__3245] :
( t(Vvar__4__z__3245,Vvar__0__A__3223)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__3223,Vvar__1__R__3224,Vvar__2__x__3243,Vvar__3__y__3244)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__3223,Vvar__1__R__3224,Vvar__3__y__3244,Vvar__4__z__3245)
& Vvar__2___24Anonymous__3226 = Vvar__4__z__3245
& Vvar__1___24Anonymous__3225 = Vvar__2__x__3243 ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
! [Vvar__0__A__3284,Vvar__1__R__3285,Vvar__2__x__3286,Vvar__3___24Anonymous__3287] :
( cType___24t(Vvar__0__A__3284)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3284,Vvar__1__R__3285)
=> ( t(Vvar__2__x__3286,Vvar__0__A__3284)
=> ( t(Vvar__3___24Anonymous__3287,Vvar__0__A__3284)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__3284,Vvar__1__R__3285,Vvar__2__x__3286,Vvar__3___24Anonymous__3287)
=> ( Vvar__3___24Anonymous__3287 = Vvar__2__x__3286
| ? [Vvar__3__y__3295] :
( t(Vvar__3__y__3295,Vvar__0__A__3284)
& ? [Vvar__4__z__3296] :
( t(Vvar__4__z__3296,Vvar__0__A__3284)
& ( p(happ(happ(Vvar__1__R__3285,Vvar__2__x__3286),Vvar__3__y__3295))
| p(happ(happ(Vvar__1__R__3285,Vvar__3__y__3295),Vvar__2__x__3286)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__3284,Vvar__1__R__3285,Vvar__3__y__3295,Vvar__4__z__3296)
& Vvar__3___24Anonymous__3287 = Vvar__4__z__3296 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
! [Vvar__0__A__3319,Vvar__1__R__3320,Vvar__2__x__3321,Vvar__3___24Anonymous__3322] :
( cType___24t(Vvar__0__A__3319)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3319,Vvar__1__R__3320)
=> ( t(Vvar__2__x__3321,Vvar__0__A__3319)
=> ( t(Vvar__3___24Anonymous__3322,Vvar__0__A__3319)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__3319,Vvar__1__R__3320,Vvar__2__x__3321,Vvar__3___24Anonymous__3322)
=> ( Vvar__3___24Anonymous__3322 = Vvar__2__x__3321
| ? [Vvar__3__y__3330] :
( t(Vvar__3__y__3330,Vvar__0__A__3319)
& ? [Vvar__4__z__3331] :
( t(Vvar__4__z__3331,Vvar__0__A__3319)
& ( p(happ(happ(Vvar__1__R__3320,Vvar__3__y__3330),Vvar__4__z__3331))
| p(happ(happ(Vvar__1__R__3320,Vvar__4__z__3331),Vvar__3__y__3330)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__3319,Vvar__1__R__3320,Vvar__2__x__3321,Vvar__3__y__3330)
& Vvar__3___24Anonymous__3322 = Vvar__4__z__3331 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
! [Vvar__0__A__119,Vvar__1__R__120,Vvar__2__x__121,Vvar__3___24Anonymous__122] :
( cType___24t(Vvar__0__A__119)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__119,Vvar__1__R__120)
=> ( t(Vvar__2__x__121,Vvar__0__A__119)
=> ( t(Vvar__3___24Anonymous__122,Vvar__0__A__119)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__119,Vvar__1__R__120,Vvar__2__x__121,Vvar__3___24Anonymous__122)
=> ( ? [Vvar__3__y__127] :
( t(Vvar__3__y__127,Vvar__0__A__119)
& p(happ(happ(Vvar__1__R__120,Vvar__2__x__121),Vvar__3__y__127))
& Vvar__3___24Anonymous__122 = Vvar__3__y__127 )
| Vvar__3___24Anonymous__122 = Vvar__2__x__121
| ? [Vvar__3__y__135] :
( t(Vvar__3__y__135,Vvar__0__A__119)
& ? [Vvar__4__z__136] :
( t(Vvar__4__z__136,Vvar__0__A__119)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__119,Vvar__1__R__120,Vvar__2__x__121,Vvar__3__y__135)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__119,Vvar__1__R__120,Vvar__3__y__135,Vvar__4__z__136)
& Vvar__3___24Anonymous__122 = Vvar__4__z__136 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
! [Vvar__0__A__3161,Vvar__1__R__3162,Vvar__2__x__3163,Vvar__3___24Anonymous__3164] :
( cType___24t(Vvar__0__A__3161)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3161,Vvar__1__R__3162)
=> ( t(Vvar__2__x__3163,Vvar__0__A__3161)
=> ( t(Vvar__3___24Anonymous__3164,Vvar__0__A__3161)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__3161,Vvar__1__R__3162,Vvar__2__x__3163,Vvar__3___24Anonymous__3164)
=> ( Vvar__3___24Anonymous__3164 = Vvar__2__x__3163
| ? [Vvar__3__y__3172] :
( t(Vvar__3__y__3172,Vvar__0__A__3161)
& ? [Vvar__4__z__3173] :
( t(Vvar__4__z__3173,Vvar__0__A__3161)
& p(happ(happ(Vvar__1__R__3162,Vvar__2__x__3163),Vvar__3__y__3172))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__3161,Vvar__1__R__3162,Vvar__3__y__3172,Vvar__4__z__3173)
& Vvar__3___24Anonymous__3164 = Vvar__4__z__3173 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
! [Vvar__0__A__3196,Vvar__1__R__3197,Vvar__2__x__3198,Vvar__3___24Anonymous__3199] :
( cType___24t(Vvar__0__A__3196)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3196,Vvar__1__R__3197)
=> ( t(Vvar__2__x__3198,Vvar__0__A__3196)
=> ( t(Vvar__3___24Anonymous__3199,Vvar__0__A__3196)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__3196,Vvar__1__R__3197,Vvar__2__x__3198,Vvar__3___24Anonymous__3199)
=> ( Vvar__3___24Anonymous__3199 = Vvar__2__x__3198
| ? [Vvar__3__y__3207] :
( t(Vvar__3__y__3207,Vvar__0__A__3196)
& ? [Vvar__4__z__3208] :
( t(Vvar__4__z__3208,Vvar__0__A__3196)
& p(happ(happ(Vvar__1__R__3197,Vvar__3__y__3207),Vvar__4__z__3208))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__3196,Vvar__1__R__3197,Vvar__2__x__3198,Vvar__3__y__3207)
& Vvar__3___24Anonymous__3199 = Vvar__4__z__3208 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
! [Vvar__0__A__102,Vvar__1__R__103,Vvar__2__x__104,Vvar__3___24Anonymous__105] :
( cType___24t(Vvar__0__A__102)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__102,Vvar__1__R__103)
=> ( t(Vvar__2__x__104,Vvar__0__A__102)
=> ( t(Vvar__3___24Anonymous__105,Vvar__0__A__102)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__102,Vvar__1__R__103,Vvar__2__x__104,Vvar__3___24Anonymous__105)
=> ( ? [Vvar__3__y__110] :
( t(Vvar__3__y__110,Vvar__0__A__102)
& p(happ(happ(Vvar__1__R__103,Vvar__2__x__104),Vvar__3__y__110))
& Vvar__3___24Anonymous__105 = Vvar__3__y__110 )
| ? [Vvar__3__y__115] :
( t(Vvar__3__y__115,Vvar__0__A__102)
& ? [Vvar__4__z__116] :
( t(Vvar__4__z__116,Vvar__0__A__102)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__102,Vvar__1__R__103,Vvar__2__x__104,Vvar__3__y__115)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__102,Vvar__1__R__103,Vvar__3__y__115,Vvar__4__z__116)
& Vvar__3___24Anonymous__105 = Vvar__4__z__116 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
! [Vvar__0__A__232,Vvar__1__R__233,Vvar__2__x__234,Vvar__3___24Anonymous__235] :
( cType___24t(Vvar__0__A__232)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__232,Vvar__1__R__233)
=> ( t(Vvar__2__x__234,Vvar__0__A__232)
=> ( t(Vvar__3___24Anonymous__235,Vvar__0__A__232)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__232,Vvar__1__R__233,Vvar__2__x__234,Vvar__3___24Anonymous__235)
=> ( ? [Vvar__3__y__240] :
( t(Vvar__3__y__240,Vvar__0__A__232)
& p(happ(happ(Vvar__1__R__233,Vvar__2__x__234),Vvar__3__y__240))
& Vvar__3___24Anonymous__235 = Vvar__3__y__240 )
| ? [Vvar__3__y__245] :
( t(Vvar__3__y__245,Vvar__0__A__232)
& ? [Vvar__4__z__246] :
( t(Vvar__4__z__246,Vvar__0__A__232)
& p(happ(happ(Vvar__1__R__233,Vvar__2__x__234),Vvar__3__y__245))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__232,Vvar__1__R__233,Vvar__3__y__245,Vvar__4__z__246)
& Vvar__3___24Anonymous__235 = Vvar__4__z__246 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
! [Vvar__0__A__3095,Vvar__1__R__3096,Vvar__2__x__3097,Vvar__3___24Anonymous__3098] :
( cType___24t(Vvar__0__A__3095)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3095,Vvar__1__R__3096)
=> ( t(Vvar__2__x__3097,Vvar__0__A__3095)
=> ( t(Vvar__3___24Anonymous__3098,Vvar__0__A__3095)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__3095,Vvar__1__R__3096,Vvar__2__x__3097,Vvar__3___24Anonymous__3098)
=> ( ? [Vvar__3__y__3103] :
( t(Vvar__3__y__3103,Vvar__0__A__3095)
& p(happ(happ(Vvar__1__R__3096,Vvar__2__x__3097),Vvar__3__y__3103))
& Vvar__3___24Anonymous__3098 = Vvar__3__y__3103 )
| ? [Vvar__3__y__3108] :
( t(Vvar__3__y__3108,Vvar__0__A__3095)
& ? [Vvar__4__z__3109] :
( t(Vvar__4__z__3109,Vvar__0__A__3095)
& p(happ(happ(Vvar__1__R__3096,Vvar__3__y__3108),Vvar__4__z__3109))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__3095,Vvar__1__R__3096,Vvar__2__x__3097,Vvar__3__y__3108)
& Vvar__3___24Anonymous__3098 = Vvar__4__z__3109 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Permutation.Permutation',axiom,
! [Vvar__0__A__1346,Vvar__1___24Anonymous__1347,Vvar__2___24Anonymous__1348] :
( cType___24t(Vvar__0__A__1346)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1346,Vvar__1___24Anonymous__1347)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1346,Vvar__2___24Anonymous__1348)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__1346,Vvar__1___24Anonymous__1347,Vvar__2___24Anonymous__1348)
=> ( ( Vvar__2___24Anonymous__1348 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1346)
& Vvar__1___24Anonymous__1347 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1346) )
| ? [Vvar__1__x__1352] :
( t(Vvar__1__x__1352,Vvar__0__A__1346)
& ? [Vvar__2__l__1353] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1346,Vvar__2__l__1353)
& ? [Vvar__3__l_27__1354] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1346,Vvar__3__l_27__1354)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__1346,Vvar__2__l__1353,Vvar__3__l_27__1354)
& Vvar__2___24Anonymous__1348 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1346,Vvar__1__x__1352,Vvar__3__l_27__1354)
& Vvar__1___24Anonymous__1347 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1346,Vvar__1__x__1352,Vvar__2__l__1353) ) ) )
| ? [Vvar__1__x__1357] :
( t(Vvar__1__x__1357,Vvar__0__A__1346)
& ? [Vvar__2__y__1358] :
( t(Vvar__2__y__1358,Vvar__0__A__1346)
& ? [Vvar__3__l__1359] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1346,Vvar__3__l__1359)
& Vvar__2___24Anonymous__1348 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1346,Vvar__1__x__1357,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1346,Vvar__2__y__1358,Vvar__3__l__1359))
& Vvar__1___24Anonymous__1347 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1346,Vvar__2__y__1358,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1346,Vvar__1__x__1357,Vvar__3__l__1359)) ) ) )
| ? [Vvar__1__l__1361] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1346,Vvar__1__l__1361)
& ? [Vvar__2__l_27__1362] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1346,Vvar__2__l_27__1362)
& ? [Vvar__3__l_27_27__1363] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1346,Vvar__3__l_27_27__1363)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__1346,Vvar__1__l__1361,Vvar__2__l_27__1362)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__1346,Vvar__2__l_27__1362,Vvar__3__l_27_27__1363)
& Vvar__2___24Anonymous__1348 = Vvar__3__l_27_27__1363
& Vvar__1___24Anonymous__1347 = Vvar__1__l__1361 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__24255,Vvar__1__R__24256,Vvar__2__a__24261,Vvar__3___24Anonymous__24262] :
( cType___24t(Vvar__0__A__24255)
=> ( c_24__type__24292___24t(Vvar__0__A__24255,Vvar__1__R__24256,Vvar__2__a__24261,Vvar__3___24Anonymous__24262,Vvar__1__R__24256)
=> ( t(Vvar__2__a__24261,Vvar__0__A__24255)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24255,Vvar__3___24Anonymous__24262)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__24255,Vvar__1__R__24256,Vvar__2__a__24261,Vvar__3___24Anonymous__24262)
=> ( Vvar__3___24Anonymous__24262 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24255)
| ? [Vvar__3__b__24278] :
( t(Vvar__3__b__24278,Vvar__0__A__24255)
& ? [Vvar__4__l__24279] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24255,Vvar__4__l__24279)
& p(happ(happ(Vvar__1__R__24256,Vvar__2__a__24261),Vvar__3__b__24278))
& Vvar__3___24Anonymous__24262 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24255,Vvar__3__b__24278,Vvar__4__l__24279) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__24212,Vvar__1__R__24213,Vvar__2___24Anonymous__24218] :
( cType___24t(Vvar__0__A__24212)
=> ( c_24__type__24253___24t(Vvar__0__A__24212,Vvar__1__R__24213,Vvar__2___24Anonymous__24218,Vvar__1__R__24213)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24212,Vvar__2___24Anonymous__24218)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__24212,Vvar__1__R__24213,Vvar__2___24Anonymous__24218)
=> ( Vvar__2___24Anonymous__24218 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24212)
| ? [Vvar__2__a__24232] :
( t(Vvar__2__a__24232,Vvar__0__A__24212)
& Vvar__2___24Anonymous__24218 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24212,Vvar__2__a__24232,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24212)) )
| ? [Vvar__2__a__24239] :
( t(Vvar__2__a__24239,Vvar__0__A__24212)
& ? [Vvar__3__b__24240] :
( t(Vvar__3__b__24240,Vvar__0__A__24212)
& ? [Vvar__4__l__24241] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24212,Vvar__4__l__24241)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__24212,Vvar__1__R__24213,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24212,Vvar__3__b__24240,Vvar__4__l__24241))
& p(happ(happ(Vvar__1__R__24213,Vvar__2__a__24239),Vvar__3__b__24240))
& Vvar__2___24Anonymous__24218 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24212,Vvar__2__a__24239,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24212,Vvar__3__b__24240,Vvar__4__l__24241)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__24294,Vvar__1__R__24295,Vvar__2___24Anonymous__24300] :
( cType___24t(Vvar__0__A__24294)
=> ( c_24__type__24327___24t(Vvar__0__A__24294,Vvar__1__R__24295,Vvar__2___24Anonymous__24300,Vvar__1__R__24295)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24294,Vvar__2___24Anonymous__24300)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__24294,Vvar__1__R__24295,Vvar__2___24Anonymous__24300)
=> ( Vvar__2___24Anonymous__24300 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24294)
| ? [Vvar__2__a__24314] :
( t(Vvar__2__a__24314,Vvar__0__A__24294)
& ? [Vvar__3__l__24315] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24294,Vvar__3__l__24315)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__24294,Vvar__1__R__24295,Vvar__3__l__24315)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__24294,Vvar__1__R__24295,Vvar__2__a__24314,Vvar__3__l__24315)
& Vvar__2___24Anonymous__24300 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24294,Vvar__2__a__24314,Vvar__3__l__24315) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__24329,Vvar__1__R__24330,Vvar__2___24Anonymous__24335] :
( cType___24t(Vvar__0__A__24329)
=> ( c_24__type__24362___24t(Vvar__0__A__24329,Vvar__1__R__24330,Vvar__2___24Anonymous__24335,Vvar__1__R__24330)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24329,Vvar__2___24Anonymous__24335)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__24329,Vvar__1__R__24330,Vvar__2___24Anonymous__24335)
=> ( Vvar__2___24Anonymous__24335 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24329)
| ? [Vvar__2__a__24349] :
( t(Vvar__2__a__24349,Vvar__0__A__24329)
& ? [Vvar__3__l__24350] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24329,Vvar__3__l__24350)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__24329,Vvar__1__R__24330,Vvar__3__l__24350)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__24329,happ(Vvar__1__R__24330,Vvar__2__a__24349),Vvar__3__l__24350)
& Vvar__2___24Anonymous__24335 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24329,Vvar__2__a__24349,Vvar__3__l__24350) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX5266] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX5266)
=> ? [Vvar__0___24Anonymous__5267] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__5267)
& ? [Vvar__1___24Anonymous__5268] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__5268)
& ? [Vvar__2___24Anonymous__5269] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__5269)
& ? [Vvar__3___24Anonymous__5270] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__5270)
& ? [Vvar__4___24Anonymous__5271] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__5271)
& ? [Vvar__5___24Anonymous__5272] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__5272)
& ? [Vvar__6___24Anonymous__5273] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__5273)
& ? [Vvar__7___24Anonymous__5274] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__5274)
& VX5266 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__5267,Vvar__1___24Anonymous__5268,Vvar__2___24Anonymous__5269,Vvar__3___24Anonymous__5270,Vvar__4___24Anonymous__5271,Vvar__5___24Anonymous__5272,Vvar__6___24Anonymous__5273,Vvar__7___24Anonymous__5274) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX15802] :
( cCoq_2eStrings_2eString_2estring___24t(VX15802)
=> ( VX15802 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__15803] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__15803)
& ? [Vvar__1___24Anonymous__15804] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__15804)
& VX15802 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__15803,Vvar__1___24Anonymous__15804) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__8918,Vvar__1__lt__8919,Vvar__2__eq__8924,Vvar__3__x__8929,Vvar__4__y__8930,VX8931] :
( cType___24t(Vvar__0__X__8918)
=> ( c_24__type__8991___24t(Vvar__0__X__8918,Vvar__1__lt__8919,Vvar__2__eq__8924,Vvar__3__x__8929,Vvar__4__y__8930,Vvar__1__lt__8919)
=> ( c_24__type__9010___24t(Vvar__0__X__8918,Vvar__1__lt__8919,Vvar__2__eq__8924,Vvar__3__x__8929,Vvar__4__y__8930,Vvar__2__eq__8924)
=> ( t(Vvar__3__x__8929,Vvar__0__X__8918)
=> ( t(Vvar__4__y__8930,Vvar__0__X__8918)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__8918,Vvar__1__lt__8919,Vvar__2__eq__8924,Vvar__3__x__8929,Vvar__4__y__8930,VX8931)
=> ( ( p(happ(happ(Vvar__1__lt__8919,Vvar__3__x__8929),Vvar__4__y__8930))
& VX8931 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__8918,Vvar__1__lt__8919,Vvar__2__eq__8924,Vvar__3__x__8929,Vvar__4__y__8930) )
| ( p(happ(happ(Vvar__2__eq__8924,Vvar__3__x__8929),Vvar__4__y__8930))
& VX8931 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__8918,Vvar__1__lt__8919,Vvar__2__eq__8924,Vvar__3__x__8929,Vvar__4__y__8930) )
| ( p(happ(happ(Vvar__1__lt__8919,Vvar__4__y__8930),Vvar__3__x__8929))
& VX8931 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__8918,Vvar__1__lt__8919,Vvar__2__eq__8924,Vvar__3__x__8929,Vvar__4__y__8930) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__24422,Vvar__1___24Anonymous__24423] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__24422)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__24423)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__24422,Vvar__1___24Anonymous__24423)
=> ( ? [Vvar__0__a__24425] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__24425)
& ? [Vvar__1__s__24426] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__24426)
& Vvar__1___24Anonymous__24423 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__24425,Vvar__1__s__24426)
& Vvar__0___24Anonymous__24422 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__24427] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__24427)
& ? [Vvar__1__s1__24428] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__24428)
& ? [Vvar__2__s2__24429] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__24429)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__24428,Vvar__2__s2__24429)
& Vvar__1___24Anonymous__24423 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__24427,Vvar__2__s2__24429)
& Vvar__0___24Anonymous__24422 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__24427,Vvar__1__s1__24428) ) ) )
| ? [Vvar__0__a__24431] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__24431)
& ? [Vvar__1__b__24432] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__24432)
& ? [Vvar__2__s1__24433] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__24433)
& ? [Vvar__3__s2__24434] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__24434)
& cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__24431),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__24432))
& Vvar__1___24Anonymous__24423 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__24432,Vvar__3__s2__24434)
& Vvar__0___24Anonymous__24422 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__24431,Vvar__2__s1__24433) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX9110] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX9110)
=> ( VX9110 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX9110 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX9110 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__7728,VX7729] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7728)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__7728,VX7729)
=> ( ? [Vvar__0__n__7730] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__7730)
& Vvar__0___24Anonymous__7728 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__7730)
& VX7729 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__7730) )
| ? [Vvar__0__n__7731] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__7731)
& ? [Vvar__1___24Anonymous__7732] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__7731,Vvar__1___24Anonymous__7732)
& Vvar__0___24Anonymous__7728 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__7731)
& VX7729 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__7731,Vvar__1___24Anonymous__7732) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__16292,Vvar__1___24Anonymous__16293,VX16294] :
( cType___24t(Vvar__0__A__16292)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__16293)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__16292,Vvar__1___24Anonymous__16293,VX16294)
=> ( ( Vvar__1___24Anonymous__16293 = cCoq_2eInit_2eDatatypes_2eO
& VX16294 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__16292) )
| ? [Vvar__1__h__16297] :
( t(Vvar__1__h__16297,Vvar__0__A__16292)
& ? [Vvar__2__n__16298] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__16298)
& ? [Vvar__3___24Anonymous__16299] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__16292,Vvar__2__n__16298,Vvar__3___24Anonymous__16299)
& Vvar__1___24Anonymous__16293 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__16298)
& VX16294 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__16292,Vvar__1__h__16297,Vvar__2__n__16298,Vvar__3___24Anonymous__16299) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__16414,Vvar__1__b__16415,Vvar__2__d__16416] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__16414)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__16415)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__16416)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__16414,Vvar__1__b__16415,Vvar__2__d__16416)
=> ? [Vvar__3__u__16421] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__16421)
& ? [Vvar__4__v__16422] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__16422)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__16421,Vvar__0__a__16414),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__16422,Vvar__1__b__16415)) = Vvar__2__d__16416
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__16389,Vvar__1__b__16390,VX16391] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__16389)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__16390)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__16389,Vvar__1__b__16390,VX16391)
=> ? [Vvar__2__u__16394] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__16394)
& ? [Vvar__3__v__16395] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__16395)
& ? [Vvar__4__d__16396] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__16396)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__16394,Vvar__0__a__16389),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__16395,Vvar__1__b__16390)) = Vvar__4__d__16396
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__16389,Vvar__1__b__16390,Vvar__4__d__16396)
& VX16391 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__16389,Vvar__1__b__16390,Vvar__2__u__16394,Vvar__3__v__16395,Vvar__4__d__16396) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__16361,Vvar__1__b__16362,Vvar__2__g__16363] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__16361)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__16362)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__16363)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__16361,Vvar__1__b__16362,Vvar__2__g__16363)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__16363,Vvar__0__a__16361)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__16363,Vvar__1__b__16362)
& ! [Vvar__var__var__var__var__5__x__16371__16374__16377__16380__16383] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__16371__16374__16377__16380__16383)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__16371__16374__16377__16380__16383,Vvar__0__a__16361)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__16371__16374__16377__16380__16383,Vvar__1__b__16362)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__16371__16374__16377__16380__16383,Vvar__2__g__16363) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__16424] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__16424)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__16424)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__16424)
& ! [Vvar__var__var__2__n__16429__16431__16433] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__16429__16431__16433)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__16429__16431__16433)
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__16429__16431__16433,Vvar__0__p__16424) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__16429__16431__16433,Vvar__0__p__16424) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__23103,Vvar__1__p__23104,VX23105] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__23103)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__23104)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__23103,Vvar__1__p__23104,VX23105)
=> ? [Vvar__2__q__23108] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__23108)
& ? [Vvar__3__r__23109] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__23109)
& Vvar__0__x__23103 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__23108,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__23104)),Vvar__3__r__23109)
& cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__23109)
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__23109,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__23104))
& VX23105 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__23103,Vvar__1__p__23104,Vvar__2__q__23108,Vvar__3__r__23109) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
! [Vvar__0__T__5697,Vvar__1__F__5698] :
( cType___24t(Vvar__0__T__5697)
=> ( t(Vvar__1__F__5698,Vvar__0__T__5697)
=> ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__5697,Vvar__1__F__5698)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
! [Vvar__0__T__5702,Vvar__1__F__5703] :
( cType___24t(Vvar__0__T__5702)
=> ( t(Vvar__1__F__5703,Vvar__0__T__5702)
=> ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__5702,Vvar__1__F__5703)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX5757] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX5757)
=> ( VX5757 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__5758] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5758)
& ? [Vvar__1___24Anonymous__5759] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__5759)
& VX5757 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__5758,Vvar__1___24Anonymous__5759) ) )
| ? [Vvar__0___24Anonymous__5760] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5760)
& ? [Vvar__1___24Anonymous__5761] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__5761)
& VX5757 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__5760,Vvar__1___24Anonymous__5761) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__1490,VX1491] :
( cType___24t(Vvar__0__C__1490)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__1490,VX1491)
=> ( ? [Vvar__1___24Anonymous__1493] :
( t(Vvar__1___24Anonymous__1493,Vvar__0__C__1490)
& VX1491 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__1490,Vvar__1___24Anonymous__1493) )
| ? [Vvar__1___24Anonymous__1495] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1495)
& VX1491 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__1490,Vvar__1___24Anonymous__1495) )
| ? [Vvar__1___24Anonymous__1497] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__1490,Vvar__1___24Anonymous__1497)
& ? [Vvar__2___24Anonymous__1498] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__1490,Vvar__2___24Anonymous__1498)
& VX1491 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__1490,Vvar__1___24Anonymous__1497,Vvar__2___24Anonymous__1498) ) )
| ? [Vvar__1___24Anonymous__1500] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__1490,Vvar__1___24Anonymous__1500)
& ? [Vvar__2___24Anonymous__1501] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__1490,Vvar__2___24Anonymous__1501)
& VX1491 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__1490,Vvar__1___24Anonymous__1500,Vvar__2___24Anonymous__1501) ) )
| ? [Vvar__1___24Anonymous__1503] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__1490,Vvar__1___24Anonymous__1503)
& ? [Vvar__2___24Anonymous__1504] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__1490,Vvar__2___24Anonymous__1504)
& VX1491 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__1490,Vvar__1___24Anonymous__1503,Vvar__2___24Anonymous__1504) ) )
| ? [Vvar__1___24Anonymous__1506] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__1490,Vvar__1___24Anonymous__1506)
& VX1491 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__1490,Vvar__1___24Anonymous__1506) )
| ? [Vvar__1___24Anonymous__1508] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__1490,Vvar__1___24Anonymous__1508)
& ? [Vvar__2___24Anonymous__1509] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__1509)
& VX1491 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__1490,Vvar__1___24Anonymous__1508,Vvar__2___24Anonymous__1509) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__5710,VX5711] :
( cType___24t(Vvar__0__C__5710)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__5710,VX5711)
=> ( ? [Vvar__1___24Anonymous__5713] :
( t(Vvar__1___24Anonymous__5713,Vvar__0__C__5710)
& VX5711 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__5710,Vvar__1___24Anonymous__5713) )
| ? [Vvar__1___24Anonymous__5715] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5715)
& ? [Vvar__2___24Anonymous__5716] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__5710,Vvar__2___24Anonymous__5716)
& VX5711 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__5710,Vvar__1___24Anonymous__5715,Vvar__2___24Anonymous__5716) ) )
| ? [Vvar__1___24Anonymous__5718] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__5710,Vvar__1___24Anonymous__5718)
& ? [Vvar__2___24Anonymous__5719] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5719)
& ? [Vvar__3___24Anonymous__5720] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__5710,Vvar__3___24Anonymous__5720)
& VX5711 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__5710,Vvar__1___24Anonymous__5718,Vvar__2___24Anonymous__5719,Vvar__3___24Anonymous__5720) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__7840,Vvar__1__rO__7841,Vvar__2__rI__7842,Vvar__3__rplus__7843,Vvar__4__rtimes__7848,Vvar__5__rminus__7853,Vvar__6__ropp__7858,Vvar__7__req__7861,Vvar__8__rle__7866,Vvar__9__rlt__7871] :
( cType___24t(Vvar__0__R__7840)
=> ( t(Vvar__1__rO__7841,Vvar__0__R__7840)
=> ( t(Vvar__2__rI__7842,Vvar__0__R__7840)
=> ( c_24__type__8272___24t(Vvar__0__R__7840,Vvar__1__rO__7841,Vvar__2__rI__7842,Vvar__3__rplus__7843,Vvar__4__rtimes__7848,Vvar__5__rminus__7853,Vvar__6__ropp__7858,Vvar__7__req__7861,Vvar__8__rle__7866,Vvar__9__rlt__7871,Vvar__3__rplus__7843)
=> ( c_24__type__8373___24t(Vvar__0__R__7840,Vvar__1__rO__7841,Vvar__2__rI__7842,Vvar__3__rplus__7843,Vvar__4__rtimes__7848,Vvar__5__rminus__7853,Vvar__6__ropp__7858,Vvar__7__req__7861,Vvar__8__rle__7866,Vvar__9__rlt__7871,Vvar__4__rtimes__7848)
=> ( c_24__type__8474___24t(Vvar__0__R__7840,Vvar__1__rO__7841,Vvar__2__rI__7842,Vvar__3__rplus__7843,Vvar__4__rtimes__7848,Vvar__5__rminus__7853,Vvar__6__ropp__7858,Vvar__7__req__7861,Vvar__8__rle__7866,Vvar__9__rlt__7871,Vvar__5__rminus__7853)
=> ( c_24__type__8564___24t(Vvar__0__R__7840,Vvar__1__rO__7841,Vvar__2__rI__7842,Vvar__3__rplus__7843,Vvar__4__rtimes__7848,Vvar__5__rminus__7853,Vvar__6__ropp__7858,Vvar__7__req__7861,Vvar__8__rle__7866,Vvar__9__rlt__7871,Vvar__6__ropp__7858)
=> ( c_24__type__8665___24t(Vvar__0__R__7840,Vvar__1__rO__7841,Vvar__2__rI__7842,Vvar__3__rplus__7843,Vvar__4__rtimes__7848,Vvar__5__rminus__7853,Vvar__6__ropp__7858,Vvar__7__req__7861,Vvar__8__rle__7866,Vvar__9__rlt__7871,Vvar__7__req__7861)
=> ( c_24__type__8766___24t(Vvar__0__R__7840,Vvar__1__rO__7841,Vvar__2__rI__7842,Vvar__3__rplus__7843,Vvar__4__rtimes__7848,Vvar__5__rminus__7853,Vvar__6__ropp__7858,Vvar__7__req__7861,Vvar__8__rle__7866,Vvar__9__rlt__7871,Vvar__8__rle__7866)
=> ( c_24__type__8867___24t(Vvar__0__R__7840,Vvar__1__rO__7841,Vvar__2__rI__7842,Vvar__3__rplus__7843,Vvar__4__rtimes__7848,Vvar__5__rminus__7853,Vvar__6__ropp__7858,Vvar__7__req__7861,Vvar__8__rle__7866,Vvar__9__rlt__7871,Vvar__9__rlt__7871)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__7840,Vvar__1__rO__7841,Vvar__2__rI__7842,Vvar__3__rplus__7843,Vvar__4__rtimes__7848,Vvar__5__rminus__7853,Vvar__6__ropp__7858,Vvar__7__req__7861,Vvar__8__rle__7866,Vvar__9__rlt__7871)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__7840,Vvar__7__req__7861)
& ! [Vvar__var__var__var__var__11__x1__7915__7921__8026__8032__8038] :
( t(Vvar__var__var__var__var__11__x1__7915__7921__8026__8032__8038,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__12__x2__7916__7922__8027__8033__8039] :
( t(Vvar__var__var__var__var__12__x2__7916__7922__8027__8033__8039,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__7__req__7861,Vvar__var__var__var__var__11__x1__7915__7921__8026__8032__8038),Vvar__var__var__var__var__12__x2__7916__7922__8027__8033__8039))
=> ! [Vvar__var__var__var__var__14__y1__7917__7923__8028__8034__8040] :
( t(Vvar__var__var__var__var__14__y1__7917__7923__8028__8034__8040,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__15__y2__7918__7924__8029__8035__8041] :
( t(Vvar__var__var__var__var__15__y2__7918__7924__8029__8035__8041,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__7__req__7861,Vvar__var__var__var__var__14__y1__7917__7923__8028__8034__8040),Vvar__var__var__var__var__15__y2__7918__7924__8029__8035__8041))
=> p(happ(happ(Vvar__7__req__7861,happ(happ(Vvar__3__rplus__7843,Vvar__var__var__var__var__11__x1__7915__7921__8026__8032__8038),Vvar__var__var__var__var__14__y1__7917__7923__8028__8034__8040)),happ(happ(Vvar__3__rplus__7843,Vvar__var__var__var__var__12__x2__7916__7922__8027__8033__8039),Vvar__var__var__var__var__15__y2__7918__7924__8029__8035__8041))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__7928__7934__8044__8050__8056] :
( t(Vvar__var__var__var__var__12__x1__7928__7934__8044__8050__8056,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__13__x2__7929__7935__8045__8051__8057] :
( t(Vvar__var__var__var__var__13__x2__7929__7935__8045__8051__8057,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__7__req__7861,Vvar__var__var__var__var__12__x1__7928__7934__8044__8050__8056),Vvar__var__var__var__var__13__x2__7929__7935__8045__8051__8057))
=> ! [Vvar__var__var__var__var__15__y1__7930__7936__8046__8052__8058] :
( t(Vvar__var__var__var__var__15__y1__7930__7936__8046__8052__8058,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__16__y2__7931__7937__8047__8053__8059] :
( t(Vvar__var__var__var__var__16__y2__7931__7937__8047__8053__8059,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__7__req__7861,Vvar__var__var__var__var__15__y1__7930__7936__8046__8052__8058),Vvar__var__var__var__var__16__y2__7931__7937__8047__8053__8059))
=> p(happ(happ(Vvar__7__req__7861,happ(happ(Vvar__4__rtimes__7848,Vvar__var__var__var__var__12__x1__7928__7934__8044__8050__8056),Vvar__var__var__var__var__15__y1__7930__7936__8046__8052__8058)),happ(happ(Vvar__4__rtimes__7848,Vvar__var__var__var__var__13__x2__7929__7935__8045__8051__8057),Vvar__var__var__var__var__16__y2__7931__7937__8047__8053__8059))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__7941__7944__8062__8065__8068] :
( t(Vvar__var__var__var__var__13__x1__7941__7944__8062__8065__8068,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__14__x2__7942__7945__8063__8066__8069] :
( t(Vvar__var__var__var__var__14__x2__7942__7945__8063__8066__8069,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__7__req__7861,Vvar__var__var__var__var__13__x1__7941__7944__8062__8065__8068),Vvar__var__var__var__var__14__x2__7942__7945__8063__8066__8069))
=> p(happ(happ(Vvar__7__req__7861,happ(Vvar__6__ropp__7858,Vvar__var__var__var__var__13__x1__7941__7944__8062__8065__8068)),happ(Vvar__6__ropp__7858,Vvar__var__var__var__var__14__x2__7942__7945__8063__8066__8069))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__7948__7954__8071__8077__8083] :
( t(Vvar__var__var__var__var__14__x1__7948__7954__8071__8077__8083,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__15__x2__7949__7955__8072__8078__8084] :
( t(Vvar__var__var__var__var__15__x2__7949__7955__8072__8078__8084,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__7__req__7861,Vvar__var__var__var__var__14__x1__7948__7954__8071__8077__8083),Vvar__var__var__var__var__15__x2__7949__7955__8072__8078__8084))
=> ! [Vvar__var__var__var__var__17__y1__7950__7956__8073__8079__8085] :
( t(Vvar__var__var__var__var__17__y1__7950__7956__8073__8079__8085,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__18__y2__7951__7957__8074__8080__8086] :
( t(Vvar__var__var__var__var__18__y2__7951__7957__8074__8080__8086,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__7__req__7861,Vvar__var__var__var__var__17__y1__7950__7956__8073__8079__8085),Vvar__var__var__var__var__18__y2__7951__7957__8074__8080__8086))
=> ( p(happ(happ(Vvar__8__rle__7866,Vvar__var__var__var__var__14__x1__7948__7954__8071__8077__8083),Vvar__var__var__var__var__17__y1__7950__7956__8073__8079__8085))
<=> p(happ(happ(Vvar__8__rle__7866,Vvar__var__var__var__var__15__x2__7949__7955__8072__8078__8084),Vvar__var__var__var__var__18__y2__7951__7957__8074__8080__8086)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__7961__7967__8089__8095__8101] :
( t(Vvar__var__var__var__var__15__x1__7961__7967__8089__8095__8101,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__16__x2__7962__7968__8090__8096__8102] :
( t(Vvar__var__var__var__var__16__x2__7962__7968__8090__8096__8102,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__7__req__7861,Vvar__var__var__var__var__15__x1__7961__7967__8089__8095__8101),Vvar__var__var__var__var__16__x2__7962__7968__8090__8096__8102))
=> ! [Vvar__var__var__var__var__18__y1__7963__7969__8091__8097__8103] :
( t(Vvar__var__var__var__var__18__y1__7963__7969__8091__8097__8103,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__19__y2__7964__7970__8092__8098__8104] :
( t(Vvar__var__var__var__var__19__y2__7964__7970__8092__8098__8104,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__7__req__7861,Vvar__var__var__var__var__18__y1__7963__7969__8091__8097__8103),Vvar__var__var__var__var__19__y2__7964__7970__8092__8098__8104))
=> ( p(happ(happ(Vvar__9__rlt__7871,Vvar__var__var__var__var__15__x1__7961__7967__8089__8095__8101),Vvar__var__var__var__var__18__y1__7963__7969__8091__8097__8103))
<=> p(happ(happ(Vvar__9__rlt__7871,Vvar__var__var__var__var__16__x2__7962__7968__8090__8096__8102),Vvar__var__var__var__var__19__y2__7964__7970__8092__8098__8104)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__7840,Vvar__1__rO__7841,Vvar__2__rI__7842,Vvar__3__rplus__7843,Vvar__4__rtimes__7848,Vvar__5__rminus__7853,Vvar__6__ropp__7858,Vvar__7__req__7861)
& ! [Vvar__var__var__var__17__n__7975__7976__8107__8108] :
( t(Vvar__var__var__var__17__n__7975__7976__8107__8108,Vvar__0__R__7840)
=> p(happ(happ(Vvar__8__rle__7866,Vvar__var__var__var__17__n__7975__7976__8107__8108),Vvar__var__var__var__17__n__7975__7976__8107__8108)) )
& ! [Vvar__var__var__var__var__18__n__7978__7982__8109__8113__8117] :
( t(Vvar__var__var__var__var__18__n__7978__7982__8109__8113__8117,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__19__m__7979__7983__8110__8114__8118] :
( t(Vvar__var__var__var__var__19__m__7979__7983__8110__8114__8118,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__8__rle__7866,Vvar__var__var__var__var__18__n__7978__7982__8109__8113__8117),Vvar__var__var__var__var__19__m__7979__7983__8110__8114__8118))
=> ( p(happ(happ(Vvar__8__rle__7866,Vvar__var__var__var__var__19__m__7979__7983__8110__8114__8118),Vvar__var__var__var__var__18__n__7978__7982__8109__8113__8117))
=> p(happ(happ(Vvar__7__req__7861,Vvar__var__var__var__var__18__n__7978__7982__8109__8113__8117),Vvar__var__var__var__var__19__m__7979__7983__8110__8114__8118)) ) ) ) )
& ! [Vvar__var__var__var__19__n__7987__7992__8121__8126] :
( t(Vvar__var__var__var__19__n__7987__7992__8121__8126,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__20__m__7988__7993__8122__8127] :
( t(Vvar__var__var__var__20__m__7988__7993__8122__8127,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__21__p__7989__7994__8123__8128] :
( t(Vvar__var__var__var__21__p__7989__7994__8123__8128,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__8__rle__7866,Vvar__var__var__var__19__n__7987__7992__8121__8126),Vvar__var__var__var__20__m__7988__7993__8122__8127))
=> ( p(happ(happ(Vvar__8__rle__7866,Vvar__var__var__var__20__m__7988__7993__8122__8127),Vvar__var__var__var__21__p__7989__7994__8123__8128))
=> p(happ(happ(Vvar__8__rle__7866,Vvar__var__var__var__19__n__7987__7992__8121__8126),Vvar__var__var__var__21__p__7989__7994__8123__8128)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__7998__8000__8131__8133__8135__8137] :
( t(Vvar__var__var__var__var__var__20__n__7998__8000__8131__8133__8135__8137,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__var__21__m__7999__8001__8132__8134__8136__8138] :
( t(Vvar__var__var__var__var__var__21__m__7999__8001__8132__8134__8136__8138,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__9__rlt__7871,Vvar__var__var__var__var__var__20__n__7998__8000__8131__8133__8135__8137),Vvar__var__var__var__var__var__21__m__7999__8001__8132__8134__8136__8138))
<=> ( p(happ(happ(Vvar__8__rle__7866,Vvar__var__var__var__var__var__20__n__7998__8000__8131__8133__8135__8137),Vvar__var__var__var__var__var__21__m__7999__8001__8132__8134__8136__8138))
& ~ p(happ(happ(Vvar__7__req__7861,Vvar__var__var__var__var__var__20__n__7998__8000__8131__8133__8135__8137),Vvar__var__var__var__var__var__21__m__7999__8001__8132__8134__8136__8138)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__8003__8005__8139__8141__8143] :
( t(Vvar__var__var__var__var__21__n__8003__8005__8139__8141__8143,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__22__m__8004__8006__8140__8142__8144] :
( t(Vvar__var__var__var__var__22__m__8004__8006__8140__8142__8144,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__9__rlt__7871,Vvar__var__var__var__var__21__n__8003__8005__8139__8141__8143),Vvar__var__var__var__var__22__m__8004__8006__8140__8142__8144))
| p(happ(happ(Vvar__7__req__7861,Vvar__var__var__var__var__21__n__8003__8005__8139__8141__8143),Vvar__var__var__var__var__22__m__8004__8006__8140__8142__8144))
| p(happ(happ(Vvar__9__rlt__7871,Vvar__var__var__var__var__22__m__8004__8006__8140__8142__8144),Vvar__var__var__var__var__21__n__8003__8005__8139__8141__8143)) ) ) )
& ! [Vvar__var__var__var__var__22__n__8008__8012__8145__8149__8153] :
( t(Vvar__var__var__var__var__22__n__8008__8012__8145__8149__8153,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__23__m__8009__8013__8146__8150__8154] :
( t(Vvar__var__var__var__var__23__m__8009__8013__8146__8150__8154,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__24__p__8010__8014__8147__8151__8155] :
( t(Vvar__var__var__var__var__24__p__8010__8014__8147__8151__8155,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__8__rle__7866,Vvar__var__var__var__var__22__n__8008__8012__8145__8149__8153),Vvar__var__var__var__var__23__m__8009__8013__8146__8150__8154))
=> p(happ(happ(Vvar__8__rle__7866,happ(happ(Vvar__3__rplus__7843,Vvar__var__var__var__var__24__p__8010__8014__8147__8151__8155),Vvar__var__var__var__var__22__n__8008__8012__8145__8149__8153)),happ(happ(Vvar__3__rplus__7843,Vvar__var__var__var__var__24__p__8010__8014__8147__8151__8155),Vvar__var__var__var__var__23__m__8009__8013__8146__8150__8154))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__8017__8021__8157__8161__8165__8169] :
( t(Vvar__var__var__var__var__var__23__n__8017__8021__8157__8161__8165__8169,Vvar__0__R__7840)
=> ! [Vvar__var__var__var__var__var__24__m__8018__8022__8158__8162__8166__8170] :
( t(Vvar__var__var__var__var__var__24__m__8018__8022__8158__8162__8166__8170,Vvar__0__R__7840)
=> ( p(happ(happ(Vvar__9__rlt__7871,Vvar__1__rO__7841),Vvar__var__var__var__var__var__23__n__8017__8021__8157__8161__8165__8169))
=> ( p(happ(happ(Vvar__9__rlt__7871,Vvar__1__rO__7841),Vvar__var__var__var__var__var__24__m__8018__8022__8158__8162__8166__8170))
=> p(happ(happ(Vvar__9__rlt__7871,Vvar__1__rO__7841),happ(happ(Vvar__4__rtimes__7848,Vvar__var__var__var__var__var__23__n__8017__8021__8157__8161__8165__8169),Vvar__var__var__var__var__var__24__m__8018__8022__8158__8162__8166__8170))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__7861,Vvar__1__rO__7841),Vvar__2__rI__7842))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX2806] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX2806)
=> ( VX2806 = cCoq_2emicromega_2eRMicromega_2eC0
| VX2806 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__2807] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__2807)
& VX2806 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__2807) )
| ? [Vvar__0__r__2808] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__2808)
& VX2806 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__2808) )
| ? [Vvar__0__r1__2809] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__2809)
& ? [Vvar__1__r2__2810] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__2810)
& VX2806 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__2809,Vvar__1__r2__2810) ) )
| ? [Vvar__0__r1__2811] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__2811)
& ? [Vvar__1__r2__2812] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__2812)
& VX2806 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__2811,Vvar__1__r2__2812) ) )
| ? [Vvar__0__r1__2813] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__2813)
& ? [Vvar__1__r2__2814] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__2814)
& VX2806 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__2813,Vvar__1__r2__2814) ) )
| ? [Vvar__0__r1__2815] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__2815)
& ? [Vvar__1__z__2816] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__2816)
& VX2806 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__2815,Vvar__1__z__2816) ) )
| ? [Vvar__0__r__2817] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__2817)
& VX2806 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__2817) )
| ? [Vvar__0__r__2818] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__2818)
& VX2806 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__2818) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__3635,VX3636] :
( cType___24t(Vvar__0__T__3635)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__3635,VX3636)
=> ? [Vvar__1__Flhs__3638] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__3635,Vvar__1__Flhs__3638)
& ? [Vvar__2__Fop__3639] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__3639)
& ? [Vvar__3__Frhs__3640] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__3635,Vvar__3__Frhs__3640)
& VX3636 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__3635,Vvar__1__Flhs__3638,Vvar__2__Fop__3639,Vvar__3__Frhs__3640) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX3360] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX3360)
=> ( VX3360 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX3360 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX3360 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX3360 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX9393] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX9393)
=> ( VX9393 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX9393 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX9393 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX9393 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX9393 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX9393 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__9247,VX9248] :
( cType___24t(Vvar__0__C__9247)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__9247,VX9248)
=> ( ? [Vvar__1___24Anonymous__9250] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__9250)
& VX9248 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__9247,Vvar__1___24Anonymous__9250) )
| ? [Vvar__1___24Anonymous__9252] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__9247,Vvar__1___24Anonymous__9252)
& VX9248 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__9247,Vvar__1___24Anonymous__9252) )
| ? [Vvar__1___24Anonymous__9254] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__9247,Vvar__1___24Anonymous__9254)
& ? [Vvar__2___24Anonymous__9255] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__9247,Vvar__2___24Anonymous__9255)
& VX9248 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__9247,Vvar__1___24Anonymous__9254,Vvar__2___24Anonymous__9255) ) )
| ? [Vvar__1___24Anonymous__9257] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__9247,Vvar__1___24Anonymous__9257)
& ? [Vvar__2___24Anonymous__9258] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__9247,Vvar__2___24Anonymous__9258)
& VX9248 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__9247,Vvar__1___24Anonymous__9257,Vvar__2___24Anonymous__9258) ) )
| ? [Vvar__1___24Anonymous__9260] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__9247,Vvar__1___24Anonymous__9260)
& ? [Vvar__2___24Anonymous__9261] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__9247,Vvar__2___24Anonymous__9261)
& VX9248 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__9247,Vvar__1___24Anonymous__9260,Vvar__2___24Anonymous__9261) ) )
| ? [Vvar__1___24Anonymous__9263] :
( t(Vvar__1___24Anonymous__9263,Vvar__0__C__9247)
& VX9248 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__9247,Vvar__1___24Anonymous__9263) )
| VX9248 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__9247) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767] :
( cType___24t(Vvar__0__R__17698)
=> ( t(Vvar__1__rO__17699,Vvar__0__R__17698)
=> ( t(Vvar__2__rI__17700,Vvar__0__R__17698)
=> ( c_24__type__18231___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__3__rplus__17701)
=> ( c_24__type__18577___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__4__rtimes__17706)
=> ( c_24__type__18923___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__5__rminus__17711)
=> ( c_24__type__19246___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__6__ropp__17716)
=> ( c_24__type__19592___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__7__req__17719)
=> ( c_24__type__19938___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__8__rle__17724)
=> ( cType___24t(Vvar__9__C__17729)
=> ( t(Vvar__10__cO__17730,Vvar__9__C__17729)
=> ( t(Vvar__11__cI__17731,Vvar__9__C__17729)
=> ( c_24__type__20284___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__12__cplus__17732)
=> ( c_24__type__20630___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__13__ctimes__17737)
=> ( c_24__type__20976___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__14__cminus__17742)
=> ( c_24__type__21299___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__15__copp__17747)
=> ( c_24__type__21645___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__16__ceqb__17750)
=> ( c_24__type__21991___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__17__cleb__17755)
=> ( c_24__type__22314___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__18__phi__17760)
=> ( cType___24t(Vvar__19__E__17763)
=> ( c_24__type__22637___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__20__pow__phi__17764)
=> ( c_24__type__22983___24t(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767,Vvar__21__rpow__17767)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__8__rle__17724,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__17__cleb__17755,Vvar__18__phi__17760,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__17698,Vvar__1__rO__17699,Vvar__2__rI__17700,Vvar__3__rplus__17701,Vvar__4__rtimes__17706,Vvar__5__rminus__17711,Vvar__6__ropp__17716,Vvar__7__req__17719,Vvar__9__C__17729,Vvar__10__cO__17730,Vvar__11__cI__17731,Vvar__12__cplus__17732,Vvar__13__ctimes__17737,Vvar__14__cminus__17742,Vvar__15__copp__17747,Vvar__16__ceqb__17750,Vvar__18__phi__17760)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__17698,Vvar__2__rI__17700,Vvar__4__rtimes__17706,Vvar__7__req__17719,Vvar__19__E__17763,Vvar__20__pow__phi__17764,Vvar__21__rpow__17767)
& ! [Vvar__var__var__var__var__var__24__x__17850__17853__17863__17866__17869__17872] :
( t(Vvar__var__var__var__var__var__24__x__17850__17853__17863__17866__17869__17872,Vvar__9__C__17729)
=> ! [Vvar__var__var__var__var__var__25__y__17851__17854__17864__17867__17870__17873] :
( t(Vvar__var__var__var__var__var__25__y__17851__17854__17864__17867__17870__17873,Vvar__9__C__17729)
=> ( happ(happ(Vvar__16__ceqb__17750,Vvar__var__var__var__var__var__24__x__17850__17853__17863__17866__17869__17872),Vvar__var__var__var__var__var__25__y__17851__17854__17864__17867__17870__17873) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__17719,happ(Vvar__18__phi__17760,Vvar__var__var__var__var__var__24__x__17850__17853__17863__17866__17869__17872)),happ(Vvar__18__phi__17760,Vvar__var__var__var__var__var__25__y__17851__17854__17864__17867__17870__17873))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__17857__17860__17875__17878__17881__17884] :
( t(Vvar__var__var__var__var__var__25__x__17857__17860__17875__17878__17881__17884,Vvar__9__C__17729)
=> ! [Vvar__var__var__var__var__var__26__y__17858__17861__17876__17879__17882__17885] :
( t(Vvar__var__var__var__var__var__26__y__17858__17861__17876__17879__17882__17885,Vvar__9__C__17729)
=> ( happ(happ(Vvar__17__cleb__17755,Vvar__var__var__var__var__var__25__x__17857__17860__17875__17878__17881__17884),Vvar__var__var__var__var__var__26__y__17858__17861__17876__17879__17882__17885) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__17724,happ(Vvar__18__phi__17760,Vvar__var__var__var__var__var__25__x__17857__17860__17875__17878__17881__17884)),happ(Vvar__18__phi__17760,Vvar__var__var__var__var__var__26__y__17858__17861__17876__17879__17882__17885))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,VX15816] :
( cType___24t(Vvar__0__TA__15812)
=> ( cType___24t(Vvar__1__TX__15813)
=> ( cType___24t(Vvar__2__AA__15814)
=> ( cType___24t(Vvar__3__AF__15815)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,VX15816)
=> ( VX15816 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815)
| VX15816 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815)
| ? [Vvar__4___24Anonymous__15829] :
( t(Vvar__4___24Anonymous__15829,Vvar__1__TX__15813)
& VX15816 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__4___24Anonymous__15829) )
| ? [Vvar__4___24Anonymous__15834] :
( t(Vvar__4___24Anonymous__15834,Vvar__0__TA__15812)
& ? [Vvar__5___24Anonymous__15835] :
( t(Vvar__5___24Anonymous__15835,Vvar__2__AA__15814)
& VX15816 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__4___24Anonymous__15834,Vvar__5___24Anonymous__15835) ) )
| ? [Vvar__4___24Anonymous__15840] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__4___24Anonymous__15840)
& ? [Vvar__5___24Anonymous__15841] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__5___24Anonymous__15841)
& VX15816 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__4___24Anonymous__15840,Vvar__5___24Anonymous__15841) ) )
| ? [Vvar__4___24Anonymous__15846] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__4___24Anonymous__15846)
& ? [Vvar__5___24Anonymous__15847] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__5___24Anonymous__15847)
& VX15816 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__4___24Anonymous__15846,Vvar__5___24Anonymous__15847) ) )
| ? [Vvar__4___24Anonymous__15852] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__4___24Anonymous__15852)
& VX15816 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__4___24Anonymous__15852) )
| ? [Vvar__4___24Anonymous__15857] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__4___24Anonymous__15857)
& ? [Vvar__5___24Anonymous__15858] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__15815,Vvar__5___24Anonymous__15858)
& ? [Vvar__6___24Anonymous__15859] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__6___24Anonymous__15859)
& VX15816 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__15812,Vvar__1__TX__15813,Vvar__2__AA__15814,Vvar__3__AF__15815,Vvar__4___24Anonymous__15857,Vvar__5___24Anonymous__15858,Vvar__6___24Anonymous__15859) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__16255,VX16256] :
( cType___24t(Vvar__0__A__16255)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__16255,VX16256)
=> ( VX16256 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__16255)
| ? [Vvar__1___24Anonymous__16259] :
( t(Vvar__1___24Anonymous__16259,Vvar__0__A__16255)
& VX16256 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__16255,Vvar__1___24Anonymous__16259) )
| ? [Vvar__1___24Anonymous__16261] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__16255,Vvar__1___24Anonymous__16261)
& ? [Vvar__2___24Anonymous__16262] :
( t(Vvar__2___24Anonymous__16262,Vvar__0__A__16255)
& ? [Vvar__3___24Anonymous__16263] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__16255,Vvar__3___24Anonymous__16263)
& VX16256 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__16255,Vvar__1___24Anonymous__16261,Vvar__2___24Anonymous__16262,Vvar__3___24Anonymous__16263) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
! [Vvar__0___24Anonymous__16499] :
( cProp___24t(Vvar__0___24Anonymous__16499)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__16499)
=> ( ? [Vvar__0__P__16501] :
( cProp___24t(Vvar__0__P__16501)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__16501)
& Vvar__0___24Anonymous__16499 = Vvar__0__P__16501 )
| ? [Vvar__0__s__16503] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__16503)
& Vvar__0___24Anonymous__16499 = c_24__prop__16512___24a2(Vvar__0___24Anonymous__16499,Vvar__0__s__16503) )
| ? [Vvar__0__s1__16505] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__16505)
& ? [Vvar__1__s2__16506] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__16506)
& Vvar__0___24Anonymous__16499 = c_24__prop__16513___24a3(Vvar__0___24Anonymous__16499,Vvar__0__s1__16505,Vvar__1__s2__16506) ) )
| ? [Vvar__0__s1__16509] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__16509)
& ? [Vvar__1__s2__16510] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__16510)
& Vvar__0___24Anonymous__16499 = c_24__prop__16514___24a3(Vvar__0___24Anonymous__16499,Vvar__0__s1__16509,Vvar__1__s2__16510) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__16468] :
( cProp___24t(Vvar__0___24Anonymous__16468)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__16468)
=> ( ? [Vvar__0__S__16470] :
( cType___24t(Vvar__0__S__16470)
& ? [Vvar__1__x__16471] :
( t(Vvar__1__x__16471,Vvar__0__S__16470)
& ? [Vvar__2__y__16472] :
( t(Vvar__2__y__16472,Vvar__0__S__16470)
& Vvar__0___24Anonymous__16468 = c_24__prop__16492___24a4(Vvar__0___24Anonymous__16468,Vvar__0__S__16470,Vvar__1__x__16471,Vvar__2__y__16472) ) ) )
| ? [Vvar__0__x__16473] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__16473)
& ? [Vvar__1__y__16474] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__16474)
& Vvar__0___24Anonymous__16468 = c_24__prop__16493___24a3(Vvar__0___24Anonymous__16468,Vvar__0__x__16473,Vvar__1__y__16474) ) )
| ? [Vvar__0__x__16475] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__16475)
& ? [Vvar__1__s__16476] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__16476)
& Vvar__0___24Anonymous__16468 = c_24__prop__16494___24a3(Vvar__0___24Anonymous__16468,Vvar__0__x__16475,Vvar__1__s__16476) ) )
| Vvar__0___24Anonymous__16468 = c_24True
| Vvar__0___24Anonymous__16468 = c_24False
| ? [Vvar__0__P__16477] :
( cProp___24t(Vvar__0__P__16477)
& ? [Vvar__1__Q__16478] :
( cProp___24t(Vvar__1__Q__16478)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__16477)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__16478)
& Vvar__0___24Anonymous__16468 = c_24__prop__16495___24a3(Vvar__0___24Anonymous__16468,Vvar__0__P__16477,Vvar__1__Q__16478) ) )
| ? [Vvar__0__P__16481] :
( cProp___24t(Vvar__0__P__16481)
& ? [Vvar__1__Q__16482] :
( cProp___24t(Vvar__1__Q__16482)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__16481)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__16482)
& Vvar__0___24Anonymous__16468 = c_24__prop__16496___24a3(Vvar__0___24Anonymous__16468,Vvar__0__P__16481,Vvar__1__Q__16482) ) )
| ? [Vvar__0__P__16485] :
( cProp___24t(Vvar__0__P__16485)
& ? [Vvar__1__Q__16486] :
( cProp___24t(Vvar__1__Q__16486)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__16485)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__16486)
& Vvar__0___24Anonymous__16468 = c_24__prop__16497___24a3(Vvar__0___24Anonymous__16468,Vvar__0__P__16485,Vvar__1__Q__16486) ) )
| ? [Vvar__0__P__16490] :
( cProp___24t(Vvar__0__P__16490)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__16490)
& Vvar__0___24Anonymous__16468 = c_24__prop__16498___24a2(Vvar__0___24Anonymous__16468,Vvar__0__P__16490) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX16318] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX16318)
=> ( VX16318 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__16319] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__16319)
& ? [Vvar__1___24Anonymous__16320] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__16320)
& VX16318 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__16319,Vvar__1___24Anonymous__16320) ) )
| ? [Vvar__0___24Anonymous__16321] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__16321)
& ? [Vvar__1___24Anonymous__16322] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__16322)
& VX16318 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__16321,Vvar__1___24Anonymous__16322) ) )
| ? [Vvar__0___24Anonymous__16323] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__16323)
& ? [Vvar__1___24Anonymous__16324] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__16324)
& ? [Vvar__2___24Anonymous__16325] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__16325)
& VX16318 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__16323,Vvar__1___24Anonymous__16324,Vvar__2___24Anonymous__16325) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__24374,Vvar__1__env__24375,Vvar__2__env_27__24378,Vvar__3__x__24381] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__24374)
=> ( c_24__type__24402___24t(Vvar__0__fr__24374,Vvar__1__env__24375,Vvar__2__env_27__24378,Vvar__3__x__24381,Vvar__1__env__24375)
=> ( c_24__type__24411___24t(Vvar__0__fr__24374,Vvar__1__env__24375,Vvar__2__env_27__24378,Vvar__3__x__24381,Vvar__2__env_27__24378)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__24381)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__24374,Vvar__1__env__24375,Vvar__2__env_27__24378,Vvar__3__x__24381)
=> ( happ(Vvar__1__env__24375,Vvar__3__x__24381) = happ(Vvar__2__env_27__24378,Vvar__3__x__24381)
& happ(Vvar__1__env__24375,Vvar__3__x__24381) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__24378,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__24374,Vvar__3__x__24381))),happ(Vvar__2__env_27__24378,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__24374,Vvar__3__x__24381))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__24378,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__24374,Vvar__3__x__24381))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__24378,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__24374,Vvar__3__x__24381))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__17330,VX17331] :
( cType___24t(Vvar__0__C__17330)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17330,VX17331)
=> ( VX17331 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__17330)
| VX17331 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__17330)
| ? [Vvar__1___24Anonymous__17335] :
( t(Vvar__1___24Anonymous__17335,Vvar__0__C__17330)
& VX17331 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__17330,Vvar__1___24Anonymous__17335) )
| ? [Vvar__1___24Anonymous__17337] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17337)
& VX17331 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__17330,Vvar__1___24Anonymous__17337) )
| ? [Vvar__1___24Anonymous__17339] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17330,Vvar__1___24Anonymous__17339)
& ? [Vvar__2___24Anonymous__17340] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17330,Vvar__2___24Anonymous__17340)
& VX17331 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__17330,Vvar__1___24Anonymous__17339,Vvar__2___24Anonymous__17340) ) )
| ? [Vvar__1___24Anonymous__17342] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17330,Vvar__1___24Anonymous__17342)
& ? [Vvar__2___24Anonymous__17343] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17330,Vvar__2___24Anonymous__17343)
& VX17331 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__17330,Vvar__1___24Anonymous__17342,Vvar__2___24Anonymous__17343) ) )
| ? [Vvar__1___24Anonymous__17345] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17330,Vvar__1___24Anonymous__17345)
& ? [Vvar__2___24Anonymous__17346] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17330,Vvar__2___24Anonymous__17346)
& VX17331 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__17330,Vvar__1___24Anonymous__17345,Vvar__2___24Anonymous__17346) ) )
| ? [Vvar__1___24Anonymous__17348] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17330,Vvar__1___24Anonymous__17348)
& VX17331 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__17330,Vvar__1___24Anonymous__17348) )
| ? [Vvar__1___24Anonymous__17350] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17330,Vvar__1___24Anonymous__17350)
& VX17331 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__17330,Vvar__1___24Anonymous__17350) )
| ? [Vvar__1___24Anonymous__17352] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17330,Vvar__1___24Anonymous__17352)
& ? [Vvar__2___24Anonymous__17353] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17330,Vvar__2___24Anonymous__17353)
& VX17331 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__17330,Vvar__1___24Anonymous__17352,Vvar__2___24Anonymous__17353) ) )
| ? [Vvar__1___24Anonymous__17355] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17330,Vvar__1___24Anonymous__17355)
& ? [Vvar__2___24Anonymous__17356] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__17356)
& VX17331 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__17330,Vvar__1___24Anonymous__17355,Vvar__2___24Anonymous__17356) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__5845,Vvar__1__rO__5846,Vvar__2__rI__5847,Vvar__3__radd__5848,Vvar__4__rmul__5853,Vvar__5__rsub__5858,Vvar__6__ropp__5863,Vvar__7__rdiv__5866,Vvar__8__rinv__5871,Vvar__9__req__5874] :
( cType___24t(Vvar__0__R__5845)
=> ( t(Vvar__1__rO__5846,Vvar__0__R__5845)
=> ( t(Vvar__2__rI__5847,Vvar__0__R__5845)
=> ( c_24__type__6039___24t(Vvar__0__R__5845,Vvar__1__rO__5846,Vvar__2__rI__5847,Vvar__3__radd__5848,Vvar__4__rmul__5853,Vvar__5__rsub__5858,Vvar__6__ropp__5863,Vvar__7__rdiv__5866,Vvar__8__rinv__5871,Vvar__9__req__5874,Vvar__3__radd__5848)
=> ( c_24__type__6132___24t(Vvar__0__R__5845,Vvar__1__rO__5846,Vvar__2__rI__5847,Vvar__3__radd__5848,Vvar__4__rmul__5853,Vvar__5__rsub__5858,Vvar__6__ropp__5863,Vvar__7__rdiv__5866,Vvar__8__rinv__5871,Vvar__9__req__5874,Vvar__4__rmul__5853)
=> ( c_24__type__6225___24t(Vvar__0__R__5845,Vvar__1__rO__5846,Vvar__2__rI__5847,Vvar__3__radd__5848,Vvar__4__rmul__5853,Vvar__5__rsub__5858,Vvar__6__ropp__5863,Vvar__7__rdiv__5866,Vvar__8__rinv__5871,Vvar__9__req__5874,Vvar__5__rsub__5858)
=> ( c_24__type__6307___24t(Vvar__0__R__5845,Vvar__1__rO__5846,Vvar__2__rI__5847,Vvar__3__radd__5848,Vvar__4__rmul__5853,Vvar__5__rsub__5858,Vvar__6__ropp__5863,Vvar__7__rdiv__5866,Vvar__8__rinv__5871,Vvar__9__req__5874,Vvar__6__ropp__5863)
=> ( c_24__type__6400___24t(Vvar__0__R__5845,Vvar__1__rO__5846,Vvar__2__rI__5847,Vvar__3__radd__5848,Vvar__4__rmul__5853,Vvar__5__rsub__5858,Vvar__6__ropp__5863,Vvar__7__rdiv__5866,Vvar__8__rinv__5871,Vvar__9__req__5874,Vvar__7__rdiv__5866)
=> ( c_24__type__6482___24t(Vvar__0__R__5845,Vvar__1__rO__5846,Vvar__2__rI__5847,Vvar__3__radd__5848,Vvar__4__rmul__5853,Vvar__5__rsub__5858,Vvar__6__ropp__5863,Vvar__7__rdiv__5866,Vvar__8__rinv__5871,Vvar__9__req__5874,Vvar__8__rinv__5871)
=> ( c_24__type__6575___24t(Vvar__0__R__5845,Vvar__1__rO__5846,Vvar__2__rI__5847,Vvar__3__radd__5848,Vvar__4__rmul__5853,Vvar__5__rsub__5858,Vvar__6__ropp__5863,Vvar__7__rdiv__5866,Vvar__8__rinv__5871,Vvar__9__req__5874,Vvar__9__req__5874)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__5845,Vvar__1__rO__5846,Vvar__2__rI__5847,Vvar__3__radd__5848,Vvar__4__rmul__5853,Vvar__5__rsub__5858,Vvar__6__ropp__5863,Vvar__7__rdiv__5866,Vvar__8__rinv__5871,Vvar__9__req__5874)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__5845,Vvar__1__rO__5846,Vvar__2__rI__5847,Vvar__3__radd__5848,Vvar__4__rmul__5853,Vvar__5__rsub__5858,Vvar__6__ropp__5863,Vvar__9__req__5874)
& ~ p(happ(happ(Vvar__9__req__5874,Vvar__2__rI__5847),Vvar__1__rO__5846))
& ! [Vvar__var__var__var__var__var__var__12__p__5917__5919__5926__5928__5930__5932__5934] :
( t(Vvar__var__var__var__var__var__var__12__p__5917__5919__5926__5928__5930__5932__5934,Vvar__0__R__5845)
=> ! [Vvar__var__var__var__var__var__var__13__q__5918__5920__5927__5929__5931__5933__5935] :
( t(Vvar__var__var__var__var__var__var__13__q__5918__5920__5927__5929__5931__5933__5935,Vvar__0__R__5845)
=> p(happ(happ(Vvar__9__req__5874,happ(happ(Vvar__7__rdiv__5866,Vvar__var__var__var__var__var__var__12__p__5917__5919__5926__5928__5930__5932__5934),Vvar__var__var__var__var__var__var__13__q__5918__5920__5927__5929__5931__5933__5935)),happ(happ(Vvar__4__rmul__5853,Vvar__var__var__var__var__var__var__12__p__5917__5919__5926__5928__5930__5932__5934),happ(Vvar__8__rinv__5871,Vvar__var__var__var__var__var__var__13__q__5918__5920__5927__5929__5931__5933__5935)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__5922__5924__5936__5938__5940__5942__5944__5946] :
( t(Vvar__var__var__var__var__var__var__var__13__p__5922__5924__5936__5938__5940__5942__5944__5946,Vvar__0__R__5845)
=> ( ~ p(happ(happ(Vvar__9__req__5874,Vvar__var__var__var__var__var__var__var__13__p__5922__5924__5936__5938__5940__5942__5944__5946),Vvar__1__rO__5846))
=> p(happ(happ(Vvar__9__req__5874,happ(happ(Vvar__4__rmul__5853,happ(Vvar__8__rinv__5871,Vvar__var__var__var__var__var__var__var__13__p__5922__5924__5936__5938__5940__5942__5944__5946)),Vvar__var__var__var__var__var__var__var__13__p__5922__5924__5936__5938__5940__5942__5944__5946)),Vvar__2__rI__5847)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__6595,Vvar__1__rO__6596,Vvar__2__rI__6597,Vvar__3__radd__6598,Vvar__4__rmul__6603,Vvar__5__rsub__6608,Vvar__6__ropp__6613,Vvar__7__rdiv__6616,Vvar__8__rinv__6621,Vvar__9__req__6624] :
( cType___24t(Vvar__0__R__6595)
=> ( t(Vvar__1__rO__6596,Vvar__0__R__6595)
=> ( t(Vvar__2__rI__6597,Vvar__0__R__6595)
=> ( c_24__type__6789___24t(Vvar__0__R__6595,Vvar__1__rO__6596,Vvar__2__rI__6597,Vvar__3__radd__6598,Vvar__4__rmul__6603,Vvar__5__rsub__6608,Vvar__6__ropp__6613,Vvar__7__rdiv__6616,Vvar__8__rinv__6621,Vvar__9__req__6624,Vvar__3__radd__6598)
=> ( c_24__type__6882___24t(Vvar__0__R__6595,Vvar__1__rO__6596,Vvar__2__rI__6597,Vvar__3__radd__6598,Vvar__4__rmul__6603,Vvar__5__rsub__6608,Vvar__6__ropp__6613,Vvar__7__rdiv__6616,Vvar__8__rinv__6621,Vvar__9__req__6624,Vvar__4__rmul__6603)
=> ( c_24__type__6975___24t(Vvar__0__R__6595,Vvar__1__rO__6596,Vvar__2__rI__6597,Vvar__3__radd__6598,Vvar__4__rmul__6603,Vvar__5__rsub__6608,Vvar__6__ropp__6613,Vvar__7__rdiv__6616,Vvar__8__rinv__6621,Vvar__9__req__6624,Vvar__5__rsub__6608)
=> ( c_24__type__7057___24t(Vvar__0__R__6595,Vvar__1__rO__6596,Vvar__2__rI__6597,Vvar__3__radd__6598,Vvar__4__rmul__6603,Vvar__5__rsub__6608,Vvar__6__ropp__6613,Vvar__7__rdiv__6616,Vvar__8__rinv__6621,Vvar__9__req__6624,Vvar__6__ropp__6613)
=> ( c_24__type__7150___24t(Vvar__0__R__6595,Vvar__1__rO__6596,Vvar__2__rI__6597,Vvar__3__radd__6598,Vvar__4__rmul__6603,Vvar__5__rsub__6608,Vvar__6__ropp__6613,Vvar__7__rdiv__6616,Vvar__8__rinv__6621,Vvar__9__req__6624,Vvar__7__rdiv__6616)
=> ( c_24__type__7232___24t(Vvar__0__R__6595,Vvar__1__rO__6596,Vvar__2__rI__6597,Vvar__3__radd__6598,Vvar__4__rmul__6603,Vvar__5__rsub__6608,Vvar__6__ropp__6613,Vvar__7__rdiv__6616,Vvar__8__rinv__6621,Vvar__9__req__6624,Vvar__8__rinv__6621)
=> ( c_24__type__7325___24t(Vvar__0__R__6595,Vvar__1__rO__6596,Vvar__2__rI__6597,Vvar__3__radd__6598,Vvar__4__rmul__6603,Vvar__5__rsub__6608,Vvar__6__ropp__6613,Vvar__7__rdiv__6616,Vvar__8__rinv__6621,Vvar__9__req__6624,Vvar__9__req__6624)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__6595,Vvar__1__rO__6596,Vvar__2__rI__6597,Vvar__3__radd__6598,Vvar__4__rmul__6603,Vvar__5__rsub__6608,Vvar__6__ropp__6613,Vvar__7__rdiv__6616,Vvar__8__rinv__6621,Vvar__9__req__6624)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__6595,Vvar__1__rO__6596,Vvar__2__rI__6597,Vvar__3__radd__6598,Vvar__4__rmul__6603,Vvar__5__rsub__6608,Vvar__6__ropp__6613,Vvar__9__req__6624)
& ~ p(happ(happ(Vvar__9__req__6624,Vvar__2__rI__6597),Vvar__1__rO__6596))
& ! [Vvar__var__var__var__var__var__var__12__p__6667__6669__6676__6678__6680__6682__6684] :
( t(Vvar__var__var__var__var__var__var__12__p__6667__6669__6676__6678__6680__6682__6684,Vvar__0__R__6595)
=> ! [Vvar__var__var__var__var__var__var__13__q__6668__6670__6677__6679__6681__6683__6685] :
( t(Vvar__var__var__var__var__var__var__13__q__6668__6670__6677__6679__6681__6683__6685,Vvar__0__R__6595)
=> p(happ(happ(Vvar__9__req__6624,happ(happ(Vvar__7__rdiv__6616,Vvar__var__var__var__var__var__var__12__p__6667__6669__6676__6678__6680__6682__6684),Vvar__var__var__var__var__var__var__13__q__6668__6670__6677__6679__6681__6683__6685)),happ(happ(Vvar__4__rmul__6603,Vvar__var__var__var__var__var__var__12__p__6667__6669__6676__6678__6680__6682__6684),happ(Vvar__8__rinv__6621,Vvar__var__var__var__var__var__var__13__q__6668__6670__6677__6679__6681__6683__6685)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__6672__6674__6686__6688__6690__6692__6694__6696] :
( t(Vvar__var__var__var__var__var__var__var__13__p__6672__6674__6686__6688__6690__6692__6694__6696,Vvar__0__R__6595)
=> ( ~ p(happ(happ(Vvar__9__req__6624,Vvar__var__var__var__var__var__var__var__13__p__6672__6674__6686__6688__6690__6692__6694__6696),Vvar__1__rO__6596))
=> p(happ(happ(Vvar__9__req__6624,happ(happ(Vvar__4__rmul__6603,happ(Vvar__8__rinv__6621,Vvar__var__var__var__var__var__var__var__13__p__6672__6674__6686__6688__6690__6692__6694__6696)),Vvar__var__var__var__var__var__var__var__13__p__6672__6674__6686__6688__6690__6692__6694__6696)),Vvar__2__rI__6597)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__17657,VX17658] :
( cType___24t(Vvar__0__C__17657)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__17657,VX17658)
=> ? [Vvar__1__num__17660] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__17657,Vvar__1__num__17660)
& ? [Vvar__2__denum__17661] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__17657,Vvar__2__denum__17661)
& ? [Vvar__3__condition__17662] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__17657),Vvar__3__condition__17662)
& VX17658 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__17657,Vvar__1__num__17660,Vvar__2__denum__17661,Vvar__3__condition__17662) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__6581,VX6582] :
( cType___24t(Vvar__0__C__6581)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__6581,VX6582)
=> ? [Vvar__1__rsplit__left__6584] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6581,Vvar__1__rsplit__left__6584)
& ? [Vvar__2__rsplit__common__6585] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6581,Vvar__2__rsplit__common__6585)
& ? [Vvar__3__rsplit__right__6586] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6581,Vvar__3__rsplit__right__6586)
& VX6582 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__6581,Vvar__1__rsplit__left__6584,Vvar__2__rsplit__common__6585,Vvar__3__rsplit__right__6586) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__7331,Vvar__1__rO__7332,Vvar__2__rI__7333,Vvar__3__radd__7334,Vvar__4__rmul__7339,Vvar__5__rdiv__7344,Vvar__6__rinv__7349,Vvar__7__req__7352] :
( cType___24t(Vvar__0__R__7331)
=> ( t(Vvar__1__rO__7332,Vvar__0__R__7331)
=> ( t(Vvar__2__rI__7333,Vvar__0__R__7331)
=> ( c_24__type__7479___24t(Vvar__0__R__7331,Vvar__1__rO__7332,Vvar__2__rI__7333,Vvar__3__radd__7334,Vvar__4__rmul__7339,Vvar__5__rdiv__7344,Vvar__6__rinv__7349,Vvar__7__req__7352,Vvar__3__radd__7334)
=> ( c_24__type__7542___24t(Vvar__0__R__7331,Vvar__1__rO__7332,Vvar__2__rI__7333,Vvar__3__radd__7334,Vvar__4__rmul__7339,Vvar__5__rdiv__7344,Vvar__6__rinv__7349,Vvar__7__req__7352,Vvar__4__rmul__7339)
=> ( c_24__type__7605___24t(Vvar__0__R__7331,Vvar__1__rO__7332,Vvar__2__rI__7333,Vvar__3__radd__7334,Vvar__4__rmul__7339,Vvar__5__rdiv__7344,Vvar__6__rinv__7349,Vvar__7__req__7352,Vvar__5__rdiv__7344)
=> ( c_24__type__7659___24t(Vvar__0__R__7331,Vvar__1__rO__7332,Vvar__2__rI__7333,Vvar__3__radd__7334,Vvar__4__rmul__7339,Vvar__5__rdiv__7344,Vvar__6__rinv__7349,Vvar__7__req__7352,Vvar__6__rinv__7349)
=> ( c_24__type__7722___24t(Vvar__0__R__7331,Vvar__1__rO__7332,Vvar__2__rI__7333,Vvar__3__radd__7334,Vvar__4__rmul__7339,Vvar__5__rdiv__7344,Vvar__6__rinv__7349,Vvar__7__req__7352,Vvar__7__req__7352)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__7331,Vvar__1__rO__7332,Vvar__2__rI__7333,Vvar__3__radd__7334,Vvar__4__rmul__7339,Vvar__5__rdiv__7344,Vvar__6__rinv__7349,Vvar__7__req__7352)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__7331,Vvar__1__rO__7332,Vvar__2__rI__7333,Vvar__3__radd__7334,Vvar__4__rmul__7339,Vvar__7__req__7352)
& ~ p(happ(happ(Vvar__7__req__7352,Vvar__2__rI__7333),Vvar__1__rO__7332))
& ! [Vvar__var__var__var__var__var__var__10__p__7387__7389__7396__7398__7400__7402__7404] :
( t(Vvar__var__var__var__var__var__var__10__p__7387__7389__7396__7398__7400__7402__7404,Vvar__0__R__7331)
=> ! [Vvar__var__var__var__var__var__var__11__q__7388__7390__7397__7399__7401__7403__7405] :
( t(Vvar__var__var__var__var__var__var__11__q__7388__7390__7397__7399__7401__7403__7405,Vvar__0__R__7331)
=> p(happ(happ(Vvar__7__req__7352,happ(happ(Vvar__5__rdiv__7344,Vvar__var__var__var__var__var__var__10__p__7387__7389__7396__7398__7400__7402__7404),Vvar__var__var__var__var__var__var__11__q__7388__7390__7397__7399__7401__7403__7405)),happ(happ(Vvar__4__rmul__7339,Vvar__var__var__var__var__var__var__10__p__7387__7389__7396__7398__7400__7402__7404),happ(Vvar__6__rinv__7349,Vvar__var__var__var__var__var__var__11__q__7388__7390__7397__7399__7401__7403__7405)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__7392__7394__7406__7408__7410__7412__7414__7416] :
( t(Vvar__var__var__var__var__var__var__var__11__p__7392__7394__7406__7408__7410__7412__7414__7416,Vvar__0__R__7331)
=> ( ~ p(happ(happ(Vvar__7__req__7352,Vvar__var__var__var__var__var__var__var__11__p__7392__7394__7406__7408__7410__7412__7414__7416),Vvar__1__rO__7332))
=> p(happ(happ(Vvar__7__req__7352,happ(happ(Vvar__4__rmul__7339,happ(Vvar__6__rinv__7349,Vvar__var__var__var__var__var__var__var__11__p__7392__7394__7406__7408__7410__7412__7414__7416)),Vvar__var__var__var__var__var__var__var__11__p__7392__7394__7406__7408__7410__7412__7414__7416)),Vvar__2__rI__7333)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
! [VX7828] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX7828)
=> ? [Vvar__0__hypo__type__7829] :
( cType___24t(Vvar__0__hypo__type__7829)
& ? [Vvar__1__hypo__proof__7830] :
( t(Vvar__1__hypo__proof__7830,Vvar__0__hypo__type__7829)
& VX7828 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__7829,Vvar__1__hypo__proof__7830) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX9441] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX9441)
=> ( VX9441 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__9442] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9442)
& ? [Vvar__1___24Anonymous__9443] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__9443)
& VX9441 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__9442,Vvar__1___24Anonymous__9443) ) )
| ? [Vvar__0___24Anonymous__9444] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9444)
& ? [Vvar__1___24Anonymous__9445] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__9445)
& VX9441 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__9444,Vvar__1___24Anonymous__9445) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__9462,VX9463] :
( cType___24t(Vvar__0__C__9462)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9462,VX9463)
=> ( VX9463 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__9462)
| VX9463 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__9462)
| ? [Vvar__1___24Anonymous__9467] :
( t(Vvar__1___24Anonymous__9467,Vvar__0__C__9462)
& VX9463 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__9462,Vvar__1___24Anonymous__9467) )
| ? [Vvar__1___24Anonymous__9469] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__9469)
& VX9463 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__9462,Vvar__1___24Anonymous__9469) )
| ? [Vvar__1___24Anonymous__9471] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9462,Vvar__1___24Anonymous__9471)
& ? [Vvar__2___24Anonymous__9472] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9462,Vvar__2___24Anonymous__9472)
& VX9463 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__9462,Vvar__1___24Anonymous__9471,Vvar__2___24Anonymous__9472) ) )
| ? [Vvar__1___24Anonymous__9474] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9462,Vvar__1___24Anonymous__9474)
& ? [Vvar__2___24Anonymous__9475] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9462,Vvar__2___24Anonymous__9475)
& VX9463 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__9462,Vvar__1___24Anonymous__9474,Vvar__2___24Anonymous__9475) ) )
| ? [Vvar__1___24Anonymous__9477] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9462,Vvar__1___24Anonymous__9477)
& ? [Vvar__2___24Anonymous__9478] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9462,Vvar__2___24Anonymous__9478)
& VX9463 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__9462,Vvar__1___24Anonymous__9477,Vvar__2___24Anonymous__9478) ) )
| ? [Vvar__1___24Anonymous__9480] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9462,Vvar__1___24Anonymous__9480)
& VX9463 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__9462,Vvar__1___24Anonymous__9480) )
| ? [Vvar__1___24Anonymous__9482] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9462,Vvar__1___24Anonymous__9482)
& ? [Vvar__2___24Anonymous__9483] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__9483)
& VX9463 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__9462,Vvar__1___24Anonymous__9482,Vvar__2___24Anonymous__9483) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__9394,VX9395] :
( cType___24t(Vvar__0__C__9394)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__9394,VX9395)
=> ( ? [Vvar__1___24Anonymous__9397] :
( t(Vvar__1___24Anonymous__9397,Vvar__0__C__9394)
& VX9395 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__9394,Vvar__1___24Anonymous__9397) )
| ? [Vvar__1___24Anonymous__9399] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__9399)
& ? [Vvar__2___24Anonymous__9400] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__9394,Vvar__2___24Anonymous__9400)
& VX9395 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__9394,Vvar__1___24Anonymous__9399,Vvar__2___24Anonymous__9400) ) )
| ? [Vvar__1___24Anonymous__9402] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__9394,Vvar__1___24Anonymous__9402)
& ? [Vvar__2___24Anonymous__9403] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__9403)
& ? [Vvar__3___24Anonymous__9404] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__9394,Vvar__3___24Anonymous__9404)
& VX9395 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__9394,Vvar__1___24Anonymous__9402,Vvar__2___24Anonymous__9403,Vvar__3___24Anonymous__9404) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__9990,Vvar__1__rO__9991,Vvar__2__rI__9992,Vvar__3__radd__9993,Vvar__4__rmul__9998,Vvar__5__rsub__10003,Vvar__6__ropp__10008,Vvar__7__req__10011] :
( cType___24t(Vvar__0__R__9990)
=> ( t(Vvar__1__rO__9991,Vvar__0__R__9990)
=> ( t(Vvar__2__rI__9992,Vvar__0__R__9990)
=> ( c_24__type__10239___24t(Vvar__0__R__9990,Vvar__1__rO__9991,Vvar__2__rI__9992,Vvar__3__radd__9993,Vvar__4__rmul__9998,Vvar__5__rsub__10003,Vvar__6__ropp__10008,Vvar__7__req__10011,Vvar__3__radd__9993)
=> ( c_24__type__10302___24t(Vvar__0__R__9990,Vvar__1__rO__9991,Vvar__2__rI__9992,Vvar__3__radd__9993,Vvar__4__rmul__9998,Vvar__5__rsub__10003,Vvar__6__ropp__10008,Vvar__7__req__10011,Vvar__4__rmul__9998)
=> ( c_24__type__10365___24t(Vvar__0__R__9990,Vvar__1__rO__9991,Vvar__2__rI__9992,Vvar__3__radd__9993,Vvar__4__rmul__9998,Vvar__5__rsub__10003,Vvar__6__ropp__10008,Vvar__7__req__10011,Vvar__5__rsub__10003)
=> ( c_24__type__10419___24t(Vvar__0__R__9990,Vvar__1__rO__9991,Vvar__2__rI__9992,Vvar__3__radd__9993,Vvar__4__rmul__9998,Vvar__5__rsub__10003,Vvar__6__ropp__10008,Vvar__7__req__10011,Vvar__6__ropp__10008)
=> ( c_24__type__10482___24t(Vvar__0__R__9990,Vvar__1__rO__9991,Vvar__2__rI__9992,Vvar__3__radd__9993,Vvar__4__rmul__9998,Vvar__5__rsub__10003,Vvar__6__ropp__10008,Vvar__7__req__10011,Vvar__7__req__10011)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__9990,Vvar__1__rO__9991,Vvar__2__rI__9992,Vvar__3__radd__9993,Vvar__4__rmul__9998,Vvar__5__rsub__10003,Vvar__6__ropp__10008,Vvar__7__req__10011)
=> ( ! [Vvar__var__var__var__var__var__8__x__10044__10045__10098__10099__10100__10101] :
( t(Vvar__var__var__var__var__var__8__x__10044__10045__10098__10099__10100__10101,Vvar__0__R__9990)
=> p(happ(happ(Vvar__7__req__10011,happ(happ(Vvar__3__radd__9993,Vvar__1__rO__9991),Vvar__var__var__var__var__var__8__x__10044__10045__10098__10099__10100__10101)),Vvar__var__var__var__var__var__8__x__10044__10045__10098__10099__10100__10101)) )
& ! [Vvar__var__var__var__var__9__x__10047__10049__10102__10104__10106] :
( t(Vvar__var__var__var__var__9__x__10047__10049__10102__10104__10106,Vvar__0__R__9990)
=> ! [Vvar__var__var__var__var__10__y__10048__10050__10103__10105__10107] :
( t(Vvar__var__var__var__var__10__y__10048__10050__10103__10105__10107,Vvar__0__R__9990)
=> p(happ(happ(Vvar__7__req__10011,happ(happ(Vvar__3__radd__9993,Vvar__var__var__var__var__9__x__10047__10049__10102__10104__10106),Vvar__var__var__var__var__10__y__10048__10050__10103__10105__10107)),happ(happ(Vvar__3__radd__9993,Vvar__var__var__var__var__10__y__10048__10050__10103__10105__10107),Vvar__var__var__var__var__9__x__10047__10049__10102__10104__10106))) ) )
& ! [Vvar__var__var__var__var__10__x__10052__10055__10108__10111__10114] :
( t(Vvar__var__var__var__var__10__x__10052__10055__10108__10111__10114,Vvar__0__R__9990)
=> ! [Vvar__var__var__var__var__11__y__10053__10056__10109__10112__10115] :
( t(Vvar__var__var__var__var__11__y__10053__10056__10109__10112__10115,Vvar__0__R__9990)
=> ! [Vvar__var__var__var__var__12__z__10054__10057__10110__10113__10116] :
( t(Vvar__var__var__var__var__12__z__10054__10057__10110__10113__10116,Vvar__0__R__9990)
=> p(happ(happ(Vvar__7__req__10011,happ(happ(Vvar__3__radd__9993,Vvar__var__var__var__var__10__x__10052__10055__10108__10111__10114),happ(happ(Vvar__3__radd__9993,Vvar__var__var__var__var__11__y__10053__10056__10109__10112__10115),Vvar__var__var__var__var__12__z__10054__10057__10110__10113__10116))),happ(happ(Vvar__3__radd__9993,happ(happ(Vvar__3__radd__9993,Vvar__var__var__var__var__10__x__10052__10055__10108__10111__10114),Vvar__var__var__var__var__11__y__10053__10056__10109__10112__10115)),Vvar__var__var__var__var__12__z__10054__10057__10110__10113__10116))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__10059__10060__10117__10118__10119__10120] :
( t(Vvar__var__var__var__var__var__11__x__10059__10060__10117__10118__10119__10120,Vvar__0__R__9990)
=> p(happ(happ(Vvar__7__req__10011,happ(happ(Vvar__4__rmul__9998,Vvar__2__rI__9992),Vvar__var__var__var__var__var__11__x__10059__10060__10117__10118__10119__10120)),Vvar__var__var__var__var__var__11__x__10059__10060__10117__10118__10119__10120)) )
& ! [Vvar__var__var__var__var__var__12__x__10062__10063__10121__10122__10123__10124] :
( t(Vvar__var__var__var__var__var__12__x__10062__10063__10121__10122__10123__10124,Vvar__0__R__9990)
=> p(happ(happ(Vvar__7__req__10011,happ(happ(Vvar__4__rmul__9998,Vvar__1__rO__9991),Vvar__var__var__var__var__var__12__x__10062__10063__10121__10122__10123__10124)),Vvar__1__rO__9991)) )
& ! [Vvar__var__var__var__var__13__x__10065__10067__10125__10127__10129] :
( t(Vvar__var__var__var__var__13__x__10065__10067__10125__10127__10129,Vvar__0__R__9990)
=> ! [Vvar__var__var__var__var__14__y__10066__10068__10126__10128__10130] :
( t(Vvar__var__var__var__var__14__y__10066__10068__10126__10128__10130,Vvar__0__R__9990)
=> p(happ(happ(Vvar__7__req__10011,happ(happ(Vvar__4__rmul__9998,Vvar__var__var__var__var__13__x__10065__10067__10125__10127__10129),Vvar__var__var__var__var__14__y__10066__10068__10126__10128__10130)),happ(happ(Vvar__4__rmul__9998,Vvar__var__var__var__var__14__y__10066__10068__10126__10128__10130),Vvar__var__var__var__var__13__x__10065__10067__10125__10127__10129))) ) )
& ! [Vvar__var__var__var__var__14__x__10070__10073__10131__10134__10137] :
( t(Vvar__var__var__var__var__14__x__10070__10073__10131__10134__10137,Vvar__0__R__9990)
=> ! [Vvar__var__var__var__var__15__y__10071__10074__10132__10135__10138] :
( t(Vvar__var__var__var__var__15__y__10071__10074__10132__10135__10138,Vvar__0__R__9990)
=> ! [Vvar__var__var__var__var__16__z__10072__10075__10133__10136__10139] :
( t(Vvar__var__var__var__var__16__z__10072__10075__10133__10136__10139,Vvar__0__R__9990)
=> p(happ(happ(Vvar__7__req__10011,happ(happ(Vvar__4__rmul__9998,Vvar__var__var__var__var__14__x__10070__10073__10131__10134__10137),happ(happ(Vvar__4__rmul__9998,Vvar__var__var__var__var__15__y__10071__10074__10132__10135__10138),Vvar__var__var__var__var__16__z__10072__10075__10133__10136__10139))),happ(happ(Vvar__4__rmul__9998,happ(happ(Vvar__4__rmul__9998,Vvar__var__var__var__var__14__x__10070__10073__10131__10134__10137),Vvar__var__var__var__var__15__y__10071__10074__10132__10135__10138)),Vvar__var__var__var__var__16__z__10072__10075__10133__10136__10139))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__10077__10080__10140__10143__10146__10149] :
( t(Vvar__var__var__var__var__var__15__x__10077__10080__10140__10143__10146__10149,Vvar__0__R__9990)
=> ! [Vvar__var__var__var__var__var__16__y__10078__10081__10141__10144__10147__10150] :
( t(Vvar__var__var__var__var__var__16__y__10078__10081__10141__10144__10147__10150,Vvar__0__R__9990)
=> ! [Vvar__var__var__var__var__var__17__z__10079__10082__10142__10145__10148__10151] :
( t(Vvar__var__var__var__var__var__17__z__10079__10082__10142__10145__10148__10151,Vvar__0__R__9990)
=> p(happ(happ(Vvar__7__req__10011,happ(happ(Vvar__4__rmul__9998,happ(happ(Vvar__3__radd__9993,Vvar__var__var__var__var__var__15__x__10077__10080__10140__10143__10146__10149),Vvar__var__var__var__var__var__16__y__10078__10081__10141__10144__10147__10150)),Vvar__var__var__var__var__var__17__z__10079__10082__10142__10145__10148__10151)),happ(happ(Vvar__3__radd__9993,happ(happ(Vvar__4__rmul__9998,Vvar__var__var__var__var__var__15__x__10077__10080__10140__10143__10146__10149),Vvar__var__var__var__var__var__17__z__10079__10082__10142__10145__10148__10151)),happ(happ(Vvar__4__rmul__9998,Vvar__var__var__var__var__var__16__y__10078__10081__10141__10144__10147__10150),Vvar__var__var__var__var__var__17__z__10079__10082__10142__10145__10148__10151)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__10084__10086__10152__10154__10156__10158] :
( t(Vvar__var__var__var__var__var__16__x__10084__10086__10152__10154__10156__10158,Vvar__0__R__9990)
=> ! [Vvar__var__var__var__var__var__17__y__10085__10087__10153__10155__10157__10159] :
( t(Vvar__var__var__var__var__var__17__y__10085__10087__10153__10155__10157__10159,Vvar__0__R__9990)
=> p(happ(happ(Vvar__7__req__10011,happ(Vvar__6__ropp__10008,happ(happ(Vvar__4__rmul__9998,Vvar__var__var__var__var__var__16__x__10084__10086__10152__10154__10156__10158),Vvar__var__var__var__var__var__17__y__10085__10087__10153__10155__10157__10159))),happ(happ(Vvar__4__rmul__9998,happ(Vvar__6__ropp__10008,Vvar__var__var__var__var__var__16__x__10084__10086__10152__10154__10156__10158)),Vvar__var__var__var__var__var__17__y__10085__10087__10153__10155__10157__10159))) ) )
& ! [Vvar__var__var__var__var__var__17__x__10089__10091__10160__10162__10164__10166] :
( t(Vvar__var__var__var__var__var__17__x__10089__10091__10160__10162__10164__10166,Vvar__0__R__9990)
=> ! [Vvar__var__var__var__var__var__18__y__10090__10092__10161__10163__10165__10167] :
( t(Vvar__var__var__var__var__var__18__y__10090__10092__10161__10163__10165__10167,Vvar__0__R__9990)
=> p(happ(happ(Vvar__7__req__10011,happ(Vvar__6__ropp__10008,happ(happ(Vvar__3__radd__9993,Vvar__var__var__var__var__var__17__x__10089__10091__10160__10162__10164__10166),Vvar__var__var__var__var__var__18__y__10090__10092__10161__10163__10165__10167))),happ(happ(Vvar__3__radd__9993,happ(Vvar__6__ropp__10008,Vvar__var__var__var__var__var__17__x__10089__10091__10160__10162__10164__10166)),happ(Vvar__6__ropp__10008,Vvar__var__var__var__var__var__18__y__10090__10092__10161__10163__10165__10167)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__10094__10096__10168__10170__10172__10174__10176] :
( t(Vvar__var__var__var__var__var__var__18__x__10094__10096__10168__10170__10172__10174__10176,Vvar__0__R__9990)
=> ! [Vvar__var__var__var__var__var__var__19__y__10095__10097__10169__10171__10173__10175__10177] :
( t(Vvar__var__var__var__var__var__var__19__y__10095__10097__10169__10171__10173__10175__10177,Vvar__0__R__9990)
=> p(happ(happ(Vvar__7__req__10011,happ(happ(Vvar__5__rsub__10003,Vvar__var__var__var__var__var__var__18__x__10094__10096__10168__10170__10172__10174__10176),Vvar__var__var__var__var__var__var__19__y__10095__10097__10169__10171__10173__10175__10177)),happ(happ(Vvar__3__radd__9993,Vvar__var__var__var__var__var__var__18__x__10094__10096__10168__10170__10172__10174__10176),happ(Vvar__6__ropp__10008,Vvar__var__var__var__var__var__var__19__y__10095__10097__10169__10171__10173__10175__10177)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__15030,Vvar__1__rI__15031,Vvar__2__rmul__15032,Vvar__3__req__15037,Vvar__4__Cpow__15042,Vvar__5__Cp__phi__15043,Vvar__6__rpow__15046] :
( cType___24t(Vvar__0__R__15030)
=> ( t(Vvar__1__rI__15031,Vvar__0__R__15030)
=> ( c_24__type__15132___24t(Vvar__0__R__15030,Vvar__1__rI__15031,Vvar__2__rmul__15032,Vvar__3__req__15037,Vvar__4__Cpow__15042,Vvar__5__Cp__phi__15043,Vvar__6__rpow__15046,Vvar__2__rmul__15032)
=> ( c_24__type__15176___24t(Vvar__0__R__15030,Vvar__1__rI__15031,Vvar__2__rmul__15032,Vvar__3__req__15037,Vvar__4__Cpow__15042,Vvar__5__Cp__phi__15043,Vvar__6__rpow__15046,Vvar__3__req__15037)
=> ( cType___24t(Vvar__4__Cpow__15042)
=> ( c_24__type__15212___24t(Vvar__0__R__15030,Vvar__1__rI__15031,Vvar__2__rmul__15032,Vvar__3__req__15037,Vvar__4__Cpow__15042,Vvar__5__Cp__phi__15043,Vvar__6__rpow__15046,Vvar__5__Cp__phi__15043)
=> ( c_24__type__15256___24t(Vvar__0__R__15030,Vvar__1__rI__15031,Vvar__2__rmul__15032,Vvar__3__req__15037,Vvar__4__Cpow__15042,Vvar__5__Cp__phi__15043,Vvar__6__rpow__15046,Vvar__6__rpow__15046)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__15030,Vvar__1__rI__15031,Vvar__2__rmul__15032,Vvar__3__req__15037,Vvar__4__Cpow__15042,Vvar__5__Cp__phi__15043,Vvar__6__rpow__15046)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__15074__15076__15078__15080__15082__15084__15086__15088] :
( t(Vvar__var__var__var__var__var__var__var__7__r__15074__15076__15078__15080__15082__15084__15086__15088,Vvar__0__R__15030)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__15075__15077__15079__15081__15083__15085__15087__15089] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__15075__15077__15079__15081__15083__15085__15087__15089)
=> p(happ(happ(Vvar__3__req__15037,happ(happ(Vvar__6__rpow__15046,Vvar__var__var__var__var__var__var__var__7__r__15074__15076__15078__15080__15082__15084__15086__15088),happ(Vvar__5__Cp__phi__15043,Vvar__var__var__var__var__var__var__var__8__n__15075__15077__15079__15081__15083__15085__15087__15089))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__15030,Vvar__1__rI__15031,Vvar__2__rmul__15032,Vvar__var__var__var__var__var__var__var__7__r__15074__15076__15078__15080__15082__15084__15086__15088,Vvar__var__var__var__var__var__var__var__8__n__15075__15077__15079__15081__15083__15085__15087__15089))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__11215,Vvar__1__radd__11216,Vvar__2__rmul__11221,Vvar__3__ropp__11226,Vvar__4__req__11229] :
( cType___24t(Vvar__0__R__11215)
=> ( c_24__type__11320___24t(Vvar__0__R__11215,Vvar__1__radd__11216,Vvar__2__rmul__11221,Vvar__3__ropp__11226,Vvar__4__req__11229,Vvar__1__radd__11216)
=> ( c_24__type__11350___24t(Vvar__0__R__11215,Vvar__1__radd__11216,Vvar__2__rmul__11221,Vvar__3__ropp__11226,Vvar__4__req__11229,Vvar__2__rmul__11221)
=> ( c_24__type__11374___24t(Vvar__0__R__11215,Vvar__1__radd__11216,Vvar__2__rmul__11221,Vvar__3__ropp__11226,Vvar__4__req__11229,Vvar__3__ropp__11226)
=> ( c_24__type__11404___24t(Vvar__0__R__11215,Vvar__1__radd__11216,Vvar__2__rmul__11221,Vvar__3__ropp__11226,Vvar__4__req__11229,Vvar__4__req__11229)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__11215,Vvar__1__radd__11216,Vvar__2__rmul__11221,Vvar__3__ropp__11226,Vvar__4__req__11229)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11434___24a5(Vvar__0__R__11215,Vvar__1__radd__11216,Vvar__2__rmul__11221,Vvar__3__ropp__11226,Vvar__4__req__11229),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__11215,c_24__type__11458___24a5(Vvar__0__R__11215,Vvar__1__radd__11216,Vvar__2__rmul__11221,Vvar__3__ropp__11226,Vvar__4__req__11229),Vvar__4__req__11229,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__11215,Vvar__0__R__11215,Vvar__4__req__11229,Vvar__4__req__11229)),Vvar__1__radd__11216)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11491___24a5(Vvar__0__R__11215,Vvar__1__radd__11216,Vvar__2__rmul__11221,Vvar__3__ropp__11226,Vvar__4__req__11229),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__11215,c_24__type__11515___24a5(Vvar__0__R__11215,Vvar__1__radd__11216,Vvar__2__rmul__11221,Vvar__3__ropp__11226,Vvar__4__req__11229),Vvar__4__req__11229,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__11215,Vvar__0__R__11215,Vvar__4__req__11229,Vvar__4__req__11229)),Vvar__2__rmul__11221)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11542___24a5(Vvar__0__R__11215,Vvar__1__radd__11216,Vvar__2__rmul__11221,Vvar__3__ropp__11226,Vvar__4__req__11229),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__11215,Vvar__0__R__11215,Vvar__4__req__11229,Vvar__4__req__11229),Vvar__3__ropp__11226)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX15261] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX15261)
=> ( VX15261 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__15262] :
( cType___24t(Vvar__0__R__15262)
& ? [Vvar__1__req__15263] :
( c_24__type__90___24t(Vvar__0__R__15262,Vvar__1__req__15263)
& ? [Vvar__2__reqb__15268] :
( c_24__type__15342___24t(Vvar__0__R__15262,Vvar__2__reqb__15268)
& ! [Vvar__var__3__x__15274__15277] :
( t(Vvar__var__3__x__15274__15277,Vvar__0__R__15262)
=> ! [Vvar__var__4__y__15275__15278] :
( t(Vvar__var__4__y__15275__15278,Vvar__0__R__15262)
=> ( happ(happ(Vvar__2__reqb__15268,Vvar__var__3__x__15274__15277),Vvar__var__4__y__15275__15278) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__15263,Vvar__var__3__x__15274__15277),Vvar__var__4__y__15275__15278)) ) ) )
& VX15261 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__15262,Vvar__1__req__15263,Vvar__2__reqb__15268) ) ) )
| ? [Vvar__0__R__15280] :
( cType___24t(Vvar__0__R__15280)
& ? [Vvar__1__rO__15281] :
( t(Vvar__1__rO__15281,Vvar__0__R__15280)
& ? [Vvar__2__rI__15282] :
( t(Vvar__2__rI__15282,Vvar__0__R__15280)
& ? [Vvar__3__radd__15283] :
( c_24__type__3364___24t(Vvar__0__R__15280,Vvar__3__radd__15283)
& ? [Vvar__4__rmul__15288] :
( c_24__type__3364___24t(Vvar__0__R__15280,Vvar__4__rmul__15288)
& ? [Vvar__5__rsub__15293] :
( c_24__type__3364___24t(Vvar__0__R__15280,Vvar__5__rsub__15293)
& ? [Vvar__6__ropp__15298] :
( c_24__type__3373___24t(Vvar__0__R__15280,Vvar__6__ropp__15298)
& ? [Vvar__7__req__15301] :
( c_24__type__90___24t(Vvar__0__R__15280,Vvar__7__req__15301)
& ? [Vvar__8__C__15306] :
( cType___24t(Vvar__8__C__15306)
& ? [Vvar__9__cO__15307] :
( t(Vvar__9__cO__15307,Vvar__8__C__15306)
& ? [Vvar__10__cI__15308] :
( t(Vvar__10__cI__15308,Vvar__8__C__15306)
& ? [Vvar__11__cadd__15309] :
( c_24__type__3389___24t(Vvar__0__R__15280,Vvar__8__C__15306,Vvar__11__cadd__15309)
& ? [Vvar__12__cmul__15314] :
( c_24__type__3389___24t(Vvar__0__R__15280,Vvar__8__C__15306,Vvar__12__cmul__15314)
& ? [Vvar__13__csub__15319] :
( c_24__type__3389___24t(Vvar__0__R__15280,Vvar__8__C__15306,Vvar__13__csub__15319)
& ? [Vvar__14__copp__15324] :
( c_24__type__3403___24t(Vvar__0__R__15280,Vvar__8__C__15306,Vvar__14__copp__15324)
& ? [Vvar__15__ceqb__15327] :
( c_24__type__3410___24t(Vvar__0__R__15280,Vvar__8__C__15306,Vvar__15__ceqb__15327)
& ? [Vvar__16__phi__15332] :
( c_24__type__3419___24t(Vvar__0__R__15280,Vvar__8__C__15306,Vvar__16__phi__15332)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__15280,Vvar__1__rO__15281,Vvar__2__rI__15282,Vvar__3__radd__15283,Vvar__4__rmul__15288,Vvar__5__rsub__15293,Vvar__6__ropp__15298,Vvar__7__req__15301,Vvar__8__C__15306,Vvar__9__cO__15307,Vvar__10__cI__15308,Vvar__11__cadd__15309,Vvar__12__cmul__15314,Vvar__13__csub__15319,Vvar__14__copp__15324,Vvar__15__ceqb__15327,Vvar__16__phi__15332)
& VX15261 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__15280,Vvar__1__rO__15281,Vvar__2__rI__15282,Vvar__3__radd__15283,Vvar__4__rmul__15288,Vvar__5__rsub__15293,Vvar__6__ropp__15298,Vvar__7__req__15301,Vvar__8__C__15306,Vvar__9__cO__15307,Vvar__10__cI__15308,Vvar__11__cadd__15309,Vvar__12__cmul__15314,Vvar__13__csub__15319,Vvar__14__copp__15324,Vvar__15__ceqb__15327,Vvar__16__phi__15332) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595] :
( cType___24t(Vvar__0__R__12543)
=> ( t(Vvar__1__rO__12544,Vvar__0__R__12543)
=> ( t(Vvar__2__rI__12545,Vvar__0__R__12543)
=> ( c_24__type__12939___24t(Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595,Vvar__3__radd__12546)
=> ( c_24__type__13152___24t(Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595,Vvar__4__rmul__12551)
=> ( c_24__type__13365___24t(Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595,Vvar__5__rsub__12556)
=> ( c_24__type__13560___24t(Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595,Vvar__6__ropp__12561)
=> ( c_24__type__13773___24t(Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595,Vvar__7__req__12564)
=> ( cType___24t(Vvar__8__C__12569)
=> ( t(Vvar__9__cO__12570,Vvar__8__C__12569)
=> ( t(Vvar__10__cI__12571,Vvar__8__C__12569)
=> ( c_24__type__13986___24t(Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595,Vvar__11__cadd__12572)
=> ( c_24__type__14199___24t(Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595,Vvar__12__cmul__12577)
=> ( c_24__type__14412___24t(Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595,Vvar__13__csub__12582)
=> ( c_24__type__14607___24t(Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595,Vvar__14__copp__12587)
=> ( c_24__type__14820___24t(Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595,Vvar__15__ceqb__12590)
=> ( c_24__type__15015___24t(Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595,Vvar__16__phi__12595)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__12543,Vvar__1__rO__12544,Vvar__2__rI__12545,Vvar__3__radd__12546,Vvar__4__rmul__12551,Vvar__5__rsub__12556,Vvar__6__ropp__12561,Vvar__7__req__12564,Vvar__8__C__12569,Vvar__9__cO__12570,Vvar__10__cI__12571,Vvar__11__cadd__12572,Vvar__12__cmul__12577,Vvar__13__csub__12582,Vvar__14__copp__12587,Vvar__15__ceqb__12590,Vvar__16__phi__12595)
=> ( p(happ(happ(Vvar__7__req__12564,happ(Vvar__16__phi__12595,Vvar__9__cO__12570)),Vvar__1__rO__12544))
& p(happ(happ(Vvar__7__req__12564,happ(Vvar__16__phi__12595,Vvar__10__cI__12571)),Vvar__2__rI__12545))
& ! [Vvar__var__var__var__var__var__var__19__x__12657__12659__12681__12683__12685__12687__12689] :
( t(Vvar__var__var__var__var__var__var__19__x__12657__12659__12681__12683__12685__12687__12689,Vvar__8__C__12569)
=> ! [Vvar__var__var__var__var__var__var__20__y__12658__12660__12682__12684__12686__12688__12690] :
( t(Vvar__var__var__var__var__var__var__20__y__12658__12660__12682__12684__12686__12688__12690,Vvar__8__C__12569)
=> p(happ(happ(Vvar__7__req__12564,happ(Vvar__16__phi__12595,happ(happ(Vvar__11__cadd__12572,Vvar__var__var__var__var__var__var__19__x__12657__12659__12681__12683__12685__12687__12689),Vvar__var__var__var__var__var__var__20__y__12658__12660__12682__12684__12686__12688__12690))),happ(happ(Vvar__3__radd__12546,happ(Vvar__16__phi__12595,Vvar__var__var__var__var__var__var__19__x__12657__12659__12681__12683__12685__12687__12689)),happ(Vvar__16__phi__12595,Vvar__var__var__var__var__var__var__20__y__12658__12660__12682__12684__12686__12688__12690)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__12662__12664__12691__12693__12695__12697__12699] :
( t(Vvar__var__var__var__var__var__var__20__x__12662__12664__12691__12693__12695__12697__12699,Vvar__8__C__12569)
=> ! [Vvar__var__var__var__var__var__var__21__y__12663__12665__12692__12694__12696__12698__12700] :
( t(Vvar__var__var__var__var__var__var__21__y__12663__12665__12692__12694__12696__12698__12700,Vvar__8__C__12569)
=> p(happ(happ(Vvar__7__req__12564,happ(Vvar__16__phi__12595,happ(happ(Vvar__13__csub__12582,Vvar__var__var__var__var__var__var__20__x__12662__12664__12691__12693__12695__12697__12699),Vvar__var__var__var__var__var__var__21__y__12663__12665__12692__12694__12696__12698__12700))),happ(happ(Vvar__5__rsub__12556,happ(Vvar__16__phi__12595,Vvar__var__var__var__var__var__var__20__x__12662__12664__12691__12693__12695__12697__12699)),happ(Vvar__16__phi__12595,Vvar__var__var__var__var__var__var__21__y__12663__12665__12692__12694__12696__12698__12700)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__12667__12669__12701__12703__12705__12707__12709] :
( t(Vvar__var__var__var__var__var__var__21__x__12667__12669__12701__12703__12705__12707__12709,Vvar__8__C__12569)
=> ! [Vvar__var__var__var__var__var__var__22__y__12668__12670__12702__12704__12706__12708__12710] :
( t(Vvar__var__var__var__var__var__var__22__y__12668__12670__12702__12704__12706__12708__12710,Vvar__8__C__12569)
=> p(happ(happ(Vvar__7__req__12564,happ(Vvar__16__phi__12595,happ(happ(Vvar__12__cmul__12577,Vvar__var__var__var__var__var__var__21__x__12667__12669__12701__12703__12705__12707__12709),Vvar__var__var__var__var__var__var__22__y__12668__12670__12702__12704__12706__12708__12710))),happ(happ(Vvar__4__rmul__12551,happ(Vvar__16__phi__12595,Vvar__var__var__var__var__var__var__21__x__12667__12669__12701__12703__12705__12707__12709)),happ(Vvar__16__phi__12595,Vvar__var__var__var__var__var__var__22__y__12668__12670__12702__12704__12706__12708__12710)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__12672__12673__12711__12712__12713__12714__12715] :
( t(Vvar__var__var__var__var__var__var__22__x__12672__12673__12711__12712__12713__12714__12715,Vvar__8__C__12569)
=> p(happ(happ(Vvar__7__req__12564,happ(Vvar__16__phi__12595,happ(Vvar__14__copp__12587,Vvar__var__var__var__var__var__var__22__x__12672__12673__12711__12712__12713__12714__12715))),happ(Vvar__6__ropp__12561,happ(Vvar__16__phi__12595,Vvar__var__var__var__var__var__var__22__x__12672__12673__12711__12712__12713__12714__12715)))) )
& ! [Vvar__var__var__var__var__var__23__x__12675__12678__12716__12719__12722__12725] :
( t(Vvar__var__var__var__var__var__23__x__12675__12678__12716__12719__12722__12725,Vvar__8__C__12569)
=> ! [Vvar__var__var__var__var__var__24__y__12676__12679__12717__12720__12723__12726] :
( t(Vvar__var__var__var__var__var__24__y__12676__12679__12717__12720__12723__12726,Vvar__8__C__12569)
=> ( happ(happ(Vvar__15__ceqb__12590,Vvar__var__var__var__var__var__23__x__12675__12678__12716__12719__12722__12725),Vvar__var__var__var__var__var__24__y__12676__12679__12717__12720__12723__12726) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__12564,happ(Vvar__16__phi__12595,Vvar__var__var__var__var__var__23__x__12675__12678__12716__12719__12722__12725)),happ(Vvar__16__phi__12595,Vvar__var__var__var__var__var__24__y__12676__12679__12717__12720__12723__12726))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__10506,Vvar__1__rO__10507,Vvar__2__rI__10508,Vvar__3__radd__10509,Vvar__4__rmul__10514,Vvar__5__rsub__10519,Vvar__6__ropp__10524,Vvar__7__req__10527] :
( cType___24t(Vvar__0__R__10506)
=> ( t(Vvar__1__rO__10507,Vvar__0__R__10506)
=> ( t(Vvar__2__rI__10508,Vvar__0__R__10506)
=> ( c_24__type__10730___24t(Vvar__0__R__10506,Vvar__1__rO__10507,Vvar__2__rI__10508,Vvar__3__radd__10509,Vvar__4__rmul__10514,Vvar__5__rsub__10519,Vvar__6__ropp__10524,Vvar__7__req__10527,Vvar__3__radd__10509)
=> ( c_24__type__10793___24t(Vvar__0__R__10506,Vvar__1__rO__10507,Vvar__2__rI__10508,Vvar__3__radd__10509,Vvar__4__rmul__10514,Vvar__5__rsub__10519,Vvar__6__ropp__10524,Vvar__7__req__10527,Vvar__4__rmul__10514)
=> ( c_24__type__10856___24t(Vvar__0__R__10506,Vvar__1__rO__10507,Vvar__2__rI__10508,Vvar__3__radd__10509,Vvar__4__rmul__10514,Vvar__5__rsub__10519,Vvar__6__ropp__10524,Vvar__7__req__10527,Vvar__5__rsub__10519)
=> ( c_24__type__10910___24t(Vvar__0__R__10506,Vvar__1__rO__10507,Vvar__2__rI__10508,Vvar__3__radd__10509,Vvar__4__rmul__10514,Vvar__5__rsub__10519,Vvar__6__ropp__10524,Vvar__7__req__10527,Vvar__6__ropp__10524)
=> ( c_24__type__10973___24t(Vvar__0__R__10506,Vvar__1__rO__10507,Vvar__2__rI__10508,Vvar__3__radd__10509,Vvar__4__rmul__10514,Vvar__5__rsub__10519,Vvar__6__ropp__10524,Vvar__7__req__10527,Vvar__7__req__10527)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__10506,Vvar__1__rO__10507,Vvar__2__rI__10508,Vvar__3__radd__10509,Vvar__4__rmul__10514,Vvar__5__rsub__10519,Vvar__6__ropp__10524,Vvar__7__req__10527)
=> ( ! [Vvar__var__var__var__var__var__8__x__10560__10561__10604__10605__10606__10607] :
( t(Vvar__var__var__var__var__var__8__x__10560__10561__10604__10605__10606__10607,Vvar__0__R__10506)
=> p(happ(happ(Vvar__7__req__10527,happ(happ(Vvar__3__radd__10509,Vvar__1__rO__10507),Vvar__var__var__var__var__var__8__x__10560__10561__10604__10605__10606__10607)),Vvar__var__var__var__var__var__8__x__10560__10561__10604__10605__10606__10607)) )
& ! [Vvar__var__var__var__var__9__x__10563__10565__10608__10610__10612] :
( t(Vvar__var__var__var__var__9__x__10563__10565__10608__10610__10612,Vvar__0__R__10506)
=> ! [Vvar__var__var__var__var__10__y__10564__10566__10609__10611__10613] :
( t(Vvar__var__var__var__var__10__y__10564__10566__10609__10611__10613,Vvar__0__R__10506)
=> p(happ(happ(Vvar__7__req__10527,happ(happ(Vvar__3__radd__10509,Vvar__var__var__var__var__9__x__10563__10565__10608__10610__10612),Vvar__var__var__var__var__10__y__10564__10566__10609__10611__10613)),happ(happ(Vvar__3__radd__10509,Vvar__var__var__var__var__10__y__10564__10566__10609__10611__10613),Vvar__var__var__var__var__9__x__10563__10565__10608__10610__10612))) ) )
& ! [Vvar__var__var__var__var__10__x__10568__10571__10614__10617__10620] :
( t(Vvar__var__var__var__var__10__x__10568__10571__10614__10617__10620,Vvar__0__R__10506)
=> ! [Vvar__var__var__var__var__11__y__10569__10572__10615__10618__10621] :
( t(Vvar__var__var__var__var__11__y__10569__10572__10615__10618__10621,Vvar__0__R__10506)
=> ! [Vvar__var__var__var__var__12__z__10570__10573__10616__10619__10622] :
( t(Vvar__var__var__var__var__12__z__10570__10573__10616__10619__10622,Vvar__0__R__10506)
=> p(happ(happ(Vvar__7__req__10527,happ(happ(Vvar__3__radd__10509,Vvar__var__var__var__var__10__x__10568__10571__10614__10617__10620),happ(happ(Vvar__3__radd__10509,Vvar__var__var__var__var__11__y__10569__10572__10615__10618__10621),Vvar__var__var__var__var__12__z__10570__10573__10616__10619__10622))),happ(happ(Vvar__3__radd__10509,happ(happ(Vvar__3__radd__10509,Vvar__var__var__var__var__10__x__10568__10571__10614__10617__10620),Vvar__var__var__var__var__11__y__10569__10572__10615__10618__10621)),Vvar__var__var__var__var__12__z__10570__10573__10616__10619__10622))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__10575__10576__10623__10624__10625__10626] :
( t(Vvar__var__var__var__var__var__11__x__10575__10576__10623__10624__10625__10626,Vvar__0__R__10506)
=> p(happ(happ(Vvar__7__req__10527,happ(happ(Vvar__4__rmul__10514,Vvar__2__rI__10508),Vvar__var__var__var__var__var__11__x__10575__10576__10623__10624__10625__10626)),Vvar__var__var__var__var__var__11__x__10575__10576__10623__10624__10625__10626)) )
& ! [Vvar__var__var__var__var__12__x__10578__10580__10627__10629__10631] :
( t(Vvar__var__var__var__var__12__x__10578__10580__10627__10629__10631,Vvar__0__R__10506)
=> ! [Vvar__var__var__var__var__13__y__10579__10581__10628__10630__10632] :
( t(Vvar__var__var__var__var__13__y__10579__10581__10628__10630__10632,Vvar__0__R__10506)
=> p(happ(happ(Vvar__7__req__10527,happ(happ(Vvar__4__rmul__10514,Vvar__var__var__var__var__12__x__10578__10580__10627__10629__10631),Vvar__var__var__var__var__13__y__10579__10581__10628__10630__10632)),happ(happ(Vvar__4__rmul__10514,Vvar__var__var__var__var__13__y__10579__10581__10628__10630__10632),Vvar__var__var__var__var__12__x__10578__10580__10627__10629__10631))) ) )
& ! [Vvar__var__var__var__var__13__x__10583__10586__10633__10636__10639] :
( t(Vvar__var__var__var__var__13__x__10583__10586__10633__10636__10639,Vvar__0__R__10506)
=> ! [Vvar__var__var__var__var__14__y__10584__10587__10634__10637__10640] :
( t(Vvar__var__var__var__var__14__y__10584__10587__10634__10637__10640,Vvar__0__R__10506)
=> ! [Vvar__var__var__var__var__15__z__10585__10588__10635__10638__10641] :
( t(Vvar__var__var__var__var__15__z__10585__10588__10635__10638__10641,Vvar__0__R__10506)
=> p(happ(happ(Vvar__7__req__10527,happ(happ(Vvar__4__rmul__10514,Vvar__var__var__var__var__13__x__10583__10586__10633__10636__10639),happ(happ(Vvar__4__rmul__10514,Vvar__var__var__var__var__14__y__10584__10587__10634__10637__10640),Vvar__var__var__var__var__15__z__10585__10588__10635__10638__10641))),happ(happ(Vvar__4__rmul__10514,happ(happ(Vvar__4__rmul__10514,Vvar__var__var__var__var__13__x__10583__10586__10633__10636__10639),Vvar__var__var__var__var__14__y__10584__10587__10634__10637__10640)),Vvar__var__var__var__var__15__z__10585__10588__10635__10638__10641))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__10590__10593__10642__10645__10648__10651] :
( t(Vvar__var__var__var__var__var__14__x__10590__10593__10642__10645__10648__10651,Vvar__0__R__10506)
=> ! [Vvar__var__var__var__var__var__15__y__10591__10594__10643__10646__10649__10652] :
( t(Vvar__var__var__var__var__var__15__y__10591__10594__10643__10646__10649__10652,Vvar__0__R__10506)
=> ! [Vvar__var__var__var__var__var__16__z__10592__10595__10644__10647__10650__10653] :
( t(Vvar__var__var__var__var__var__16__z__10592__10595__10644__10647__10650__10653,Vvar__0__R__10506)
=> p(happ(happ(Vvar__7__req__10527,happ(happ(Vvar__4__rmul__10514,happ(happ(Vvar__3__radd__10509,Vvar__var__var__var__var__var__14__x__10590__10593__10642__10645__10648__10651),Vvar__var__var__var__var__var__15__y__10591__10594__10643__10646__10649__10652)),Vvar__var__var__var__var__var__16__z__10592__10595__10644__10647__10650__10653)),happ(happ(Vvar__3__radd__10509,happ(happ(Vvar__4__rmul__10514,Vvar__var__var__var__var__var__14__x__10590__10593__10642__10645__10648__10651),Vvar__var__var__var__var__var__16__z__10592__10595__10644__10647__10650__10653)),happ(happ(Vvar__4__rmul__10514,Vvar__var__var__var__var__var__15__y__10591__10594__10643__10646__10649__10652),Vvar__var__var__var__var__var__16__z__10592__10595__10644__10647__10650__10653)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__10597__10599__10654__10656__10658__10660__10662] :
( t(Vvar__var__var__var__var__var__var__15__x__10597__10599__10654__10656__10658__10660__10662,Vvar__0__R__10506)
=> ! [Vvar__var__var__var__var__var__var__16__y__10598__10600__10655__10657__10659__10661__10663] :
( t(Vvar__var__var__var__var__var__var__16__y__10598__10600__10655__10657__10659__10661__10663,Vvar__0__R__10506)
=> p(happ(happ(Vvar__7__req__10527,happ(happ(Vvar__5__rsub__10519,Vvar__var__var__var__var__var__var__15__x__10597__10599__10654__10656__10658__10660__10662),Vvar__var__var__var__var__var__var__16__y__10598__10600__10655__10657__10659__10661__10663)),happ(happ(Vvar__3__radd__10509,Vvar__var__var__var__var__var__var__15__x__10597__10599__10654__10656__10658__10660__10662),happ(Vvar__6__ropp__10524,Vvar__var__var__var__var__var__var__16__y__10598__10600__10655__10657__10659__10661__10663)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__10602__10603__10664__10665__10666__10667__10668] :
( t(Vvar__var__var__var__var__var__var__16__x__10602__10603__10664__10665__10666__10667__10668,Vvar__0__R__10506)
=> p(happ(happ(Vvar__7__req__10527,happ(happ(Vvar__3__radd__10509,Vvar__var__var__var__var__var__var__16__x__10602__10603__10664__10665__10666__10667__10668),happ(Vvar__6__ropp__10524,Vvar__var__var__var__var__var__var__16__x__10602__10603__10664__10665__10666__10667__10668))),Vvar__1__rO__10507)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__11545,Vvar__1__rO__11546,Vvar__2__rI__11547,Vvar__3__radd__11548,Vvar__4__rmul__11553,Vvar__5__req__11558,Vvar__6__C__11563,Vvar__7__cO__11564,Vvar__8__cI__11565,Vvar__9__cadd__11566,Vvar__10__cmul__11571,Vvar__11__ceqb__11576,Vvar__12__phi__11581] :
( cType___24t(Vvar__0__R__11545)
=> ( t(Vvar__1__rO__11546,Vvar__0__R__11545)
=> ( t(Vvar__2__rI__11547,Vvar__0__R__11545)
=> ( c_24__type__11798___24t(Vvar__0__R__11545,Vvar__1__rO__11546,Vvar__2__rI__11547,Vvar__3__radd__11548,Vvar__4__rmul__11553,Vvar__5__req__11558,Vvar__6__C__11563,Vvar__7__cO__11564,Vvar__8__cI__11565,Vvar__9__cadd__11566,Vvar__10__cmul__11571,Vvar__11__ceqb__11576,Vvar__12__phi__11581,Vvar__3__radd__11548)
=> ( c_24__type__11923___24t(Vvar__0__R__11545,Vvar__1__rO__11546,Vvar__2__rI__11547,Vvar__3__radd__11548,Vvar__4__rmul__11553,Vvar__5__req__11558,Vvar__6__C__11563,Vvar__7__cO__11564,Vvar__8__cI__11565,Vvar__9__cadd__11566,Vvar__10__cmul__11571,Vvar__11__ceqb__11576,Vvar__12__phi__11581,Vvar__4__rmul__11553)
=> ( c_24__type__12048___24t(Vvar__0__R__11545,Vvar__1__rO__11546,Vvar__2__rI__11547,Vvar__3__radd__11548,Vvar__4__rmul__11553,Vvar__5__req__11558,Vvar__6__C__11563,Vvar__7__cO__11564,Vvar__8__cI__11565,Vvar__9__cadd__11566,Vvar__10__cmul__11571,Vvar__11__ceqb__11576,Vvar__12__phi__11581,Vvar__5__req__11558)
=> ( cType___24t(Vvar__6__C__11563)
=> ( t(Vvar__7__cO__11564,Vvar__6__C__11563)
=> ( t(Vvar__8__cI__11565,Vvar__6__C__11563)
=> ( c_24__type__12173___24t(Vvar__0__R__11545,Vvar__1__rO__11546,Vvar__2__rI__11547,Vvar__3__radd__11548,Vvar__4__rmul__11553,Vvar__5__req__11558,Vvar__6__C__11563,Vvar__7__cO__11564,Vvar__8__cI__11565,Vvar__9__cadd__11566,Vvar__10__cmul__11571,Vvar__11__ceqb__11576,Vvar__12__phi__11581,Vvar__9__cadd__11566)
=> ( c_24__type__12298___24t(Vvar__0__R__11545,Vvar__1__rO__11546,Vvar__2__rI__11547,Vvar__3__radd__11548,Vvar__4__rmul__11553,Vvar__5__req__11558,Vvar__6__C__11563,Vvar__7__cO__11564,Vvar__8__cI__11565,Vvar__9__cadd__11566,Vvar__10__cmul__11571,Vvar__11__ceqb__11576,Vvar__12__phi__11581,Vvar__10__cmul__11571)
=> ( c_24__type__12423___24t(Vvar__0__R__11545,Vvar__1__rO__11546,Vvar__2__rI__11547,Vvar__3__radd__11548,Vvar__4__rmul__11553,Vvar__5__req__11558,Vvar__6__C__11563,Vvar__7__cO__11564,Vvar__8__cI__11565,Vvar__9__cadd__11566,Vvar__10__cmul__11571,Vvar__11__ceqb__11576,Vvar__12__phi__11581,Vvar__11__ceqb__11576)
=> ( c_24__type__12534___24t(Vvar__0__R__11545,Vvar__1__rO__11546,Vvar__2__rI__11547,Vvar__3__radd__11548,Vvar__4__rmul__11553,Vvar__5__req__11558,Vvar__6__C__11563,Vvar__7__cO__11564,Vvar__8__cI__11565,Vvar__9__cadd__11566,Vvar__10__cmul__11571,Vvar__11__ceqb__11576,Vvar__12__phi__11581,Vvar__12__phi__11581)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__11545,Vvar__1__rO__11546,Vvar__2__rI__11547,Vvar__3__radd__11548,Vvar__4__rmul__11553,Vvar__5__req__11558,Vvar__6__C__11563,Vvar__7__cO__11564,Vvar__8__cI__11565,Vvar__9__cadd__11566,Vvar__10__cmul__11571,Vvar__11__ceqb__11576,Vvar__12__phi__11581)
=> ( p(happ(happ(Vvar__5__req__11558,happ(Vvar__12__phi__11581,Vvar__7__cO__11564)),Vvar__1__rO__11546))
& p(happ(happ(Vvar__5__req__11558,happ(Vvar__12__phi__11581,Vvar__8__cI__11565)),Vvar__2__rI__11547))
& ! [Vvar__var__var__var__var__var__var__15__x__11627__11629__11643__11645__11647__11649__11651] :
( t(Vvar__var__var__var__var__var__var__15__x__11627__11629__11643__11645__11647__11649__11651,Vvar__6__C__11563)
=> ! [Vvar__var__var__var__var__var__var__16__y__11628__11630__11644__11646__11648__11650__11652] :
( t(Vvar__var__var__var__var__var__var__16__y__11628__11630__11644__11646__11648__11650__11652,Vvar__6__C__11563)
=> p(happ(happ(Vvar__5__req__11558,happ(Vvar__12__phi__11581,happ(happ(Vvar__9__cadd__11566,Vvar__var__var__var__var__var__var__15__x__11627__11629__11643__11645__11647__11649__11651),Vvar__var__var__var__var__var__var__16__y__11628__11630__11644__11646__11648__11650__11652))),happ(happ(Vvar__3__radd__11548,happ(Vvar__12__phi__11581,Vvar__var__var__var__var__var__var__15__x__11627__11629__11643__11645__11647__11649__11651)),happ(Vvar__12__phi__11581,Vvar__var__var__var__var__var__var__16__y__11628__11630__11644__11646__11648__11650__11652)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__11632__11634__11653__11655__11657__11659__11661] :
( t(Vvar__var__var__var__var__var__var__16__x__11632__11634__11653__11655__11657__11659__11661,Vvar__6__C__11563)
=> ! [Vvar__var__var__var__var__var__var__17__y__11633__11635__11654__11656__11658__11660__11662] :
( t(Vvar__var__var__var__var__var__var__17__y__11633__11635__11654__11656__11658__11660__11662,Vvar__6__C__11563)
=> p(happ(happ(Vvar__5__req__11558,happ(Vvar__12__phi__11581,happ(happ(Vvar__10__cmul__11571,Vvar__var__var__var__var__var__var__16__x__11632__11634__11653__11655__11657__11659__11661),Vvar__var__var__var__var__var__var__17__y__11633__11635__11654__11656__11658__11660__11662))),happ(happ(Vvar__4__rmul__11553,happ(Vvar__12__phi__11581,Vvar__var__var__var__var__var__var__16__x__11632__11634__11653__11655__11657__11659__11661)),happ(Vvar__12__phi__11581,Vvar__var__var__var__var__var__var__17__y__11633__11635__11654__11656__11658__11660__11662)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__11637__11640__11663__11666__11669__11672] :
( t(Vvar__var__var__var__var__var__17__x__11637__11640__11663__11666__11669__11672,Vvar__6__C__11563)
=> ! [Vvar__var__var__var__var__var__18__y__11638__11641__11664__11667__11670__11673] :
( t(Vvar__var__var__var__var__var__18__y__11638__11641__11664__11667__11670__11673,Vvar__6__C__11563)
=> ( happ(happ(Vvar__11__ceqb__11576,Vvar__var__var__var__var__var__17__x__11637__11640__11663__11666__11669__11672),Vvar__var__var__var__var__var__18__y__11638__11641__11664__11667__11670__11673) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__11558,happ(Vvar__12__phi__11581,Vvar__var__var__var__var__var__17__x__11637__11640__11663__11666__11669__11672)),happ(Vvar__12__phi__11581,Vvar__var__var__var__var__var__18__y__11638__11641__11664__11667__11670__11673))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__9726,Vvar__1__rO__9727,Vvar__2__rI__9728,Vvar__3__radd__9729,Vvar__4__rmul__9734,Vvar__5__req__9739] :
( cType___24t(Vvar__0__R__9726)
=> ( t(Vvar__1__rO__9727,Vvar__0__R__9726)
=> ( t(Vvar__2__rI__9728,Vvar__0__R__9726)
=> ( c_24__type__9894___24t(Vvar__0__R__9726,Vvar__1__rO__9727,Vvar__2__rI__9728,Vvar__3__radd__9729,Vvar__4__rmul__9734,Vvar__5__req__9739,Vvar__3__radd__9729)
=> ( c_24__type__9933___24t(Vvar__0__R__9726,Vvar__1__rO__9727,Vvar__2__rI__9728,Vvar__3__radd__9729,Vvar__4__rmul__9734,Vvar__5__req__9739,Vvar__4__rmul__9734)
=> ( c_24__type__9972___24t(Vvar__0__R__9726,Vvar__1__rO__9727,Vvar__2__rI__9728,Vvar__3__radd__9729,Vvar__4__rmul__9734,Vvar__5__req__9739,Vvar__5__req__9739)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__9726,Vvar__1__rO__9727,Vvar__2__rI__9728,Vvar__3__radd__9729,Vvar__4__rmul__9734,Vvar__5__req__9739)
=> ( ! [Vvar__var__var__var__var__var__6__n__9764__9765__9803__9804__9805__9806] :
( t(Vvar__var__var__var__var__var__6__n__9764__9765__9803__9804__9805__9806,Vvar__0__R__9726)
=> p(happ(happ(Vvar__5__req__9739,happ(happ(Vvar__3__radd__9729,Vvar__1__rO__9727),Vvar__var__var__var__var__var__6__n__9764__9765__9803__9804__9805__9806)),Vvar__var__var__var__var__var__6__n__9764__9765__9803__9804__9805__9806)) )
& ! [Vvar__var__var__var__var__7__n__9767__9769__9807__9809__9811] :
( t(Vvar__var__var__var__var__7__n__9767__9769__9807__9809__9811,Vvar__0__R__9726)
=> ! [Vvar__var__var__var__var__8__m__9768__9770__9808__9810__9812] :
( t(Vvar__var__var__var__var__8__m__9768__9770__9808__9810__9812,Vvar__0__R__9726)
=> p(happ(happ(Vvar__5__req__9739,happ(happ(Vvar__3__radd__9729,Vvar__var__var__var__var__7__n__9767__9769__9807__9809__9811),Vvar__var__var__var__var__8__m__9768__9770__9808__9810__9812)),happ(happ(Vvar__3__radd__9729,Vvar__var__var__var__var__8__m__9768__9770__9808__9810__9812),Vvar__var__var__var__var__7__n__9767__9769__9807__9809__9811))) ) )
& ! [Vvar__var__var__var__var__8__n__9772__9775__9813__9816__9819] :
( t(Vvar__var__var__var__var__8__n__9772__9775__9813__9816__9819,Vvar__0__R__9726)
=> ! [Vvar__var__var__var__var__9__m__9773__9776__9814__9817__9820] :
( t(Vvar__var__var__var__var__9__m__9773__9776__9814__9817__9820,Vvar__0__R__9726)
=> ! [Vvar__var__var__var__var__10__p__9774__9777__9815__9818__9821] :
( t(Vvar__var__var__var__var__10__p__9774__9777__9815__9818__9821,Vvar__0__R__9726)
=> p(happ(happ(Vvar__5__req__9739,happ(happ(Vvar__3__radd__9729,Vvar__var__var__var__var__8__n__9772__9775__9813__9816__9819),happ(happ(Vvar__3__radd__9729,Vvar__var__var__var__var__9__m__9773__9776__9814__9817__9820),Vvar__var__var__var__var__10__p__9774__9777__9815__9818__9821))),happ(happ(Vvar__3__radd__9729,happ(happ(Vvar__3__radd__9729,Vvar__var__var__var__var__8__n__9772__9775__9813__9816__9819),Vvar__var__var__var__var__9__m__9773__9776__9814__9817__9820)),Vvar__var__var__var__var__10__p__9774__9777__9815__9818__9821))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__9779__9780__9822__9823__9824__9825] :
( t(Vvar__var__var__var__var__var__9__n__9779__9780__9822__9823__9824__9825,Vvar__0__R__9726)
=> p(happ(happ(Vvar__5__req__9739,happ(happ(Vvar__4__rmul__9734,Vvar__2__rI__9728),Vvar__var__var__var__var__var__9__n__9779__9780__9822__9823__9824__9825)),Vvar__var__var__var__var__var__9__n__9779__9780__9822__9823__9824__9825)) )
& ! [Vvar__var__var__var__var__var__10__n__9782__9783__9826__9827__9828__9829] :
( t(Vvar__var__var__var__var__var__10__n__9782__9783__9826__9827__9828__9829,Vvar__0__R__9726)
=> p(happ(happ(Vvar__5__req__9739,happ(happ(Vvar__4__rmul__9734,Vvar__1__rO__9727),Vvar__var__var__var__var__var__10__n__9782__9783__9826__9827__9828__9829)),Vvar__1__rO__9727)) )
& ! [Vvar__var__var__var__var__11__n__9785__9787__9830__9832__9834] :
( t(Vvar__var__var__var__var__11__n__9785__9787__9830__9832__9834,Vvar__0__R__9726)
=> ! [Vvar__var__var__var__var__12__m__9786__9788__9831__9833__9835] :
( t(Vvar__var__var__var__var__12__m__9786__9788__9831__9833__9835,Vvar__0__R__9726)
=> p(happ(happ(Vvar__5__req__9739,happ(happ(Vvar__4__rmul__9734,Vvar__var__var__var__var__11__n__9785__9787__9830__9832__9834),Vvar__var__var__var__var__12__m__9786__9788__9831__9833__9835)),happ(happ(Vvar__4__rmul__9734,Vvar__var__var__var__var__12__m__9786__9788__9831__9833__9835),Vvar__var__var__var__var__11__n__9785__9787__9830__9832__9834))) ) )
& ! [Vvar__var__var__var__var__12__n__9790__9793__9836__9839__9842] :
( t(Vvar__var__var__var__var__12__n__9790__9793__9836__9839__9842,Vvar__0__R__9726)
=> ! [Vvar__var__var__var__var__13__m__9791__9794__9837__9840__9843] :
( t(Vvar__var__var__var__var__13__m__9791__9794__9837__9840__9843,Vvar__0__R__9726)
=> ! [Vvar__var__var__var__var__14__p__9792__9795__9838__9841__9844] :
( t(Vvar__var__var__var__var__14__p__9792__9795__9838__9841__9844,Vvar__0__R__9726)
=> p(happ(happ(Vvar__5__req__9739,happ(happ(Vvar__4__rmul__9734,Vvar__var__var__var__var__12__n__9790__9793__9836__9839__9842),happ(happ(Vvar__4__rmul__9734,Vvar__var__var__var__var__13__m__9791__9794__9837__9840__9843),Vvar__var__var__var__var__14__p__9792__9795__9838__9841__9844))),happ(happ(Vvar__4__rmul__9734,happ(happ(Vvar__4__rmul__9734,Vvar__var__var__var__var__12__n__9790__9793__9836__9839__9842),Vvar__var__var__var__var__13__m__9791__9794__9837__9840__9843)),Vvar__var__var__var__var__14__p__9792__9795__9838__9841__9844))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__9797__9800__9845__9848__9851__9854] :
( t(Vvar__var__var__var__var__var__13__n__9797__9800__9845__9848__9851__9854,Vvar__0__R__9726)
=> ! [Vvar__var__var__var__var__var__14__m__9798__9801__9846__9849__9852__9855] :
( t(Vvar__var__var__var__var__var__14__m__9798__9801__9846__9849__9852__9855,Vvar__0__R__9726)
=> ! [Vvar__var__var__var__var__var__15__p__9799__9802__9847__9850__9853__9856] :
( t(Vvar__var__var__var__var__var__15__p__9799__9802__9847__9850__9853__9856,Vvar__0__R__9726)
=> p(happ(happ(Vvar__5__req__9739,happ(happ(Vvar__4__rmul__9734,happ(happ(Vvar__3__radd__9729,Vvar__var__var__var__var__var__13__n__9797__9800__9845__9848__9851__9854),Vvar__var__var__var__var__var__14__m__9798__9801__9846__9849__9852__9855)),Vvar__var__var__var__var__var__15__p__9799__9802__9847__9850__9853__9856)),happ(happ(Vvar__3__radd__9729,happ(happ(Vvar__4__rmul__9734,Vvar__var__var__var__var__var__13__n__9797__9800__9845__9848__9851__9854),Vvar__var__var__var__var__var__15__p__9799__9802__9847__9850__9853__9856)),happ(happ(Vvar__4__rmul__9734,Vvar__var__var__var__var__var__14__m__9798__9801__9846__9849__9852__9855),Vvar__var__var__var__var__var__15__p__9799__9802__9847__9850__9853__9856)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__10993,Vvar__1__radd__10994,Vvar__2__rmul__10999,Vvar__3__req__11004] :
( cType___24t(Vvar__0__R__10993)
=> ( c_24__type__11079___24t(Vvar__0__R__10993,Vvar__1__radd__10994,Vvar__2__rmul__10999,Vvar__3__req__11004,Vvar__1__radd__10994)
=> ( c_24__type__11102___24t(Vvar__0__R__10993,Vvar__1__radd__10994,Vvar__2__rmul__10999,Vvar__3__req__11004,Vvar__2__rmul__10999)
=> ( c_24__type__11125___24t(Vvar__0__R__10993,Vvar__1__radd__10994,Vvar__2__rmul__10999,Vvar__3__req__11004,Vvar__3__req__11004)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__10993,Vvar__1__radd__10994,Vvar__2__rmul__10999,Vvar__3__req__11004)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11148___24a4(Vvar__0__R__10993,Vvar__1__radd__10994,Vvar__2__rmul__10999,Vvar__3__req__11004),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__10993,c_24__type__11166___24a4(Vvar__0__R__10993,Vvar__1__radd__10994,Vvar__2__rmul__10999,Vvar__3__req__11004),Vvar__3__req__11004,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__10993,Vvar__0__R__10993,Vvar__3__req__11004,Vvar__3__req__11004)),Vvar__1__radd__10994)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11192___24a4(Vvar__0__R__10993,Vvar__1__radd__10994,Vvar__2__rmul__10999,Vvar__3__req__11004),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__10993,c_24__type__11210___24a4(Vvar__0__R__10993,Vvar__1__radd__10994,Vvar__2__rmul__10999,Vvar__3__req__11004),Vvar__3__req__11004,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__10993,Vvar__0__R__10993,Vvar__3__req__11004,Vvar__3__req__11004)),Vvar__2__rmul__10999)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [VX9153] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX9153)
=> ( VX9153 = cHammer_2eTactics_2eReconstr_2eEmpty
| VX9153 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).
fof('$_inversion_hahn.HahnBase.Equality.mixin_of',axiom,
! [Vvar__0__T__16438,VX16439] :
( cType___24t(Vvar__0__T__16438)
=> ( chahn_2eHahnBase_2eEquality_2emixin__of___24t(Vvar__0__T__16438,VX16439)
=> ? [Vvar__1__op__16441] :
( c_24__type__15342___24t(Vvar__0__T__16438,Vvar__1__op__16441)
& ? [Vvar__2___24Anonymous__16446] :
( chahn_2eHahnBase_2eEquality_2eaxiom___24t(Vvar__0__T__16438,Vvar__1__op__16441,Vvar__2___24Anonymous__16446)
& VX16439 = chahn_2eHahnBase_2eEquality_2eMixin___24a3(Vvar__0__T__16438,Vvar__1__op__16441,Vvar__2___24Anonymous__16446) ) ) ) ) ).
fof('$_inversion_hahn.HahnBase.Equality.type',axiom,
! [VX16458] :
( chahn_2eHahnBase_2eEquality_2etype___24t(VX16458)
=> ? [Vvar__0__sort__16459] :
( cType___24t(Vvar__0__sort__16459)
& ? [Vvar__1___24Anonymous__16460] :
( chahn_2eHahnBase_2eEquality_2emixin__of___24t(Vvar__0__sort__16459,Vvar__1___24Anonymous__16460)
& ? [Vvar__2___24Anonymous__16461] :
( cType___24t(Vvar__2___24Anonymous__16461)
& VX16458 = chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__16459,Vvar__1___24Anonymous__16460,Vvar__2___24Anonymous__16461) ) ) ) ) ).
fof('$_lam_14',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__14___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(c_24True) ) ).
fof('$_lam_1415',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__1415___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ).
fof('$_lam_17688',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__17688___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_17696',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__17696___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_18',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__18___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(c_24False) ) ).
fof('$_lam_1942',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__1942___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__4),Vv__CANONICAL__3) ).
fof('$_lam_1954',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__1954___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('$_lam_1962',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__1962___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(c_24False) ) ).
fof('$_lam_1983',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__1983___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('$_lam_1994',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__1994___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2einter__rel___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_2005',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__2005___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('$_lam_2016',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__2016___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2eminus__rel___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__2) ).
fof('$_lam_2045',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__2045___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(c_24True) ) ).
fof('$_lam_2048',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__2048___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = chahn_2eHahnRelationsBasic_2epow__rel___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ).
fof('$_lam_2053',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__2053___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('$_lam_2067',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__2067___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___24a1(Vv__CANONICAL__0),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(Vv__CANONICAL__0),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(Vv__CANONICAL__0),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(Vv__CANONICAL__0),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__1) ) ).
fof('$_lam_2094',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__2094___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ! [Vv__CANONICAL__3] :
( c_24__type__1764___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,chahn_2eHahnRelationsBasic_2ebunion___24a4(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__0,c_24__lam__2045___24a1(Vv__CANONICAL__0),c_24__lam__2100___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3))),chahn_2eHahnRelationsBasic_2ebunion___24a4(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__0,c_24__lam__2045___24a1(Vv__CANONICAL__0),c_24__lam__2108___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ).
fof('$_lam_2100',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__2100___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__1,Vv__CANONICAL__2) ).
fof('$_lam_2108',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__2108___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_2115',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__2115___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_2118',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__2118___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 ).
fof('$_lam_2124',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__2124___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) ).
fof('$_lam_2130',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__2130___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('$_lam_2139',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__2139___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_2148',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__2148___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_2189',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__2189___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__4))
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5))
& p(happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ) ) ).
fof('$_lam_2213',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__2213___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_2223',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__2223___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2erestr__rel___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_2239',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__2239___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('$_lam_2245',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__2245___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_2265',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__2265___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(Vv__CANONICAL__2,Vv__CANONICAL__4) ).
fof('$_lam_2277',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__2277___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ).
fof('$_lam_2345',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__2345___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(Vv__CANONICAL__3,Vv__CANONICAL__4) ).
fof('$_lam_2358',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__2358___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_2383',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__2383___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(cCoq_2eLists_2eList_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1)) ) ).
fof('$_lam_2620',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__2620___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
| p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ).
fof('$_lam_2628',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__2628___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(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ).
fof('$_lam_3062',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__3062___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_3066',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__3066___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_32',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__32___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
& p(happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ).
fof('$_lam_3359',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__3359___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> p(happ(happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4)),happ(Vv__CANONICAL__2,Vv__CANONICAL__5))) ) ).
fof('$_lam_43',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__43___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ).
fof('$_lam_5004',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__5004___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_5105',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__5105___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_prop_16492',axiom,
! [Vvar__0___24Anonymous__16468,Vvar__0__S__16470,Vvar__1__x__16471,Vvar__2__y__16472] :
( p(c_24__prop__16492___24a4(Vvar__0___24Anonymous__16468,Vvar__0__S__16470,Vvar__1__x__16471,Vvar__2__y__16472))
<=> Vvar__1__x__16471 = Vvar__2__y__16472 ) ).
fof('$_prop_16493',axiom,
! [Vvar__0___24Anonymous__16468,Vvar__0__x__16473,Vvar__1__y__16474] :
( p(c_24__prop__16493___24a3(Vvar__0___24Anonymous__16468,Vvar__0__x__16473,Vvar__1__y__16474))
<=> Vvar__0__x__16473 = Vvar__1__y__16474 ) ).
fof('$_prop_16494',axiom,
! [Vvar__0___24Anonymous__16468,Vvar__0__x__16475,Vvar__1__s__16476] :
( p(c_24__prop__16494___24a3(Vvar__0___24Anonymous__16468,Vvar__0__x__16475,Vvar__1__s__16476))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__16475,Vvar__1__s__16476) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_16495',axiom,
! [Vvar__0___24Anonymous__16468,Vvar__0__P__16477,Vvar__1__Q__16478] :
( p(c_24__prop__16495___24a3(Vvar__0___24Anonymous__16468,Vvar__0__P__16477,Vvar__1__Q__16478))
<=> ( p(Vvar__0__P__16477)
& p(Vvar__1__Q__16478) ) ) ).
fof('$_prop_16496',axiom,
! [Vvar__0___24Anonymous__16468,Vvar__0__P__16481,Vvar__1__Q__16482] :
( p(c_24__prop__16496___24a3(Vvar__0___24Anonymous__16468,Vvar__0__P__16481,Vvar__1__Q__16482))
<=> ( p(Vvar__0__P__16481)
| p(Vvar__1__Q__16482) ) ) ).
fof('$_prop_16497',axiom,
! [Vvar__0___24Anonymous__16468,Vvar__0__P__16485,Vvar__1__Q__16486] :
( p(c_24__prop__16497___24a3(Vvar__0___24Anonymous__16468,Vvar__0__P__16485,Vvar__1__Q__16486))
<=> ( p(Vvar__0__P__16485)
=> p(Vvar__1__Q__16486) ) ) ).
fof('$_prop_16498',axiom,
! [Vvar__0___24Anonymous__16468,Vvar__0__P__16490] :
( p(c_24__prop__16498___24a2(Vvar__0___24Anonymous__16468,Vvar__0__P__16490))
<=> ~ p(Vvar__0__P__16490) ) ).
fof('$_prop_16512',axiom,
! [Vvar__0___24Anonymous__16499,Vvar__0__s__16503] :
( p(c_24__prop__16512___24a2(Vvar__0___24Anonymous__16499,Vvar__0__s__16503))
<=> ! [Vvar__1__a__16504] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__16504)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__16504,Vvar__0__s__16503) ) ) ).
fof('$_prop_16513',axiom,
! [Vvar__0___24Anonymous__16499,Vvar__0__s1__16505,Vvar__1__s2__16506] :
( p(c_24__prop__16513___24a3(Vvar__0___24Anonymous__16499,Vvar__0__s1__16505,Vvar__1__s2__16506))
<=> ! [Vvar__2__a__16507] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__16507)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__16507,Vvar__0__s1__16505)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__16507,Vvar__1__s2__16506) ) ) ) ).
fof('$_prop_16514',axiom,
! [Vvar__0___24Anonymous__16499,Vvar__0__s1__16509,Vvar__1__s2__16510] :
( p(c_24__prop__16514___24a3(Vvar__0___24Anonymous__16499,Vvar__0__s1__16509,Vvar__1__s2__16510))
<=> ! [Vvar__2__a__16511] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__16511)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__16511,Vvar__0__s1__16509)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__16511,Vvar__1__s2__16510) ) ) ) ).
fof('$_prop_2473',axiom,
! [V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457] :
( p(c_24__prop__2473___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457)) ) ).
fof('$_prop_2485',axiom,
! [V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457] :
( p(c_24__prop__2485___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2456,Vvar__2___24Anonymous__2457)) ) ).
fof('$_type_1022',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1023] :
( c_24__type__1022___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1023)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__1023,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_10239',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__10240] :
( c_24__type__10239___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__10240)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10240,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_10302',axiom,
! [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__10303] :
( c_24__type__10302___24t(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__10303)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10303,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_10365',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__10366] :
( c_24__type__10365___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__10366)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10366,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_10419',axiom,
! [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__10420] :
( c_24__type__10419___24t(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__10420)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__10420,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_10482',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__10483] :
( c_24__type__10482___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__10483)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__10483,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_1057',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1058] :
( c_24__type__1057___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1058)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__1058,Vv__CANONICAL__3)) ) ) ).
fof('$_type_10730',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__10731] :
( c_24__type__10730___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__10731)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10731,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_10793',axiom,
! [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__10794] :
( c_24__type__10793___24t(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__10794)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10794,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_10856',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__10857] :
( c_24__type__10856___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__10857)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10857,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_10910',axiom,
! [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__10911] :
( c_24__type__10910___24t(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__10911)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__10911,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_10973',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__10974] :
( c_24__type__10973___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__10974)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__10974,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_11079',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11080] :
( c_24__type__11079___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11080)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11080,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11102',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11103] :
( c_24__type__11102___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11103)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11103,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11125',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11126] :
( c_24__type__11125___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11126)
<=> ! [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__11126,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_11148',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11149] :
( c_24__type__11148___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11149)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11149,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11166',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11167] :
( c_24__type__11166___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11167)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__11167,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_11192',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11193] :
( c_24__type__11192___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11193)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11193,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11210',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11211] :
( c_24__type__11210___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11211)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__11211,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_11320',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11321] :
( c_24__type__11320___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11321)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11321,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11350',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11351] :
( c_24__type__11350___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11351)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11351,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11374',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11375] :
( c_24__type__11374___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11375)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__11375,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_11404',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11405] :
( c_24__type__11404___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11405)
<=> ! [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__11405,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_11434',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11435] :
( c_24__type__11434___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11435)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11435,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11458',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11459] :
( c_24__type__11458___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11459)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__11459,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_11491',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11492] :
( c_24__type__11491___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11492)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11492,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11515',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11516] :
( c_24__type__11515___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11516)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__11516,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_11542',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11543] :
( c_24__type__11542___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11543)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__11543,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_11798',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__11799] :
( c_24__type__11798___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__11799)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11799,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11923',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__11924] :
( c_24__type__11923___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__11924)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11924,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12048',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__12049] :
( c_24__type__12048___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__12049)
<=> ! [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__12049,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_12173',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__12174] :
( c_24__type__12173___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__12174)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__12174,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_12298',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__12299] :
( c_24__type__12298___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__12299)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__12299,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_12423',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__12424] :
( c_24__type__12423___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__12424)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__12424,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_12534',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__12535] :
( c_24__type__12534___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__12535)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__12535,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_12939',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__12940] :
( c_24__type__12939___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__12940)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12940,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13152',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13153] :
( c_24__type__13152___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13153)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13153,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13365',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__13366] :
( c_24__type__13365___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__13366)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13366,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1344',axiom,
! [Vvar__1345] :
( c_24__type__1344___24t(Vvar__1345)
<=> ! [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__1345,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_13560',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__13561] :
( c_24__type__13560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__13561)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__13561,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_1368',axiom,
! [Vvar__1369] :
( c_24__type__1368___24t(Vvar__1369)
<=> ! [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__1369,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13773',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__13774] :
( c_24__type__13773___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__13774)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__13774,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_1397',axiom,
! [Vvar__1398] :
( c_24__type__1397___24t(Vvar__1398)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__1398,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13986',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__13987] :
( c_24__type__13986___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__13987)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__13987,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_14199',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14200] :
( c_24__type__14199___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14200)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__14200,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_1427',axiom,
! [Vvar__1428] :
( c_24__type__1427___24t(Vvar__1428)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__1428,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1429',axiom,
! [Vvar__1430] :
( c_24__type__1429___24t(Vvar__1430)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1430,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14412',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__14413] :
( c_24__type__14412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__14413)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__14413,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_1448',axiom,
! [Vvar__1449] :
( c_24__type__1448___24t(Vvar__1449)
<=> ! [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__1449,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_145',axiom,
! [Vvar__146] :
( c_24__type__145___24t(Vvar__146)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__146,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1450',axiom,
! [Vvar__1451] :
( c_24__type__1450___24t(Vvar__1451)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__1451,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1452',axiom,
! [Vvar__1453] :
( c_24__type__1452___24t(Vvar__1453)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__1453,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1457',axiom,
! [Vvar__1458] :
( c_24__type__1457___24t(Vvar__1458)
<=> ! [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__1458,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1460',axiom,
! [Vv__CANONICAL__0,Vvar__1461] :
( c_24__type__1460___24t(Vv__CANONICAL__0,Vvar__1461)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__1461,Vv__CANONICAL__1)) ) ) ).
fof('$_type_14607',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14608] :
( c_24__type__14607___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14608)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__14608,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_1473',axiom,
! [Vvar__1474] :
( c_24__type__1473___24t(Vvar__1474)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__1474,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14820',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14821] :
( c_24__type__14820___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14821)
<=> ! [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__14821,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_1485',axiom,
! [Vvar__1486] :
( c_24__type__1485___24t(Vvar__1486)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1486,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_15015',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__15016] :
( c_24__type__15015___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__15016)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__15016,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_15028',axiom,
! [Vvar__15029] :
( c_24__type__15028___24t(Vvar__15029)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15029,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15132',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15133] :
( c_24__type__15132___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15133)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15133,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15176',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15177] :
( c_24__type__15176___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15177)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__15177,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_15212',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15213] :
( c_24__type__15212___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15213)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__15213,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_15256',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15257] :
( c_24__type__15256___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15257)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__15257,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15342',axiom,
! [Vv__CANONICAL__0,Vvar__15343] :
( c_24__type__15342___24t(Vv__CANONICAL__0,Vvar__15343)
<=> ! [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__15343,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_15490',axiom,
! [Vvar__15491] :
( c_24__type__15490___24t(Vvar__15491)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__90___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__15500___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__15491,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_15500',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15501] :
( c_24__type__15500___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15501)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__15501,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_15533',axiom,
! [Vvar__15534] :
( c_24__type__15533___24t(Vvar__15534)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__90___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__15543___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__15500___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__15534,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_15543',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15544] :
( c_24__type__15543___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15544)
<=> ! [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__15544,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_15613',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15614] :
( c_24__type__15613___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15614)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__15614,Vv__CANONICAL__2)) ) ) ).
fof('$_type_15617',axiom,
! [Vvar__15618] :
( c_24__type__15617___24t(Vvar__15618)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__15618,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15652',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15653] :
( c_24__type__15652___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15653)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__15653,Vv__CANONICAL__3)) ) ) ).
fof('$_type_15660',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15661] :
( c_24__type__15660___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15661)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__15661,Vv__CANONICAL__3)) ) ) ).
fof('$_type_15668',axiom,
! [Vvar__15669] :
( c_24__type__15668___24t(Vvar__15669)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__15669,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_15698',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15699] :
( c_24__type__15698___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15699)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__15699,Vv__CANONICAL__2)) ) ) ).
fof('$_type_157',axiom,
! [Vvar__158] :
( c_24__type__157___24t(Vvar__158)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__158,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_15702',axiom,
! [Vvar__15703] :
( c_24__type__15702___24t(Vvar__15703)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__15703,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15737',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15738] :
( c_24__type__15737___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15738)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__15738,Vv__CANONICAL__3)) ) ) ).
fof('$_type_15745',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15746] :
( c_24__type__15745___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15746)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__15746,Vv__CANONICAL__3)) ) ) ).
fof('$_type_15753',axiom,
! [Vvar__15754] :
( c_24__type__15753___24t(Vvar__15754)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5369___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__15754,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_15779',axiom,
! [Vvar__15780] :
( c_24__type__15779___24t(Vvar__15780)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__15780,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15800',axiom,
! [Vvar__15801] :
( c_24__type__15800___24t(Vvar__15801)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ( p(c_24False)
=> t(happ(Vvar__15801,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15866',axiom,
! [Vvar__15867] :
( c_24__type__15866___24t(Vvar__15867)
<=> ! [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__15867,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_163',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__164] :
( c_24__type__163___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__164)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__164,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_16301',axiom,
! [Vvar__16302] :
( c_24__type__16301___24t(Vvar__16302)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__16302,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16535',axiom,
! [Vvar__16536] :
( c_24__type__16535___24t(Vvar__16536)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__16536,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_1654',axiom,
! [Vvar__1655] :
( c_24__type__1654___24t(Vvar__1655)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1656___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1655,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1656',axiom,
! [Vvar__1657] :
( c_24__type__1656___24t(Vvar__1657)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1657,Vv__CANONICAL__0)) ) ) ).
fof('$_type_16595',axiom,
! [Vvar__16596] :
( c_24__type__16595___24t(Vvar__16596)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__16596,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1661',axiom,
! [Vv__CANONICAL__0,Vvar__1662] :
( c_24__type__1661___24t(Vv__CANONICAL__0,Vvar__1662)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__1662,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_16993',axiom,
! [Vvar__16994] :
( c_24__type__16993___24t(Vvar__16994)
<=> ! [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__16994,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1701',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1702] :
( c_24__type__1701___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1702)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__163___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__1702,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_17082',axiom,
! [Vvar__17083] :
( c_24__type__17082___24t(Vvar__17083)
<=> ! [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__17083,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17155',axiom,
! [Vvar__17156] :
( c_24__type__17155___24t(Vvar__17156)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__17156,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17182',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17183] :
( c_24__type__17182___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17183)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__17183,Vv__CANONICAL__3)) ) ) ).
fof('$_type_17203',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17204] :
( c_24__type__17203___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17204)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__17204,Vv__CANONICAL__3)) ) ) ).
fof('$_type_1721',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1722] :
( c_24__type__1721___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1722)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__163___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__1722,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_17238',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17239] :
( c_24__type__17238___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17239)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__17239,Vv__CANONICAL__5)) ) ) ).
fof('$_type_17246',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17247] :
( c_24__type__17246___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17247)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__17247,Vv__CANONICAL__5)) ) ) ).
fof('$_type_17248',axiom,
! [Vvar__17249] :
( c_24__type__17248___24t(Vvar__17249)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__17249,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17253',axiom,
! [Vvar__17254] :
( c_24__type__17253___24t(Vvar__17254)
<=> ! [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__17254,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17280',axiom,
! [Vvar__17281] :
( c_24__type__17280___24t(Vvar__17281)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cProp___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__17281,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1729',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1730] :
( c_24__type__1729___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1730)
<=> ! [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__1730,Vv__CANONICAL__2)) ) ) ).
fof('$_type_1761',axiom,
! [Vv__CANONICAL__0,Vvar__1762] :
( c_24__type__1761___24t(Vv__CANONICAL__0,Vvar__1762)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__1762,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_1764',axiom,
! [Vv__CANONICAL__0,Vvar__1765] :
( c_24__type__1764___24t(Vv__CANONICAL__0,Vvar__1765)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__1765,Vv__CANONICAL__1)) ) ) ).
fof('$_type_17680',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__17681] :
( c_24__type__17680___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__17681)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__17681,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_1813',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1814] :
( c_24__type__1813___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1814)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__163___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__1814,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_1821',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1822] :
( c_24__type__1821___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1822)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(Vvar__1822,Vv__CANONICAL__2)) ) ) ).
fof('$_type_18231',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__18232] :
( c_24__type__18231___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__18232)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18232,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18577',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__18578] :
( c_24__type__18577___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__18578)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18578,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18923',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__18924] :
( c_24__type__18923___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__18924)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18924,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19246',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__19247] :
( c_24__type__19246___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__19247)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__19247,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_195',axiom,
! [Vvar__196] :
( c_24__type__195___24t(Vvar__196)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__163___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__196,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_19592',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__19593] :
( c_24__type__19592___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__19593)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__19593,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_19938',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__19939] :
( c_24__type__19938___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__19939)
<=> ! [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__19939,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_20284',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__20285] :
( c_24__type__20284___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__20285)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__20285,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_20630',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__20631] :
( c_24__type__20630___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__20631)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__20631,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_207',axiom,
! [Vvar__208] :
( c_24__type__207___24t(Vvar__208)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__163___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__208,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_20976',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__20977] :
( c_24__type__20976___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__20977)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__20977,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_21',axiom,
! [Vv__CANONICAL__0,Vvar__22] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vvar__22)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22,Vv__CANONICAL__1)) ) ) ).
fof('$_type_2111',axiom,
! [Vvar__2112] :
( c_24__type__2111___24t(Vvar__2112)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2112,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21299',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__21300] :
( c_24__type__21299___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__21300)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__21300,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_21645',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__21646] :
( c_24__type__21645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__21646)
<=> ! [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__21646,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_219',axiom,
! [Vvar__220] :
( c_24__type__219___24t(Vvar__220)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__163___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__220,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_21991',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__21992] :
( c_24__type__21991___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__21992)
<=> ! [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__21992,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_22314',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__22315] :
( c_24__type__22314___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__22315)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__22315,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_22637',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__22638] :
( c_24__type__22637___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__22638)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__22638,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_22983',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__22984] :
( c_24__type__22983___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__22984)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__22984,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22992',axiom,
! [Vvar__22993] :
( c_24__type__22992___24t(Vvar__22993)
<=> ! [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__22993,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22995',axiom,
! [Vvar__22996] :
( c_24__type__22995___24t(Vvar__22996)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__22996,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_230',axiom,
! [Vvar__231] :
( c_24__type__230___24t(Vvar__231)
<=> ! [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__231,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23037',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23038] :
( c_24__type__23037___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23038)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23038,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_23072',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23073] :
( c_24__type__23072___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23073)
<=> ! [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__23073,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_23101',axiom,
! [Vvar__23102] :
( c_24__type__23101___24t(Vvar__23102)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__23102,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23125',axiom,
! [Vvar__23126] :
( c_24__type__23125___24t(Vvar__23126)
<=> ! [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__23126,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23157',axiom,
! [Vvar__23158] :
( c_24__type__23157___24t(Vvar__23158)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__23158,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23172',axiom,
! [Vvar__23173] :
( c_24__type__23172___24t(Vvar__23173)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3364___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__23173,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_23189',axiom,
! [Vvar__23190] :
( c_24__type__23189___24t(Vvar__23190)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__23190,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2336',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2337] :
( c_24__type__2336___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2337)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__2337,Vv__CANONICAL__3)) ) ) ).
fof('$_type_23395',axiom,
! [Vvar__23396] :
( c_24__type__23395___24t(Vvar__23396)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__23396,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23405',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23406] :
( c_24__type__23405___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23406)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__23406,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_23410',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23411] :
( c_24__type__23410___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23411)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__23411,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_23416',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23417] :
( c_24__type__23416___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23417)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__23417,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_23421',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23422] :
( c_24__type__23421___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23422)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__23422,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_23453',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23454] :
( c_24__type__23453___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23454)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__23454,Vv__CANONICAL__3)) ) ) ).
fof('$_type_23477',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23478] :
( c_24__type__23477___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23478)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__23478,Vv__CANONICAL__3)) ) ) ).
fof('$_type_23524',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23525] :
( c_24__type__23524___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23525)
<=> ! [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__23525,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_23559',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23560] :
( c_24__type__23559___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23560)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23560,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_23564',axiom,
! [Vvar__23565] :
( c_24__type__23564___24t(Vvar__23565)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__23565,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23569',axiom,
! [Vvar__23570] :
( c_24__type__23569___24t(Vvar__23570)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__23570,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23594',axiom,
! [Vvar__23595] :
( c_24__type__23594___24t(Vvar__23595)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21___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__23595,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23646',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23647] :
( c_24__type__23646___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23647)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23647,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_23744',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23745] :
( c_24__type__23744___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23745)
<=> ! [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__23745,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_24170',axiom,
! [Vvar__24171] :
( c_24__type__24170___24t(Vvar__24171)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__24171,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_24210',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24211] :
( c_24__type__24210___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24211)
<=> ! [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__24211,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_24253',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24254] :
( c_24__type__24253___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24254)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24254,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_2427',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2428] :
( c_24__type__2427___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2428)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(Vvar__2428,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_24292',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24293] :
( c_24__type__24292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24293)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24293,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_24327',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24328] :
( c_24__type__24327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24328)
<=> ! [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__24328,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_24362',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24363] :
( c_24__type__24362___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24363)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24363,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_24371',axiom,
! [Vvar__24372] :
( c_24__type__24371___24t(Vvar__24372)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21___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__24372,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_2439',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2440] :
( c_24__type__2439___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2440)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__2440,Vv__CANONICAL__2)) ) ) ).
fof('$_type_24402',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24403] :
( c_24__type__24402___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24403)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__24403,Vv__CANONICAL__4)) ) ) ).
fof('$_type_24411',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24412] :
( c_24__type__24411___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24412)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__24412,Vv__CANONICAL__4)) ) ) ).
fof('$_type_24418',axiom,
! [Vvar__24419] :
( c_24__type__24418___24t(Vvar__24419)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__24419,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2487',axiom,
! [Vvar__2488] :
( c_24__type__2487___24t(Vvar__2488)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__2488,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2520',axiom,
! [Vvar__2521] :
( c_24__type__2520___24t(Vvar__2521)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__163___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2521,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2525',axiom,
! [Vvar__2526] :
( c_24__type__2525___24t(Vvar__2526)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__2526,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2535',axiom,
! [Vvar__2536] :
( c_24__type__2535___24t(Vvar__2536)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__2536,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2543',axiom,
! [Vvar__2544] :
( c_24__type__2543___24t(Vvar__2544)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__2544,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2557',axiom,
! [Vvar__2558] :
( c_24__type__2557___24t(Vvar__2558)
<=> ! [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__2558,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2588',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2589] :
( c_24__type__2588___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2589)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__2589,Vv__CANONICAL__2)) ) ) ).
fof('$_type_2611',axiom,
! [Vv__CANONICAL__0,Vvar__2612] :
( c_24__type__2611___24t(Vv__CANONICAL__0,Vvar__2612)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__2612,Vv__CANONICAL__1)) ) ) ).
fof('$_type_266',axiom,
! [Vv__CANONICAL__0,Vvar__267] :
( c_24__type__266___24t(Vv__CANONICAL__0,Vvar__267)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__267,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_271',axiom,
! [Vv__CANONICAL__0,Vvar__272] :
( c_24__type__271___24t(Vv__CANONICAL__0,Vvar__272)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__272,Vv__CANONICAL__1)) ) ) ).
fof('$_type_2759',axiom,
! [Vvar__2760] :
( c_24__type__2759___24t(Vvar__2760)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__2760,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2767',axiom,
! [Vvar__2768] :
( c_24__type__2767___24t(Vvar__2768)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2768,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2795',axiom,
! [Vvar__2796] :
( c_24__type__2795___24t(Vvar__2796)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2796,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_297',axiom,
! [Vvar__298] :
( c_24__type__297___24t(Vvar__298)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__163___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)
=> cProp___24t(happ(happ(happ(happ(Vvar__298,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2992',axiom,
! [Vvar__2993] :
( c_24__type__2992___24t(Vvar__2993)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__2993,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2995',axiom,
! [Vvar__2996] :
( c_24__type__2995___24t(Vvar__2996)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__2996,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2998',axiom,
! [Vvar__2999] :
( c_24__type__2998___24t(Vvar__2999)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2999,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_336',axiom,
! [Vvar__337] :
( c_24__type__336___24t(Vvar__337)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__337,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3364',axiom,
! [Vv__CANONICAL__0,Vvar__3365] :
( c_24__type__3364___24t(Vv__CANONICAL__0,Vvar__3365)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3365,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3373',axiom,
! [Vv__CANONICAL__0,Vvar__3374] :
( c_24__type__3373___24t(Vv__CANONICAL__0,Vvar__3374)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__3374,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_3389',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3390] :
( c_24__type__3389___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3390)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__3390,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_3403',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3404] :
( c_24__type__3403___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3404)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__3404,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_3410',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3411] :
( c_24__type__3410___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3411)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__3411,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_3419',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3420] :
( c_24__type__3419___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3420)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__3420,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_357',axiom,
! [Vvar__358] :
( c_24__type__357___24t(Vvar__358)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__358,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_374',axiom,
! [Vvar__375] :
( c_24__type__374___24t(Vvar__375)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__21___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__375,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_4',axiom,
! [Vv__CANONICAL__0,Vvar__5] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vvar__5)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__5,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_429',axiom,
! [Vv__CANONICAL__0,Vvar__430] :
( c_24__type__429___24t(Vv__CANONICAL__0,Vvar__430)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__21___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__430,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_4344',axiom,
! [Vvar__4345] :
( c_24__type__4344___24t(Vvar__4345)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__4345,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_47',axiom,
! [Vvar__48] :
( c_24__type__47___24t(Vvar__48)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__48,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_474',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__475] :
( c_24__type__474___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__475)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(happ(Vvar__475,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_479',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__480] :
( c_24__type__479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__480)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(Vvar__480,Vv__CANONICAL__2)) ) ) ).
fof('$_type_486',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__487] :
( c_24__type__486___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__487)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(Vvar__487,Vv__CANONICAL__2)) ) ) ).
fof('$_type_4891',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__4892] :
( c_24__type__4891___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__4892)
<=> ! [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__4892,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_4919',axiom,
! [Vvar__4920] :
( c_24__type__4919___24t(Vvar__4920)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__90___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4920,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4925',axiom,
! [Vvar__4926] :
( c_24__type__4925___24t(Vvar__4926)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__4926,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4931',axiom,
! [Vvar__4932] :
( c_24__type__4931___24t(Vvar__4932)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4932,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4935',axiom,
! [Vvar__4936] :
( c_24__type__4935___24t(Vvar__4936)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4936,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4974',axiom,
! [Vv__CANONICAL__0,Vvar__4975] :
( c_24__type__4974___24t(Vv__CANONICAL__0,Vvar__4975)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__4975,Vv__CANONICAL__1)) ) ) ).
fof('$_type_4987',axiom,
! [Vvar__4988] :
( c_24__type__4987___24t(Vvar__4988)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__4989___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eN0))
=> ! [Vv__CANONICAL__2] :
( c_24__type__4994___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__4988,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4989',axiom,
! [Vvar__4990] :
( c_24__type__4989___24t(Vvar__4990)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__4990,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4994',axiom,
! [Vv__CANONICAL__0,Vvar__4995] :
( c_24__type__4994___24t(Vv__CANONICAL__0,Vvar__4995)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__4995,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_4999',axiom,
! [Vv__CANONICAL__0,Vvar__5000] :
( c_24__type__4999___24t(Vv__CANONICAL__0,Vvar__5000)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__5000,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_5016',axiom,
! [Vvar__5017] :
( c_24__type__5016___24t(Vvar__5017)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5021___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__5017,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_5021',axiom,
! [Vv__CANONICAL__0,Vvar__5022] :
( c_24__type__5021___24t(Vv__CANONICAL__0,Vvar__5022)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5022,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5034',axiom,
! [Vv__CANONICAL__0,Vvar__5035] :
( c_24__type__5034___24t(Vv__CANONICAL__0,Vvar__5035)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5021___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(Vvar__5035,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_5045',axiom,
! [Vv__CANONICAL__0,Vvar__5046] :
( c_24__type__5045___24t(Vv__CANONICAL__0,Vvar__5046)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__5021___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__5046,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5054',axiom,
! [Vv__CANONICAL__0,Vvar__5055] :
( c_24__type__5054___24t(Vv__CANONICAL__0,Vvar__5055)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__5055,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_5117',axiom,
! [Vvar__5118] :
( c_24__type__5117___24t(Vvar__5118)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5122___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__5118,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_5122',axiom,
! [Vv__CANONICAL__0,Vvar__5123] :
( c_24__type__5122___24t(Vv__CANONICAL__0,Vvar__5123)
<=> ! [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__5123,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5135',axiom,
! [Vv__CANONICAL__0,Vvar__5136] :
( c_24__type__5135___24t(Vv__CANONICAL__0,Vvar__5136)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5122___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(Vvar__5136,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_5146',axiom,
! [Vv__CANONICAL__0,Vvar__5147] :
( c_24__type__5146___24t(Vv__CANONICAL__0,Vvar__5147)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__5122___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__5147,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5155',axiom,
! [Vv__CANONICAL__0,Vvar__5156] :
( c_24__type__5155___24t(Vv__CANONICAL__0,Vvar__5156)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__5156,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_5217',axiom,
! [Vvar__5218] :
( c_24__type__5217___24t(Vvar__5218)
<=> ! [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__5218,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5221',axiom,
! [Vvar__5222] :
( c_24__type__5221___24t(Vvar__5222)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__5222,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5291',axiom,
! [Vvar__5292] :
( c_24__type__5291___24t(Vvar__5292)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__5292,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5293',axiom,
! [Vvar__5294] :
( c_24__type__5293___24t(Vvar__5294)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__5294,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5303',axiom,
! [Vvar__5304] :
( c_24__type__5303___24t(Vvar__5304)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__5304,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5330',axiom,
! [Vvar__5331] :
( c_24__type__5330___24t(Vvar__5331)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__5331,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5347',axiom,
! [Vvar__5348] :
( c_24__type__5347___24t(Vvar__5348)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__5348,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5355',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5356] :
( c_24__type__5355___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5356)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cProp___24t(happ(happ(Vvar__5356,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_5362',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5363] :
( c_24__type__5362___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5363)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__5363,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_5366',axiom,
! [Vvar__5367] :
( c_24__type__5366___24t(Vvar__5367)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__5367,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5369',axiom,
! [Vv__CANONICAL__0,Vvar__5370] :
( c_24__type__5369___24t(Vv__CANONICAL__0,Vvar__5370)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__5370,Vv__CANONICAL__1)) ) ) ).
fof('$_type_5374',axiom,
! [Vv__CANONICAL__0,Vvar__5375] :
( c_24__type__5374___24t(Vv__CANONICAL__0,Vvar__5375)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__5375,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_5379',axiom,
! [Vvar__5380] :
( c_24__type__5379___24t(Vvar__5380)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5380,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5447',axiom,
! [Vvar__5448] :
( c_24__type__5447___24t(Vvar__5448)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__5448,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5450',axiom,
! [Vvar__5451] :
( c_24__type__5450___24t(Vvar__5451)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__5451,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5474',axiom,
! [Vvar__5475] :
( c_24__type__5474___24t(Vvar__5475)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__5475,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_552',axiom,
! [Vvar__553] :
( c_24__type__552___24t(Vvar__553)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21___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__553,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5534',axiom,
! [Vvar__5535] :
( c_24__type__5534___24t(Vvar__5535)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5535,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5708',axiom,
! [Vv__CANONICAL__0,Vvar__5709] :
( c_24__type__5708___24t(Vv__CANONICAL__0,Vvar__5709)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__5709,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_575',axiom,
! [Vvar__576] :
( c_24__type__575___24t(Vvar__576)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__576,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_5807',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__5808] :
( c_24__type__5807___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__5808)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__5808,Vv__CANONICAL__6)) ) ) ).
fof('$_type_581',axiom,
! [Vvar__582] :
( c_24__type__581___24t(Vvar__582)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__582,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5835',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__5836] :
( c_24__type__5835___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__5836)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__5836,Vv__CANONICAL__6)) ) ) ).
fof('$_type_588',axiom,
! [Vvar__589] :
( c_24__type__588___24t(Vvar__589)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__589,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_600',axiom,
! [Vvar__601] :
( c_24__type__600___24t(Vvar__601)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__601,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_6039',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6040] :
( c_24__type__6039___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6040)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6040,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_61',axiom,
! [Vv__CANONICAL__0,Vvar__62] :
( c_24__type__61___24t(Vv__CANONICAL__0,Vvar__62)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__62,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_6132',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6133] :
( c_24__type__6132___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6133)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6133,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6225',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6226] :
( c_24__type__6225___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6226)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6226,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6307',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6308] :
( c_24__type__6307___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6308)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__6308,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_6400',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6401] :
( c_24__type__6400___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6401)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6401,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_644',axiom,
! [Vvar__645] :
( c_24__type__644___24t(Vvar__645)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__163___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__650___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__645,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_6482',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6483] :
( c_24__type__6482___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6483)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__6483,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_650',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__651] :
( c_24__type__650___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__651)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__651,Vv__CANONICAL__2)) ) ) ).
fof('$_type_6575',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6576] :
( c_24__type__6575___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6576)
<=> ! [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__6576,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_66',axiom,
! [Vvar__67] :
( c_24__type__66___24t(Vvar__67)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__67,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_667',axiom,
! [Vvar__668] :
( c_24__type__667___24t(Vvar__668)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__163___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__673___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__668,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_673',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__674] :
( c_24__type__673___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__674)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__674,Vv__CANONICAL__2)) ) ) ).
fof('$_type_6789',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6790] :
( c_24__type__6789___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6790)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6790,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6882',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6883] :
( c_24__type__6882___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6883)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6883,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_694',axiom,
! [Vvar__695] :
( c_24__type__694___24t(Vvar__695)
<=> ! [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__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__702___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__695,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_6975',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6976] :
( c_24__type__6975___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6976)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6976,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7',axiom,
! [Vv__CANONICAL__0,Vvar__8] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vvar__8)
<=> ! [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__8,Vv__CANONICAL__1)) ) ) ).
fof('$_type_702',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__703] :
( c_24__type__702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__703)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__703,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_7057',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__7058] :
( c_24__type__7057___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__7058)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__7058,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_7150',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7151] :
( c_24__type__7150___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7151)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7151,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_72',axiom,
! [Vvar__73] :
( c_24__type__72___24t(Vvar__73)
<=> ! [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__73,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7232',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7233] :
( c_24__type__7232___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7233)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__7233,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_7325',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__7326] :
( c_24__type__7325___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__7326)
<=> ! [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__7326,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_7479',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__7480] :
( c_24__type__7479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__7480)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7480,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_75',axiom,
! [Vvar__76] :
( c_24__type__75___24t(Vvar__76)
<=> ! [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__76,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7542',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__7543] :
( c_24__type__7542___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__7543)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7543,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7605',axiom,
! [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__7606] :
( c_24__type__7605___24t(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__7606)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7606,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7659',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__7660] :
( c_24__type__7659___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__7660)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__7660,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_7722',axiom,
! [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__7723] :
( c_24__type__7722___24t(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__7723)
<=> ! [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__7723,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_7733',axiom,
! [Vvar__7734] :
( c_24__type__7733___24t(Vvar__7734)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__7734,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7749',axiom,
! [Vvar__7750] :
( c_24__type__7749___24t(Vvar__7750)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__163___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__7750,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7785',axiom,
! [Vvar__7786] :
( c_24__type__7785___24t(Vvar__7786)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3364___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3364___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__7786,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_8272',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__8273] :
( c_24__type__8272___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__8273)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8273,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_83',axiom,
! [Vvar__84] :
( c_24__type__83___24t(Vvar__84)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__21___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__84,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8373',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__8374] :
( c_24__type__8373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__8374)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8374,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8474',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__8475] :
( c_24__type__8474___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__8475)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8475,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8564',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__8565] :
( c_24__type__8564___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__8565)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__8565,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_8665',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__8666] :
( c_24__type__8665___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__8666)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__8666,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_8766',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__8767] :
( c_24__type__8766___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__8767)
<=> ! [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__8767,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_8867',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__8868] :
( c_24__type__8867___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__8868)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__8868,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_8991',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8992] :
( c_24__type__8991___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8992)
<=> ! [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__8992,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_90',axiom,
! [Vv__CANONICAL__0,Vvar__91] :
( c_24__type__90___24t(Vv__CANONICAL__0,Vvar__91)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__91,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_9010',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9011] :
( c_24__type__9010___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9011)
<=> ! [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__9011,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_9030',axiom,
! [Vvar__9031] :
( c_24__type__9030___24t(Vvar__9031)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__90___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__90___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__9031,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_92',axiom,
! [Vvar__93] :
( c_24__type__92___24t(Vvar__93)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__93,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9213',axiom,
! [Vvar__9214] :
( c_24__type__9213___24t(Vvar__9214)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__9214,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_97',axiom,
! [Vvar__98] :
( c_24__type__97___24t(Vvar__98)
<=> ! [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__98,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9700',axiom,
! [Vvar__9701] :
( c_24__type__9700___24t(Vvar__9701)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3364___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__9701,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_9721',axiom,
! [Vvar__9722] :
( c_24__type__9721___24t(Vvar__9722)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3364___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__9722,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_9894',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__9895] :
( c_24__type__9894___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__9895)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9895,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9933',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__9934] :
( c_24__type__9933___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__9934)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9934,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9972',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__9973] :
( c_24__type__9972___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__9973)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__9973,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_typeof_A',axiom,
cType___24t(cA) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__2795___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
c_24__type__2795___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
c_24__type__2795___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__5117___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__17248___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__5447___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
c_24__type__17253___24t(cCoq_2eBool_2eBool_2eifb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__5303___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.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
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.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('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__17280___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_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__1450___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__1427___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__1448___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__5447___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__1485___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_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__1457___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.length',axiom,
c_24__type__1473___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__92___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__5450___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__1452___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__92___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__5447___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__16993___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__5474___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__5474___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.xorb',axiom,
c_24__type__5447___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_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.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
c_24__type__5379___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__2759___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__2759___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__2759___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__2759___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__1427___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__2759___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.t',axiom,
cType___24t(cCoq_2eInit_2eNat_2et) ).
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__1429___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__2795___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__2795___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.except',axiom,
c_24__type__15800___24t(cCoq_2eInit_2eSpecif_2eexcept) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__24371___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__15617___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__15668___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__15702___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__15753___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__4344___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__15779___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__4919___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__1344___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__15490___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__15490___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__15533___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__15533___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on',axiom,
c_24__type__5366___24t(cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalChoice_on',axiom,
c_24__type__5347___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalChoice_on_rel',axiom,
c_24__type__5330___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on',axiom,
c_24__type__5379___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ProofIrrelevance',axiom,
cProp___24t(cCoq_2eLogic_2eChoiceFacts_2eProofIrrelevance) ).
fof('$_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.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.weak_generalized_excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eweak__generalized__excluded__middle) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__5534___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.FinFun.Bijective',axiom,
c_24__type__7749___24t(cCoq_2eLogic_2eFinFun_2eBijective) ).
fof('$_typeof_Coq.Logic.FinFun.Injective',axiom,
c_24__type__7749___24t(cCoq_2eLogic_2eFinFun_2eInjective) ).
fof('$_typeof_Coq.Logic.FinFun.Surjective',axiom,
c_24__type__7749___24t(cCoq_2eLogic_2eFinFun_2eSurjective) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__4931___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__4931___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNat.N.peano_rect',axiom,
c_24__type__4987___24t(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect) ).
fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
c_24__type__5016___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__4925___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.t',axiom,
cType___24t(cCoq_2eNArith_2eBinNatDef_2eN_2et) ).
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('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__5293___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__1397___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__1397___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__5291___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__5291___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
c_24__type__16595___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).
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('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
c_24__type__24418___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
c_24__type__5291___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__16535___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__23172___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.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__23569___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__17082___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__23564___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
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('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__2995___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__2998___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__2992___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__2995___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__2992___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__17155___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__9213___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
c_24__type__230___24t(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.commut',axiom,
c_24__type__97___24t(cCoq_2eRelations_2eRelation__Definitions_2ecommut) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.equiv',axiom,
c_24__type__230___24t(cCoq_2eRelations_2eRelation__Definitions_2eequiv) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.inclusion',axiom,
c_24__type__97___24t(cCoq_2eRelations_2eRelation__Definitions_2einclusion) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__230___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__92___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.same_relation',axiom,
c_24__type__97___24t(cCoq_2eRelations_2eRelation__Definitions_2esame__relation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.symmetric',axiom,
c_24__type__230___24t(cCoq_2eRelations_2eRelation__Definitions_2esymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__230___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Relations.Relation_Operators.transp',axiom,
c_24__type__145___24t(cCoq_2eRelations_2eRelation__Operators_2etransp) ).
fof('$_typeof_Coq.Relations.Relation_Operators.union',axiom,
c_24__type__157___24t(cCoq_2eRelations_2eRelation__Operators_2eunion) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__230___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__92___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__9030___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__4931___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__2795___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__2795___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__23157___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__23157___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
c_24__type__1368___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).
fof('$_typeof_Coq.Structures.OrdersTac.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('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__7733___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__16301___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
c_24__type__1368___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__1368___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__1368___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__5217___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__5217___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__5221___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__5217___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__5221___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_pos',axiom,
c_24__type__23189___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.Zeven.Zeven',axiom,
c_24__type__2767___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__2767___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__23101___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__9213___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__23125___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__92___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__92___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__23395___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__92___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__23594___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__92___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_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__92___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__92___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__92___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__15866___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__92___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__92___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__92___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__92___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__7785___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__7785___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_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.PEX',axiom,
c_24__type__22995___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__24170___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__22992___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__92___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__92___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__9700___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__15028___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__15028___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__4925___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__9721___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_HahnMinElt.min_elt',axiom,
c_24__type__47___24t(cHahnMinElt_2emin__elt) ).
fof('$_typeof_HahnMinElt.wmin_elt',axiom,
c_24__type__47___24t(cHahnMinElt_2ewmin__elt) ).
fof('$_typeof_Hammer.Tactics.Reconstr.ReconstrT',axiom,
cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).
fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
c_24__type__581___24t(cHammer_2eTactics_2eReconstr_2erdone) ).
fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
c_24__type__581___24t(cHammer_2eTactics_2eTactics_2erdone) ).
fof('$_typeof_a',axiom,
cA___24t(ca) ).
fof('$_typeof_hahn.HahnBase.Equality.mixin_of',axiom,
c_24__type__92___24t(chahn_2eHahnBase_2eEquality_2emixin__of) ).
fof('$_typeof_hahn.HahnBase.Equality.type',axiom,
cType___24t(chahn_2eHahnBase_2eEquality_2etype) ).
fof('$_typeof_hahn.HahnBase.NW',axiom,
c_24__type__1654___24t(chahn_2eHahnBase_2eNW) ).
fof('$_typeof_hahn.HahnEquational.good_ctx',axiom,
c_24__type__2111___24t(chahn_2eHahnEquational_2egood__ctx) ).
fof('$_typeof_hahn.HahnFuneq.funeq',axiom,
c_24__type__297___24t(chahn_2eHahnFuneq_2efuneq) ).
fof('$_typeof_hahn.HahnList.undup',axiom,
c_24__type__2487___24t(chahn_2eHahnList_2eundup) ).
fof('$_typeof_hahn.HahnMaxElt.max_elt',axiom,
c_24__type__47___24t(chahn_2eHahnMaxElt_2emax__elt) ).
fof('$_typeof_hahn.HahnMaxElt.wmax_elt',axiom,
c_24__type__47___24t(chahn_2eHahnMaxElt_2ewmax__elt) ).
fof('$_typeof_hahn.HahnRelationsBasic.acyclic',axiom,
c_24__type__230___24t(chahn_2eHahnRelationsBasic_2eacyclic) ).
fof('$_typeof_hahn.HahnRelationsBasic.bunion',axiom,
c_24__type__575___24t(chahn_2eHahnRelationsBasic_2ebunion) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_refl',axiom,
c_24__type__75___24t(chahn_2eHahnRelationsBasic_2eclos__refl) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_refl_sym',axiom,
c_24__type__75___24t(chahn_2eHahnRelationsBasic_2eclos__refl__sym) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_sym',axiom,
c_24__type__75___24t(chahn_2eHahnRelationsBasic_2eclos__sym) ).
fof('$_typeof_hahn.HahnRelationsBasic.codom_rel',axiom,
c_24__type__47___24t(chahn_2eHahnRelationsBasic_2ecodom__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.collect_rel',axiom,
c_24__type__219___24t(chahn_2eHahnRelationsBasic_2ecollect__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.cross_rel',axiom,
c_24__type__374___24t(chahn_2eHahnRelationsBasic_2ecross__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.dom_rel',axiom,
c_24__type__47___24t(chahn_2eHahnRelationsBasic_2edom__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eq_rel',axiom,
c_24__type__2520___24t(chahn_2eHahnRelationsBasic_2eeq__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eqv_dom_rel',axiom,
c_24__type__2525___24t(chahn_2eHahnRelationsBasic_2eeqv__dom__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eqv_rel',axiom,
c_24__type__66___24t(chahn_2eHahnRelationsBasic_2eeqv__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.functional',axiom,
c_24__type__230___24t(chahn_2eHahnRelationsBasic_2efunctional) ).
fof('$_typeof_hahn.HahnRelationsBasic.immediate',axiom,
c_24__type__75___24t(chahn_2eHahnRelationsBasic_2eimmediate) ).
fof('$_typeof_hahn.HahnRelationsBasic.inter_rel',axiom,
c_24__type__72___24t(chahn_2eHahnRelationsBasic_2einter__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.irreflexive',axiom,
c_24__type__230___24t(chahn_2eHahnRelationsBasic_2eirreflexive) ).
fof('$_typeof_hahn.HahnRelationsBasic.is_total',axiom,
c_24__type__357___24t(chahn_2eHahnRelationsBasic_2eis__total) ).
fof('$_typeof_hahn.HahnRelationsBasic.map_rel',axiom,
c_24__type__207___24t(chahn_2eHahnRelationsBasic_2emap__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.minus_rel',axiom,
c_24__type__72___24t(chahn_2eHahnRelationsBasic_2eminus__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.pow_rel',axiom,
c_24__type__2557___24t(chahn_2eHahnRelationsBasic_2epow__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_eq_rel',axiom,
c_24__type__195___24t(chahn_2eHahnRelationsBasic_2erestr__eq__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_rel',axiom,
c_24__type__552___24t(chahn_2eHahnRelationsBasic_2erestr__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_subset',axiom,
c_24__type__2535___24t(chahn_2eHahnRelationsBasic_2erestr__subset) ).
fof('$_typeof_hahn.HahnRelationsBasic.seq',axiom,
c_24__type__72___24t(chahn_2eHahnRelationsBasic_2eseq) ).
fof('$_typeof_hahn.HahnRelationsBasic.singl_rel',axiom,
c_24__type__336___24t(chahn_2eHahnRelationsBasic_2esingl__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.strict_partial_order',axiom,
c_24__type__230___24t(chahn_2eHahnRelationsBasic_2estrict__partial__order) ).
fof('$_typeof_hahn.HahnRelationsBasic.strict_total_order',axiom,
c_24__type__357___24t(chahn_2eHahnRelationsBasic_2estrict__total__order) ).
fof('$_typeof_hahn.HahnRelationsBasic.upward_closed',axiom,
c_24__type__2543___24t(chahn_2eHahnRelationsBasic_2eupward__closed) ).
fof('$_typeof_hahn.HahnSets.set_bunion',axiom,
c_24__type__694___24t(chahn_2eHahnSets_2eset__bunion) ).
fof('$_typeof_hahn.HahnSets.set_collect',axiom,
c_24__type__644___24t(chahn_2eHahnSets_2eset__collect) ).
fof('$_typeof_hahn.HahnSets.set_compl',axiom,
c_24__type__588___24t(chahn_2eHahnSets_2eset__compl) ).
fof('$_typeof_hahn.HahnSets.set_disjoint',axiom,
c_24__type__83___24t(chahn_2eHahnSets_2eset__disjoint) ).
fof('$_typeof_hahn.HahnSets.set_empty',axiom,
c_24__type__581___24t(chahn_2eHahnSets_2eset__empty) ).
fof('$_typeof_hahn.HahnSets.set_equiv',axiom,
c_24__type__83___24t(chahn_2eHahnSets_2eset__equiv) ).
fof('$_typeof_hahn.HahnSets.set_full',axiom,
c_24__type__581___24t(chahn_2eHahnSets_2eset__full) ).
fof('$_typeof_hahn.HahnSets.set_inter',axiom,
c_24__type__600___24t(chahn_2eHahnSets_2eset__inter) ).
fof('$_typeof_hahn.HahnSets.set_map',axiom,
c_24__type__667___24t(chahn_2eHahnSets_2eset__map) ).
fof('$_typeof_hahn.HahnSets.set_minus',axiom,
c_24__type__600___24t(chahn_2eHahnSets_2eset__minus) ).
fof('$_typeof_hahn.HahnSets.set_subset',axiom,
c_24__type__83___24t(chahn_2eHahnSets_2eset__subset) ).
fof('$_typeof_hahn.HahnSets.set_union',axiom,
c_24__type__600___24t(chahn_2eHahnSets_2eset__union) ).
fof('$_typeof_r',axiom,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,cr) ).
fof('$_typeof_r\'',axiom,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,cr_27) ).
fof('$_typeof_r\'\'',axiom,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,cr_27_27) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.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.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.induction',axiom,
! [V0__A] :
( c_24__type__1429___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1429,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e),V0__A)
=> ( p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(happ(V0__A,V3__n))
=> p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n))) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(happ(V0__A,V4__n)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2795,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__1429,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),cCoq_2eInit_2ePeano_2ele) ).
fof('Coq.Arith.PeanoNat.Nat.lt_exists_pred',axiom,
! [V0__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__z,V1__n)
=> ? [V3__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__k)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(V3__k)
& cCoq_2eInit_2ePeano_2ele___24a2(V0__z,V3__k) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2795,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__1429,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),cCoq_2eInit_2ePeano_2elt) ).
fof('Coq.Arith.PeanoNat.Nat.recursion_succ',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__f] :
( c_24__type__5122___24t(V0__A,V3__f)
=> ( p(happ(happ(V1__Aeq,V2__a),V2__a))
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5122___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__3373___24a1(V0__A),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),V3__f)
=> ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> p(happ(happ(V1__Aeq,cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4(V0__A,V2__a,V3__f,cCoq_2eInit_2eDatatypes_2eS___24a1(V6__n))),happ(happ(V3__f,V6__n),cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4(V0__A,V2__a,V3__f,V6__n)))) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.recursion_wd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5135___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__5146___24a1(V0__A),V1__Aeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__5122___24a1(V0__A),c_24__type__5155___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__3373___24a1(V0__A),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,V0__A,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),V1__Aeq))),cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A)) ) ) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__1429___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.Init.Wf.Acc_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__90___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__21___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V4__y),V3__x))
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V4__y) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V3__x))
=> p(happ(V2__P,V5__y)) ) )
=> p(happ(V2__P,V3__x)) ) ) )
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V4__x)
=> p(happ(V2__P,V4__x)) ) ) ) ) ) ) ).
fof('Coq.Init.Wf.Acc_intro',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__90___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V3__y),V2__x))
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V3__y) ) )
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__x) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1460___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V4__l))
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.app_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27)) ) ) ) ).
fof('Coq.Lists.List.in_app_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)))
<=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V2__l))
=> ? [V4__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
& ? [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
& V2__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V5__l2)) ) ) ) ) ) ) ).
fof('Coq.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.ClassicalDescription.unique_choice',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__702___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> cCoq_2eInit_2eLogic_2eex___24a2(V1__B,cCoq_2eInit_2eLogic_2eunique___24a2(V1__B,c_24__lam__1415___24a4(V0__A,V1__B,V2__R,V3__x))) )
=> ? [V4__f] :
( c_24__type__163___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('Coq.Logic.Classical_Prop.NNPP',axiom,
! [V0__p] :
( cProp___24t(V0__p)
=> ( ~ ~ p(V0__p)
=> p(V0__p) ) ) ).
fof('Coq.Logic.Classical_Prop.Peirce',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( ( ( p(V0__P)
=> p(c_24False) )
=> p(V0__P) )
=> p(V0__P) ) ) ).
fof('Coq.Logic.Classical_Prop.classic',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_and_or',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( p(V0__P)
=> p(V1__Q) )
=> ( ( p(V0__P)
| p(V1__Q) )
=> p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_and_or2',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ! [V2__R] :
( cProp___24t(V2__R)
=> ( ( p(V0__P)
=> p(V1__Q) )
=> ( ( p(V0__P)
| p(V2__R) )
=> ( p(V1__Q)
| p(V2__R) ) ) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.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.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
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__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__163___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__5369___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__23405___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__23410___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__163___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__17696___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__5369___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__17680___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__17688___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__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__163___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__5369___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__23416___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__23421___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.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
fof('Coq.NArith.BinNat.N.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.induction',axiom,
! [V0__A] :
( c_24__type__4935___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4935,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e),V0__A)
=> ( p(happ(V0__A,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> ( p(happ(V0__A,V3__n))
=> p(happ(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n))) ) )
=> ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__n)
=> p(happ(V0__A,V4__n)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ).
fof('Coq.NArith.BinNat.N.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m)
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4931,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__4935,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e)),cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('Coq.NArith.BinNat.N.lt_exists_pred',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__z,V1__n)
=> ? [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__k)
& V1__n = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__k)
& cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__z,V3__k) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) ) ).
fof('Coq.NArith.BinNat.N.lt_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.peano_ind',axiom,
! [V0__P] :
( c_24__type__4935___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.peano_rect_succ',axiom,
! [V0__P] :
( c_24__type__4989___24t(V0__P)
=> ! [V1__a] :
( t(V1__a,happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
=> ! [V2__f] :
( c_24__type__4999___24t(V0__P,V2__f)
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V0__P,V1__a,V2__f,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n)) = happ(happ(V2__f,V3__n),cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V0__P,V1__a,V2__f,V3__n)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.recursion_succ',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__f] :
( c_24__type__5021___24t(V0__A,V3__f)
=> ( p(happ(happ(V1__Aeq,V2__a),V2__a))
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5021___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__3373___24a1(V0__A),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),V3__f)
=> ! [V6__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V6__n)
=> p(happ(happ(V1__Aeq,cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4(V0__A,V2__a,V3__f,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V6__n))),happ(happ(V3__f,V6__n),cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4(V0__A,V2__a,V3__f,V6__n)))) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.recursion_wd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5034___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__5045___24a1(V0__A),V1__Aeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__5021___24a1(V0__A),c_24__type__5054___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__3373___24a1(V0__A),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,V0__A,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),V1__Aeq))),cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_r_clos_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a2(V0__A,V1__R),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_refl_trans_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__21___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V6__z)
=> p(happ(V3__P,V6__z)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_refl_trans_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__21___24t(V0__A,V2__P)
=> ! [V3__z] :
( t(V3__z,V0__A)
=> ( p(happ(V2__P,V3__z))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__R,V5__x),V6__y))
=> ( p(happ(V2__P,V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V3__z)
=> p(happ(V2__P,V5__x)) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V3__z)
=> p(happ(V2__P,V6__x)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_idempotent',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_is_equiv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rst1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rst1n_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rstn1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rstn1_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rstn1_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rstn1_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rstn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt1n_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt1n_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_clos_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_idempotent',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_is_preorder',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rt1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rt1n_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rtn1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rtn1_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rtn1_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rtn1_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_t1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_tn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_t1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_t1n_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_tn1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_tn1_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_transp_permute',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__R),V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__R),V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.rt1n_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__21___24t(V0__A,V2__P)
=> ! [V3__z] :
( t(V3__z,V0__A)
=> ( p(happ(V2__P,V3__z))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__R,V5__x),V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V6__y,V3__z)
=> ( p(happ(V2__P,V6__y))
=> p(happ(V2__P,V5__x)) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V6__x,V3__z)
=> p(happ(V2__P,V6__x)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_PER',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V0__A,V1__R) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_equivalence',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_order',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_preorder',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_antisym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.per_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.per_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__21___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( p(happ(V3__P,V2__x))
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__21___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( p(happ(V3__P,V2__x))
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__90___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V4__x),V5__y))
| p(happ(happ(V1__R,V5__y),V4__x)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__90___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V4__x),V5__y))
| p(happ(happ(V1__R,V5__y),V4__x)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__90___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> p(happ(happ(V2__P,V6__y),V5__x)) ) ) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ! [V8__z] :
( t(V8__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V6__x,V7__y)
=> ( p(happ(happ(V2__P,V6__x),V7__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__y,V8__z)
=> ( p(happ(happ(V2__P,V7__y),V8__z))
=> p(happ(happ(V2__P,V6__x),V8__z)) ) ) ) ) ) ) )
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ! [V8__a] :
( t(V8__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__a,V8__a)
=> p(happ(happ(V2__P,V7__a),V8__a)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__21___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V5__y),V6__z))
| p(happ(happ(V1__R,V6__z),V5__y)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__21___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V5__y),V6__z))
| p(happ(happ(V1__R,V6__z),V5__y)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__90___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> p(happ(happ(V2__P,V6__y),V5__x)) ) ) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ! [V8__z] :
( t(V8__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V6__x,V7__y)
=> ( p(happ(happ(V2__P,V6__x),V7__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__y,V8__z)
=> ( p(happ(happ(V2__P,V7__y),V8__z))
=> p(happ(happ(V2__P,V6__x),V8__z)) ) ) ) ) ) ) )
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ! [V8__a] :
( t(V8__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__a,V8__a)
=> p(happ(happ(V2__P,V7__a),V8__a)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_1n_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__90___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_1n_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__90___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__90___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V7__z)
=> ( p(happ(happ(V2__P,V6__y),V7__z))
=> p(happ(happ(V2__P,V5__x),V7__z)) ) ) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V7__a)
=> p(happ(happ(V2__P,V6__x),V7__a)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_n1_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__21___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_n1_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__21___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__90___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V7__z)
=> ( p(happ(happ(V2__P,V6__y),V7__z))
=> p(happ(happ(V2__P,V5__x),V7__z)) ) ) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V7__a)
=> p(happ(happ(V2__P,V6__x),V7__a)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_1n_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__90___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_1n_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__90___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__90___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V4__x,V5__y)
=> ( p(happ(happ(V2__P,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_n1_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__21___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_n1_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__21___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__90___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V4__x,V5__y)
=> ( p(happ(happ(V2__P,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.r_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.r_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst1n_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( ( p(happ(happ(V1__R,V2__x),V3__y))
| p(happ(happ(V1__R,V3__y),V2__x)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rstn1_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rstn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( ( p(happ(happ(V1__R,V3__y),V4__z))
| p(happ(happ(V1__R,V4__z),V3__y)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt1n_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rtn1_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rtn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t1n_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.tn1_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.tn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relations.inverse_image_of_equivalence',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V1__B,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,c_24__lam__3359___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Build_Setoid_Theory',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__A,V1__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V1__Aeq,V3__x),V3__x)) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> p(happ(happ(V1__Aeq,V4__y),V3__x)) ) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ! [V5__z] :
( t(V5__z,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> ( p(happ(happ(V1__Aeq,V4__y),V5__z))
=> p(happ(happ(V1__Aeq,V3__x),V5__z)) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.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.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_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,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('HahnMinElt.BasicProperties.max_transp',axiom,
chahn_2eHahnSets_2eset__equiv___24a3(cA,chahn_2eHahnMaxElt_2emax__elt___24a2(cA,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(cA,cr)),cHahnMinElt_2emin__elt___24a2(cA,cr)) ).
fof('HahnMinElt.BasicProperties.min_elt_union',axiom,
( cHahnMinElt_2emin__elt___24a3(cA,cr,ca)
=> ( cHahnMinElt_2emin__elt___24a3(cA,cr_27,ca)
=> cHahnMinElt_2emin__elt___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,cr,cr_27),ca) ) ) ).
fof('HahnMinElt.BasicProperties.min_elt_weaken',axiom,
( cHahnMinElt_2emin__elt___24a3(cA,cr,ca)
=> cHahnMinElt_2ewmin__elt___24a3(cA,cr,ca) ) ).
fof('HahnMinElt.BasicProperties.min_transp',axiom,
chahn_2eHahnSets_2eset__equiv___24a3(cA,cHahnMinElt_2emin__elt___24a2(cA,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(cA,cr)),chahn_2eHahnMaxElt_2emax__elt___24a2(cA,cr)) ).
fof('HahnMinElt.BasicProperties.set_equiv_min_elt',axiom,
( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(cA,cr,cr_27)
=> chahn_2eHahnSets_2eset__equiv___24a3(cA,cHahnMinElt_2emin__elt___24a2(cA,cr),cHahnMinElt_2emin__elt___24a2(cA,cr_27)) ) ).
fof('HahnMinElt.BasicProperties.set_subset_min_elt',axiom,
( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,cr_27,cr)
=> chahn_2eHahnSets_2eset__subset___24a3(cA,cHahnMinElt_2emin__elt___24a2(cA,cr),cHahnMinElt_2emin__elt___24a2(cA,cr_27)) ) ).
fof('hahn.HahnEquational.acyclic_case_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__f] :
( c_24__type__21___24t(V0__A,V2__f)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
<=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V2__f,V1__r))
& ! [V3__x] :
( t(V3__x,V0__A)
=> ( ~ p(happ(V2__f,V3__x))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V3__x,V3__x)
=> p(c_24False) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.acyclic_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)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V1__r)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnEquational.acyclic_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__271___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('hahn.HahnEquational.acyclic_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__271___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eProgram_2eBasics_2eflip___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),cCoq_2eProgram_2eBasics_2eimpl),chahn_2eHahnRelationsBasic_2eacyclic___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.acyclic_seqC',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)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27))
<=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)) ) ) ) ) ).
fof('hahn.HahnEquational.add_dom_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__s] :
( c_24__type__21___24t(V0__A,V2__s)
=> ! [V3__s_27] :
( c_24__type__21___24t(V0__A,V3__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__s)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__s_27),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,V2__s)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__s_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__s)))) ) ) ) ) ) ).
fof('hahn.HahnEquational.add_dom_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__s] :
( c_24__type__21___24t(V0__A,V2__s)
=> ! [V3__s_27] :
( c_24__type__21___24t(V0__A,V3__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__s_27),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__s)))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__s_27),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__s_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__s)))) ) ) ) ) ) ).
fof('hahn.HahnEquational.bunion_empty',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__rr] :
( c_24__type__479___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__1962___24a2(V0__B,V1__A)) ) ) ) ).
fof('hahn.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__479___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('hahn.HahnEquational.bunion_inter_compat_l',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__21___24t(V0__B,V2__s)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V3__r)
=> ! [V4__rr] :
( c_24__type__479___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__1994___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('hahn.HahnEquational.bunion_inter_compat_r',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__21___24t(V0__B,V2__s)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V3__r)
=> ! [V4__rr] :
( c_24__type__479___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__2005___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('hahn.HahnEquational.bunion_minus_compat_r',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__21___24t(V0__B,V2__s)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V3__r)
=> ! [V4__rr] :
( c_24__type__479___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__2016___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('hahn.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__474___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__21___24a1(V0__A),c_24__type__486___24a2(V0__A,V1__B),chahn_2eHahnSets_2eset__equiv___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__479___24a2(V0__A,V1__B),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V1__B),c_3d___24a1(c_24__type__479___24a2(V0__A,V1__B)),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V1__B))),chahn_2eHahnRelationsBasic_2ebunion___24a2(V0__A,V1__B)) ) ) ).
fof('hahn.HahnEquational.bunion_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__474___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__21___24a1(V0__A),c_24__type__486___24a2(V0__A,V1__B),chahn_2eHahnSets_2eset__subset___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__479___24a2(V0__A,V1__B),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V1__B),c_3d___24a1(c_24__type__479___24a2(V0__A,V1__B)),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V1__B))),chahn_2eHahnRelationsBasic_2ebunion___24a2(V0__A,V1__B)) ) ) ).
fof('hahn.HahnEquational.bunion_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__21___24t(V1__B,V2__f)
=> ! [V3__s] :
( c_24__type__650___24t(V0__A,V1__B,V3__s)
=> ! [V4__rr] :
( c_24__type__479___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__2239___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__2245___24a3(V0__A,V1__B,V4__rr)))) ) ) ) ) ) ).
fof('hahn.HahnEquational.bunion_union_l',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__21___24t(V0__B,V2__s)
=> ! [V3__s_27] :
( c_24__type__21___24t(V0__B,V3__s_27)
=> ! [V4__rr] :
( c_24__type__479___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('hahn.HahnEquational.bunion_union_r',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__21___24t(V0__B,V2__s)
=> ! [V3__rr] :
( c_24__type__479___24t(V0__B,V1__A,V3__rr)
=> ! [V4__rr_27] :
( c_24__type__479___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__1983___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('hahn.HahnEquational.clos_refl_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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_2eclos__refl___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_refl_sym_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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__sym___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_refl_sym_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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_2eclos__refl__sym___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_refl_trans_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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('hahn.HahnEquational.clos_refl_trans_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_relf_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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('hahn.HahnEquational.clos_sym_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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__sym___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_sym_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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_2eclos__sym___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_trans_imm',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V4__L] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__L)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__L)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ! [V7__b] :
( t(V7__b,V0__A)
=> ( ! [V8__c] :
( t(V8__c,V0__A)
=> ( p(happ(happ(V1__r,V6__a),V8__c))
=> ( p(happ(happ(V1__r,V8__c),V7__b))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V8__c,V4__L)) ) ) )
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V6__a,V7__b) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_imm2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V4__L] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__L)
=> ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ( ! [V7__c] :
( t(V7__c,V0__A)
=> ( p(happ(happ(V1__r,V5__a),V7__c))
=> ( p(happ(happ(V1__r,V7__c),V6__b))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V7__c,V4__L)) ) ) )
=> ( p(happ(happ(V1__r,V5__a),V6__b))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V5__a,V6__b) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_immediate1',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)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V3__a,V4__b)
=> p(happ(happ(V1__r,V3__a),V4__b)) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_immediate2',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)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ! [V4__dom] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__dom)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ( p(happ(happ(V1__r,V5__a),V6__b))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V6__b,V4__dom)) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ! [V7__b] :
( t(V7__b,V0__A)
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V6__a,V7__b) ) ) ) ) ) ) ) ) ) ).
fof('hahn.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('hahn.HahnEquational.clos_trans_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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('hahn.HahnEquational.clos_trans_mori',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_2einclusion___24a3(V0__A,V1__x,V2__y)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___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('hahn.HahnEquational.clos_trans_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.codom_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__61___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__21___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A)),chahn_2eHahnRelationsBasic_2ecodom__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.codom_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__61___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__21___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),chahn_2eHahnSets_2eset__subset___24a1(V0__A)),chahn_2eHahnRelationsBasic_2ecodom__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.collect_rel_acyclic',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r))
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V3__r) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_bunion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__163___24t(V0__A,V1__B,V3__f)
=> ! [V4__s] :
( c_24__type__1057___24t(V0__A,V1__B,V2__C,V4__s)
=> ! [V5__rr] :
( c_24__type__2336___24t(V0__A,V1__B,V2__C,V5__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V3__f,chahn_2eHahnRelationsBasic_2ebunion___24a4(V2__C,V0__A,V4__s,c_24__lam__2345___24a4(V0__A,V1__B,V2__C,V5__rr))),chahn_2eHahnRelationsBasic_2ebunion___24a4(V2__C,V1__B,V4__s,c_24__lam__2358___24a5(V0__A,V1__B,V2__C,V3__f,V5__rr))) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_compose',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__163___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__1022___24t(V0__A,V1__B,V2__C,V4__g)
=> ! [V5__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V2__C,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V2__C,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__A,V1__B,V2__C,V4__g,V3__f),V5__r),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V1__B,V2__C,V4__g,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V3__f,V5__r))) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V3__r)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_crt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [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(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V3__r,V4__r_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V4__r_27))) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_irr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r))
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V3__r) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [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(V1__B,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V4__r_27)),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V3__r,V4__r_27))) ) ) ) ) ) ).
fof('hahn.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__1813___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__163___24a2(V0__A,V1__B),c_24__type__1821___24a2(V0__A,V1__B),c_3d___24a1(c_24__type__163___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('hahn.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__1813___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__163___24a2(V0__A,V1__B),c_24__type__1821___24a2(V0__A,V1__B),c_3d___24a1(c_24__type__163___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('hahn.HahnEquational.collect_rel_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [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(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V4__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V4__r_27))) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_transp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V3__r)),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [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_2esame__relation___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V3__r,V4__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V4__r_27))) ) ) ) ) ) ).
fof('hahn.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__14___24a1(V0__A)),V1__r)) ) ) ).
fof('hahn.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('hahn.HahnEquational.cr_helper',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__d] :
( c_24__type__21___24t(V0__A,V3__d)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d),V2__r_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27))) ) ) ) ) ) ).
fof('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.HahnEquational.cr_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.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('hahn.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('hahn.HahnEquational.crsE',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__sym___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__14___24a1(V0__A)),V1__r),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnEquational.crsEE',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__sym___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__14___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnEquational.crs_inter',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,chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,V2__r_27))) ) ) ) ).
fof('hahn.HahnEquational.crs_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.crs_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)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl__sym___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__sym___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,V2__r_27))) ) ) ) ).
fof('hahn.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('hahn.HahnEquational.csE',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__sym___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnEquational.cs_inter',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,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V2__r_27))) ) ) ) ).
fof('hahn.HahnEquational.cs_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__21___24t(V0__A,V1__s)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__s,V2__r)),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__s,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V2__r))) ) ) ) ).
fof('hahn.HahnEquational.cs_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.cs_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)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__sym___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__sym___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V2__r_27))) ) ) ) ).
fof('hahn.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__2045___24a1(V0__A),c_24__lam__2053___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.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('hahn.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('hahn.HahnEquational.ct_ct',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,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__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('hahn.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('hahn.HahnEquational.ct_imm1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V4__acts] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__acts)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r),c_24__lam__2383___24a2(V0__A,V4__acts))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r))) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.ct_imm2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V4__acts] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__acts)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V1__r),c_24__lam__2383___24a2(V0__A,V4__acts))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r))) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.ct_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__7___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_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('hahn.HahnEquational.ct_ind_left_helper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__7___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__x] :
( c_24__type__90___24t(V0__A,V3__x)
=> ! [V4__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r)
=> ( V3__x = cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V4__r)
=> ! [V6__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V4__r),V6__r_27)
=> ( ! [V8__k] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V8__k)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V8__k),V6__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r,V8__k)),V6__r_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V3__x),V6__r_27) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.ct_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__7___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_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('hahn.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('hahn.HahnEquational.ct_of_cross',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__21___24t(V0__A,V1__s)
=> ! [V2__s_27] :
( c_24__type__21___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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.HahnEquational.ct_step',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,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.ct_unit',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,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.dom_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__61___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__21___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A)),chahn_2eHahnRelationsBasic_2edom__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.dom_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__61___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__21___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),chahn_2eHahnSets_2eset__subset___24a1(V0__A)),chahn_2eHahnRelationsBasic_2edom__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.fun_seq_minus_helper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__S] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__S)
=> ! [V3__T] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__T)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__R,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__S,V3__T)),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__R,V2__S),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__R,V3__T))) ) ) ) ) ) ).
fof('hahn.HahnEquational.functional_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__271___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('hahn.HahnEquational.functional_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__271___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eProgram_2eBasics_2eflip___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),cCoq_2eProgram_2eBasics_2eimpl),chahn_2eHahnRelationsBasic_2efunctional___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.good_ctx_compose',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__7___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__Q] :
( c_24__type__7___24t(V0__A,V3__Q)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V3__Q)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__2148___24a3(V0__A,V1__P,V3__Q)) ) ) ) ) ) ).
fof('hahn.HahnEquational.good_ctx_const',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__2118___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.good_ctx_id',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__2115___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.good_ctx_seq_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__7___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__2124___24a3(V0__A,V1__P,V3__r)) ) ) ) ) ).
fof('hahn.HahnEquational.good_ctx_seq_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__7___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__2130___24a3(V0__A,V1__P,V3__r)) ) ) ) ) ).
fof('hahn.HahnEquational.good_ctx_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__7___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__Q] :
( c_24__type__7___24t(V0__A,V3__Q)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V3__Q)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__2139___24a3(V0__A,V1__P,V3__Q)) ) ) ) ) ) ).
fof('hahn.HahnEquational.immediate_clos_trans_elim',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)
=> ( chahn_2eHahnRelationsBasic_2eimmediate___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__a,V3__b)
=> ( p(happ(happ(V1__r,V2__a),V3__b))
& ! [V5__c] :
( t(V5__c,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V5__c)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V5__c,V3__b)
=> p(c_24False) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.immediate_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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('hahn.HahnEquational.inclusion_ct_seq_eqv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__21___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),V2__r)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r))) ) ) ) ).
fof('hahn.HahnEquational.inclusion_ct_seq_eqv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__21___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom))) ) ) ) ).
fof('hahn.HahnEquational.inclusion_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1661___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__271___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('hahn.HahnEquational.inclusion_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1661___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__271___24a1(V0__A),cCoq_2eProgram_2eBasics_2eflip___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eProgram_2eBasics_2eimpl)),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.inclusion_r_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)
=> ! [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,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,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,chahn_2eHahnRelationsBasic_2eseq___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,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.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('hahn.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('hahn.HahnEquational.inclusion_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__21___24t(V0__A,V2__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom),V1__r),V1__r) ) ) ) ).
fof('hahn.HahnEquational.inclusion_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__21___24t(V0__A,V2__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom)),V1__r) ) ) ) ).
fof('hahn.HahnEquational.inclusion_step2_ct',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,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.inclusion_t_r_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)
=> ! [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,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r_27_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___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,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.inclusion_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_2einclusion___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_2einclusion___24a3(V0__A,V1__r,V2__r_27) ) ) ) ) ).
fof('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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__18___24a1(V0__A),V1__r),c_24__lam__18___24a1(V0__A)) ) ) ).
fof('hahn.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__18___24a1(V0__A)),c_24__lam__18___24a1(V0__A)) ) ) ).
fof('hahn.HahnEquational.inter_inclusion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__i] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__i)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__i),V1__r) ) ) ) ).
fof('hahn.HahnEquational.inter_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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('hahn.HahnEquational.inter_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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_2einter__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.inter_sym',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_2esymmetric___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnEquational.inter_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__i] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__i)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V3__i)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V3__i),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V3__i)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__i)) ) ) ) ) ) ).
fof('hahn.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('hahn.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('hahn.HahnEquational.irreflexive_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__271___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('hahn.HahnEquational.irreflexive_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__271___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eProgram_2eBasics_2eflip___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),cCoq_2eProgram_2eBasics_2eimpl),chahn_2eHahnRelationsBasic_2eirreflexive___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.is_total_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__266___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__21___24a1(V0__A),c_24__type__271___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('hahn.HahnEquational.map_rel_acyclic',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V1__B,V3__r)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_compose',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__163___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__1022___24t(V0__A,V1__B,V2__C,V4__g)
=> ! [V5__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V2__C,V5__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V2__C,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__A,V1__B,V2__C,V4__g,V3__f),V5__r),chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V3__f,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V1__B,V2__C,V4__g,V5__r))) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(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,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V1__B,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_crt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(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,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V1__B,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(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,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V1__B,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___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('hahn.HahnEquational.map_rel_irr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V1__B,V3__r)
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___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('hahn.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__1721___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__163___24a2(V0__A,V1__B),c_24__type__1729___24a2(V0__A,V1__B),c_3d___24a1(c_24__type__163___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('hahn.HahnEquational.map_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1721___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__163___24a2(V0__A,V1__B),c_24__type__1729___24a2(V0__A,V1__B),c_3d___24a1(c_24__type__163___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_2einclusion___24a1(V1__B),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A))),chahn_2eHahnRelationsBasic_2emap__rel___24a2(V0__A,V1__B)) ) ) ).
fof('hahn.HahnEquational.map_rel_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___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_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___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)),chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V1__B,V3__r,V4__r_27))) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_transp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V1__B,V3__r)),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___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('hahn.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__18___24a1(V0__A)) ) ) ).
fof('hahn.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__18___24a1(V0__A)) ) ) ) ) ).
fof('hahn.HahnEquational.minus_eqv_rel_helper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__T] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__T)
=> ! [V3__d1] :
( c_24__type__21___24t(V0__A,V3__d1)
=> ! [V4__d2] :
( c_24__type__21___24t(V0__A,V4__d2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d1),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__R,V2__T),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__d2))),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d1),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__R,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__d2))),V2__T)) ) ) ) ) ) ).
fof('hahn.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__18___24a1(V0__A),V1__r),c_24__lam__18___24a1(V0__A)) ) ) ).
fof('hahn.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__18___24a1(V0__A)),V1__r) ) ) ).
fof('hahn.HahnEquational.minus_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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('hahn.HahnEquational.minus_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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_2eProgram_2eBasics_2eflip___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A))),chahn_2eHahnRelationsBasic_2eminus__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.minus_sym',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_2esymmetric___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.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('hahn.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('hahn.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('hahn.HahnEquational.pow_rel_more_Proper',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1761___24a1(V0__X),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__X),c_24__type__1764___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('hahn.HahnEquational.pow_rel_mori_Proper',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1761___24a1(V0__X),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__X),c_24__type__1764___24a1(V0__X),cCoq_2eRelations_2eRelation__Definitions_2einclusion___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_2einclusion___24a1(V0__X))),chahn_2eHahnRelationsBasic_2epow__rel___24a1(V0__X)) ) ).
fof('hahn.HahnEquational.pow_rt',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)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V0__n),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V1__A,V2__r)) ) ) ) ).
fof('hahn.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('hahn.HahnEquational.pow_t',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_2etransitive___24a2(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V2__r,V1__n)),V2__r) ) ) ) ) ).
fof('hahn.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('hahn.HahnEquational.restrC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__21___24t(V0__A,V1__d)
=> ! [V2__d_27] :
( c_24__type__21___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('hahn.HahnEquational.restr_bunion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__21___24t(V1__B,V2__f)
=> ! [V3__s] :
( c_24__type__650___24t(V0__A,V1__B,V3__s)
=> ! [V4__rr] :
( c_24__type__479___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__2213___24a3(V0__A,V1__B,V4__rr))),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V3__s,c_24__lam__2223___24a4(V0__A,V1__B,V2__f,V4__rr))) ) ) ) ) ) ).
fof('hahn.HahnEquational.restr_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__21___24t(V0__A,V1__d)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__d,V2__r)),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__d,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r))) ) ) ) ).
fof('hahn.HahnEquational.restr_eq_bunion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__21___24t(V0__A,V1__s)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__rr] :
( c_24__type__479___24t(V0__A,V2__B,V3__rr)
=> ! [V4__C] :
( cType___24t(V4__C)
=> ! [V5__f] :
( c_24__type__1022___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__2265___24a4(V0__A,V2__B,V3__rr,V4__C))),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V2__B,V1__s,c_24__lam__2277___24a5(V0__A,V2__B,V3__rr,V4__C,V5__f))) ) ) ) ) ) ) ).
fof('hahn.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__163___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('hahn.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__1701___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__163___24a2(V0__A,V1__B),c_24__type__7___24a1(V0__A),c_3d___24a1(c_24__type__163___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('hahn.HahnEquational.restr_eq_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1701___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__163___24a2(V0__A,V1__B),c_24__type__7___24a1(V0__A),c_3d___24a1(c_24__type__163___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_2einclusion___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A))),chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a2(V0__A,V1__B)) ) ) ).
fof('hahn.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__163___24t(V0__A,V2__B,V3__f)
=> ! [V4__dom] :
( c_24__type__650___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('hahn.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__163___24t(V0__A,V2__B,V3__f)
=> ! [V4__dom] :
( c_24__type__650___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('hahn.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__163___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('hahn.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__14___24a1(V0__A),V1__r),V1__r) ) ) ).
fof('hahn.HahnEquational.restr_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__21___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('hahn.HahnEquational.restr_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__21___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('hahn.HahnEquational.restr_minus_alt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__21___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('hahn.HahnEquational.restr_relE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__21___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('hahn.HahnEquational.restr_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__429___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__21___24a1(V0__A),c_24__type__7___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('hahn.HahnEquational.restr_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__429___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__21___24a1(V0__A),c_24__type__7___24a1(V0__A),chahn_2eHahnSets_2eset__subset___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_2erestr__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.restr_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__21___24t(V0__A,V1__d)
=> ! [V2__d_27] :
( c_24__type__21___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('hahn.HahnEquational.restr_seq_compl_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__21___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,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnSets_2eset__compl___24a2(V0__A,V1__d)),V2__r)),c_24__lam__18___24a1(V0__A)) ) ) ) ).
fof('hahn.HahnEquational.restr_seq_eqv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__21___24t(V0__A,V1__f)
=> ! [V2__d] :
( c_24__type__21___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('hahn.HahnEquational.restr_seq_eqv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__21___24t(V0__A,V1__f)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__d] :
( c_24__type__21___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('hahn.HahnEquational.restr_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__21___24t(V0__A,V1__s)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__s,V2__r)) ) ) ) ) ).
fof('hahn.HahnEquational.restr_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__21___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('hahn.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__14___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.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__2045___24a1(V0__A),c_24__lam__2048___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.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__14___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)))) ) ) ).
fof('hahn.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('hahn.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('hahn.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__14___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V1__r))) ) ) ).
fof('hahn.HahnEquational.rt_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__7___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_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,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__14___24a1(V0__A))),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__refl__trans___24a2(V0__A,V3__r)),V4__r_27) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.rt_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__7___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_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,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__14___24a1(V0__A))),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__refl__trans___24a2(V0__A,V3__r)),V4__r_27) ) ) ) ) ) ) ) ).
fof('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.HahnEquational.rt_unit',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,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.HahnEquational.seqA2',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)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( chahn_2eHahnRelationsBasic_2eseq___24a5(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__r_27_27,V4__x,V5__y)
<=> chahn_2eHahnRelationsBasic_2eseq___24a5(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V3__r_27_27),V4__x,V5__y) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.seq_bunion_l',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__P] :
( c_24__type__21___24t(V0__B,V2__P)
=> ! [V3__rr] :
( c_24__type__479___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__1942___24a4(V0__B,V1__A,V3__rr,V4__r))) ) ) ) ) ) ).
fof('hahn.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__650___24t(V0__B,V1__A,V3__P)
=> ! [V4__rr] :
( c_24__type__479___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__1954___24a4(V0__B,V1__A,V2__r,V4__rr))) ) ) ) ) ) ).
fof('hahn.HahnEquational.seq_eqv_inter_ll',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__S] :
( c_24__type__21___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('hahn.HahnEquational.seq_eqv_inter_lr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__S] :
( c_24__type__21___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('hahn.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__21___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__43___24a3(V0__A,V1__r,V2__dom)) ) ) ) ).
fof('hahn.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__21___24t(V0__A,V2__dom1)
=> ! [V3__dom2] :
( c_24__type__21___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__2189___24a4(V0__A,V1__r,V2__dom1,V3__dom2)) ) ) ) ) ).
fof('hahn.HahnEquational.seq_eqv_minus_ll',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__21___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('hahn.HahnEquational.seq_eqv_minus_lr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__21___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('hahn.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__21___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__32___24a3(V0__A,V1__r,V2__dom)) ) ) ) ).
fof('hahn.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__18___24a1(V0__A),V1__r),c_24__lam__18___24a1(V0__A)) ) ) ).
fof('hahn.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__18___24a1(V0__A)),c_24__lam__18___24a1(V0__A)) ) ) ).
fof('hahn.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__14___24a1(V0__A)),V1__r),V1__r) ) ) ).
fof('hahn.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__14___24a1(V0__A))),V1__r) ) ) ).
fof('hahn.HahnEquational.seq_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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('hahn.HahnEquational.seq_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.HahnEquational.symmetricE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
<=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnEquational.symmetricEE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
<=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnEquational.symmetric_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__271___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_2esymmetric___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.tot_ex',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__mo] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__mo)
=> ! [V2__dom] :
( c_24__type__21___24t(V0__X,V2__dom)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__X,V2__dom,V1__mo)
=> ! [V4__a] :
( t(V4__a,V0__X)
=> ! [V5__b] :
( t(V5__b,V0__X)
=> ( p(happ(V2__dom,V4__a))
=> ( p(happ(V2__dom,V5__b))
=> ( ~ p(happ(happ(V1__mo,V4__a),V5__b))
=> ( V4__a != V5__b
=> p(happ(happ(V1__mo,V5__b),V4__a)) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.trailing_refl',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__e] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__e)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V3__e))) ) ) ) ) ) ).
fof('hahn.HahnEquational.transitive_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__271___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('hahn.HahnEquational.transitive_transp',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_2etransitive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.HahnEquational.transp_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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('hahn.HahnEquational.transp_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7___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)),cCoq_2eRelations_2eRelation__Operators_2etransp___24a1(V0__A)) ) ).
fof('hahn.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('hahn.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('hahn.HahnEquational.transp_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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('hahn.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__18___24a1(V0__A),V1__r),V1__r) ) ) ).
fof('hahn.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__18___24a1(V0__A)),V1__r) ) ) ).
fof('hahn.HahnEquational.union_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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('hahn.HahnEquational.union_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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))),cCoq_2eRelations_2eRelation__Operators_2eunion___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.union_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__21___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('hahn.HahnEquational.union_sym',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_2esymmetric___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnEquational.well_founded_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__271___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.HahnEquational.well_founded_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__271___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eProgram_2eBasics_2eflip___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),cCoq_2eProgram_2eBasics_2eimpl),cCoq_2eInit_2eWf_2ewell__founded___24a1(V0__A)) ) ).
fof('hahn.HahnFuneq.funeq_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_inter_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_inter_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__t)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_irreflexive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V4__t),V3__r))
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__t,V3__r)) ) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2439___24a2(V0__A,V1__B),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_2eHahnFuneq_2efuneq___24a3(V0__A,V1__B,V2__f)) ) ) ) ).
fof('hahn.HahnFuneq.funeq_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2439___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eProgram_2eBasics_2eflip___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),cCoq_2eProgram_2eBasics_2eimpl),chahn_2eHahnFuneq_2efuneq___24a3(V0__A,V1__B,V2__f)) ) ) ) ).
fof('hahn.HahnFuneq.funeq_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ! [V5__dom] :
( c_24__type__650___24t(V0__A,V1__B,V5__dom)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V5__dom,V3__r)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ! [V5__C] :
( cType___24t(V5__C)
=> ! [V6__dom] :
( c_24__type__2427___24t(V0__A,V1__B,V5__C,V6__dom)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V5__C,V6__dom,V3__r)) ) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_restr_eq_rel',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__t)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_transp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__t)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ) ).
fof('hahn.HahnList.in_undup_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,chahn_2eHahnList_2eundup___24a2(V0__A,V2__l)))
<=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V2__l)) ) ) ) ) ).
fof('hahn.HahnList.nodup_undup',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,chahn_2eHahnList_2eundup___24a2(V0__A,V1__l)) ) ) ).
fof('hahn.HahnMaxElt.max_elt_Propere',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__61___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__21___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A)),chahn_2eHahnMaxElt_2emax__elt___24a1(V0__A)) ) ).
fof('hahn.HahnMaxElt.max_elt_restr_eq',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] :
( cType___24t(V3__B)
=> ! [V4__f] :
( c_24__type__163___24t(V0__A,V3__B,V4__f)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V3__B,V4__f,V1__r),V2__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_seq1',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)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_seq2',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)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__a)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_t',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)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_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__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__a)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_weaken',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)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_max',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b)),V1__r),c_24__lam__18___24a1(V0__A)) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_max_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b))) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_max_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b))) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_max_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),c_24__lam__18___24a1(V0__A)) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_wmax',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__b)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b)),V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b))) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_wmax_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b))) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_wmax_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b))) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_wmax_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__b)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b))) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eqv_max',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,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r)),V1__r),c_24__lam__18___24a1(V0__A)) ) ) ).
fof('hahn.HahnMaxElt.seq_eqv_max_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,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnMaxElt.seq_eqv_max_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_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnMaxElt.seq_eqv_max_t',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,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),c_24__lam__18___24a1(V0__A)) ) ) ).
fof('hahn.HahnMaxElt.seq_max',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] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),c_24__lam__18___24a1(V0__A)) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_max_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)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_max_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)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> 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)),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_max_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)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)),c_24__lam__18___24a1(V0__A)) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_max',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)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),V1__r),c_24__lam__18___24a1(V0__A)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_max_r',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)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_max_rt',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)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_max_t',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)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),c_24__lam__18___24a1(V0__A)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_wmax',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)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),V1__r),chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_wmax_r',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)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_wmax_rt',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)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_wmax_t',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)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_wmax',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] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_wmax_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)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_wmax_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)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> 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)),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_wmax_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)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.set_equiv_max_elt',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)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r),chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnMaxElt.set_equiv_wmax_elt',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)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnMaxElt_2ewmax__elt___24a2(V0__A,V1__r),chahn_2eHahnMaxElt_2ewmax__elt___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnMaxElt.set_subset_max_elt',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,V1__r)
=> chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r),chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnMaxElt.set_subset_wmax_elt',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,V1__r)
=> chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnMaxElt_2ewmax__elt___24a2(V0__A,V1__r),chahn_2eHahnMaxElt_2ewmax__elt___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnMaxElt.transp_seq_eqv_max',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_2etransp___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r))),c_24__lam__18___24a1(V0__A)) ) ) ).
fof('hahn.HahnMaxElt.transp_seq_eqv_max_t',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,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r))),c_24__lam__18___24a1(V0__A)) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_Propere',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__61___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__21___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A)),chahn_2eHahnMaxElt_2ewmax__elt___24a1(V0__A)) ) ).
fof('hahn.HahnMaxElt.wmax_elt_r',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)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_restr_eq',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] :
( cType___24t(V3__B)
=> ! [V4__f] :
( c_24__type__163___24t(V0__A,V3__B,V4__f)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V3__B,V4__f,V1__r),V2__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_rt',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)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_seq1',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)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_seq2',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)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__a)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_t',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)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_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__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__a)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.acyclic_antisymmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__r) ) ) ) ).
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_refl_trans_of_transitive',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)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V3__x,V4__y)
<=> chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V3__x,V4__y) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_eq',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__163___24t(V0__A,V2__B,V3__f)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(happ(V1__r,V4__a),V5__b))
=> happ(V3__f,V4__a) = happ(V3__f,V5__b) ) ) )
=> ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V5__a,V6__b)
=> happ(V3__f,V5__a) = happ(V3__f,V6__b) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_in_rt',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__trans___24a4(V0__A,V1__r,V2__a,V3__b)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V2__a,V3__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.clos_trans_of_clos_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__x,V3__y) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_of_clos_trans1',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__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,c_24__lam__2620___24a3(V0__A,V1__r,V2__r_27),V3__x,V4__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,c_24__lam__2628___24a3(V0__A,V1__r,V2__r_27),V3__x,V4__y) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_of_transitive',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)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V3__x,V4__y)
<=> p(happ(happ(V1__r,V3__x),V4__y)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_of_transitiveD',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)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V3__x,V4__y)
=> p(happ(happ(V1__r,V3__x),V4__y)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_restrD',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__21___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r),V3__x,V4__y)
=> ( p(happ(V1__dom,V3__x))
& p(happ(V1__dom,V4__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_restr_eqD',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r),V4__x,V5__y)
=> happ(V2__f,V4__x) = happ(V2__f,V5__y) ) ) ) ) ) ) ) ).
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.functionalE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
=> ? [V3__f] :
( c_24__type__2611___24t(V0__A,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) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V5__y) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_inter_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)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_inter_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)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_minus',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)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__21___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_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)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_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)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r_27)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ( chahn_2eHahnRelationsBasic_2edom__rel___24a3(V0__A,V1__r,V5__x)
=> ( chahn_2eHahnRelationsBasic_2edom__rel___24a3(V0__A,V2__r_27,V5__x)
=> p(c_24False) ) ) )
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ) ).
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_acyclic',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)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,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__673___24t(V0__A,V1__B,V3__P)
=> ! [V4__rr] :
( c_24__type__2588___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_bunion_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__x] :
( t(V3__x,V1__B)
=> ! [V4__P] :
( c_24__type__673___24t(V0__A,V1__B,V4__P)
=> ! [V5__rr] :
( c_24__type__2588___24t(V0__A,V1__B,V5__rr)
=> ( p(happ(V4__P,V3__x))
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,happ(V5__rr,V3__x))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2ebunion___24a4(V1__B,V0__A,V4__P,V5__rr)) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_cr_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_2ereflexive___24a2(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),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_eqv_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__21___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_eqv_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__21___24t(V0__A,V1__dom)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_id_cr',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,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__14___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_id_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__14___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r_27)) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_l1',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,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V1__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_l1_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,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V3__r_27_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_l2',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,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V2__r_27) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_l2_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,V2__r_27,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V3__r_27_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_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_2einter__rel___24a3(V0__A,V1__r,V3__s),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V4__s_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_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)
=> ! [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,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_minus_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__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__s)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V3__s)
<=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__s)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_minus_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,V4__s_27,V3__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V3__s),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r_27,V4__s_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_minus_rel',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,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V1__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_r_cr',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),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,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_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_2einclusion___24a1(V0__A)) ) ).
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_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__21___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r),V2__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r),V3__r) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_restr_eq_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [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,V3__r,V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r),V4__r_27) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_restr_rel_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__21___24t(V0__A,V1__dom)
=> ! [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_2einclusion___24a3(V0__A,V2__r,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r),V3__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_rt_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_2ereflexive___24a2(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__refl__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ) ).
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_ind_right',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,V2__r_27,V1__r),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_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,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_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_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,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V3__r_27_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_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)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_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,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_refl',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_2etransitive___24a2(V0__A,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)),V3__r_27_27) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_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)
=> ! [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,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r_27_27))
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r_27_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r_27_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_cr',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,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)) ) ) ) ) ).
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_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_2einclusion___24a3(V0__A,V1__r,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__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_ind_right',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_2eseq___24a3(V0__A,V2__r_27,V1__r),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_t_t2',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__trans___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),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_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_2einclusion___24a1(V0__A)) ) ).
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_minus',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,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V2__r_27)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_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,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V3__s),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V4__s_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_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)
=> ! [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,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.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.irreflexive_inclusion',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)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__21___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r)
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r))
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V3__r) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_seqC',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)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27))
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_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)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27))
<=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
& chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.is_total_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__21___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__dom,V2__r)
=> chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__dom,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.r_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V2__x,V2__x) ) ) ) ).
fof('hahn.HahnRelationsBasic.r_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V3__y))
=> chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V2__x,V3__y) ) ) ) ) ) ).
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_inter',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_2einter__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
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.reflexive_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_2ereflexive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_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_2ereflexive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.restr_eq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__163___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
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.strict_partial_order_antisymmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,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.trans_irr_acyclic',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.trans_irr_antisymmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__r) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.transitive_cr',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_2etransitive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ) ).
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_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__21___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__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('hahn.HahnRelationsBasic.upward_closed_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__P] :
( c_24__type__21___24t(V0__A,V2__P)
=> ( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V1__r,V2__P)
=> chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__P) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.upward_closed_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__P] :
( c_24__type__21___24t(V0__A,V2__P)
=> ( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V1__r,V2__P)
=> chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__P) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.upward_closed_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)
=> ! [V3__P] :
( c_24__type__21___24t(V0__A,V3__P)
=> ( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V1__r,V3__P)
=> ( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V2__r_27,V3__P)
=> chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__P) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.hahn_inclusion_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_2einclusion___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('hahn.HahnRewrite.rewrite_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_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r),V1__r) ) ) ) ).
fof('hahn.HahnRewrite.rewrite_trans_seq_cr_cr',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_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnRewrite.rewrite_trans_seq_cr_l',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_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),V1__r),V1__r) ) ) ) ).
fof('hahn.HahnRewrite.rewrite_trans_seq_cr_r',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_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),V1__r) ) ) ) ).
fof('hahn.HahnRewrite.seq2',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,V1__r1,V2__r2),V3__r)
=> ! [V5__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V5__s)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V5__s)) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.seq3',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)
=> ! [V4__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V3__r3)),V4__r)
=> ! [V6__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,V6__s))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r,V6__s)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.seq4',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)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,V4__r4))),V5__r)
=> ! [V7__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,V7__s)))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r,V7__s)) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.seq5',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)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r5] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r5)
=> ! [V6__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,V5__r5)))),V6__r)
=> ! [V8__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V8__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,V8__s))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__r,V8__s)) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.seq6',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)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r5] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r5)
=> ! [V6__r6] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r6)
=> ! [V7__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,V6__r6))))),V7__r)
=> ! [V9__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V9__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__r6,V9__s)))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V7__r,V9__s)) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin2',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_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,V2__r2),V3__r)
=> ! [V5__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V5__s)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V5__s)) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin3',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)
=> ! [V4__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V3__r3)),V4__r)
=> ! [V6__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,V6__s))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r,V6__s)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin4',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)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,V4__r4))),V5__r)
=> ! [V7__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,V7__s)))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r,V7__s)) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin5',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)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r5] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r5)
=> ! [V6__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,V5__r5)))),V6__r)
=> ! [V8__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V8__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,V8__s))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__r,V8__s)) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin6',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)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r5] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r5)
=> ! [V6__r6] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r6)
=> ! [V7__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,V6__r6))))),V7__r)
=> ! [V9__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V9__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__r6,V9__s)))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V7__r,V9__s)) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.transitiveI',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,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r),V1__r)
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r) ) ) ) ).
fof('hahn.HahnSets.set_equiv_rel_Reflexive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(c_24__type__21___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A)) ) ).
fof('$adef_$_lam_2383_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__2383,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__2383___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_2223_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2223,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2223___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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_2130_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2130,V_24X1),V_24X2),V_24X3) = c_24__lam__2130___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_lam_1983_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1983,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1983___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_2628_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__2628,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__2628___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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.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.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.FinFun.Injective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eInjective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eInjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_2108_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2108,V_24X1),V_24X2),V_24X3) = c_24__lam__2108___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Even.even_$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('$adef_$_let_4_P\'_4957_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__4__P_27__4957,V_24X1),V_24X2) = c_24__let__4__P_27__4957___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_2118_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2118,V_24X1),V_24X2) = c_24__lam__2118___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.transp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2etransp,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.PER_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ePER,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$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('$adef_hahn.HahnSets.set_full_$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('$adef_$_lam_1415_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__1415,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__1415___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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_$_lam_32_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__32,V_24X1),V_24X2),V_24X3) = c_24__lam__32___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Decimal.D0_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).
fof('$adef_$_lam_17688_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__17688,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__17688___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.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_$_lam_5105_$a1',axiom,
! [V_24X1] : happ(c_24__lam__5105,V_24X1) = c_24__lam__5105___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('$adef_hahn.HahnSets.set_collect_$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('$adef_Coq.Program.Basics.flip_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eProgram_2eBasics_2eflip,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eProgram_2eBasics_2eflip___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('$adef_$_lam_2358_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2358,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2358___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.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_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_32_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__32,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__32___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_2345_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2345,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2345___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_2124_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2124,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2124___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_2005_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2005,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2005___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_2053_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2053,V_24X1),V_24X2),V_24X3) = c_24__lam__2053___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$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('$adef_hahn.HahnRelationsBasic.restr_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2erestr__rel,V_24X1) = chahn_2eHahnRelationsBasic_2erestr__rel___24a1(V_24X1) ).
fof('$adef_Coq.Init.Logic.ex2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eLogic_2eex2,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eLogic_2eex2___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_hahn.HahnRelationsBasic.restr_eq_rel_$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('$adef_hahn.HahnRelationsBasic.immediate_$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('$adef_$_lam_2045_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__2045,V_24X1),V_24X2))
<=> c_24__lam__2045___24a2(V_24X1,V_24X2) ) ).
fof('$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.Init.Logic.ex_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eLogic_2eex,V_24X1),V_24X2))
<=> cCoq_2eInit_2eLogic_2eex___24a2(V_24X1,V_24X2) ) ).
fof('$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_hahn.HahnSets.set_subset_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnSets_2eset__subset,V_24X1) = chahn_2eHahnSets_2eset__subset___24a1(V_24X1) ).
fof('$adef_Coq.Sorting.Sorted.LocallySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eLocallySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_hahn.HahnRelationsBasic.eq_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eeq__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2eeq__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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_$_lam_17696_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__17696,V_24X1),V_24X2),V_24X3) = c_24__lam__17696___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Definitions.inclusion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2einclusion,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.Pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2ePos,V_24X1) = cCoq_2eInit_2eDecimal_2ePos___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$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('$adef_$_lam_2277_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2277,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2277___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_2345_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2345,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2345___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Arith.Between.P_nth_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eArith_2eBetween_2eP__nth,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eArith_2eBetween_2eP__nth___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_hahn.HahnMaxElt.max_elt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnMaxElt_2emax__elt,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnMaxElt_2emax__elt___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$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('$adef_hahn.HahnRelationsBasic.strict_partial_order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnRelationsBasic_2estrict__partial__order,V_24X1),V_24X2))
<=> chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V_24X1,V_24X2) ) ).
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('$adef_hahn.HahnMaxElt.max_elt_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnMaxElt_2emax__elt,V_24X1) = chahn_2eHahnMaxElt_2emax__elt___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.eq_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eDatatypes_2eeq__true,V_24X1))
<=> cCoq_2eInit_2eDatatypes_2eeq__true___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Decimal.D6_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).
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('$adef_Coq.micromega.VarMap.Elt_$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('$adef_hahn.HahnMaxElt.wmax_elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnMaxElt_2ewmax__elt,V_24X1),V_24X2) = chahn_2eHahnMaxElt_2ewmax__elt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$23942_$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_2423942,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2423942___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.dom_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnRelationsBasic_2edom__rel,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnRelationsBasic_2edom__rel___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Operators.transp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2etransp,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2etransp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnList.undup_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnList_2eundup,V_24X1),V_24X2) = chahn_2eHahnList_2eundup___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2277_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__2277,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__2277___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.NArith.BinNat.N.peano_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(V_24X1) ).
fof('$adef_Coq.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_hahn.HahnRelationsBasic.strict_total_order_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnRelationsBasic_2estrict__total__order,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnRelationsBasic_2estrict__total__order___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_hahn.HahnRelationsBasic.clos_sym_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eclos__sym,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eclos__sym___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D4_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.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_$_lam_43_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__43,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__43___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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_18_$a1',axiom,
! [V_24X1] : happ(c_24__lam__18,V_24X1) = c_24__lam__18___24a1(V_24X1) ).
fof('$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.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_$_prop_16513_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16513,V_24X1),V_24X2),V_24X3) = c_24__prop__16513___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_hahn.HahnRelationsBasic.codom_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2ecodom__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_1994_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1994,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1994___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.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_hahn.HahnRelationsBasic.codom_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnRelationsBasic_2ecodom__rel,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnRelationsBasic_2ecodom__rel___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Classes.RelationClasses.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).
fof('$adef_$_lam_2213_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2213,V_24X1),V_24X2),V_24X3) = c_24__lam__2213___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1983_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1983,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1983___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_fix_16592_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__16592__v__CANONICAL__0,V_24X1) = c_24__fix__16592__v__CANONICAL__0___24a1(V_24X1) ).
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('$adef_$_lam_2245_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2245,V_24X1),V_24X2),V_24X3) = c_24__lam__2245___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_3066_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__3066,V_24X1),V_24X2),V_24X3) = c_24__lam__3066___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_2053_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2053,V_24X1),V_24X2) = c_24__lam__2053___24a2(V_24X1,V_24X2) ).
fof('$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.Relations.Relation_Definitions.commut_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ecommut,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Definitions_2ecommut___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_2118_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2118,V_24X1),V_24X2),V_24X3) = c_24__lam__2118___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_hahn.HahnRelationsBasic.clos_sym_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eclos__sym,V_24X1) = chahn_2eHahnRelationsBasic_2eclos__sym___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$9206_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_249206,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_249206___24a1(V_24X1) ).
fof('$adef_$_lam_2016_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2016,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2016___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_2213_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2213,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2213___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Arith.Between.between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ebetween,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ebetween___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.peano_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnMaxElt.max_elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnMaxElt_2emax__elt,V_24X1),V_24X2) = chahn_2eHahnMaxElt_2emax__elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2067_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__2067,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__2067___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_$_lam_14_$a1',axiom,
! [V_24X1] : happ(c_24__lam__14,V_24X1) = c_24__lam__14___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('$adef_$_let_4_P\'_4957_$a1',axiom,
! [V_24X1] : happ(c_24__let__4__P_27__4957,V_24X1) = c_24__let__4__P_27__4957___24a1(V_24X1) ).
fof('$adef_$_prop_2485_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__2485,V_24X1),V_24X2),V_24X3) = c_24__prop__2485___24a3(V_24X1,V_24X2,V_24X3) ).
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_5004_$a1',axiom,
! [V_24X1] : happ(c_24__lam__5004,V_24X1) = c_24__lam__5004___24a1(V_24X1) ).
fof('$adef_hahn.HahnBase.NW_$a1',axiom,
! [V_24X1] :
( p(happ(chahn_2eHahnBase_2eNW,V_24X1))
<=> chahn_2eHahnBase_2eNW___24a1(V_24X1) ) ).
fof('$adef_Coq.NArith.BinNat.N.recursion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnRelationsBasic.dom_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2edom__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2edom__rel___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1962_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1962,V_24X1),V_24X2) = c_24__lam__1962___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_16514_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16514,V_24X1),V_24X2),V_24X3) = c_24__prop__16514___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_2016_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2016,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2016___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_prop_16492_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__16492,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__16492___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_let_5_f\'_4958_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__5__f_27__4958,V_24X1),V_24X2) = c_24__let__5__f_27__4958___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('$adef_HahnMinElt.wmin_elt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cHahnMinElt_2ewmin__elt,V_24X1),V_24X2),V_24X3))
<=> cHahnMinElt_2ewmin__elt___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('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$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('$adef_$_lam_3062_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__3062,V_24X1),V_24X2),V_24X3) = c_24__lam__3062___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_HahnMinElt.min_elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cHahnMinElt_2emin__elt,V_24X1),V_24X2) = cHahnMinElt_2emin__elt___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_2108_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2108,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2108___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Between.exists_between_$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('$adef_$_lam_2094_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2094,V_24X1),V_24X2) = c_24__lam__2094___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_lam_2115_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2115,V_24X1),V_24X2) = c_24__lam__2115___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('$adef_$_case_Coq.Numbers.BinNums.positive$16576_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2416576,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2416576___24a2(V_24X1,V_24X2) ).
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('$adef_$_let_var_6_p_9709_9711_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__9709__9711,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__9709__9711___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_3359_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__3359,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__3359___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnSets.set_union_$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('$adef_$_lam_2383_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2383,V_24X1),V_24X2) = c_24__lam__2383___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnSets.set_compl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnSets_2eset__compl,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnSets_2eset__compl___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.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.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_$_lam_2223_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2223,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2223___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_2139_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2139,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2139___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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_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_$_lam_3359_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__3359,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__3359___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_lam_3066_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__3066,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__3066___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_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_$_lam_17696_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__17696,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__17696___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).
fof('$adef_Coq.Program.Basics.compose_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eProgram_2eBasics_2ecompose,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eProgram_2eBasics_2ecompose___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_hahn.HahnRelationsBasic.singl_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2esingl__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2esingl__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_2094_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__2094,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__2094___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_let_var_6_p_9707_9710_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__9707__9710,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__9707__9710___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_hahn.HahnRelationsBasic.clos_refl_sym_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eclos__refl__sym,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sorting.Sorted.HdRel_$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('$adef_Coq.Relations.Relation_Operators.clos_trans_$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('$adef_hahn.HahnRelationsBasic.acyclic_$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('$adef_$_prop_2473_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__2473,V_24X1),V_24X2),V_24X3) = c_24__prop__2473___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_17688_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__17688,V_24X1),V_24X2),V_24X3) = c_24__lam__17688___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_2048_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2048,V_24X1),V_24X2) = c_24__lam__2048___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.codom_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2ecodom__rel,V_24X1) = chahn_2eHahnRelationsBasic_2ecodom__rel___24a1(V_24X1) ).
fof('$adef_$_lam_2130_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2130,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2130___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.SetoidList.transpose2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose2,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$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('$adef_Coq.Classes.RelationClasses.Reflexive_$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('$adef_Coq.Arith.EqNat.eq_nat_$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('$adef_hahn.HahnEquational.good_ctx_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnEquational_2egood__ctx,V_24X1),V_24X2))
<=> chahn_2eHahnEquational_2egood__ctx___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.Forall2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eList_2eForall2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.Tauto.A_$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_2189_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__2189,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__2189___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_hahn.HahnMaxElt.wmax_elt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnMaxElt_2ewmax__elt,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_case_Coq.Numbers.BinNums.N$4971_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eN_244971,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eNumbers_2eBinNums_2eN_244971___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('$adef_$_lam_2620_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2620,V_24X1),V_24X2),V_24X3) = c_24__lam__2620___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_Coq.Init.Datatypes.CompGtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.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_$_lam_2100_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2100,V_24X1),V_24X2) = c_24__lam__2100___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
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('$adef_hahn.HahnRelationsBasic.map_rel_$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_2005_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2005,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2005___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_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_hahn.HahnRelationsBasic.clos_refl_sym_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eclos__refl__sym,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_24074_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__24074__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__24074__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_2189_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2189,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2189___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_$_lam_18_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__18,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__18___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_hahn.HahnRelationsBasic.singl_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2esingl__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_1942_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1942,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1942___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).
fof('$adef_$_lam_2124_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2124,V_24X1),V_24X2),V_24X3) = c_24__lam__2124___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_case_Coq.Numbers.BinNums.Z$9201_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_249201,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_249201___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_2265_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2265,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2265___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_lam_2148_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2148,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2148___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.same_relation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esame__relation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).
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('$adef_Coq.NArith.BinNat.N.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.equiv_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequiv,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.negb_$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_2265_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2265,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2265___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ClassicalDescription.excluded_middle_informative_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative,V_24X1) = cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(V_24X1) ).
fof('$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.HahnFuneq.funeq_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnFuneq_2efuneq,V_24X1),V_24X2),V_24X3) = chahn_2eHahnFuneq_2efuneq___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_let_5_f\'_4958_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__5__f_27__4958,V_24X1),V_24X2),V_24X3) = c_24__let__5__f_27__4958___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_2245_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2245,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2245___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_3062_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__3062,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__3062___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_1962_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__1962,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__1962___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_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_$_lam_2148_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2148,V_24X1),V_24X2),V_24X3) = c_24__lam__2148___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.ForallOrdPairs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallOrdPairs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_$_lam_2358_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__2358,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__2358___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_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_$_lam_1415_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1415,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1415___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNat.N.peano_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Nat.sub_$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('$adef_hahn.HahnBase.Equality.Mixin_$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('$adef_Coq.ZArith.BinInt.Z.divide_$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('$adef_Coq.setoid_ring.Field_theory.FEI_$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('$adef_Coq.Init.Logic.unique_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eunique,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eunique___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('$adef_Coq.setoid_ring.Ring_theory.power_theory_$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('$adef_$_lam_1954_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1954,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1954___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.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_$_lam_2628_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2628,V_24X1),V_24X2),V_24X3) = c_24__lam__2628___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('$adef_hahn.HahnRelationsBasic.restr_subset_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2erestr__subset,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2erestr__subset___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_5004_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__5004,V_24X1),V_24X2) = c_24__lam__5004___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_16512_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__16512,V_24X1),V_24X2) = c_24__prop__16512___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_$_lam_2239_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2239,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2239___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_2100_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2100,V_24X1),V_24X2),V_24X3) = c_24__lam__2100___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_prop_16496_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16496,V_24X1),V_24X2),V_24X3) = c_24__prop__16496___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_$_case_Coq.Init.Datatypes.list$24029_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2424029,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2424029___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_5105_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__5105,V_24X1),V_24X2) = c_24__lam__5105___24a2(V_24X1,V_24X2) ).
fof('$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_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_$_case_Coq.Init.Datatypes.nat$9184_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_249184,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_249184___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.mknegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.dom_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2edom__rel,V_24X1) = chahn_2eHahnRelationsBasic_2edom__rel___24a1(V_24X1) ).
fof('$adef_$_lam_14_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__14,V_24X1),V_24X2))
<=> c_24__lam__14___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_lam_2067_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2067,V_24X1),V_24X2) = c_24__lam__2067___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.existT2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Relations.Relation_Operators.union_$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('$adef_Coq.Lists.SetoidList.InA_$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('$adef_hahn.HahnMaxElt.wmax_elt_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnMaxElt_2ewmax__elt,V_24X1) = chahn_2eHahnMaxElt_2ewmax__elt___24a1(V_24X1) ).
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('$adef_$_prop_16495_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16495,V_24X1),V_24X2),V_24X3) = c_24__prop__16495___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_2045_$a1',axiom,
! [V_24X1] : happ(c_24__lam__2045,V_24X1) = c_24__lam__2045___24a1(V_24X1) ).
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('$adef_$_lam_2115_$a1',axiom,
! [V_24X1] : happ(c_24__lam__2115,V_24X1) = c_24__lam__2115___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_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_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Operators.Ltl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eLtl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_1994_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1994,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1994___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_16498_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__16498,V_24X1),V_24X2) = c_24__prop__16498___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_16493_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16493,V_24X1),V_24X2),V_24X3) = c_24__prop__16493___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_43_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__43,V_24X1),V_24X2),V_24X3) = c_24__lam__43___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_HahnMinElt.min_elt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cHahnMinElt_2emin__elt,V_24X1),V_24X2),V_24X3))
<=> cHahnMinElt_2emin__elt___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_hahn.HahnFuneq.funeq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnFuneq_2efuneq,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnFuneq_2efuneq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_hahn.HahnRelationsBasic.clos_sym_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eclos__sym,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_2139_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2139,V_24X1),V_24X2),V_24X3) = c_24__lam__2139___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_2620_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__2620,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__2620___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_sym_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eclos__refl__sym,V_24X1) = chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a1(V_24X1) ).
fof('$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_$_lam_2239_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2239,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2239___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Init.Specif.left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Specif.sigT_$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('$adef_Coq.setoid_ring.Field_theory.semi_field_theory_$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('$adef_$_prop_16494_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16494,V_24X1),V_24X2),V_24X3) = c_24__prop__16494___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_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.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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.Relations.Relation_Definitions.symmetric_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2esymmetric,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a1(V_24X1) ).
fof('$adef_$_prop_16497_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__16497,V_24X1),V_24X2),V_24X3) = c_24__prop__16497___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_2048_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2048,V_24X1),V_24X2),V_24X3) = c_24__lam__2048___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Specif.sig2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_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_$_lam_1954_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1954,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1954___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$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('$adef_hahn.HahnSets.set_compl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnSets_2eset__compl,V_24X1),V_24X2) = chahn_2eHahnSets_2eset__compl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.upward_closed_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnRelationsBasic_2eupward__closed,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnRelationsBasic_2eupward__closed___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('$adef_hahn.HahnRelationsBasic.functional_$a2',axiom,
! [V_24X1,V_24X2] :
( p(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('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Peano.gt_$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('$adef_$_lam_1942_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1942,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1942___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$tdef_$_type_21',axiom,
! [V_24X1,V_24Y] :
( c_24__type__21___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__21___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4994',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4994___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4994___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2525',axiom,
! [V_24Y] :
( c_24__type__2525___24t(V_24Y)
<=> t(V_24Y,c_24__type__2525) ) ).
fof('$tdef_$_type_24418',axiom,
! [V_24Y] :
( c_24__type__24418___24t(V_24Y)
<=> t(V_24Y,c_24__type__24418) ) ).
fof('$tdef_$_type_11350',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__11350___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__11350___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_17253',axiom,
! [V_24Y] :
( c_24__type__17253___24t(V_24Y)
<=> t(V_24Y,c_24__type__17253) ) ).
fof('$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_$_type_11542',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__11542___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__11542___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_17238',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17238___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17238___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_5374',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5374___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5374___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21645',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__21645___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__21645___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_5369',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5369___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5369___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8665',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__8665___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__8665___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_1764',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1764___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1764___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23037',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23037___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23037___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_23172',axiom,
! [V_24Y] :
( c_24__type__23172___24t(V_24Y)
<=> t(V_24Y,c_24__type__23172) ) ).
fof('$tdef_$_type_6482',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__6482___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__6482___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.EnvRing.Mon',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2eMon) ) ).
fof('$tdef_$_type_1450',axiom,
! [V_24Y] :
( c_24__type__1450___24t(V_24Y)
<=> t(V_24Y,c_24__type__1450) ) ).
fof('$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_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_374',axiom,
! [V_24Y] :
( c_24__type__374___24t(V_24Y)
<=> t(V_24Y,c_24__type__374) ) ).
fof('$tdef_$_type_6307',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__6307___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__6307___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_2427',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2427___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2427___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_10302',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__10302___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__10302___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_6882',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__6882___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__6882___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_19246',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__19246___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__19246___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_5045',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5045___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5045___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1460',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1460___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1460___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23524',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23524___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23524___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2998',axiom,
! [V_24Y] :
( c_24__type__2998___24t(V_24Y)
<=> t(V_24Y,c_24__type__2998) ) ).
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_Coq.Reals.RIneq.posreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).
fof('$tdef_$_type_10365',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__10365___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__10365___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_13365',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__13365___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__13365___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Init.Datatypes.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_24292',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__24292___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__24292___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_16595',axiom,
! [V_24Y] :
( c_24__type__16595___24t(V_24Y)
<=> t(V_24Y,c_24__type__16595) ) ).
fof('$tdef_$_type_5221',axiom,
! [V_24Y] :
( c_24__type__5221___24t(V_24Y)
<=> t(V_24Y,c_24__type__5221) ) ).
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_581',axiom,
! [V_24Y] :
( c_24__type__581___24t(V_24Y)
<=> t(V_24Y,c_24__type__581) ) ).
fof('$tdef_$_type_14820',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__14820___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__14820___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_9010',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9010___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9010___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_17203',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__17203___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__17203___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_357',axiom,
! [V_24Y] :
( c_24__type__357___24t(V_24Y)
<=> t(V_24Y,c_24__type__357) ) ).
fof('$tdef_$_type_297',axiom,
! [V_24Y] :
( c_24__type__297___24t(V_24Y)
<=> t(V_24Y,c_24__type__297) ) ).
fof('$tdef_$_type_23569',axiom,
! [V_24Y] :
( c_24__type__23569___24t(V_24Y)
<=> t(V_24Y,c_24__type__23569) ) ).
fof('$tdef_$_type_195',axiom,
! [V_24Y] :
( c_24__type__195___24t(V_24Y)
<=> t(V_24Y,c_24__type__195) ) ).
fof('$tdef_$_type_17155',axiom,
! [V_24Y] :
( c_24__type__17155___24t(V_24Y)
<=> t(V_24Y,c_24__type__17155) ) ).
fof('$tdef_$_type_1452',axiom,
! [V_24Y] :
( c_24__type__1452___24t(V_24Y)
<=> t(V_24Y,c_24__type__1452) ) ).
fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
fof('$tdef_$_type_4987',axiom,
! [V_24Y] :
( c_24__type__4987___24t(V_24Y)
<=> t(V_24Y,c_24__type__4987) ) ).
fof('$tdef_$_type_8564',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__8564___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__8564___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4919',axiom,
! [V_24Y] :
( c_24__type__4919___24t(V_24Y)
<=> t(V_24Y,c_24__type__4919) ) ).
fof('$tdef_$_type_15753',axiom,
! [V_24Y] :
( c_24__type__15753___24t(V_24Y)
<=> t(V_24Y,c_24__type__15753) ) ).
fof('$tdef_$_type_1429',axiom,
! [V_24Y] :
( c_24__type__1429___24t(V_24Y)
<=> t(V_24Y,c_24__type__1429) ) ).
fof('$tdef_$_type_24253',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24253___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24253___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_24371',axiom,
! [V_24Y] :
( c_24__type__24371___24t(V_24Y)
<=> t(V_24Y,c_24__type__24371) ) ).
fof('$tdef_$_type_23594',axiom,
! [V_24Y] :
( c_24__type__23594___24t(V_24Y)
<=> t(V_24Y,c_24__type__23594) ) ).
fof('$tdef_$_type_1761',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1761___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1761___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15660',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__15660___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__15660___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_15015',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__15015___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__15015___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_3389',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3389___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3389___24a2(V_24X1,V_24X2)) ) ).
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_$_type_21299',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__21299___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__21299___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_4',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1397',axiom,
! [V_24Y] :
( c_24__type__1397___24t(V_24Y)
<=> t(V_24Y,c_24__type__1397) ) ).
fof('$tdef_$_type_23559',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23559___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23559___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_11102',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__11102___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__11102___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ) ).
fof('$tdef_$_type_4999',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4999___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4999___24a1(V_24X1)) ) ).
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_$_type_5534',axiom,
! [V_24Y] :
( c_24__type__5534___24t(V_24Y)
<=> t(V_24Y,c_24__type__5534) ) ).
fof('$tdef_$_type_5330',axiom,
! [V_24Y] :
( c_24__type__5330___24t(V_24Y)
<=> t(V_24Y,c_24__type__5330) ) ).
fof('$tdef_$_type_15668',axiom,
! [V_24Y] :
( c_24__type__15668___24t(V_24Y)
<=> t(V_24Y,c_24__type__15668) ) ).
fof('$tdef_$_type_9721',axiom,
! [V_24Y] :
( c_24__type__9721___24t(V_24Y)
<=> t(V_24Y,c_24__type__9721) ) ).
fof('$tdef_$_type_23410',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__23410___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__23410___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23189',axiom,
! [V_24Y] :
( c_24__type__23189___24t(V_24Y)
<=> t(V_24Y,c_24__type__23189) ) ).
fof('$tdef_$_type_6975',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6975___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6975___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_15613',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15613___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15613___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_20976',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__20976___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__20976___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_6400',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6400___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6400___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_7542',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__7542___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__7542___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_$_type_5303',axiom,
! [V_24Y] :
( c_24__type__5303___24t(V_24Y)
<=> t(V_24Y,c_24__type__5303) ) ).
fof('$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_2557',axiom,
! [V_24Y] :
( c_24__type__2557___24t(V_24Y)
<=> t(V_24Y,c_24__type__2557) ) ).
fof('$tdef_$_type_1368',axiom,
! [V_24Y] :
( c_24__type__1368___24t(V_24Y)
<=> t(V_24Y,c_24__type__1368) ) ).
fof('$tdef_$_type_11434',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__11434___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__11434___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_5835',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__5835___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__5835___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_11923',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__11923___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__11923___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('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.N',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).
fof('$tdef_Coq.Init.Specif.sig2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_11192',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__11192___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__11192___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_12298',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__12298___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__12298___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_Coq.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_5474',axiom,
! [V_24Y] :
( c_24__type__5474___24t(V_24Y)
<=> t(V_24Y,c_24__type__5474) ) ).
fof('$tdef_$_type_2520',axiom,
! [V_24Y] :
( c_24__type__2520___24t(V_24Y)
<=> t(V_24Y,c_24__type__2520) ) ).
fof('$tdef_$_type_3410',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3410___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3410___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1654',axiom,
! [V_24Y] :
( c_24__type__1654___24t(V_24Y)
<=> t(V_24Y,c_24__type__1654) ) ).
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_$_type_5291',axiom,
! [V_24Y] :
( c_24__type__5291___24t(V_24Y)
<=> t(V_24Y,c_24__type__5291) ) ).
fof('$tdef_$_type_266',axiom,
! [V_24X1,V_24Y] :
( c_24__type__266___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__266___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6225',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6225___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6225___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$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_552',axiom,
! [V_24Y] :
( c_24__type__552___24t(V_24Y)
<=> t(V_24Y,c_24__type__552) ) ).
fof('$tdef_$_type_15500',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15500___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15500___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7605',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__7605___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__7605___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4344',axiom,
! [V_24Y] :
( c_24__type__4344___24t(V_24Y)
<=> t(V_24Y,c_24__type__4344) ) ).
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_$_type_23646',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23646___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23646___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_14607',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__14607___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__14607___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_336',axiom,
! [V_24Y] :
( c_24__type__336___24t(V_24Y)
<=> t(V_24Y,c_24__type__336) ) ).
fof('$tdef_$_type_15800',axiom,
! [V_24Y] :
( c_24__type__15800___24t(V_24Y)
<=> t(V_24Y,c_24__type__15800) ) ).
fof('$tdef_$_type_15543',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15543___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15543___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15652',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__15652___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__15652___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_5034',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5034___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5034___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6575',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6575___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6575___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_8766',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__8766___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__8766___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_15779',axiom,
! [V_24Y] :
( c_24__type__15779___24t(V_24Y)
<=> t(V_24Y,c_24__type__15779) ) ).
fof('$tdef_$_type_14412',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__14412___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__14412___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_5155',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5155___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5155___24a1(V_24X1)) ) ).
fof('$tdef_$_type_9933',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__9933___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__9933___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_15176',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__15176___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__15176___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_12048',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__12048___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__12048___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_23421',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__23421___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__23421___24a2(V_24X1,V_24X2)) ) ).
fof('$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_673',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__673___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__673___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).
fof('$tdef_$_type_23072',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23072___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23072___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_1457',axiom,
! [V_24Y] :
( c_24__type__1457___24t(V_24Y)
<=> t(V_24Y,c_24__type__1457) ) ).
fof('$tdef_$_type_20630',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__20630___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__20630___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_19592',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__19592___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__19592___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_61',axiom,
! [V_24X1,V_24Y] :
( c_24__type__61___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__61___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_11491',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__11491___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__11491___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_5217',axiom,
! [V_24Y] :
( c_24__type__5217___24t(V_24Y)
<=> t(V_24Y,c_24__type__5217) ) ).
fof('$tdef_$_type_230',axiom,
! [V_24Y] :
( c_24__type__230___24t(V_24Y)
<=> t(V_24Y,c_24__type__230) ) ).
fof('$tdef_$_type_10856',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__10856___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__10856___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_5366',axiom,
! [V_24Y] :
( c_24__type__5366___24t(V_24Y)
<=> t(V_24Y,c_24__type__5366) ) ).
fof('$tdef_$_type_2588',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2588___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2588___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8272',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__8272___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__8272___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Datatypes.sum',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2esum___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2336',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2336___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2336___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_429',axiom,
! [V_24X1,V_24Y] :
( c_24__type__429___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__429___24a1(V_24X1)) ) ).
fof('$tdef_$_type_486',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__486___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__486___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11210',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__11210___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__11210___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Strings.Ascii.ascii',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).
fof('$tdef_$_type_24402',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__24402___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__24402___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_23744',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23744___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23744___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_72',axiom,
! [V_24Y] :
( c_24__type__72___24t(V_24Y)
<=> t(V_24Y,c_24__type__72) ) ).
fof('$tdef_$_type_1485',axiom,
! [V_24Y] :
( c_24__type__1485___24t(V_24Y)
<=> t(V_24Y,c_24__type__1485) ) ).
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_$_type_5016',axiom,
! [V_24Y] :
( c_24__type__5016___24t(V_24Y)
<=> t(V_24Y,c_24__type__5016) ) ).
fof('$tdef_$_type_1057',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1057___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1057___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_650',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__650___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__650___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9894',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__9894___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__9894___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_9030',axiom,
! [V_24Y] :
( c_24__type__9030___24t(V_24Y)
<=> t(V_24Y,c_24__type__9030) ) ).
fof('$tdef_$_type_23395',axiom,
! [V_24Y] :
( c_24__type__23395___24t(V_24Y)
<=> t(V_24Y,c_24__type__23395) ) ).
fof('$tdef_$_type_575',axiom,
! [V_24Y] :
( c_24__type__575___24t(V_24Y)
<=> t(V_24Y,c_24__type__575) ) ).
fof('$tdef_$_type_219',axiom,
! [V_24Y] :
( c_24__type__219___24t(V_24Y)
<=> t(V_24Y,c_24__type__219) ) ).
fof('$tdef_$_type_1813',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1813___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1813___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_16993',axiom,
! [V_24Y] :
( c_24__type__16993___24t(V_24Y)
<=> t(V_24Y,c_24__type__16993) ) ).
fof('$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_5054',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5054___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5054___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6789',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__6789___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__6789___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_90',axiom,
! [V_24X1,V_24Y] :
( c_24__type__90___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__90___24a1(V_24X1)) ) ).
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_15866',axiom,
! [V_24Y] :
( c_24__type__15866___24t(V_24Y)
<=> t(V_24Y,c_24__type__15866) ) ).
fof('$tdef_$_type_8867',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__8867___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__8867___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_24362',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24362___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24362___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_10419',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__10419___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__10419___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_2543',axiom,
! [V_24Y] :
( c_24__type__2543___24t(V_24Y)
<=> t(V_24Y,c_24__type__2543) ) ).
fof('$tdef_$_type_3373',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3373___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3373___24a1(V_24X1)) ) ).
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_Coq.micromega.RingMicromega.Op2',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp2) ) ).
fof('$tdef_$_type_271',axiom,
! [V_24X1,V_24Y] :
( c_24__type__271___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__271___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23564',axiom,
! [V_24Y] :
( c_24__type__23564___24t(V_24Y)
<=> t(V_24Y,c_24__type__23564) ) ).
fof('$tdef_$_type_1729',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1729___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1729___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7150',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__7150___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__7150___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_75',axiom,
! [V_24Y] :
( c_24__type__75___24t(V_24Y)
<=> t(V_24Y,c_24__type__75) ) ).
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_$_type_11125',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__11125___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__11125___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Decimal.int',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).
fof('$tdef_$_type_5379',axiom,
! [V_24Y] :
( c_24__type__5379___24t(V_24Y)
<=> t(V_24Y,c_24__type__5379) ) ).
fof('$tdef_$_type_83',axiom,
! [V_24Y] :
( c_24__type__83___24t(V_24Y)
<=> t(V_24Y,c_24__type__83) ) ).
fof('$tdef_$_type_4931',axiom,
! [V_24Y] :
( c_24__type__4931___24t(V_24Y)
<=> t(V_24Y,c_24__type__4931) ) ).
fof('$tdef_$_type_10910',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__10910___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__10910___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_13152',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__13152___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__13152___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_12939',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__12939___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__12939___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_15745',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__15745___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__15745___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_24170',axiom,
! [V_24Y] :
( c_24__type__24170___24t(V_24Y)
<=> t(V_24Y,c_24__type__24170) ) ).
fof('$tdef_$_type_19938',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__19938___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__19938___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.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_$_type_22983',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__22983___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__22983___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_5122',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5122___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5122___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1721',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1721___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1721___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7232',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7232___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7232___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_12423',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__12423___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__12423___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_11374',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__11374___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__11374___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_8474',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__8474___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__8474___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4925',axiom,
! [V_24Y] :
( c_24__type__4925___24t(V_24Y)
<=> t(V_24Y,c_24__type__4925) ) ).
fof('$tdef_$_type_2759',axiom,
! [V_24Y] :
( c_24__type__2759___24t(V_24Y)
<=> t(V_24Y,c_24__type__2759) ) ).
fof('$tdef_$_type_23101',axiom,
! [V_24Y] :
( c_24__type__23101___24t(V_24Y)
<=> t(V_24Y,c_24__type__23101) ) ).
fof('$tdef_$_type_11458',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__11458___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__11458___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_15737',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__15737___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__15737___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_24411',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__24411___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__24411___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_145',axiom,
! [V_24Y] :
( c_24__type__145___24t(V_24Y)
<=> t(V_24Y,c_24__type__145) ) ).
fof('$tdef_$_type_6039',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6039___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6039___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_18577',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__18577___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__18577___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_5117',axiom,
! [V_24Y] :
( c_24__type__5117___24t(V_24Y)
<=> t(V_24Y,c_24__type__5117) ) ).
fof('$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_$_type_694',axiom,
! [V_24Y] :
( c_24__type__694___24t(V_24Y)
<=> t(V_24Y,c_24__type__694) ) ).
fof('$tdef_$_type_23157',axiom,
! [V_24Y] :
( c_24__type__23157___24t(V_24Y)
<=> t(V_24Y,c_24__type__23157) ) ).
fof('$tdef_Coq.Init.Specif.sigT',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2487',axiom,
! [V_24Y] :
( c_24__type__2487___24t(V_24Y)
<=> t(V_24Y,c_24__type__2487) ) ).
fof('$tdef_$_type_5135',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5135___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5135___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12534',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__12534___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__12534___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_24327',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24327___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24327___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_A',axiom,
! [V_24Y] :
( cA___24t(V_24Y)
<=> t(V_24Y,cA) ) ).
fof('$tdef_$_type_11079',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__11079___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__11079___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_18923',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__18923___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__18923___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_15702',axiom,
! [V_24Y] :
( c_24__type__15702___24t(V_24Y)
<=> t(V_24Y,c_24__type__15702) ) ).
fof('$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_1448',axiom,
! [V_24Y] :
( c_24__type__1448___24t(V_24Y)
<=> t(V_24Y,c_24__type__1448) ) ).
fof('$tdef_$_type_15698',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15698___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15698___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22992',axiom,
! [V_24Y] :
( c_24__type__22992___24t(V_24Y)
<=> t(V_24Y,c_24__type__22992) ) ).
fof('$tdef_$_type_12173',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__12173___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__12173___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('$tdef_Coq.micromega.EnvRing.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8991',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__8991___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__8991___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_15617',axiom,
! [V_24Y] :
( c_24__type__15617___24t(V_24Y)
<=> t(V_24Y,c_24__type__15617) ) ).
fof('$tdef_$_type_8373',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__8373___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__8373___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_14199',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__14199___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__14199___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_23125',axiom,
! [V_24Y] :
( c_24__type__23125___24t(V_24Y)
<=> t(V_24Y,c_24__type__23125) ) ).
fof('$tdef_$_type_24210',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__24210___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__24210___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_2995',axiom,
! [V_24Y] :
( c_24__type__2995___24t(V_24Y)
<=> t(V_24Y,c_24__type__2995) ) ).
fof('$tdef_$_type_15533',axiom,
! [V_24Y] :
( c_24__type__15533___24t(V_24Y)
<=> t(V_24Y,c_24__type__15533) ) ).
fof('$tdef_$_type_11798',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__11798___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__11798___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_18231',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__18231___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__18231___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Structures.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_$_type_15212',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__15212___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__15212___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_10973',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__10973___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__10973___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4974',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4974___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4974___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2767',axiom,
! [V_24Y] :
( c_24__type__2767___24t(V_24Y)
<=> t(V_24Y,c_24__type__2767) ) ).
fof('$tdef_$_type_1661',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1661___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1661___24a1(V_24X1)) ) ).
fof('$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_17248',axiom,
! [V_24Y] :
( c_24__type__17248___24t(V_24Y)
<=> t(V_24Y,c_24__type__17248) ) ).
fof('$tdef_$_type_9213',axiom,
! [V_24Y] :
( c_24__type__9213___24t(V_24Y)
<=> t(V_24Y,c_24__type__9213) ) ).
fof('$tdef_$_type_5293',axiom,
! [V_24Y] :
( c_24__type__5293___24t(V_24Y)
<=> t(V_24Y,c_24__type__5293) ) ).
fof('$tdef_$_type_23405',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__23405___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__23405___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15490',axiom,
! [V_24Y] :
( c_24__type__15490___24t(V_24Y)
<=> t(V_24Y,c_24__type__15490) ) ).
fof('$tdef_$_type_15342',axiom,
! [V_24X1,V_24Y] :
( c_24__type__15342___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__15342___24a1(V_24X1)) ) ).
fof('$tdef_$_type_644',axiom,
! [V_24Y] :
( c_24__type__644___24t(V_24Y)
<=> t(V_24Y,c_24__type__644) ) ).
fof('$tdef_$_type_2795',axiom,
! [V_24Y] :
( c_24__type__2795___24t(V_24Y)
<=> t(V_24Y,c_24__type__2795) ) ).
fof('$tdef_$_type_157',axiom,
! [V_24Y] :
( c_24__type__157___24t(V_24Y)
<=> t(V_24Y,c_24__type__157) ) ).
fof('$tdef_$_type_23453',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23453___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23453___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Bool.Bool.reflect',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_667',axiom,
! [V_24Y] :
( c_24__type__667___24t(V_24Y)
<=> t(V_24Y,c_24__type__667) ) ).
fof('$tdef_$_type_5146',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5146___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5146___24a1(V_24X1)) ) ).
fof('$tdef_$_type_10730',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__10730___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__10730___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13986',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__13986___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__13986___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_22314',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__22314___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__22314___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_2111',axiom,
! [V_24Y] :
( c_24__type__2111___24t(V_24Y)
<=> t(V_24Y,c_24__type__2111) ) ).
fof('$tdef_$_type_13773',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__13773___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__13773___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_10482',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__10482___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__10482___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_5355',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5355___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5355___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_588',axiom,
! [V_24Y] :
( c_24__type__588___24t(V_24Y)
<=> t(V_24Y,c_24__type__588) ) ).
fof('$tdef_$_type_207',axiom,
! [V_24Y] :
( c_24__type__207___24t(V_24Y)
<=> t(V_24Y,c_24__type__207) ) ).
fof('$tdef_$_type_1656',axiom,
! [V_24Y] :
( c_24__type__1656___24t(V_24Y)
<=> t(V_24Y,c_24__type__1656) ) ).
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_$_type_3403',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3403___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3403___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_$_type_4989',axiom,
! [V_24Y] :
( c_24__type__4989___24t(V_24Y)
<=> t(V_24Y,c_24__type__4989) ) ).
fof('$tdef_$_type_17280',axiom,
! [V_24Y] :
( c_24__type__17280___24t(V_24Y)
<=> t(V_24Y,c_24__type__17280) ) ).
fof('$tdef_hahn.HahnBase.Equality.type',axiom,
! [V_24Y] :
( chahn_2eHahnBase_2eEquality_2etype___24t(V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2etype) ) ).
fof('$tdef_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [V_24X1,V_24Y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_$_type_2439',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2439___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2439___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9972',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__9972___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__9972___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$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_20284',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__20284___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__20284___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_5450',axiom,
! [V_24Y] :
( c_24__type__5450___24t(V_24Y)
<=> t(V_24Y,c_24__type__5450) ) ).
fof('$tdef_$_type_5807',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__5807___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__5807___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_2535',axiom,
! [V_24Y] :
( c_24__type__2535___24t(V_24Y)
<=> t(V_24Y,c_24__type__2535) ) ).
fof('$tdef_$_type_7722',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__7722___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__7722___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_7749',axiom,
! [V_24Y] :
( c_24__type__7749___24t(V_24Y)
<=> t(V_24Y,c_24__type__7749) ) ).
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_$_type_11320',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__11320___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__11320___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_9700',axiom,
! [V_24Y] :
( c_24__type__9700___24t(V_24Y)
<=> t(V_24Y,c_24__type__9700) ) ).
fof('$tdef_$_type_17680',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__17680___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__17680___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2992',axiom,
! [V_24Y] :
( c_24__type__2992___24t(V_24Y)
<=> t(V_24Y,c_24__type__2992) ) ).
fof('$tdef_$_type_4891',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__4891___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__4891___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_702',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__702___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__702___24a2(V_24X1,V_24X2)) ) ).
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_$_type_7057',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7057___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7057___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_23416',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__23416___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__23416___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15256',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__15256___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__15256___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$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_$_type_23477',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23477___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23477___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_47',axiom,
! [V_24Y] :
( c_24__type__47___24t(V_24Y)
<=> t(V_24Y,c_24__type__47) ) ).
fof('$tdef_$_type_10793',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__10793___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__10793___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_7479',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__7479___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__7479___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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_5708',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5708___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5708___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4935',axiom,
! [V_24Y] :
( c_24__type__4935___24t(V_24Y)
<=> t(V_24Y,c_24__type__4935) ) ).
fof('$tdef_$_type_15132',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__15132___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__15132___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_22637',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__22637___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__22637___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_7733',axiom,
! [V_24Y] :
( c_24__type__7733___24t(V_24Y)
<=> t(V_24Y,c_24__type__7733) ) ).
fof('$tdef_$_type_3419',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3419___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3419___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5447',axiom,
! [V_24Y] :
( c_24__type__5447___24t(V_24Y)
<=> t(V_24Y,c_24__type__5447) ) ).
fof('$tdef_$_type_16301',axiom,
! [V_24Y] :
( c_24__type__16301___24t(V_24Y)
<=> t(V_24Y,c_24__type__16301) ) ).
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_$_type_600',axiom,
! [V_24Y] :
( c_24__type__600___24t(V_24Y)
<=> t(V_24Y,c_24__type__600) ) ).
fof('$tdef_$_type_7659',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__7659___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__7659___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_66',axiom,
! [V_24Y] :
( c_24__type__66___24t(V_24Y)
<=> t(V_24Y,c_24__type__66) ) ).
fof('$tdef_$_type_10239',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__10239___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__10239___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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_1821',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1821___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1821___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_17182',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__17182___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__17182___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_22995',axiom,
! [V_24Y] :
( c_24__type__22995___24t(V_24Y)
<=> t(V_24Y,c_24__type__22995) ) ).
fof('$tdef_$_type_5362',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5362___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5362___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5021',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5021___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5021___24a1(V_24X1)) ) ).
fof('$tdef_$_type_16535',axiom,
! [V_24Y] :
( c_24__type__16535___24t(V_24Y)
<=> t(V_24Y,c_24__type__16535) ) ).
fof('$tdef_$_type_17246',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17246___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17246___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_97',axiom,
! [V_24Y] :
( c_24__type__97___24t(V_24Y)
<=> t(V_24Y,c_24__type__97) ) ).
fof('$tdef_$_type_474',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__474___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__474___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7325',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__7325___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__7325___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).
fof('$tdef_$_type_92',axiom,
! [V_24Y] :
( c_24__type__92___24t(V_24Y)
<=> t(V_24Y,c_24__type__92) ) ).
fof('$tdef_$_type_15028',axiom,
! [V_24Y] :
( c_24__type__15028___24t(V_24Y)
<=> t(V_24Y,c_24__type__15028) ) ).
fof('$tdef_$_type_479',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__479___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__479___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7',axiom,
! [V_24X1,V_24Y] :
( c_24__type__7___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__7___24a1(V_24X1)) ) ).
fof('$tdef_$_type_11148',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__11148___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__11148___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_163',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__163___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__163___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1427',axiom,
! [V_24Y] :
( c_24__type__1427___24t(V_24Y)
<=> t(V_24Y,c_24__type__1427) ) ).
fof('$tdef_$_type_2611',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2611___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2611___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13560',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__13560___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__13560___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('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$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_11166',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__11166___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__11166___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
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_$_type_7785',axiom,
! [V_24Y] :
( c_24__type__7785___24t(V_24Y)
<=> t(V_24Y,c_24__type__7785) ) ).
fof('$tdef_$_type_1473',axiom,
! [V_24Y] :
( c_24__type__1473___24t(V_24Y)
<=> t(V_24Y,c_24__type__1473) ) ).
fof('$tdef_$_type_11404',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__11404___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__11404___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_6132',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6132___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6132___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_21991',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__21991___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__21991___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_1022',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1022___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1022___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_5347',axiom,
! [V_24Y] :
( c_24__type__5347___24t(V_24Y)
<=> t(V_24Y,c_24__type__5347) ) ).
fof('$tdef_$_type_1701',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1701___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1701___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11515',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__11515___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__11515___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3364',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3364___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3364___24a1(V_24X1)) ) ).
fof('$tdef_$_type_17082',axiom,
! [V_24Y] :
( c_24__type__17082___24t(V_24Y)
<=> t(V_24Y,c_24__type__17082) ) ).
fof('$tdef_$_type_1344',axiom,
! [V_24Y] :
( c_24__type__1344___24t(V_24Y)
<=> t(V_24Y,c_24__type__1344) ) ).
fof('_HAMMER_GOAL',conjecture,
( cHahnMinElt_2emin__elt___24a3(cA,cr,ca)
=> cHahnMinElt_2emin__elt___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,cr),ca) ) ).
%------------------------------------------------------------------------------