TPTP Problem File: SEV661+1.p
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%------------------------------------------------------------------------------
% File : SEV661+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - N N proper
% 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 : N.N.proper.p [Kal26]
% Status : Theorem
% Rating : 0.70 v9.3.0
% Syntax : Number of formulae : 2457 (1094 unt; 0 def)
% Number of atoms : 7792 (2355 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 5435 ( 100 ~; 662 |;1164 &)
% ( 762 <=>;2747 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 6 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 395 ( 394 usr; 0 prp; 1-23 aty)
% Number of functors : 1358 (1358 usr; 891 con; 0-22 aty)
% Number of variables : 7309 (6885 !; 424 ?)
% 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.prod$27866',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__27879___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__27871] :
( t(Vvar__2___24Anonymous__27871,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__27872] :
( t(Vvar__3___24Anonymous__27872,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__27871,Vvar__3___24Anonymous__27872)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2427866___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__27871)),Vvar__3___24Anonymous__27872)))) ) ) ) ) ) ) ) ) ).
fof('$_def_$_let_var_6_p_26880_26883',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__26879] : c_24__let__var__6__p__26880__26883___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__26879) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__26879) ).
fof('$_def_$_let_var_6_p_26882_26884',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__26881] : c_24__let__var__6__p__26882__26884___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__26881) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__26881) ).
fof('$_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('$_def_Coq.Bool.Bvector.Bvector',axiom,
cCoq_2eBool_2eBvector_2eBvector = cCoq_2eVectors_2eVectorDef_2et___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__30690] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__30690)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__30690) ) ).
fof('$_def_Coq.Init.Datatypes.CompOpp',axiom,
! [V0__r] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__r)
=> ( ( V0__r = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eEq )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eGt )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ).
fof('$_def_Coq.Init.Datatypes.CompSpecT',axiom,
! [V0__A,V1__eq,V2__lt,V3__x,V4__y] : cCoq_2eInit_2eDatatypes_2eCompSpecT___24a5(V0__A,V1__eq,V2__lt,V3__x,V4__y) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a3(happ(happ(V1__eq,V3__x),V4__y),happ(happ(V2__lt,V3__x),V4__y),happ(happ(V2__lt,V4__y),V3__x)) ).
fof('$_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__12093] :
( t(Vvar__1___24Anonymous__12093,V0__A)
& ? [Vvar__2___24Anonymous__12094] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12094)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12093,Vvar__2___24Anonymous__12094)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12093,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__12094,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__12062] :
( t(Vvar__2___24Anonymous__12062,V0__A)
& ? [Vvar__3___24Anonymous__12063] :
( t(Vvar__3___24Anonymous__12063,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__12062,Vvar__3___24Anonymous__12063)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__12062 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__11993___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
| ? [Vvar__0___24Anonymous__11991] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11991)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11991)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__11991),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__11991)) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.negb',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_def_Coq.Init.Datatypes.orb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = V1__b2 ) ) ) ).
fof('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__12074] :
( t(Vvar__2___24Anonymous__12074,V0__A)
& ? [Vvar__3___24Anonymous__12075] :
( t(Vvar__3___24Anonymous__12075,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__12074,Vvar__3___24Anonymous__12075)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__12075 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.xorb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__18150] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18150)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18150)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__18150,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.compare',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__32473] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32473)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32473)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__32474] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32474)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32474)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__32477] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32477)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32477)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__32474,Vvar__0___24Anonymous__32477) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.div2',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__32488] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32488)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32488)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32488)
& ( ( Vvar__0___24Anonymous__32488 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__32491] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32491)
& Vvar__0___24Anonymous__32488 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32491)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__32491)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.leb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__6198] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6198)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6198)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__6201] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6201)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6201)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__6198,Vvar__0___24Anonymous__6201) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__29624] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29624)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29624)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__29627] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29627)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29627)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__29624,Vvar__0___24Anonymous__29627)) ) ) ) ) ) ) ) ).
fof('$_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__32482] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32482)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32482)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__32485] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32485)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32485)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__32482,Vvar__0___24Anonymous__32485)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__18155] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18155)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18155)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__18155,V2__m)) ) ) ) ).
fof('$_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__29616] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29616)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29616)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__29616 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__29618] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29618)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29618)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__29621] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29621)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29621)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__29618,Vvar__0___24Anonymous__29621) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Wf.well_founded',axiom,
! [V0__A,V1__R] :
( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__a) ) ) ).
fof('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__18107] :
( t(Vvar__1___24Anonymous__18107,V0__A)
& ? [Vvar__2___24Anonymous__18108] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__18108)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__18107,Vvar__2___24Anonymous__18108)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__18107 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__18108) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd',axiom,
! [V0__A,V1__default,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = V1__default )
| ? [Vvar__1___24Anonymous__32431] :
( t(Vvar__1___24Anonymous__32431,V0__A)
& ? [Vvar__2___24Anonymous__32432] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__32432)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__32431,Vvar__2___24Anonymous__32432)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__32431 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__32452] :
( t(Vvar__1___24Anonymous__32452,V0__A)
& ? [Vvar__2___24Anonymous__32453] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__32453)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__32452,Vvar__2___24Anonymous__32453)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__32452),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__32453)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__18119] :
( t(Vvar__1___24Anonymous__18119,V0__A)
& ? [Vvar__2___24Anonymous__18120] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__18120)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__18119,Vvar__2___24Anonymous__18120)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__18119 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__18122] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18122)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18122)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__18129] :
( t(Vvar__1___24Anonymous__18129,V0__A)
& ? [Vvar__2___24Anonymous__18130] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__18130)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__18129,Vvar__2___24Anonymous__18130)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__18122,Vvar__2___24Anonymous__18130,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.tl',axiom,
! [V0__A,V1__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__32442] :
( t(Vvar__1___24Anonymous__32442,V0__A)
& ? [Vvar__2___24Anonymous__32443] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__32443)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__32442,Vvar__2___24Anonymous__32443)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__32443 ) ) ) ) ) ).
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.NArith.BinNat.N.Bezout',axiom,
! [V0__n,V1__m,V2__p] :
( cCoq_2eNArith_2eBinNat_2eN_2eBezout___24a3(V0__n,V1__m,V2__p)
<=> ? [V3__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__a)
& ? [V4__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__b)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V3__a,V0__n) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V4__b,V1__m)) ) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.Even',axiom,
! [V0__n] :
( cCoq_2eNArith_2eBinNat_2eN_2eEven___24a1(V0__n)
<=> ? [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
& V0__n = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__m) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.Private_OrderTac.Tac.interp_ord',axiom,
! [V0__o] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V0__o)
=> ( ( V0__o = cCoq_2eStructures_2eOrdersTac_2eOEQ
& cCoq_2eNArith_2eBinNat_2eN_2ePrivate__OrderTac_2eTac_2einterp__ord___24a1(V0__o) = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) )
| ( V0__o = cCoq_2eStructures_2eOrdersTac_2eOLT
& cCoq_2eNArith_2eBinNat_2eN_2ePrivate__OrderTac_2eTac_2einterp__ord___24a1(V0__o) = cCoq_2eNArith_2eBinNat_2eN_2elt )
| ( V0__o = cCoq_2eStructures_2eOrdersTac_2eOLE
& cCoq_2eNArith_2eBinNat_2eN_2ePrivate__OrderTac_2eTac_2einterp__ord___24a1(V0__o) = cCoq_2eNArith_2eBinNat_2eN_2ele ) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.Private_Tac.interp_ord',axiom,
! [V0__o] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V0__o)
=> ( ( V0__o = cCoq_2eStructures_2eOrdersTac_2eOEQ
& cCoq_2eNArith_2eBinNat_2eN_2ePrivate__Tac_2einterp__ord___24a1(V0__o) = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) )
| ( V0__o = cCoq_2eStructures_2eOrdersTac_2eOLT
& cCoq_2eNArith_2eBinNat_2eN_2ePrivate__Tac_2einterp__ord___24a1(V0__o) = cCoq_2eNArith_2eBinNat_2eN_2elt )
| ( V0__o = cCoq_2eStructures_2eOrdersTac_2eOLE
& cCoq_2eNArith_2eBinNat_2eN_2ePrivate__Tac_2einterp__ord___24a1(V0__o) = cCoq_2eNArith_2eBinNat_2eN_2ele ) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.b2n',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.divide',axiom,
! [V0__p,V1__q] :
( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__p,V1__q)
<=> ? [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__r)
& V1__q = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__r,V0__p) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.eq',axiom,
cCoq_2eNArith_2eBinNat_2eN_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.NArith.BinNat.N.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNat.N.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lcm',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eBinNat_2eN_2elcm___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__a,cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V1__b,cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b))) ).
fof('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y))
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.le_alt',axiom,
! [V0__n,V1__m] :
( cCoq_2eNArith_2eBinNat_2eN_2ele__alt___24a2(V0__n,V1__m)
<=> ? [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V0__n) = V1__m ) ) ).
fof('$_def_Coq.NArith.BinNat.N.lnot',axiom,
! [V0__a,V1__n] : cCoq_2eNArith_2eBinNat_2eN_2elnot___24a2(V0__a,V1__n) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,cCoq_2eNArith_2eBinNat_2eN_2eones___24a1(V1__n)) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( p(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('$_def_Coq.NArith.BinNat.N.lt_alt',axiom,
! [V0__n,V1__m] :
( cCoq_2eNArith_2eBinNat_2eN_2elt__alt___24a2(V0__n,V1__m)
<=> ? [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V2__p),V0__n) = V1__m ) ) ).
fof('$_def_Coq.NArith.BinNat.N.max_case',axiom,
! [V0__n,V1__m,V2__P,V3__X,V4__X0] : cCoq_2eNArith_2eBinNat_2eN_2emax__case___24a5(V0__n,V1__m,V2__P,V3__X,V4__X0) = cCoq_2eNArith_2eBinNat_2eN_2emax__case__strong___24a5(V0__n,V1__m,c_24__lam__35768___24a3(V0__n,V1__m,V2__P),c_24__lam__35775___24a4(V0__n,V1__m,V2__P,V3__X),c_24__lam__35782___24a4(V0__n,V1__m,V2__P,V4__X0)) ).
fof('$_def_Coq.NArith.BinNat.N.min_case',axiom,
! [V0__n,V1__m,V2__P,V3__X,V4__X0] : cCoq_2eNArith_2eBinNat_2eN_2emin__case___24a5(V0__n,V1__m,V2__P,V3__X,V4__X0) = cCoq_2eNArith_2eBinNat_2eN_2emin__case__strong___24a5(V0__n,V1__m,c_24__lam__45270___24a3(V0__n,V1__m,V2__P),c_24__lam__45277___24a4(V0__n,V1__m,V2__P,V3__X),c_24__lam__45284___24a4(V0__n,V1__m,V2__P,V4__X0)) ).
fof('$_def_Coq.NArith.BinNat.N.ones',axiom,
! [V0__n] : cCoq_2eNArith_2eBinNat_2eN_2eones___24a1(V0__n) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n)) ).
fof('$_def_Coq.NArith.BinNat.N.peano_rec',axiom,
! [V0__P] : cCoq_2eNArith_2eBinNat_2eN_2epeano__rec___24a1(V0__P) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(V0__P) ).
fof('$_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__29388___24a1(V0__A)) ).
fof('$_def_Coq.NArith.BinNat.N.sqrt_up',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__a) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNat_2eN_2esqrt__up___24a1(V0__a) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__a) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNat_2eN_2esqrt__up___24a1(V0__a) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__a))) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__a) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNat_2eN_2esqrt__up___24a1(V0__a) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__11633] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11633)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11633)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__11636] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11636)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11636)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__11633,Vvar__0___24Anonymous__11636)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.compare',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__11638] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11638)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11638)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__11639] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11639)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11639)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__11642] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11642)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11642)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__11639,Vvar__0___24Anonymous__11642) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.NArith.BinNatDef.N.div2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__28106] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28106)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28106)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28106)
& ( ? [Vvar__0___24Anonymous__28110] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28110)
& Vvar__0___24Anonymous__28106 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28110)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28110) )
| ? [Vvar__0___24Anonymous__28111] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28111)
& Vvar__0___24Anonymous__28106 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28111)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28111) )
| ( Vvar__0___24Anonymous__28106 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div_eucl',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
| ? [Vvar__0___24Anonymous__28119] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28119)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28119)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,V0__a) )
| ? [Vvar__0___24Anonymous__28122] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28122)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28122)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__28119,V1__b) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__28099] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28099)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28099)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28099)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__6155] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6155)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6155)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__6156] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6156)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6156)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__6159] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6159)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6159)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__6156,Vvar__0___24Anonymous__6159) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__28112] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28112)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28112)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28112)
& ( ? [Vvar__0___24Anonymous__28116] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28116)
& Vvar__0___24Anonymous__28112 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28116)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__28117] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28117)
& Vvar__0___24Anonymous__28112 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28117)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__28112 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.gcd',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = V1__b )
| ? [Vvar__0___24Anonymous__28126] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28126)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28126)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = V0__a )
| ? [Vvar__0___24Anonymous__28129] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28129)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28129)
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__28126,Vvar__0___24Anonymous__28129)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.iter',axiom,
! [V0__n,V1__A,V2__f,V3__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cType___24t(V1__A)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eiter___24a4(V0__n,V1__A,V2__f,V3__x) = V3__x )
| ? [Vvar__0___24Anonymous__30669] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30669)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30669)
& cCoq_2eNArith_2eBinNatDef_2eN_2eiter___24a4(V0__n,V1__A,V2__f,V3__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__A,V2__f,V3__x,Vvar__0___24Anonymous__30669) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.land',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__11649] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11649)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11649)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__11652] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11652)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11652)
& cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(Vvar__0___24Anonymous__11649,Vvar__0___24Anonymous__11652) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.ldiff',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V1__n,V2__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__28132] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28132)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28132)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__28135] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28135)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28135)
& cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eldiff___24a2(Vvar__0___24Anonymous__28132,Vvar__0___24Anonymous__28135) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.log2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__276] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__276)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__276)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__276)
& ( ? [Vvar__0___24Anonymous__280] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__280)
& Vvar__0___24Anonymous__276 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__280)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__280)) )
| ? [Vvar__0___24Anonymous__281] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__281)
& Vvar__0___24Anonymous__276 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__281)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__281)) )
| ( Vvar__0___24Anonymous__276 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.lor',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__284] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__284)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__284)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__287] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__287)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__287)
& cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(Vvar__0___24Anonymous__284,Vvar__0___24Anonymous__287)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.ltb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.lxor',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__11654] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11654)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11654)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__11657] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11657)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11657)
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__11654,Vvar__0___24Anonymous__11657) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.max',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V0__n ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.min',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V1__n_27 ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.modulo',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__322] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__322)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__322)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__325] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__325)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__325)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__322,Vvar__0___24Anonymous__325)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.odd',axiom,
! [V0__n] : cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n)) ).
fof('$_def_Coq.NArith.BinNatDef.N.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__28146] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28146)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28146)
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__28146)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.one',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2eone = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_def_Coq.NArith.BinNatDef.N.pow',axiom,
! [V0__n,V1__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__p)
=> ( ( V1__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__327] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__327)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__327)
& ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__330] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__330)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__330)
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(Vvar__0___24Anonymous__330,Vvar__0___24Anonymous__327)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__6143] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6143)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6143)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__6143) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.shiftl',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl___24a2(V0__a,V1__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__11659] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11659)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11659)
& cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl___24a2(V0__a,V1__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eshiftl___24a2(Vvar__0___24Anonymous__11659,V1__n)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.shiftl_nat',axiom,
! [V0__a] : cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(c_24__lam__28137,V0__a,c_24__lam__28138) ).
fof('$_def_Coq.NArith.BinNatDef.N.shiftr',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eshiftr___24a2(V0__a,V1__n) = V0__a )
| ? [Vvar__0___24Anonymous__28144] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28144)
& V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28144)
& cCoq_2eNArith_2eBinNatDef_2eN_2eshiftr___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2,V0__a,Vvar__0___24Anonymous__28144) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.shiftr_nat',axiom,
! [V0__a] : cCoq_2eNArith_2eBinNatDef_2eN_2eshiftr__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(c_24__lam__28137,V0__a,c_24__lam__28142) ).
fof('$_def_Coq.NArith.BinNatDef.N.size',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esize___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__34999] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34999)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34999)
& cCoq_2eNArith_2eBinNatDef_2eN_2esize___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__34999)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.size_nat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esize__nat___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__35000] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35000)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35000)
& cCoq_2eNArith_2eBinNatDef_2eN_2esize__nat___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__35000) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.sqrt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__11648] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11648)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11648)
& cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(Vvar__0___24Anonymous__11648)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.square',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esquare___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__28118] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28118)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28118)
& cCoq_2eNArith_2eBinNatDef_2eN_2esquare___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esquare___24a1(Vvar__0___24Anonymous__28118)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.sub',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__6144] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6144)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6144)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__6149] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6149)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6144)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6149)
=> ( V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6149)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__6144,Vvar__0___24Anonymous__6149) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__6152] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6152)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__6144,Vvar__0___24Anonymous__6149) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__6152)
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6152) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__6144,Vvar__0___24Anonymous__6149) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__6142] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6142)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6142)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__6142)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ_double',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__28098] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28098)
& V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28098)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28098)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__28100] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28100)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28100)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__28100) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
! [Vvar__29135] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__29135)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__29135) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__11661] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11661)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11661)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__11661,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.testbit_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat___24a1(V0__a) = c_24__lam__321 )
| ? [Vvar__0___24Anonymous__332] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__332)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__332)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(Vvar__0___24Anonymous__332) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__11663] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11663)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11663)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__11663) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.two',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2etwo = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.NArith.BinNatDef.N.zero',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2ezero = cCoq_2eNumbers_2eBinNums_2eN0 ).
fof('$_def_Coq.NArith.Ndec.Nleb',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eNat_2eleb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V1__b)) ).
fof('$_def_Coq.NArith.Ndigits.Neven',axiom,
! [V0__n] :
( cCoq_2eNArith_2eNdigits_2eNeven___24a1(V0__n)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_def_Coq.NArith.Ndigits.Nless',axiom,
! [V0__a,V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__18165] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18165)
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__18165)
& cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,V1__a_27) = cCoq_2eNArith_2eNdigits_2eNless__aux___24a3(V0__a,V1__a_27,Vvar__0___24Anonymous__18165) ) ) ) ) ).
fof('$_def_Coq.NArith.Ndigits.Nodd',axiom,
! [V0__n] :
( cCoq_2eNArith_2eNdigits_2eNodd___24a1(V0__n)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_def_Coq.NArith.Ndigits.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eNdigits_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.Numbers.BinNums.N_rec',axiom,
! [V0__P] : cCoq_2eNumbers_2eBinNums_2eN__rec___24a1(V0__P) = cCoq_2eNumbers_2eBinNums_2eN__rect___24a1(V0__P) ).
fof('$_def_Coq.Numbers.BinNums.N_rect',axiom,
! [V0__P,V1__f,V2__f,V3__n] :
( c_24__type__30789___24t(V0__P,V0__P)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> ( ( V3__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNumbers_2eBinNums_2eN__rect___24a4(V0__P,V1__f,V2__f,V3__n) = V1__f )
| ? [Vvar__0___24Anonymous__30787] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30787)
& V3__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30787)
& cCoq_2eNumbers_2eBinNums_2eN__rect___24a4(V0__P,V1__f,V2__f,V3__n) = happ(V2__f,Vvar__0___24Anonymous__30787) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.le',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.mask2cmp',axiom,
! [V0__p] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V0__p)
=> ( ( V0__p = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPos_2ePos_2emask2cmp___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__35200] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35200)
& V0__p = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__35200)
& cCoq_2ePArith_2eBinPos_2ePos_2emask2cmp___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2eGt )
| ( V0__p = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPos_2ePos_2emask2cmp___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
! [V0__c,V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = V0__c )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eLt )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.Ndouble',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2ePArith_2eBinPosDef_2ePos_2eNdouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__28620] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28620)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28620)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eNdouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28620)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.Nsucc_double',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2ePArith_2eBinPosDef_2ePos_2eNsucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__28619] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28619)
& V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28619)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eNsucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28619)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__28567] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28567)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28567)
& ( ? [Vvar__0___24Anonymous__28571] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28571)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28571)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__28566__1__add__carry___24a2(Vvar__0___24Anonymous__28567,Vvar__0___24Anonymous__28571)) )
| ? [Vvar__0___24Anonymous__28572] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28572)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28572)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__28567,Vvar__0___24Anonymous__28572)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__28567)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__28573] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28573)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28573)
& ( ? [Vvar__0___24Anonymous__28577] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28577)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28577)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__28573,Vvar__0___24Anonymous__28577)) )
| ? [Vvar__0___24Anonymous__28578] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28578)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28578)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__28573,Vvar__0___24Anonymous__28578)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28573) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__28579] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28579)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28579)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__28579)) )
| ? [Vvar__0___24Anonymous__28580] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28580)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28580)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28580) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.compare',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.div2',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__28614] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28614)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28614)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__28614 )
| ? [Vvar__0___24Anonymous__28615] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28615)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28615)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__28615 )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.eqb',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__35053] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35053)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35053)
& ( ? [Vvar__0___24Anonymous__35057] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35057)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35057)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__35053,Vvar__0___24Anonymous__35057) )
| ? [Vvar__0___24Anonymous__35058] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35058)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35058)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__35059] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35059)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35059)
& ( ? [Vvar__0___24Anonymous__35063] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35063)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35063)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__35064] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35064)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35064)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__35059,Vvar__0___24Anonymous__35064) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__35065] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35065)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35065)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__35066] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35066)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35066)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__28599] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28599)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28599)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__28599),Vvar__0___24Anonymous__28599)) )
| ? [Vvar__0___24Anonymous__28600] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28600)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28600)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__28600),Vvar__0___24Anonymous__28600) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.lor',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__35071] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35071)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35071)
& ( ? [Vvar__0___24Anonymous__35075] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35075)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35075)
& cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(V1__p,V2__q) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(Vvar__0___24Anonymous__35071,Vvar__0___24Anonymous__35075)) )
| ? [Vvar__0___24Anonymous__35076] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35076)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35076)
& cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(V1__p,V2__q) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(Vvar__0___24Anonymous__35071,Vvar__0___24Anonymous__35076)) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(V1__p,V2__q) = V1__p ) ) ) ) )
| ? [Vvar__0___24Anonymous__35077] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35077)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35077)
& ( ? [Vvar__0___24Anonymous__35081] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35081)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35081)
& cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(V1__p,V2__q) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(Vvar__0___24Anonymous__35077,Vvar__0___24Anonymous__35081)) )
| ? [Vvar__0___24Anonymous__35082] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35082)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35082)
& cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(V1__p,V2__q) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(Vvar__0___24Anonymous__35077,Vvar__0___24Anonymous__35082)) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(V1__p,V2__q) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35077) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__35083] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35083)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35083)
& cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(V1__p,V2__q) = V2__q )
| ? [Vvar__0___24Anonymous__35084] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35084)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35084)
& cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(V1__p,V2__q) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35084) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(V1__p,V2__q) = V2__q ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__11707] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11707)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__11707)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__y,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__11707,V2__y))) )
| ? [Vvar__0___24Anonymous__11708] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11708)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11708)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__11708,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__28678] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28678)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28678)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__28678)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred_N',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( ? [Vvar__0___24Anonymous__28596] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28596)
& V0__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28596)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28596)) )
| ? [Vvar__0___24Anonymous__28597] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28597)
& V0__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28597)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__28597)) )
| ( V0__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__35040] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35040)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35040)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35040)) )
| ? [Vvar__0___24Anonymous__35041] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35041)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35041)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__35041)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.shiftl',axiom,
! [V0__p,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2ePArith_2eBinPosDef_2ePos_2eshiftl___24a2(V0__p,V1__n) = V0__p )
| ? [Vvar__0___24Anonymous__28639] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28639)
& V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__28639)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eshiftl___24a2(V0__p,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2exO,V0__p,Vvar__0___24Anonymous__28639) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__35050] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35050)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35050)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__35050)) )
| ? [Vvar__0___24Anonymous__35051] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35051)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35051)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__35051)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__35047] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35047)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35047)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__35047)) )
| ? [Vvar__0___24Anonymous__35048] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35048)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35048)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__35048)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__35042] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35042)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__35042)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__35042 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__11704] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11704)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__11704)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__11704)) )
| ? [Vvar__0___24Anonymous__11705] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11705)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11705)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__11705) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.testbit',axiom,
! [V1__p,V2__n] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__35092] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35092)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35092)
& ( ( V2__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V1__p,V2__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__35095] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35095)
& V2__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35095)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V1__p,V2__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__35092,cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35095)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__35096] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35096)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35096)
& ( ( V2__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V1__p,V2__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__35099] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35099)
& V2__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35099)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V1__p,V2__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__35096,cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35099)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ( V2__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V1__p,V2__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__35100] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35100)
& V2__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35100)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V1__p,V2__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__28646] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28646)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28646)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__28659___24a1(Vvar__0___24Anonymous__28646) )
| ? [Vvar__0___24Anonymous__28650] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28650)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28650)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__28666___24a1(Vvar__0___24Anonymous__28650) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__28670 ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
! [V0__x] : cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd,V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
| ? [Vvar__0___24Anonymous__32690] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32690)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32690)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__32690) )
| ? [Vvar__0___24Anonymous__32691] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32691)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32691)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__32691)) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__14___24a1(V0__A) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Strings.Ascii.ascii_of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eStrings_2eAscii_2eascii__of__N___24a1(V0__n) = cCoq_2eStrings_2eAscii_2ezero )
| ? [Vvar__0___24Anonymous__30693] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30693)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30693)
& cCoq_2eStrings_2eAscii_2eascii__of__N___24a1(V0__n) = cCoq_2eStrings_2eAscii_2eascii__of__pos___24a1(Vvar__0___24Anonymous__30693) ) ) ) ).
fof('$_def_Coq.Strings.ByteVector.ByteVector',axiom,
cCoq_2eStrings_2eByteVector_2eByteVector = cCoq_2eVectors_2eVectorDef_2et___24a1(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.eq_dec',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq__dec = cCoq_2eNArith_2eBinNat_2eN_2eeq__dec ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt = cCoq_2eNArith_2eBinNat_2eN_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [Vvar__29136] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__29136)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__29136) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_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('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__30691] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30691)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30691)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30691) )
| ? [Vvar__0___24Anonymous__30692] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30692)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30692)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30692) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__29047] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29047)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29047)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29047) )
| ? [Vvar__0___24Anonymous__29048] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29048)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29048)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29048) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__29043] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29043)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29043)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__29043) )
| ? [Vvar__0___24Anonymous__29044] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29044)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29044)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__29044) ) ) ) ).
fof('$_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__28989] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28989)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__28989)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__28993] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28993)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__28993)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__28989,Vvar__0___24Anonymous__28993)) )
| ? [Vvar__0___24Anonymous__28994] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28994)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__28994)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__28989,Vvar__0___24Anonymous__28994) ) ) ) ) )
| ? [Vvar__0___24Anonymous__28995] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28995)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__28995)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__28999] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28999)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__28999)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__28999,Vvar__0___24Anonymous__28995) )
| ? [Vvar__0___24Anonymous__29000] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29000)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29000)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__28995,Vvar__0___24Anonymous__29000)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.compare',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__29025] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29025)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29025)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__29026] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29026)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29026)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__29027] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29027)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29027)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__29031] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29031)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29031)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__29027,Vvar__0___24Anonymous__29031) )
| ? [Vvar__0___24Anonymous__29032] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29032)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29032)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__29033] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29033)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29033)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__29037] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29037)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29037)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__29038] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29038)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29038)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__29033,Vvar__0___24Anonymous__29038)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__29060] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__29060)
& ? [Vvar__3___24Anonymous__29061] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__29061)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__29060,Vvar__3___24Anonymous__29061)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__29060 ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.min',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__35276] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__35276)
& ? [Vvar__3___24Anonymous__35277] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__35277)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__35276,Vvar__3___24Anonymous__35277)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__35277 ) ) ) ) ).
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__29009] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29009)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29009)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__29013] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29013)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29013)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__29009,Vvar__0___24Anonymous__29013)) )
| ? [Vvar__0___24Anonymous__29014] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29014)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29014)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__29009,Vvar__0___24Anonymous__29014)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__29015] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29015)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29015)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__29019] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29019)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29019)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__29015,Vvar__0___24Anonymous__29019)) )
| ? [Vvar__0___24Anonymous__29020] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29020)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29020)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__29015,Vvar__0___24Anonymous__29020)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__29053] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29053)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29053)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29053) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__29004] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29004)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29004)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29004) )
| ? [Vvar__0___24Anonymous__29005] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29005)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29005)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29005) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__29022] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29022)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29022)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__29022) )
| ? [Vvar__0___24Anonymous__29023] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29023)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29023)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pred',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.quot',axiom,
! [V0__a,V1__b] : cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.rem',axiom,
! [V0__a,V1__b] : cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b)) ).
fof('$_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.to_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__29051] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29051)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29051)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29051) )
| ? [Vvar__0___24Anonymous__29052] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29052)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29052)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__35270] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35270)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35270)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__35270) )
| ? [Vvar__0___24Anonymous__35271] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35271)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35271)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__12235___24a1(V0__D) ).
fof('$_def_Coq.micromega.Env.nth',axiom,
! [V0__D,V1__n,V2__e] : cCoq_2emicromega_2eEnv_2enth___24a3(V0__D,V1__n,V2__e) = happ(V2__e,V1__n) ).
fof('$_def_Coq.micromega.EnvRing.P1',axiom,
! [V0__C,V1__cI] : cCoq_2emicromega_2eEnvRing_2eP1___24a2(V0__C,V1__cI) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V0__C,V1__cI) ).
fof('$_def_Coq.micromega.RMicromega.INZ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2emicromega_2eRMicromega_2eINZ___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__32681] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32681)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__32681)
& cCoq_2emicromega_2eRMicromega_2eINZ___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32681)) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_conj',axiom,
! [V1__A,V2__eval,V3__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__19866] :
( t(Vvar__1___24Anonymous__19866,V1__A)
& ? [Vvar__2___24Anonymous__19867] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__19867)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__19867)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__19866,Vvar__2___24Anonymous__19867)
& ( ( Vvar__2___24Anonymous__19867 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(happ(V2__eval,Vvar__1___24Anonymous__19866)) ) )
| ? [Vvar__1___24Anonymous__19878] :
( t(Vvar__1___24Anonymous__19878,V1__A)
& ? [Vvar__2___24Anonymous__19879] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__19879)
& Vvar__2___24Anonymous__19867 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__19878,Vvar__2___24Anonymous__19879)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__19866))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__19867) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__19847] :
( t(Vvar__1___24Anonymous__19847,V1__A)
& ? [Vvar__2___24Anonymous__19848] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__19848)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__19847,Vvar__2___24Anonymous__19848)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__19847))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__19848,V4__goal) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.NFormula',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C) = cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_def_Coq.micromega.RingMicromega.PolC',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V0__C) ).
fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).
fof('$_def_Coq.micromega.RingMicromega.cneqb',axiom,
! [V0__C,V1__ceqb,V2__x,V3__y] : cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V0__C,V1__ceqb,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2enegb___24a1(happ(happ(V1__ceqb,V2__x),V3__y)) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op1',axiom,
! [V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V5__o)
=> ( ( V5__o = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__20450___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__20458___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__20466___24a3(V0__R,V1__rO,V4__rlt) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__20474___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op2',axiom,
! [V0__R,V1__req,V2__rle,V3__rlt,V4__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V4__o)
=> ( ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V1__req )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__21925___24a2(V0__R,V1__req) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V2__rle )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__21933___24a2(V0__R,V2__rle) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__21941___24a2(V0__R,V3__rlt) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__21949___24a2(V0__R,V3__rlt) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.eval_pexpr',axiom,
! [V0__R,V1__rplus,V2__rtimes,V3__rminus,V4__ropp,V5__C,V6__phi,V7__E,V8__pow__phi,V9__rpow] : cCoq_2emicromega_2eRingMicromega_2eeval__pexpr___24a10(V0__R,V1__rplus,V2__rtimes,V3__rminus,V4__ropp,V5__C,V6__phi,V7__E,V8__pow__phi,V9__rpow) = cCoq_2emicromega_2eEnvRing_2ePEeval___24a10(V0__R,V1__rplus,V2__rtimes,V3__rminus,V4__ropp,V5__C,V6__phi,V7__E,V8__pow__phi,V9__rpow) ).
fof('$_def_Coq.micromega.RingMicromega.eval_pol',axiom,
! [V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi] : cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a5(V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi) = cCoq_2emicromega_2eEnvRing_2ePphi___24a5(V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi) ).
fof('$_def_Coq.micromega.RingMicromega.eval_sexpr',axiom,
! [V0__R,V1__rplus,V2__rtimes,V3__rminus,V4__ropp,V5__E,V6__pow__phi,V7__rpow,V8__S,V9__phiS] : cCoq_2emicromega_2eRingMicromega_2eeval__sexpr___24a10(V0__R,V1__rplus,V2__rtimes,V3__rminus,V4__ropp,V5__E,V6__pow__phi,V7__rpow,V8__S,V9__phiS) = cCoq_2emicromega_2eEnvRing_2ePEeval___24a10(V0__R,V1__rplus,V2__rtimes,V3__rminus,V4__ropp,V8__S,V9__phiS,V5__E,V6__pow__phi,V7__rpow) ).
fof('$_def_Coq.micromega.Tauto.clause',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.omega.PreOmega.Z_of_N\'',axiom,
cCoq_2eomega_2ePreOmega_2eZ__of__N_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N ).
fof('$_def_Coq.setoid_ring.ArithRing.protected_to_nat',axiom,
cCoq_2esetoid__ring_2eArithRing_2eprotected__to__nat = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat ).
fof('$_def_Coq.setoid_ring.BinList.jump',axiom,
! [V0__A,V2__p,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( ? [Vvar__0___24Anonymous__30780] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30780)
& V2__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30780)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__30780,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__30780,cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l))) )
| ? [Vvar__0___24Anonymous__30781] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30781)
& V2__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30781)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__30781,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__30781,V3__l)) )
| ( V2__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.FEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V9__C)
=> ( cType___24t(V11__Cpow)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,V16__pe)
=> ( ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V1__rO )
| ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__15607] :
( t(Vvar__1___24Anonymous__15607,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__15607)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V10__phi,Vvar__1___24Anonymous__15607) )
| ? [Vvar__1___24Anonymous__15609] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15609)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__15609)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__15609,V15__l) )
| ? [Vvar__1___24Anonymous__15611] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15611)
& ? [Vvar__2___24Anonymous__15612] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__15612)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__15611,Vvar__2___24Anonymous__15612)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__15611)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__15612)) ) )
| ? [Vvar__1___24Anonymous__15615] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15615)
& ? [Vvar__2___24Anonymous__15616] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__15616)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__15615,Vvar__2___24Anonymous__15616)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__15615)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__15616)) ) )
| ? [Vvar__1___24Anonymous__15619] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15619)
& ? [Vvar__2___24Anonymous__15620] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__15620)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__15619,Vvar__2___24Anonymous__15620)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__15619)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__15620)) ) )
| ? [Vvar__1___24Anonymous__15623] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15623)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__15623)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__15623)) )
| ? [Vvar__1___24Anonymous__15625] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15625)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__15625)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V8__rinv,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__15625)) )
| ? [Vvar__1___24Anonymous__15627] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15627)
& ? [Vvar__2___24Anonymous__15628] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__15628)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__15627,Vvar__2___24Anonymous__15628)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V7__rdiv,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__15627)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__15628)) ) )
| ? [Vvar__1___24Anonymous__15631] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__15631)
& ? [Vvar__2___24Anonymous__15632] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__15632)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__15631,Vvar__2___24Anonymous__15632)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V13__rpow,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__15631)),happ(V12__Cp__phi,Vvar__2___24Anonymous__15632)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__17585] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__17585)
& ? [Vvar__2___24Anonymous__17586] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__17586)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__17585,Vvar__2___24Anonymous__17586)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__17585),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__17586,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__e,V14__e_27] :
( cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__e,V14__e_27)
<=> ! [V15__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V15__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V15__l,V13__e)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V15__l,V14__e_27))) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.NtoZ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eField__theory_2eNtoZ___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__29548] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29548)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29548)
& cCoq_2esetoid__ring_2eField__theory_2eNtoZ___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29548) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.PCond',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__le)
=> ( ( V15__le = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__15936] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__15936)
& ? [Vvar__2___24Anonymous__15937] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__15937)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__15937)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__15936,Vvar__2___24Anonymous__15937)
& ( ( Vvar__2___24Anonymous__15937 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__15936)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__15948] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__15948)
& ? [Vvar__2___24Anonymous__15949] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__15949)
& Vvar__2___24Anonymous__15937 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__15948,Vvar__2___24Anonymous__15949)
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ( ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__15936)),V1__rO))
& cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__15937) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.ZtoN',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eField__theory_2eZtoN___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__31063] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31063)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31063)
& cCoq_2esetoid__ring_2eField__theory_2eZtoN___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31063) )
| ? [Vvar__0___24Anonymous__31064] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31064)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31064)
& cCoq_2esetoid__ring_2eField__theory_2eZtoN___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nopp',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNopp = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nsub',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNsub = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_def_Coq.setoid_ring.InitialRing.NwO',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNwO = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
! [Vvar__18070] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__18070)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__18070) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
=> ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
| ? [Vvar__0___24Anonymous__29584] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29584)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29584)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__29584) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN1',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
=> ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN1___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
| ? [Vvar__0___24Anonymous__18030] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18030)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__18030)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN1___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__18030) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiNword',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w] :
( cType___24t(V0__R)
=> ( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V8__w)
=> ( ( V8__w = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = V1__rO )
| ? [Vvar__1___24Anonymous__32283] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__32283)
& ? [Vvar__2___24Anonymous__32284] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__32284)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__32283)
=> ( V8__w = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__32283,Vvar__2___24Anonymous__32284)
& ( ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__32284)
=> ( Vvar__1___24Anonymous__32283 = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( Vvar__2___24Anonymous__32284 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,Vvar__1___24Anonymous__32283) )
| ? [Vvar__1___24Anonymous__32305] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__32305)
& ? [Vvar__2___24Anonymous__32306] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__32306)
& Vvar__2___24Anonymous__32284 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__32305,Vvar__2___24Anonymous__32306)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = happ(V6__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,Vvar__2___24Anonymous__32284)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__32308] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32308)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__32284)
=> ( Vvar__1___24Anonymous__32283 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__32308)
& ( ( Vvar__2___24Anonymous__32284 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,Vvar__1___24Anonymous__32283) )
| ? [Vvar__1___24Anonymous__32315] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__32315)
& ? [Vvar__2___24Anonymous__32316] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__32316)
& Vvar__2___24Anonymous__32284 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__32315,Vvar__2___24Anonymous__32316)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,Vvar__1___24Anonymous__32283)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,Vvar__2___24Anonymous__32284)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__29550] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29550)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29550)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29550)
& ( ? [Vvar__0___24Anonymous__29554] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29554)
& Vvar__0___24Anonymous__29550 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29554)
& 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__29550))) )
| ? [Vvar__0___24Anonymous__29555] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29555)
& Vvar__0___24Anonymous__29550 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29555)
& 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__29550))) )
| ( Vvar__0___24Anonymous__29550 = 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__29556] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29556)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29556)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29556)
& ( ? [Vvar__0___24Anonymous__29560] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29560)
& Vvar__0___24Anonymous__29556 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29560)
& 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__29556)) )
| ? [Vvar__0___24Anonymous__29561] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29561)
& Vvar__0___24Anonymous__29556 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29561)
& 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__29556)) )
| ( Vvar__0___24Anonymous__29556 = 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__17997] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17997)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17997)
& 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__17997))) )
| ? [Vvar__0___24Anonymous__17998] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17998)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17998)
& 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__17998)) )
| ( 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('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__32212] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32212)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32212)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__32212) )
| ? [Vvar__0___24Anonymous__32213] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32213)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32213)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__32213)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.triv_div',axiom,
! [V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y] :
( cType___24t(V0__C)
=> ( c_24__type__1938___24t(V0__C,V3__ceqb)
=> ( t(V4__x,V0__C)
=> ( t(V5__y,V0__C)
=> ( ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V2__cI,V1__cO) )
| ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V1__cO,V4__x) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring.bool_eq',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V1__b2) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.P0',axiom,
! [V0__C,V1__cO] : cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V0__C,V1__cO) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,V1__cO) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.P1',axiom,
! [V0__C,V1__cI] : cCoq_2esetoid__ring_2eRing__polynom_2eP1___24a2(V0__C,V1__cI) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,V1__cI) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V7__C)
=> ( cType___24t(V9__Cpow)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,V14__pe)
=> ( ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V1__rO )
| ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__2297] :
( t(Vvar__1___24Anonymous__2297,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__2297)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V8__phi,Vvar__1___24Anonymous__2297) )
| ? [Vvar__1___24Anonymous__2299] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2299)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__2299)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__2299,V13__l) )
| ? [Vvar__1___24Anonymous__2301] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__2301)
& ? [Vvar__2___24Anonymous__2302] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__2302)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__2301,Vvar__2___24Anonymous__2302)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__2301)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__2302)) ) )
| ? [Vvar__1___24Anonymous__2305] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__2305)
& ? [Vvar__2___24Anonymous__2306] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__2306)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__2305,Vvar__2___24Anonymous__2306)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__2305)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__2306)) ) )
| ? [Vvar__1___24Anonymous__2309] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__2309)
& ? [Vvar__2___24Anonymous__2310] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__2310)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__2309,Vvar__2___24Anonymous__2310)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__2309)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__2310)) ) )
| ? [Vvar__1___24Anonymous__2313] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__2313)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__2313)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__2313)) )
| ? [Vvar__1___24Anonymous__2315] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__2315)
& ? [Vvar__2___24Anonymous__2316] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2316)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__2315,Vvar__2___24Anonymous__2316)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V11__rpow,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__2315)),happ(V10__Cp__phi,Vvar__2___24Anonymous__2316)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Peq',axiom,
! [V0__C,V1__ceqb,V3__P,V4__P_27] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V3__P)
=> ( ? [Vvar__1___24Anonymous__23501] :
( t(Vvar__1___24Anonymous__23501,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__23501)
& ( ? [Vvar__1___24Anonymous__23511] :
( t(Vvar__1___24Anonymous__23511,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__23511)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__23501),Vvar__1___24Anonymous__23511) )
| ? [Vvar__1___24Anonymous__23513] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23513)
& ? [Vvar__2___24Anonymous__23514] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__23514)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__23513,Vvar__2___24Anonymous__23514)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__23517] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23517)
& ? [Vvar__2___24Anonymous__23518] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23518)
& ? [Vvar__3___24Anonymous__23519] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__23519)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__23517,Vvar__2___24Anonymous__23518,Vvar__3___24Anonymous__23519)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__23524] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23524)
& ? [Vvar__2___24Anonymous__23525] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__23525)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__23524,Vvar__2___24Anonymous__23525)
& ( ? [Vvar__1___24Anonymous__23545] :
( t(Vvar__1___24Anonymous__23545,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__23545)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__23547] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23547)
& ? [Vvar__2___24Anonymous__23548] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__23548)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23524)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23547)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__23547,Vvar__2___24Anonymous__23548)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__23524,Vvar__1___24Anonymous__23547) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__23525,Vvar__2___24Anonymous__23548) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__23524,Vvar__1___24Anonymous__23547) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__23524,Vvar__1___24Anonymous__23547) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__23553] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23553)
& ? [Vvar__2___24Anonymous__23554] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23554)
& ? [Vvar__3___24Anonymous__23555] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__23555)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__23553,Vvar__2___24Anonymous__23554,Vvar__3___24Anonymous__23555)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__23560] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23560)
& ? [Vvar__2___24Anonymous__23561] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23561)
& ? [Vvar__3___24Anonymous__23562] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__23562)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__23560,Vvar__2___24Anonymous__23561,Vvar__3___24Anonymous__23562)
& ( ? [Vvar__1___24Anonymous__23595] :
( t(Vvar__1___24Anonymous__23595,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__23595)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__23597] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23597)
& ? [Vvar__2___24Anonymous__23598] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__23598)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__23597,Vvar__2___24Anonymous__23598)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__23601] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23601)
& ? [Vvar__2___24Anonymous__23602] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23602)
& ? [Vvar__3___24Anonymous__23603] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__23603)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23561)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23602)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__23601,Vvar__2___24Anonymous__23602,Vvar__3___24Anonymous__23603)
& ( ( cType___24t(V0__C)
=> ( c_24__type__1938___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23560)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23601)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__23561,Vvar__2___24Anonymous__23602) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__23560,Vvar__1___24Anonymous__23601) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__3___24Anonymous__23562,Vvar__3___24Anonymous__23603) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__23560,Vvar__1___24Anonymous__23601) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__23561,Vvar__2___24Anonymous__23602) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__23561,Vvar__2___24Anonymous__23602) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_Coq.setoid_ring.Ring_theory.IDphi',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRopp',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRsub',axiom,
! [V0__R,V1__radd,V2__x,V3__y] : cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V0__R,V1__radd,V2__x,V3__y) = happ(happ(V1__radd,V2__x),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V3__y)) ).
fof('$_def_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
! [V0__C,V1__c] : cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V0__C,V1__c) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__C) ).
fof('$_def_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__2507] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2507)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2507)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__2507) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__26879] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26879)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26879)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__26880__26883___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__26879)),c_24__let__var__6__p__26880__26883___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__26879))) )
| ? [Vvar__0___24Anonymous__26881] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26881)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26881)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__26882__26884___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__26881)),c_24__let__var__6__p__26882__26884___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__26881)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_ExtLib.Core.Type.equal',axiom,
! [V0__T,V1__type] :
( cType___24t(V0__T)
=> ( cExtLib_2eCore_2eType_2etype___24t(V0__T,V1__type)
=> ? [Vvar__1__equal__58] :
( c_24__type__14___24t(V0__T,Vvar__1__equal__58)
& ? [Vvar__2__proper__63] :
( c_24__type__8___24t(V0__T,Vvar__2__proper__63)
& V1__type = cExtLib_2eCore_2eType_2eBuild__type___24a3(V0__T,Vvar__1__equal__58,Vvar__2__proper__63)
& cExtLib_2eCore_2eType_2eequal___24a2(V0__T,V1__type) = Vvar__1__equal__58 ) ) ) ) ).
fof('$_def_ExtLib.Core.Type.proper',axiom,
! [V0__T,V1__type] :
( cType___24t(V0__T)
=> ( cExtLib_2eCore_2eType_2etype___24t(V0__T,V1__type)
=> ? [Vvar__1__equal__85] :
( c_24__type__14___24t(V0__T,Vvar__1__equal__85)
& ? [Vvar__2__proper__90] :
( c_24__type__8___24t(V0__T,Vvar__2__proper__90)
& V1__type = cExtLib_2eCore_2eType_2eBuild__type___24a3(V0__T,Vvar__1__equal__85,Vvar__2__proper__90)
& cExtLib_2eCore_2eType_2eproper___24a2(V0__T,V1__type) = Vvar__2__proper__90 ) ) ) ) ).
fof('$_def_ExtLib.Structures.Proper.PReflexive',axiom,
! [V0__T,V1__wf,V2__R] :
( cExtLib_2eStructures_2eProper_2ePReflexive___24a3(V0__T,V1__wf,V2__R)
<=> ! [V3__x] :
( t(V3__x,V0__T)
=> ( p(happ(V1__wf,V3__x))
=> p(happ(happ(V2__R,V3__x),V3__x)) ) ) ) ).
fof('$_def_N.type_N',axiom,
cN_2etype__N = cExtLib_2eCore_2eType_2eBuild__type___24a3(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_24__lam__35284) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__362,Vvar__1___24Anonymous__363,Vvar__0__P__364,Vvar__1___24Anonymous__365] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__362) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__364) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__29507,Vvar__1__Plt__29508,Vvar__2__Pgt__29509,Vvar__3___24Anonymous__29510,Vvar__0__Peq__29511,Vvar__1__Plt__29512,Vvar__2__Pgt__29513,Vvar__3___24Anonymous__29514] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__29507,Vvar__1__Plt__29508,Vvar__2__Pgt__29509) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__29511,Vvar__1__Plt__29512,Vvar__2__Pgt__29513) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__312] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__312) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__12020,Vvar__1___24Anonymous__12021,Vvar__0__A__12022] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__12020,Vvar__1___24Anonymous__12021) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__12022) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__29448,Vvar__1__B__29449,Vvar__2___24Anonymous__29450,Vvar__0__A__29451,Vvar__1__B__29452,Vvar__2___24Anonymous__29453] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__29448,Vvar__1__B__29449,Vvar__2___24Anonymous__29450) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__29451,Vvar__1__B__29452,Vvar__2___24Anonymous__29453) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__380,Vvar__0__A__381,Vvar__1___24Anonymous__382,Vvar__2___24Anonymous__383] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__380) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__381,Vvar__1___24Anonymous__382,Vvar__2___24Anonymous__383) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__12213] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__12213) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__29542,Vvar__0__d__29543] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__29542) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__29543) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__11605,Vvar__1__B__11606,Vvar__2___24Anonymous__11607,Vvar__0__A__11608,Vvar__1__B__11609,Vvar__2___24Anonymous__11610] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__11605,Vvar__1__B__11606,Vvar__2___24Anonymous__11607) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__11608,Vvar__1__B__11609) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__28077,Vvar__1__B__28078,Vvar__2___24Anonymous__28079,Vvar__0__A__28080,Vvar__1__B__28081,Vvar__2___24Anonymous__28082] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__28077,Vvar__1__B__28078) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__28080,Vvar__1__B__28081) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__304] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__304) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__11812] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11812) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__296,Vvar__0___24Anonymous__297] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__296) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__297) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__29410] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__29410) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__19655,Vvar__1__lt__19656,Vvar__2__eq__19657,Vvar__3__x__19658,Vvar__4__y__19659,Vvar__5___24Anonymous__19660,Vvar__0__X__19661,Vvar__1__lt__19662,Vvar__2__eq__19663,Vvar__3__x__19664,Vvar__4__y__19665,Vvar__5___24Anonymous__19666] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__19655,Vvar__1__lt__19656,Vvar__2__eq__19657,Vvar__3__x__19658,Vvar__4__y__19659) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__19661,Vvar__1__lt__19662,Vvar__2__eq__19663,Vvar__3__x__19664,Vvar__4__y__19665) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__32203,Vvar__0__n__32204,Vvar__1___24Anonymous__32205] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__32203) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__32204,Vvar__1___24Anonymous__32205) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__29372,Vvar__0__A__29373,Vvar__1__h__29374,Vvar__2__n__29375,Vvar__3___24Anonymous__29376] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__29372) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__29373,Vvar__1__h__29374,Vvar__2__n__29375,Vvar__3___24Anonymous__29376) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__12382,Vvar__1___24Anonymous__12383,Vvar__0__C__12384,Vvar__1___24Anonymous__12385] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__12382,Vvar__1___24Anonymous__12383) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__12384,Vvar__1___24Anonymous__12385) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__12471,Vvar__1___24Anonymous__12472,Vvar__0__C__12473,Vvar__1___24Anonymous__12474,Vvar__2___24Anonymous__12475] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__12471,Vvar__1___24Anonymous__12472) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__12473,Vvar__1___24Anonymous__12474,Vvar__2___24Anonymous__12475) ).
fof('$_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$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__20772,Vvar__1___24Anonymous__20773,Vvar__0__C__20774,Vvar__1___24Anonymous__20775] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__20772,Vvar__1___24Anonymous__20773) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__20774,Vvar__1___24Anonymous__20775) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__15491,Vvar__0__C__15492] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__15491) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__15492) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__2201,Vvar__0__C__2202] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2201) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2202) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__23472,Vvar__1___24Anonymous__23473,Vvar__0__C__23474,Vvar__1___24Anonymous__23475,Vvar__2___24Anonymous__23476] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__23472,Vvar__1___24Anonymous__23473) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__23474,Vvar__1___24Anonymous__23475,Vvar__2___24Anonymous__23476) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__24118,Vvar__1___24Anonymous__24119] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__24118,Vvar__1___24Anonymous__24119) ).
fof('$_fix_28566_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__28581] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28581)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28581)
& ( ? [Vvar__0___24Anonymous__28585] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28585)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28585)
& c_24__fix__28566__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__28566__1__add__carry___24a2(Vvar__0___24Anonymous__28581,Vvar__0___24Anonymous__28585)) )
| ? [Vvar__0___24Anonymous__28586] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28586)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28586)
& c_24__fix__28566__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__28566__1__add__carry___24a2(Vvar__0___24Anonymous__28581,Vvar__0___24Anonymous__28586)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__28566__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__28581)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__28587] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28587)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28587)
& ( ? [Vvar__0___24Anonymous__28591] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28591)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28591)
& c_24__fix__28566__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__28566__1__add__carry___24a2(Vvar__0___24Anonymous__28587,Vvar__0___24Anonymous__28591)) )
| ? [Vvar__0___24Anonymous__28592] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28592)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28592)
& c_24__fix__28566__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__28587,Vvar__0___24Anonymous__28592)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__28566__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__28587)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__28593] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28593)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28593)
& c_24__fix__28566__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__28593)) )
| ? [Vvar__0___24Anonymous__28594] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28594)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28594)
& c_24__fix__28566__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__28594)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__28566__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__370,Vvar__0__P__371,Vvar__1___24Anonymous__372,Vvar__1___24Anonymous__373] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__370) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__371)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__370 = Vvar__0__P__371 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__366,Vvar__0__P__367,Vvar__1___24Anonymous__368,Vvar__1___24Anonymous__369] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__366) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__367)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__366 = Vvar__0__P__367 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__29515,Vvar__0__Peq__29516,Vvar__1__Plt__29517,Vvar__1__Plt__29518,Vvar__2__Pgt__29519,Vvar__2__Pgt__29520,Vvar__3___24Anonymous__29521,Vvar__3___24Anonymous__29522] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__29515,Vvar__1__Plt__29517,Vvar__2__Pgt__29519) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__29516,Vvar__1__Plt__29518,Vvar__2__Pgt__29520)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__29519 = Vvar__2__Pgt__29520
& Vvar__1__Plt__29517 = Vvar__1__Plt__29518
& Vvar__0__Peq__29515 = Vvar__0__Peq__29516 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__29531,Vvar__0__Peq__29532,Vvar__1__Plt__29533,Vvar__1__Plt__29534,Vvar__2__Pgt__29535,Vvar__2__Pgt__29536,Vvar__3___24Anonymous__29537,Vvar__3___24Anonymous__29538] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__29531,Vvar__1__Plt__29533,Vvar__2__Pgt__29535) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__29532,Vvar__1__Plt__29534,Vvar__2__Pgt__29536)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__29535 = Vvar__2__Pgt__29536
& Vvar__1__Plt__29533 = Vvar__1__Plt__29534
& Vvar__0__Peq__29531 = Vvar__0__Peq__29532 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__29523,Vvar__0__Peq__29524,Vvar__1__Plt__29525,Vvar__1__Plt__29526,Vvar__2__Pgt__29527,Vvar__2__Pgt__29528,Vvar__3___24Anonymous__29529,Vvar__3___24Anonymous__29530] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__29523,Vvar__1__Plt__29525,Vvar__2__Pgt__29527) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__29524,Vvar__1__Plt__29526,Vvar__2__Pgt__29528)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__29527 = Vvar__2__Pgt__29528
& Vvar__1__Plt__29525 = Vvar__1__Plt__29526
& Vvar__0__Peq__29523 = Vvar__0__Peq__29524 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__12027,Vvar__0__A__12028] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__12027) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__12028)
=> Vvar__0__A__12027 = Vvar__0__A__12028 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__313,Vvar__0___24Anonymous__314] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__313) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__314)
=> Vvar__0___24Anonymous__313 = Vvar__0___24Anonymous__314 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__12023,Vvar__0__A__12024,Vvar__1___24Anonymous__12025,Vvar__1___24Anonymous__12026] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__12023,Vvar__1___24Anonymous__12025) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__12024,Vvar__1___24Anonymous__12026)
=> ( Vvar__1___24Anonymous__12025 = Vvar__1___24Anonymous__12026
& Vvar__0__A__12023 = Vvar__0__A__12024 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__386,Vvar__0__A__387,Vvar__1___24Anonymous__388,Vvar__1___24Anonymous__389,Vvar__2___24Anonymous__390,Vvar__2___24Anonymous__391] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__386,Vvar__1___24Anonymous__388,Vvar__2___24Anonymous__390) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__387,Vvar__1___24Anonymous__389,Vvar__2___24Anonymous__391)
=> ( Vvar__2___24Anonymous__390 = Vvar__2___24Anonymous__391
& Vvar__1___24Anonymous__388 = Vvar__1___24Anonymous__389
& Vvar__0__A__386 = Vvar__0__A__387 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__29454,Vvar__0__A__29455,Vvar__1__B__29456,Vvar__1__B__29457,Vvar__2___24Anonymous__29458,Vvar__2___24Anonymous__29459] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__29454,Vvar__1__B__29456,Vvar__2___24Anonymous__29458) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__29455,Vvar__1__B__29457,Vvar__2___24Anonymous__29459)
=> ( Vvar__2___24Anonymous__29458 = Vvar__2___24Anonymous__29459
& Vvar__1__B__29456 = Vvar__1__B__29457
& Vvar__0__A__29454 = Vvar__0__A__29455 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__29460,Vvar__0__A__29461,Vvar__1__B__29462,Vvar__1__B__29463,Vvar__2___24Anonymous__29464,Vvar__2___24Anonymous__29465] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__29460,Vvar__1__B__29462,Vvar__2___24Anonymous__29464) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__29461,Vvar__1__B__29463,Vvar__2___24Anonymous__29465)
=> ( Vvar__2___24Anonymous__29464 = Vvar__2___24Anonymous__29465
& Vvar__1__B__29462 = Vvar__1__B__29463
& Vvar__0__A__29460 = Vvar__0__A__29461 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__384,Vvar__0__A__385] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__384) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__385)
=> Vvar__0__A__384 = Vvar__0__A__385 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__12042,Vvar__0__A__12043,Vvar__1__B__12044,Vvar__1__B__12045,Vvar__2___24Anonymous__12046,Vvar__2___24Anonymous__12047,Vvar__3___24Anonymous__12048,Vvar__3___24Anonymous__12049] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__12042,Vvar__1__B__12044,Vvar__2___24Anonymous__12046,Vvar__3___24Anonymous__12048) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__12043,Vvar__1__B__12045,Vvar__2___24Anonymous__12047,Vvar__3___24Anonymous__12049)
=> ( Vvar__3___24Anonymous__12048 = Vvar__3___24Anonymous__12049
& Vvar__2___24Anonymous__12046 = Vvar__2___24Anonymous__12047
& Vvar__1__B__12044 = Vvar__1__B__12045
& Vvar__0__A__12042 = Vvar__0__A__12043 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__12214,Vvar__0___24Anonymous__12215] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__12214) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__12215)
=> Vvar__0___24Anonymous__12214 = Vvar__0___24Anonymous__12215 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__12216,Vvar__0___24Anonymous__12217] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__12216) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__12217)
=> Vvar__0___24Anonymous__12216 = Vvar__0___24Anonymous__12217 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__12218,Vvar__0___24Anonymous__12219] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__12218) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__12219)
=> Vvar__0___24Anonymous__12218 = Vvar__0___24Anonymous__12219 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__12220,Vvar__0___24Anonymous__12221] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__12220) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__12221)
=> Vvar__0___24Anonymous__12220 = Vvar__0___24Anonymous__12221 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__12222,Vvar__0___24Anonymous__12223] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__12222) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__12223)
=> Vvar__0___24Anonymous__12222 = Vvar__0___24Anonymous__12223 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__12224,Vvar__0___24Anonymous__12225] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__12224) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__12225)
=> Vvar__0___24Anonymous__12224 = Vvar__0___24Anonymous__12225 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__12226,Vvar__0___24Anonymous__12227] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__12226) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__12227)
=> Vvar__0___24Anonymous__12226 = Vvar__0___24Anonymous__12227 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__12228,Vvar__0___24Anonymous__12229] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__12228) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__12229)
=> Vvar__0___24Anonymous__12228 = Vvar__0___24Anonymous__12229 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__12230,Vvar__0___24Anonymous__12231] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__12230) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__12231)
=> Vvar__0___24Anonymous__12230 = Vvar__0___24Anonymous__12231 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__12232,Vvar__0___24Anonymous__12233] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__12232) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__12233)
=> Vvar__0___24Anonymous__12232 = Vvar__0___24Anonymous__12233 ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__29546,Vvar__0__d__29547] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__29546) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__29547)
=> Vvar__0__d__29546 = Vvar__0__d__29547 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__29544,Vvar__0__d__29545] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__29544) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__29545)
=> Vvar__0__d__29544 = Vvar__0__d__29545 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__11575,Vvar__0__A__11576,Vvar__1__P__11577,Vvar__1__P__11578,Vvar__2__x__11579,Vvar__2__x__11580,Vvar__3___24Anonymous__11581,Vvar__3___24Anonymous__11582] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__11575,Vvar__1__P__11577,Vvar__2__x__11579) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__11576,Vvar__1__P__11578,Vvar__2__x__11580)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__11579 = Vvar__2__x__11580
& Vvar__1__P__11577 = Vvar__1__P__11578
& Vvar__0__A__11575 = Vvar__0__A__11576 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__11611,Vvar__0__A__11612,Vvar__1__B__11613,Vvar__1__B__11614,Vvar__2___24Anonymous__11615,Vvar__2___24Anonymous__11616] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__11611,Vvar__1__B__11613,Vvar__2___24Anonymous__11615) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__11612,Vvar__1__B__11614,Vvar__2___24Anonymous__11616)
=> ( Vvar__2___24Anonymous__11615 = Vvar__2___24Anonymous__11616
& Vvar__1__B__11613 = Vvar__1__B__11614
& Vvar__0__A__11611 = Vvar__0__A__11612 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__11617,Vvar__0__A__11618,Vvar__1__B__11619,Vvar__1__B__11620,Vvar__2___24Anonymous__11621,Vvar__2___24Anonymous__11622] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__11617,Vvar__1__B__11619) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__11618,Vvar__1__B__11620)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__11619 = Vvar__1__B__11620
& Vvar__0__A__11617 = Vvar__0__A__11618 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__28083,Vvar__0__A__28084,Vvar__1__B__28085,Vvar__1__B__28086,Vvar__2___24Anonymous__28087,Vvar__2___24Anonymous__28088] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__28083,Vvar__1__B__28085) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__28084,Vvar__1__B__28086)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__28085 = Vvar__1__B__28086
& Vvar__0__A__28083 = Vvar__0__A__28084 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__28089,Vvar__0__A__28090,Vvar__1__B__28091,Vvar__1__B__28092,Vvar__2___24Anonymous__28093,Vvar__2___24Anonymous__28094] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__28089,Vvar__1__B__28091) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__28090,Vvar__1__B__28092)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__28091 = Vvar__1__B__28092
& Vvar__0__A__28089 = Vvar__0__A__28090 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__305,Vvar__0___24Anonymous__306] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__305) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__306)
=> Vvar__0___24Anonymous__305 = Vvar__0___24Anonymous__306 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__11815,Vvar__0___24Anonymous__11816] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11815) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11816)
=> Vvar__0___24Anonymous__11815 = Vvar__0___24Anonymous__11816 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__11813,Vvar__0___24Anonymous__11814] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11813) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11814)
=> Vvar__0___24Anonymous__11813 = Vvar__0___24Anonymous__11814 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__298,Vvar__0___24Anonymous__299] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__298) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__299)
=> Vvar__0___24Anonymous__298 = Vvar__0___24Anonymous__299 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__300,Vvar__0___24Anonymous__301] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__300) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__301)
=> Vvar__0___24Anonymous__300 = Vvar__0___24Anonymous__301 ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__29411,Vvar__0___24Anonymous__29412] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__29411) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__29412)
=> Vvar__0___24Anonymous__29411 = Vvar__0___24Anonymous__29412 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__19800,Vvar__0__Qnum__19801,Vvar__1__Qden__19802,Vvar__1__Qden__19803] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__19800,Vvar__1__Qden__19802) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__19801,Vvar__1__Qden__19803)
=> ( Vvar__1__Qden__19802 = Vvar__1__Qden__19803
& Vvar__0__Qnum__19800 = Vvar__0__Qnum__19801 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__29422,Vvar__0___24Anonymous__29423,Vvar__1___24Anonymous__29424,Vvar__1___24Anonymous__29425,Vvar__2___24Anonymous__29426,Vvar__2___24Anonymous__29427,Vvar__3___24Anonymous__29428,Vvar__3___24Anonymous__29429,Vvar__4___24Anonymous__29430,Vvar__4___24Anonymous__29431,Vvar__5___24Anonymous__29432,Vvar__5___24Anonymous__29433,Vvar__6___24Anonymous__29434,Vvar__6___24Anonymous__29435,Vvar__7___24Anonymous__29436,Vvar__7___24Anonymous__29437] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__29422,Vvar__1___24Anonymous__29424,Vvar__2___24Anonymous__29426,Vvar__3___24Anonymous__29428,Vvar__4___24Anonymous__29430,Vvar__5___24Anonymous__29432,Vvar__6___24Anonymous__29434,Vvar__7___24Anonymous__29436) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__29423,Vvar__1___24Anonymous__29425,Vvar__2___24Anonymous__29427,Vvar__3___24Anonymous__29429,Vvar__4___24Anonymous__29431,Vvar__5___24Anonymous__29433,Vvar__6___24Anonymous__29435,Vvar__7___24Anonymous__29437)
=> ( Vvar__7___24Anonymous__29436 = Vvar__7___24Anonymous__29437
& Vvar__6___24Anonymous__29434 = Vvar__6___24Anonymous__29435
& Vvar__5___24Anonymous__29432 = Vvar__5___24Anonymous__29433
& Vvar__4___24Anonymous__29430 = Vvar__4___24Anonymous__29431
& Vvar__3___24Anonymous__29428 = Vvar__3___24Anonymous__29429
& Vvar__2___24Anonymous__29426 = Vvar__2___24Anonymous__29427
& Vvar__1___24Anonymous__29424 = Vvar__1___24Anonymous__29425
& Vvar__0___24Anonymous__29422 = Vvar__0___24Anonymous__29423 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__19679,Vvar__0__X__19680,Vvar__1__lt__19681,Vvar__1__lt__19682,Vvar__2__eq__19683,Vvar__2__eq__19684,Vvar__3__x__19685,Vvar__3__x__19686,Vvar__4__y__19687,Vvar__4__y__19688,Vvar__5___24Anonymous__19689,Vvar__5___24Anonymous__19690] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__19679,Vvar__1__lt__19681,Vvar__2__eq__19683,Vvar__3__x__19685,Vvar__4__y__19687) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__19680,Vvar__1__lt__19682,Vvar__2__eq__19684,Vvar__3__x__19686,Vvar__4__y__19688)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__19687 = Vvar__4__y__19688
& Vvar__3__x__19685 = Vvar__3__x__19686
& Vvar__2__eq__19683 = Vvar__2__eq__19684
& Vvar__1__lt__19681 = Vvar__1__lt__19682
& Vvar__0__X__19679 = Vvar__0__X__19680 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__19691,Vvar__0__X__19692,Vvar__1__lt__19693,Vvar__1__lt__19694,Vvar__2__eq__19695,Vvar__2__eq__19696,Vvar__3__x__19697,Vvar__3__x__19698,Vvar__4__y__19699,Vvar__4__y__19700,Vvar__5___24Anonymous__19701,Vvar__5___24Anonymous__19702] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__19691,Vvar__1__lt__19693,Vvar__2__eq__19695,Vvar__3__x__19697,Vvar__4__y__19699) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__19692,Vvar__1__lt__19694,Vvar__2__eq__19696,Vvar__3__x__19698,Vvar__4__y__19700)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__19699 = Vvar__4__y__19700
& Vvar__3__x__19697 = Vvar__3__x__19698
& Vvar__2__eq__19695 = Vvar__2__eq__19696
& Vvar__1__lt__19693 = Vvar__1__lt__19694
& Vvar__0__X__19691 = Vvar__0__X__19692 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__19667,Vvar__0__X__19668,Vvar__1__lt__19669,Vvar__1__lt__19670,Vvar__2__eq__19671,Vvar__2__eq__19672,Vvar__3__x__19673,Vvar__3__x__19674,Vvar__4__y__19675,Vvar__4__y__19676,Vvar__5___24Anonymous__19677,Vvar__5___24Anonymous__19678] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__19667,Vvar__1__lt__19669,Vvar__2__eq__19671,Vvar__3__x__19673,Vvar__4__y__19675) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__19668,Vvar__1__lt__19670,Vvar__2__eq__19672,Vvar__3__x__19674,Vvar__4__y__19676)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__19675 = Vvar__4__y__19676
& Vvar__3__x__19673 = Vvar__3__x__19674
& Vvar__2__eq__19671 = Vvar__2__eq__19672
& Vvar__1__lt__19669 = Vvar__1__lt__19670
& Vvar__0__X__19667 = Vvar__0__X__19668 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__32206,Vvar__0__n__32207] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__32206) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__32207)
=> Vvar__0__n__32206 = Vvar__0__n__32207 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__32208,Vvar__0__n__32209,Vvar__1___24Anonymous__32210,Vvar__1___24Anonymous__32211] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__32208,Vvar__1___24Anonymous__32210) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__32209,Vvar__1___24Anonymous__32211)
=> ( Vvar__1___24Anonymous__32210 = Vvar__1___24Anonymous__32211
& Vvar__0__n__32208 = Vvar__0__n__32209 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__29379,Vvar__0__A__29380,Vvar__1__h__29381,Vvar__1__h__29382,Vvar__2__n__29383,Vvar__2__n__29384,Vvar__3___24Anonymous__29385,Vvar__3___24Anonymous__29386] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__29379,Vvar__1__h__29381,Vvar__2__n__29383,Vvar__3___24Anonymous__29385) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__29380,Vvar__1__h__29382,Vvar__2__n__29384,Vvar__3___24Anonymous__29386)
=> ( Vvar__3___24Anonymous__29385 = Vvar__3___24Anonymous__29386
& Vvar__2__n__29383 = Vvar__2__n__29384
& Vvar__1__h__29381 = Vvar__1__h__29382
& Vvar__0__A__29379 = Vvar__0__A__29380 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__29377,Vvar__0__A__29378] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__29377) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__29378)
=> Vvar__0__A__29377 = Vvar__0__A__29378 ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__12390,Vvar__0__C__12391,Vvar__1___24Anonymous__12392,Vvar__1___24Anonymous__12393] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__12390,Vvar__1___24Anonymous__12392) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__12391,Vvar__1___24Anonymous__12393)
=> ( Vvar__1___24Anonymous__12392 = Vvar__1___24Anonymous__12393
& Vvar__0__C__12390 = Vvar__0__C__12391 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__12394,Vvar__0__C__12395,Vvar__1___24Anonymous__12396,Vvar__1___24Anonymous__12397,Vvar__2___24Anonymous__12398,Vvar__2___24Anonymous__12399] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__12394,Vvar__1___24Anonymous__12396,Vvar__2___24Anonymous__12398) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__12395,Vvar__1___24Anonymous__12397,Vvar__2___24Anonymous__12399)
=> ( Vvar__2___24Anonymous__12398 = Vvar__2___24Anonymous__12399
& Vvar__1___24Anonymous__12396 = Vvar__1___24Anonymous__12397
& Vvar__0__C__12394 = Vvar__0__C__12395 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__12386,Vvar__0__C__12387,Vvar__1___24Anonymous__12388,Vvar__1___24Anonymous__12389] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__12386,Vvar__1___24Anonymous__12388) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__12387,Vvar__1___24Anonymous__12389)
=> ( Vvar__1___24Anonymous__12388 = Vvar__1___24Anonymous__12389
& Vvar__0__C__12386 = Vvar__0__C__12387 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__12406,Vvar__0__C__12407,Vvar__1___24Anonymous__12408,Vvar__1___24Anonymous__12409,Vvar__2___24Anonymous__12410,Vvar__2___24Anonymous__12411] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__12406,Vvar__1___24Anonymous__12408,Vvar__2___24Anonymous__12410) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__12407,Vvar__1___24Anonymous__12409,Vvar__2___24Anonymous__12411)
=> ( Vvar__2___24Anonymous__12410 = Vvar__2___24Anonymous__12411
& Vvar__1___24Anonymous__12408 = Vvar__1___24Anonymous__12409
& Vvar__0__C__12406 = Vvar__0__C__12407 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__12412,Vvar__0__C__12413,Vvar__1___24Anonymous__12414,Vvar__1___24Anonymous__12415] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__12412,Vvar__1___24Anonymous__12414) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__12413,Vvar__1___24Anonymous__12415)
=> ( Vvar__1___24Anonymous__12414 = Vvar__1___24Anonymous__12415
& Vvar__0__C__12412 = Vvar__0__C__12413 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__12416,Vvar__0__C__12417,Vvar__1___24Anonymous__12418,Vvar__1___24Anonymous__12419,Vvar__2___24Anonymous__12420,Vvar__2___24Anonymous__12421] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__12416,Vvar__1___24Anonymous__12418,Vvar__2___24Anonymous__12420) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__12417,Vvar__1___24Anonymous__12419,Vvar__2___24Anonymous__12421)
=> ( Vvar__2___24Anonymous__12420 = Vvar__2___24Anonymous__12421
& Vvar__1___24Anonymous__12418 = Vvar__1___24Anonymous__12419
& Vvar__0__C__12416 = Vvar__0__C__12417 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__12400,Vvar__0__C__12401,Vvar__1___24Anonymous__12402,Vvar__1___24Anonymous__12403,Vvar__2___24Anonymous__12404,Vvar__2___24Anonymous__12405] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__12400,Vvar__1___24Anonymous__12402,Vvar__2___24Anonymous__12404) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__12401,Vvar__1___24Anonymous__12403,Vvar__2___24Anonymous__12405)
=> ( Vvar__2___24Anonymous__12404 = Vvar__2___24Anonymous__12405
& Vvar__1___24Anonymous__12402 = Vvar__1___24Anonymous__12403
& Vvar__0__C__12400 = Vvar__0__C__12401 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__12486,Vvar__0__C__12487,Vvar__1___24Anonymous__12488,Vvar__1___24Anonymous__12489,Vvar__2___24Anonymous__12490,Vvar__2___24Anonymous__12491,Vvar__3___24Anonymous__12492,Vvar__3___24Anonymous__12493] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__12486,Vvar__1___24Anonymous__12488,Vvar__2___24Anonymous__12490,Vvar__3___24Anonymous__12492) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__12487,Vvar__1___24Anonymous__12489,Vvar__2___24Anonymous__12491,Vvar__3___24Anonymous__12493)
=> ( Vvar__3___24Anonymous__12492 = Vvar__3___24Anonymous__12493
& Vvar__2___24Anonymous__12490 = Vvar__2___24Anonymous__12491
& Vvar__1___24Anonymous__12488 = Vvar__1___24Anonymous__12489
& Vvar__0__C__12486 = Vvar__0__C__12487 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__12476,Vvar__0__C__12477,Vvar__1___24Anonymous__12478,Vvar__1___24Anonymous__12479] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__12476,Vvar__1___24Anonymous__12478) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__12477,Vvar__1___24Anonymous__12479)
=> ( Vvar__1___24Anonymous__12478 = Vvar__1___24Anonymous__12479
& Vvar__0__C__12476 = Vvar__0__C__12477 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__12480,Vvar__0__C__12481,Vvar__1___24Anonymous__12482,Vvar__1___24Anonymous__12483,Vvar__2___24Anonymous__12484,Vvar__2___24Anonymous__12485] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__12480,Vvar__1___24Anonymous__12482,Vvar__2___24Anonymous__12484) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__12481,Vvar__1___24Anonymous__12483,Vvar__2___24Anonymous__12485)
=> ( Vvar__2___24Anonymous__12484 = Vvar__2___24Anonymous__12485
& Vvar__1___24Anonymous__12482 = Vvar__1___24Anonymous__12483
& Vvar__0__C__12480 = Vvar__0__C__12481 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__22145,Vvar__0__T__22146,Vvar__1__Flhs__22147,Vvar__1__Flhs__22148,Vvar__2__Fop__22149,Vvar__2__Fop__22150,Vvar__3__Frhs__22151,Vvar__3__Frhs__22152] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__22145,Vvar__1__Flhs__22147,Vvar__2__Fop__22149,Vvar__3__Frhs__22151) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__22146,Vvar__1__Flhs__22148,Vvar__2__Fop__22150,Vvar__3__Frhs__22152)
=> ( Vvar__3__Frhs__22151 = Vvar__3__Frhs__22152
& Vvar__2__Fop__22149 = Vvar__2__Fop__22150
& Vvar__1__Flhs__22147 = Vvar__1__Flhs__22148
& Vvar__0__T__22145 = Vvar__0__T__22146 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__20796,Vvar__0__C__20797,Vvar__1___24Anonymous__20798,Vvar__1___24Anonymous__20799,Vvar__2___24Anonymous__20800,Vvar__2___24Anonymous__20801] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__20796,Vvar__1___24Anonymous__20798,Vvar__2___24Anonymous__20800) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__20797,Vvar__1___24Anonymous__20799,Vvar__2___24Anonymous__20801)
=> ( Vvar__2___24Anonymous__20800 = Vvar__2___24Anonymous__20801
& Vvar__1___24Anonymous__20798 = Vvar__1___24Anonymous__20799
& Vvar__0__C__20796 = Vvar__0__C__20797 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__20802,Vvar__0__C__20803,Vvar__1___24Anonymous__20804,Vvar__1___24Anonymous__20805] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__20802,Vvar__1___24Anonymous__20804) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__20803,Vvar__1___24Anonymous__20805)
=> ( Vvar__1___24Anonymous__20804 = Vvar__1___24Anonymous__20805
& Vvar__0__C__20802 = Vvar__0__C__20803 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__20776,Vvar__0__C__20777,Vvar__1___24Anonymous__20778,Vvar__1___24Anonymous__20779] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__20776,Vvar__1___24Anonymous__20778) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__20777,Vvar__1___24Anonymous__20779)
=> ( Vvar__1___24Anonymous__20778 = Vvar__1___24Anonymous__20779
& Vvar__0__C__20776 = Vvar__0__C__20777 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__20784,Vvar__0__C__20785,Vvar__1___24Anonymous__20786,Vvar__1___24Anonymous__20787,Vvar__2___24Anonymous__20788,Vvar__2___24Anonymous__20789] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__20784,Vvar__1___24Anonymous__20786,Vvar__2___24Anonymous__20788) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__20785,Vvar__1___24Anonymous__20787,Vvar__2___24Anonymous__20789)
=> ( Vvar__2___24Anonymous__20788 = Vvar__2___24Anonymous__20789
& Vvar__1___24Anonymous__20786 = Vvar__1___24Anonymous__20787
& Vvar__0__C__20784 = Vvar__0__C__20785 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__20790,Vvar__0__C__20791,Vvar__1___24Anonymous__20792,Vvar__1___24Anonymous__20793,Vvar__2___24Anonymous__20794,Vvar__2___24Anonymous__20795] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__20790,Vvar__1___24Anonymous__20792,Vvar__2___24Anonymous__20794) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__20791,Vvar__1___24Anonymous__20793,Vvar__2___24Anonymous__20795)
=> ( Vvar__2___24Anonymous__20794 = Vvar__2___24Anonymous__20795
& Vvar__1___24Anonymous__20792 = Vvar__1___24Anonymous__20793
& Vvar__0__C__20790 = Vvar__0__C__20791 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__20780,Vvar__0__C__20781,Vvar__1___24Anonymous__20782,Vvar__1___24Anonymous__20783] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__20780,Vvar__1___24Anonymous__20782) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__20781,Vvar__1___24Anonymous__20783)
=> ( Vvar__1___24Anonymous__20782 = Vvar__1___24Anonymous__20783
& Vvar__0__C__20780 = Vvar__0__C__20781 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__20806,Vvar__0__C__20807] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__20806) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__20807)
=> Vvar__0__C__20806 = Vvar__0__C__20807 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__15495,Vvar__0__C__15496] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__15495) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__15496)
=> Vvar__0__C__15495 = Vvar__0__C__15496 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__15493,Vvar__0__C__15494] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__15493) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__15494)
=> Vvar__0__C__15493 = Vvar__0__C__15494 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__15501,Vvar__0__C__15502,Vvar__1___24Anonymous__15503,Vvar__1___24Anonymous__15504] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__15501,Vvar__1___24Anonymous__15503) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__15502,Vvar__1___24Anonymous__15504)
=> ( Vvar__1___24Anonymous__15503 = Vvar__1___24Anonymous__15504
& Vvar__0__C__15501 = Vvar__0__C__15502 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__15505,Vvar__0__C__15506,Vvar__1___24Anonymous__15507,Vvar__1___24Anonymous__15508,Vvar__2___24Anonymous__15509,Vvar__2___24Anonymous__15510] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__15505,Vvar__1___24Anonymous__15507,Vvar__2___24Anonymous__15509) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__15506,Vvar__1___24Anonymous__15508,Vvar__2___24Anonymous__15510)
=> ( Vvar__2___24Anonymous__15509 = Vvar__2___24Anonymous__15510
& Vvar__1___24Anonymous__15507 = Vvar__1___24Anonymous__15508
& Vvar__0__C__15505 = Vvar__0__C__15506 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__15497,Vvar__0__C__15498,Vvar__1___24Anonymous__15499,Vvar__1___24Anonymous__15500] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__15497,Vvar__1___24Anonymous__15499) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__15498,Vvar__1___24Anonymous__15500)
=> ( Vvar__1___24Anonymous__15499 = Vvar__1___24Anonymous__15500
& Vvar__0__C__15497 = Vvar__0__C__15498 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__15531,Vvar__0__C__15532,Vvar__1___24Anonymous__15533,Vvar__1___24Anonymous__15534,Vvar__2___24Anonymous__15535,Vvar__2___24Anonymous__15536] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__15531,Vvar__1___24Anonymous__15533,Vvar__2___24Anonymous__15535) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__15532,Vvar__1___24Anonymous__15534,Vvar__2___24Anonymous__15536)
=> ( Vvar__2___24Anonymous__15535 = Vvar__2___24Anonymous__15536
& Vvar__1___24Anonymous__15533 = Vvar__1___24Anonymous__15534
& Vvar__0__C__15531 = Vvar__0__C__15532 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__15527,Vvar__0__C__15528,Vvar__1___24Anonymous__15529,Vvar__1___24Anonymous__15530] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__15527,Vvar__1___24Anonymous__15529) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__15528,Vvar__1___24Anonymous__15530)
=> ( Vvar__1___24Anonymous__15529 = Vvar__1___24Anonymous__15530
& Vvar__0__C__15527 = Vvar__0__C__15528 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__15517,Vvar__0__C__15518,Vvar__1___24Anonymous__15519,Vvar__1___24Anonymous__15520,Vvar__2___24Anonymous__15521,Vvar__2___24Anonymous__15522] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__15517,Vvar__1___24Anonymous__15519,Vvar__2___24Anonymous__15521) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__15518,Vvar__1___24Anonymous__15520,Vvar__2___24Anonymous__15522)
=> ( Vvar__2___24Anonymous__15521 = Vvar__2___24Anonymous__15522
& Vvar__1___24Anonymous__15519 = Vvar__1___24Anonymous__15520
& Vvar__0__C__15517 = Vvar__0__C__15518 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__15523,Vvar__0__C__15524,Vvar__1___24Anonymous__15525,Vvar__1___24Anonymous__15526] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__15523,Vvar__1___24Anonymous__15525) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__15524,Vvar__1___24Anonymous__15526)
=> ( Vvar__1___24Anonymous__15525 = Vvar__1___24Anonymous__15526
& Vvar__0__C__15523 = Vvar__0__C__15524 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__15537,Vvar__0__C__15538,Vvar__1___24Anonymous__15539,Vvar__1___24Anonymous__15540,Vvar__2___24Anonymous__15541,Vvar__2___24Anonymous__15542] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__15537,Vvar__1___24Anonymous__15539,Vvar__2___24Anonymous__15541) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__15538,Vvar__1___24Anonymous__15540,Vvar__2___24Anonymous__15542)
=> ( Vvar__2___24Anonymous__15541 = Vvar__2___24Anonymous__15542
& Vvar__1___24Anonymous__15539 = Vvar__1___24Anonymous__15540
& Vvar__0__C__15537 = Vvar__0__C__15538 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__15511,Vvar__0__C__15512,Vvar__1___24Anonymous__15513,Vvar__1___24Anonymous__15514,Vvar__2___24Anonymous__15515,Vvar__2___24Anonymous__15516] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__15511,Vvar__1___24Anonymous__15513,Vvar__2___24Anonymous__15515) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__15512,Vvar__1___24Anonymous__15514,Vvar__2___24Anonymous__15516)
=> ( Vvar__2___24Anonymous__15515 = Vvar__2___24Anonymous__15516
& Vvar__1___24Anonymous__15513 = Vvar__1___24Anonymous__15514
& Vvar__0__C__15511 = Vvar__0__C__15512 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__15893,Vvar__0__C__15894,Vvar__1__num__15895,Vvar__1__num__15896,Vvar__2__denum__15897,Vvar__2__denum__15898,Vvar__3__condition__15899,Vvar__3__condition__15900] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__15893,Vvar__1__num__15895,Vvar__2__denum__15897,Vvar__3__condition__15899) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__15894,Vvar__1__num__15896,Vvar__2__denum__15898,Vvar__3__condition__15900)
=> ( Vvar__3__condition__15899 = Vvar__3__condition__15900
& Vvar__2__denum__15897 = Vvar__2__denum__15898
& Vvar__1__num__15895 = Vvar__1__num__15896
& Vvar__0__C__15893 = Vvar__0__C__15894 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__16322,Vvar__0__C__16323,Vvar__1__rsplit__left__16324,Vvar__1__rsplit__left__16325,Vvar__2__rsplit__common__16326,Vvar__2__rsplit__common__16327,Vvar__3__rsplit__right__16328,Vvar__3__rsplit__right__16329] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__16322,Vvar__1__rsplit__left__16324,Vvar__2__rsplit__common__16326,Vvar__3__rsplit__right__16328) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__16323,Vvar__1__rsplit__left__16325,Vvar__2__rsplit__common__16327,Vvar__3__rsplit__right__16329)
=> ( Vvar__3__rsplit__right__16328 = Vvar__3__rsplit__right__16329
& Vvar__2__rsplit__common__16326 = Vvar__2__rsplit__common__16327
& Vvar__1__rsplit__left__16324 = Vvar__1__rsplit__left__16325
& Vvar__0__C__16322 = Vvar__0__C__16323 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__2205,Vvar__0__C__2206] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2205) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2206)
=> Vvar__0__C__2205 = Vvar__0__C__2206 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__2203,Vvar__0__C__2204] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2203) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2204)
=> Vvar__0__C__2203 = Vvar__0__C__2204 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__2211,Vvar__0__C__2212,Vvar__1___24Anonymous__2213,Vvar__1___24Anonymous__2214] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2211,Vvar__1___24Anonymous__2213) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2212,Vvar__1___24Anonymous__2214)
=> ( Vvar__1___24Anonymous__2213 = Vvar__1___24Anonymous__2214
& Vvar__0__C__2211 = Vvar__0__C__2212 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__2215,Vvar__0__C__2216,Vvar__1___24Anonymous__2217,Vvar__1___24Anonymous__2218,Vvar__2___24Anonymous__2219,Vvar__2___24Anonymous__2220] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2215,Vvar__1___24Anonymous__2217,Vvar__2___24Anonymous__2219) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2216,Vvar__1___24Anonymous__2218,Vvar__2___24Anonymous__2220)
=> ( Vvar__2___24Anonymous__2219 = Vvar__2___24Anonymous__2220
& Vvar__1___24Anonymous__2217 = Vvar__1___24Anonymous__2218
& Vvar__0__C__2215 = Vvar__0__C__2216 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__2207,Vvar__0__C__2208,Vvar__1___24Anonymous__2209,Vvar__1___24Anonymous__2210] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2207,Vvar__1___24Anonymous__2209) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2208,Vvar__1___24Anonymous__2210)
=> ( Vvar__1___24Anonymous__2209 = Vvar__1___24Anonymous__2210
& Vvar__0__C__2207 = Vvar__0__C__2208 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__2227,Vvar__0__C__2228,Vvar__1___24Anonymous__2229,Vvar__1___24Anonymous__2230,Vvar__2___24Anonymous__2231,Vvar__2___24Anonymous__2232] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2227,Vvar__1___24Anonymous__2229,Vvar__2___24Anonymous__2231) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2228,Vvar__1___24Anonymous__2230,Vvar__2___24Anonymous__2232)
=> ( Vvar__2___24Anonymous__2231 = Vvar__2___24Anonymous__2232
& Vvar__1___24Anonymous__2229 = Vvar__1___24Anonymous__2230
& Vvar__0__C__2227 = Vvar__0__C__2228 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__2233,Vvar__0__C__2234,Vvar__1___24Anonymous__2235,Vvar__1___24Anonymous__2236] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2233,Vvar__1___24Anonymous__2235) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2234,Vvar__1___24Anonymous__2236)
=> ( Vvar__1___24Anonymous__2235 = Vvar__1___24Anonymous__2236
& Vvar__0__C__2233 = Vvar__0__C__2234 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__2237,Vvar__0__C__2238,Vvar__1___24Anonymous__2239,Vvar__1___24Anonymous__2240,Vvar__2___24Anonymous__2241,Vvar__2___24Anonymous__2242] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2237,Vvar__1___24Anonymous__2239,Vvar__2___24Anonymous__2241) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2238,Vvar__1___24Anonymous__2240,Vvar__2___24Anonymous__2242)
=> ( Vvar__2___24Anonymous__2241 = Vvar__2___24Anonymous__2242
& Vvar__1___24Anonymous__2239 = Vvar__1___24Anonymous__2240
& Vvar__0__C__2237 = Vvar__0__C__2238 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__2221,Vvar__0__C__2222,Vvar__1___24Anonymous__2223,Vvar__1___24Anonymous__2224,Vvar__2___24Anonymous__2225,Vvar__2___24Anonymous__2226] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2221,Vvar__1___24Anonymous__2223,Vvar__2___24Anonymous__2225) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2222,Vvar__1___24Anonymous__2224,Vvar__2___24Anonymous__2226)
=> ( Vvar__2___24Anonymous__2225 = Vvar__2___24Anonymous__2226
& Vvar__1___24Anonymous__2223 = Vvar__1___24Anonymous__2224
& Vvar__0__C__2221 = Vvar__0__C__2222 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__23487,Vvar__0__C__23488,Vvar__1___24Anonymous__23489,Vvar__1___24Anonymous__23490,Vvar__2___24Anonymous__23491,Vvar__2___24Anonymous__23492,Vvar__3___24Anonymous__23493,Vvar__3___24Anonymous__23494] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__23487,Vvar__1___24Anonymous__23489,Vvar__2___24Anonymous__23491,Vvar__3___24Anonymous__23493) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__23488,Vvar__1___24Anonymous__23490,Vvar__2___24Anonymous__23492,Vvar__3___24Anonymous__23494)
=> ( Vvar__3___24Anonymous__23493 = Vvar__3___24Anonymous__23494
& Vvar__2___24Anonymous__23491 = Vvar__2___24Anonymous__23492
& Vvar__1___24Anonymous__23489 = Vvar__1___24Anonymous__23490
& Vvar__0__C__23487 = Vvar__0__C__23488 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__23477,Vvar__0__C__23478,Vvar__1___24Anonymous__23479,Vvar__1___24Anonymous__23480] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__23477,Vvar__1___24Anonymous__23479) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__23478,Vvar__1___24Anonymous__23480)
=> ( Vvar__1___24Anonymous__23479 = Vvar__1___24Anonymous__23480
& Vvar__0__C__23477 = Vvar__0__C__23478 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__23481,Vvar__0__C__23482,Vvar__1___24Anonymous__23483,Vvar__1___24Anonymous__23484,Vvar__2___24Anonymous__23485,Vvar__2___24Anonymous__23486] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__23481,Vvar__1___24Anonymous__23483,Vvar__2___24Anonymous__23485) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__23482,Vvar__1___24Anonymous__23484,Vvar__2___24Anonymous__23486)
=> ( Vvar__2___24Anonymous__23485 = Vvar__2___24Anonymous__23486
& Vvar__1___24Anonymous__23483 = Vvar__1___24Anonymous__23484
& Vvar__0__C__23481 = Vvar__0__C__23482 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__24124,Vvar__0___24Anonymous__24125,Vvar__1___24Anonymous__24126,Vvar__1___24Anonymous__24127] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__24124,Vvar__1___24Anonymous__24126) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__24125,Vvar__1___24Anonymous__24127)
=> ( Vvar__1___24Anonymous__24126 = Vvar__1___24Anonymous__24127
& Vvar__0___24Anonymous__24124 = Vvar__0___24Anonymous__24125 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__24120,Vvar__0___24Anonymous__24121,Vvar__1___24Anonymous__24122,Vvar__1___24Anonymous__24123] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__24120,Vvar__1___24Anonymous__24122) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__24121,Vvar__1___24Anonymous__24123)
=> ( Vvar__1___24Anonymous__24122 = Vvar__1___24Anonymous__24123
& Vvar__0___24Anonymous__24120 = Vvar__0___24Anonymous__24121 ) ) ).
fof('$_inj_ExtLib.Core.Type.Build_type',axiom,
! [Vvar__0__T__36,Vvar__0__T__37,Vvar__1__equal__38,Vvar__1__equal__39,Vvar__2__proper__40,Vvar__2__proper__41] :
( cExtLib_2eCore_2eType_2eBuild__type___24a3(Vvar__0__T__36,Vvar__1__equal__38,Vvar__2__proper__40) = cExtLib_2eCore_2eType_2eBuild__type___24a3(Vvar__0__T__37,Vvar__1__equal__39,Vvar__2__proper__41)
=> ( Vvar__2__proper__40 = Vvar__2__proper__41
& Vvar__1__equal__38 = Vvar__1__equal__39
& Vvar__0__T__36 = Vvar__0__T__37 ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__352,Vvar__1___24Anonymous__353,VX354] :
( cProp___24t(Vvar__0__P__352)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__353)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__352,Vvar__1___24Anonymous__353,VX354)
=> ( ( p(Vvar__0__P__352)
& Vvar__1___24Anonymous__353 = cCoq_2eInit_2eDatatypes_2etrue
& VX354 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__352) )
| ( ~ p(Vvar__0__P__352)
& Vvar__1___24Anonymous__353 = cCoq_2eInit_2eDatatypes_2efalse
& VX354 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__352) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX29138] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX29138)
=> ( VX29138 = cCoq_2eInit_2eByte_2ex00
| VX29138 = cCoq_2eInit_2eByte_2ex01
| VX29138 = cCoq_2eInit_2eByte_2ex02
| VX29138 = cCoq_2eInit_2eByte_2ex03
| VX29138 = cCoq_2eInit_2eByte_2ex04
| VX29138 = cCoq_2eInit_2eByte_2ex05
| VX29138 = cCoq_2eInit_2eByte_2ex06
| VX29138 = cCoq_2eInit_2eByte_2ex07
| VX29138 = cCoq_2eInit_2eByte_2ex08
| VX29138 = cCoq_2eInit_2eByte_2ex09
| VX29138 = cCoq_2eInit_2eByte_2ex0a
| VX29138 = cCoq_2eInit_2eByte_2ex0b
| VX29138 = cCoq_2eInit_2eByte_2ex0c
| VX29138 = cCoq_2eInit_2eByte_2ex0d
| VX29138 = cCoq_2eInit_2eByte_2ex0e
| VX29138 = cCoq_2eInit_2eByte_2ex0f
| VX29138 = cCoq_2eInit_2eByte_2ex10
| VX29138 = cCoq_2eInit_2eByte_2ex11
| VX29138 = cCoq_2eInit_2eByte_2ex12
| VX29138 = cCoq_2eInit_2eByte_2ex13
| VX29138 = cCoq_2eInit_2eByte_2ex14
| VX29138 = cCoq_2eInit_2eByte_2ex15
| VX29138 = cCoq_2eInit_2eByte_2ex16
| VX29138 = cCoq_2eInit_2eByte_2ex17
| VX29138 = cCoq_2eInit_2eByte_2ex18
| VX29138 = cCoq_2eInit_2eByte_2ex19
| VX29138 = cCoq_2eInit_2eByte_2ex1a
| VX29138 = cCoq_2eInit_2eByte_2ex1b
| VX29138 = cCoq_2eInit_2eByte_2ex1c
| VX29138 = cCoq_2eInit_2eByte_2ex1d
| VX29138 = cCoq_2eInit_2eByte_2ex1e
| VX29138 = cCoq_2eInit_2eByte_2ex1f
| VX29138 = cCoq_2eInit_2eByte_2ex20
| VX29138 = cCoq_2eInit_2eByte_2ex21
| VX29138 = cCoq_2eInit_2eByte_2ex22
| VX29138 = cCoq_2eInit_2eByte_2ex23
| VX29138 = cCoq_2eInit_2eByte_2ex24
| VX29138 = cCoq_2eInit_2eByte_2ex25
| VX29138 = cCoq_2eInit_2eByte_2ex26
| VX29138 = cCoq_2eInit_2eByte_2ex27
| VX29138 = cCoq_2eInit_2eByte_2ex28
| VX29138 = cCoq_2eInit_2eByte_2ex29
| VX29138 = cCoq_2eInit_2eByte_2ex2a
| VX29138 = cCoq_2eInit_2eByte_2ex2b
| VX29138 = cCoq_2eInit_2eByte_2ex2c
| VX29138 = cCoq_2eInit_2eByte_2ex2d
| VX29138 = cCoq_2eInit_2eByte_2ex2e
| VX29138 = cCoq_2eInit_2eByte_2ex2f
| VX29138 = cCoq_2eInit_2eByte_2ex30
| VX29138 = cCoq_2eInit_2eByte_2ex31
| VX29138 = cCoq_2eInit_2eByte_2ex32
| VX29138 = cCoq_2eInit_2eByte_2ex33
| VX29138 = cCoq_2eInit_2eByte_2ex34
| VX29138 = cCoq_2eInit_2eByte_2ex35
| VX29138 = cCoq_2eInit_2eByte_2ex36
| VX29138 = cCoq_2eInit_2eByte_2ex37
| VX29138 = cCoq_2eInit_2eByte_2ex38
| VX29138 = cCoq_2eInit_2eByte_2ex39
| VX29138 = cCoq_2eInit_2eByte_2ex3a
| VX29138 = cCoq_2eInit_2eByte_2ex3b
| VX29138 = cCoq_2eInit_2eByte_2ex3c
| VX29138 = cCoq_2eInit_2eByte_2ex3d
| VX29138 = cCoq_2eInit_2eByte_2ex3e
| VX29138 = cCoq_2eInit_2eByte_2ex3f
| VX29138 = cCoq_2eInit_2eByte_2ex40
| VX29138 = cCoq_2eInit_2eByte_2ex41
| VX29138 = cCoq_2eInit_2eByte_2ex42
| VX29138 = cCoq_2eInit_2eByte_2ex43
| VX29138 = cCoq_2eInit_2eByte_2ex44
| VX29138 = cCoq_2eInit_2eByte_2ex45
| VX29138 = cCoq_2eInit_2eByte_2ex46
| VX29138 = cCoq_2eInit_2eByte_2ex47
| VX29138 = cCoq_2eInit_2eByte_2ex48
| VX29138 = cCoq_2eInit_2eByte_2ex49
| VX29138 = cCoq_2eInit_2eByte_2ex4a
| VX29138 = cCoq_2eInit_2eByte_2ex4b
| VX29138 = cCoq_2eInit_2eByte_2ex4c
| VX29138 = cCoq_2eInit_2eByte_2ex4d
| VX29138 = cCoq_2eInit_2eByte_2ex4e
| VX29138 = cCoq_2eInit_2eByte_2ex4f
| VX29138 = cCoq_2eInit_2eByte_2ex50
| VX29138 = cCoq_2eInit_2eByte_2ex51
| VX29138 = cCoq_2eInit_2eByte_2ex52
| VX29138 = cCoq_2eInit_2eByte_2ex53
| VX29138 = cCoq_2eInit_2eByte_2ex54
| VX29138 = cCoq_2eInit_2eByte_2ex55
| VX29138 = cCoq_2eInit_2eByte_2ex56
| VX29138 = cCoq_2eInit_2eByte_2ex57
| VX29138 = cCoq_2eInit_2eByte_2ex58
| VX29138 = cCoq_2eInit_2eByte_2ex59
| VX29138 = cCoq_2eInit_2eByte_2ex5a
| VX29138 = cCoq_2eInit_2eByte_2ex5b
| VX29138 = cCoq_2eInit_2eByte_2ex5c
| VX29138 = cCoq_2eInit_2eByte_2ex5d
| VX29138 = cCoq_2eInit_2eByte_2ex5e
| VX29138 = cCoq_2eInit_2eByte_2ex5f
| VX29138 = cCoq_2eInit_2eByte_2ex60
| VX29138 = cCoq_2eInit_2eByte_2ex61
| VX29138 = cCoq_2eInit_2eByte_2ex62
| VX29138 = cCoq_2eInit_2eByte_2ex63
| VX29138 = cCoq_2eInit_2eByte_2ex64
| VX29138 = cCoq_2eInit_2eByte_2ex65
| VX29138 = cCoq_2eInit_2eByte_2ex66
| VX29138 = cCoq_2eInit_2eByte_2ex67
| VX29138 = cCoq_2eInit_2eByte_2ex68
| VX29138 = cCoq_2eInit_2eByte_2ex69
| VX29138 = cCoq_2eInit_2eByte_2ex6a
| VX29138 = cCoq_2eInit_2eByte_2ex6b
| VX29138 = cCoq_2eInit_2eByte_2ex6c
| VX29138 = cCoq_2eInit_2eByte_2ex6d
| VX29138 = cCoq_2eInit_2eByte_2ex6e
| VX29138 = cCoq_2eInit_2eByte_2ex6f
| VX29138 = cCoq_2eInit_2eByte_2ex70
| VX29138 = cCoq_2eInit_2eByte_2ex71
| VX29138 = cCoq_2eInit_2eByte_2ex72
| VX29138 = cCoq_2eInit_2eByte_2ex73
| VX29138 = cCoq_2eInit_2eByte_2ex74
| VX29138 = cCoq_2eInit_2eByte_2ex75
| VX29138 = cCoq_2eInit_2eByte_2ex76
| VX29138 = cCoq_2eInit_2eByte_2ex77
| VX29138 = cCoq_2eInit_2eByte_2ex78
| VX29138 = cCoq_2eInit_2eByte_2ex79
| VX29138 = cCoq_2eInit_2eByte_2ex7a
| VX29138 = cCoq_2eInit_2eByte_2ex7b
| VX29138 = cCoq_2eInit_2eByte_2ex7c
| VX29138 = cCoq_2eInit_2eByte_2ex7d
| VX29138 = cCoq_2eInit_2eByte_2ex7e
| VX29138 = cCoq_2eInit_2eByte_2ex7f
| VX29138 = cCoq_2eInit_2eByte_2ex80
| VX29138 = cCoq_2eInit_2eByte_2ex81
| VX29138 = cCoq_2eInit_2eByte_2ex82
| VX29138 = cCoq_2eInit_2eByte_2ex83
| VX29138 = cCoq_2eInit_2eByte_2ex84
| VX29138 = cCoq_2eInit_2eByte_2ex85
| VX29138 = cCoq_2eInit_2eByte_2ex86
| VX29138 = cCoq_2eInit_2eByte_2ex87
| VX29138 = cCoq_2eInit_2eByte_2ex88
| VX29138 = cCoq_2eInit_2eByte_2ex89
| VX29138 = cCoq_2eInit_2eByte_2ex8a
| VX29138 = cCoq_2eInit_2eByte_2ex8b
| VX29138 = cCoq_2eInit_2eByte_2ex8c
| VX29138 = cCoq_2eInit_2eByte_2ex8d
| VX29138 = cCoq_2eInit_2eByte_2ex8e
| VX29138 = cCoq_2eInit_2eByte_2ex8f
| VX29138 = cCoq_2eInit_2eByte_2ex90
| VX29138 = cCoq_2eInit_2eByte_2ex91
| VX29138 = cCoq_2eInit_2eByte_2ex92
| VX29138 = cCoq_2eInit_2eByte_2ex93
| VX29138 = cCoq_2eInit_2eByte_2ex94
| VX29138 = cCoq_2eInit_2eByte_2ex95
| VX29138 = cCoq_2eInit_2eByte_2ex96
| VX29138 = cCoq_2eInit_2eByte_2ex97
| VX29138 = cCoq_2eInit_2eByte_2ex98
| VX29138 = cCoq_2eInit_2eByte_2ex99
| VX29138 = cCoq_2eInit_2eByte_2ex9a
| VX29138 = cCoq_2eInit_2eByte_2ex9b
| VX29138 = cCoq_2eInit_2eByte_2ex9c
| VX29138 = cCoq_2eInit_2eByte_2ex9d
| VX29138 = cCoq_2eInit_2eByte_2ex9e
| VX29138 = cCoq_2eInit_2eByte_2ex9f
| VX29138 = cCoq_2eInit_2eByte_2exa0
| VX29138 = cCoq_2eInit_2eByte_2exa1
| VX29138 = cCoq_2eInit_2eByte_2exa2
| VX29138 = cCoq_2eInit_2eByte_2exa3
| VX29138 = cCoq_2eInit_2eByte_2exa4
| VX29138 = cCoq_2eInit_2eByte_2exa5
| VX29138 = cCoq_2eInit_2eByte_2exa6
| VX29138 = cCoq_2eInit_2eByte_2exa7
| VX29138 = cCoq_2eInit_2eByte_2exa8
| VX29138 = cCoq_2eInit_2eByte_2exa9
| VX29138 = cCoq_2eInit_2eByte_2exaa
| VX29138 = cCoq_2eInit_2eByte_2exab
| VX29138 = cCoq_2eInit_2eByte_2exac
| VX29138 = cCoq_2eInit_2eByte_2exad
| VX29138 = cCoq_2eInit_2eByte_2exae
| VX29138 = cCoq_2eInit_2eByte_2exaf
| VX29138 = cCoq_2eInit_2eByte_2exb0
| VX29138 = cCoq_2eInit_2eByte_2exb1
| VX29138 = cCoq_2eInit_2eByte_2exb2
| VX29138 = cCoq_2eInit_2eByte_2exb3
| VX29138 = cCoq_2eInit_2eByte_2exb4
| VX29138 = cCoq_2eInit_2eByte_2exb5
| VX29138 = cCoq_2eInit_2eByte_2exb6
| VX29138 = cCoq_2eInit_2eByte_2exb7
| VX29138 = cCoq_2eInit_2eByte_2exb8
| VX29138 = cCoq_2eInit_2eByte_2exb9
| VX29138 = cCoq_2eInit_2eByte_2exba
| VX29138 = cCoq_2eInit_2eByte_2exbb
| VX29138 = cCoq_2eInit_2eByte_2exbc
| VX29138 = cCoq_2eInit_2eByte_2exbd
| VX29138 = cCoq_2eInit_2eByte_2exbe
| VX29138 = cCoq_2eInit_2eByte_2exbf
| VX29138 = cCoq_2eInit_2eByte_2exc0
| VX29138 = cCoq_2eInit_2eByte_2exc1
| VX29138 = cCoq_2eInit_2eByte_2exc2
| VX29138 = cCoq_2eInit_2eByte_2exc3
| VX29138 = cCoq_2eInit_2eByte_2exc4
| VX29138 = cCoq_2eInit_2eByte_2exc5
| VX29138 = cCoq_2eInit_2eByte_2exc6
| VX29138 = cCoq_2eInit_2eByte_2exc7
| VX29138 = cCoq_2eInit_2eByte_2exc8
| VX29138 = cCoq_2eInit_2eByte_2exc9
| VX29138 = cCoq_2eInit_2eByte_2exca
| VX29138 = cCoq_2eInit_2eByte_2excb
| VX29138 = cCoq_2eInit_2eByte_2excc
| VX29138 = cCoq_2eInit_2eByte_2excd
| VX29138 = cCoq_2eInit_2eByte_2exce
| VX29138 = cCoq_2eInit_2eByte_2excf
| VX29138 = cCoq_2eInit_2eByte_2exd0
| VX29138 = cCoq_2eInit_2eByte_2exd1
| VX29138 = cCoq_2eInit_2eByte_2exd2
| VX29138 = cCoq_2eInit_2eByte_2exd3
| VX29138 = cCoq_2eInit_2eByte_2exd4
| VX29138 = cCoq_2eInit_2eByte_2exd5
| VX29138 = cCoq_2eInit_2eByte_2exd6
| VX29138 = cCoq_2eInit_2eByte_2exd7
| VX29138 = cCoq_2eInit_2eByte_2exd8
| VX29138 = cCoq_2eInit_2eByte_2exd9
| VX29138 = cCoq_2eInit_2eByte_2exda
| VX29138 = cCoq_2eInit_2eByte_2exdb
| VX29138 = cCoq_2eInit_2eByte_2exdc
| VX29138 = cCoq_2eInit_2eByte_2exdd
| VX29138 = cCoq_2eInit_2eByte_2exde
| VX29138 = cCoq_2eInit_2eByte_2exdf
| VX29138 = cCoq_2eInit_2eByte_2exe0
| VX29138 = cCoq_2eInit_2eByte_2exe1
| VX29138 = cCoq_2eInit_2eByte_2exe2
| VX29138 = cCoq_2eInit_2eByte_2exe3
| VX29138 = cCoq_2eInit_2eByte_2exe4
| VX29138 = cCoq_2eInit_2eByte_2exe5
| VX29138 = cCoq_2eInit_2eByte_2exe6
| VX29138 = cCoq_2eInit_2eByte_2exe7
| VX29138 = cCoq_2eInit_2eByte_2exe8
| VX29138 = cCoq_2eInit_2eByte_2exe9
| VX29138 = cCoq_2eInit_2eByte_2exea
| VX29138 = cCoq_2eInit_2eByte_2exeb
| VX29138 = cCoq_2eInit_2eByte_2exec
| VX29138 = cCoq_2eInit_2eByte_2exed
| VX29138 = cCoq_2eInit_2eByte_2exee
| VX29138 = cCoq_2eInit_2eByte_2exef
| VX29138 = cCoq_2eInit_2eByte_2exf0
| VX29138 = cCoq_2eInit_2eByte_2exf1
| VX29138 = cCoq_2eInit_2eByte_2exf2
| VX29138 = cCoq_2eInit_2eByte_2exf3
| VX29138 = cCoq_2eInit_2eByte_2exf4
| VX29138 = cCoq_2eInit_2eByte_2exf5
| VX29138 = cCoq_2eInit_2eByte_2exf6
| VX29138 = cCoq_2eInit_2eByte_2exf7
| VX29138 = cCoq_2eInit_2eByte_2exf8
| VX29138 = cCoq_2eInit_2eByte_2exf9
| VX29138 = cCoq_2eInit_2eByte_2exfa
| VX29138 = cCoq_2eInit_2eByte_2exfb
| VX29138 = cCoq_2eInit_2eByte_2exfc
| VX29138 = cCoq_2eInit_2eByte_2exfd
| VX29138 = cCoq_2eInit_2eByte_2exfe
| VX29138 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__11978,Vvar__1__Q__11979,Vvar__2___24Anonymous__11980] :
( cProp___24t(Vvar__0__P__11978)
=> ( cProp___24t(Vvar__1__Q__11979)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__11980)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__11978,Vvar__1__Q__11979,Vvar__2___24Anonymous__11980)
=> ( ( p(Vvar__0__P__11978)
& Vvar__2___24Anonymous__11980 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__11979)
& Vvar__2___24Anonymous__11980 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__6180,Vvar__1__Plt__6181,Vvar__2__Pgt__6182,Vvar__3___24Anonymous__6183] :
( cProp___24t(Vvar__0__Peq__6180)
=> ( cProp___24t(Vvar__1__Plt__6181)
=> ( cProp___24t(Vvar__2__Pgt__6182)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__6183)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__6180,Vvar__1__Plt__6181,Vvar__2__Pgt__6182,Vvar__3___24Anonymous__6183)
=> ( ( p(Vvar__0__Peq__6180)
& Vvar__3___24Anonymous__6183 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__6181)
& Vvar__3___24Anonymous__6183 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__6182)
& Vvar__3___24Anonymous__6183 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__29466,Vvar__1__Plt__29467,Vvar__2__Pgt__29468,Vvar__3___24Anonymous__29469,VX29470] :
( cProp___24t(Vvar__0__Peq__29466)
=> ( cProp___24t(Vvar__1__Plt__29467)
=> ( cProp___24t(Vvar__2__Pgt__29468)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__29469)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__29466,Vvar__1__Plt__29467,Vvar__2__Pgt__29468,Vvar__3___24Anonymous__29469,VX29470)
=> ( ( p(Vvar__0__Peq__29466)
& Vvar__3___24Anonymous__29469 = cCoq_2eInit_2eDatatypes_2eEq
& VX29470 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__29466,Vvar__1__Plt__29467,Vvar__2__Pgt__29468) )
| ( p(Vvar__1__Plt__29467)
& Vvar__3___24Anonymous__29469 = cCoq_2eInit_2eDatatypes_2eLt
& VX29470 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__29466,Vvar__1__Plt__29467,Vvar__2__Pgt__29468) )
| ( p(Vvar__2__Pgt__29468)
& Vvar__3___24Anonymous__29469 = cCoq_2eInit_2eDatatypes_2eGt
& VX29470 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__29466,Vvar__1__Plt__29467,Vvar__2__Pgt__29468) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX309] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX309)
=> ( VX309 = cCoq_2eInit_2eDatatypes_2etrue
| VX309 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX392] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX392)
=> ( VX392 = cCoq_2eInit_2eDatatypes_2eEq
| VX392 = cCoq_2eInit_2eDatatypes_2eLt
| VX392 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__374,VX375] :
( cType___24t(Vvar__0__A__374)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__374,VX375)
=> ( VX375 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__374)
| ? [Vvar__1___24Anonymous__378] :
( t(Vvar__1___24Anonymous__378,Vvar__0__A__374)
& ? [Vvar__2___24Anonymous__379] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__374,Vvar__2___24Anonymous__379)
& VX375 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__374,Vvar__1___24Anonymous__378,Vvar__2___24Anonymous__379) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX310] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX310)
=> ( VX310 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__311] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__311)
& VX310 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__311) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__12015,VX12016] :
( cType___24t(Vvar__0__A__12015)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__12015,VX12016)
=> ( ? [Vvar__1___24Anonymous__12018] :
( t(Vvar__1___24Anonymous__12018,Vvar__0__A__12015)
& VX12016 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__12015,Vvar__1___24Anonymous__12018) )
| VX12016 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__12015) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__12034,Vvar__1__B__12035,VX12036] :
( cType___24t(Vvar__0__A__12034)
=> ( cType___24t(Vvar__1__B__12035)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__12034,Vvar__1__B__12035,VX12036)
=> ? [Vvar__2___24Anonymous__12039] :
( t(Vvar__2___24Anonymous__12039,Vvar__0__A__12034)
& ? [Vvar__3___24Anonymous__12040] :
( t(Vvar__3___24Anonymous__12040,Vvar__1__B__12035)
& VX12036 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__12034,Vvar__1__B__12035,Vvar__2___24Anonymous__12039,Vvar__3___24Anonymous__12040) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__29438,Vvar__1__B__29439,VX29440] :
( cType___24t(Vvar__0__A__29438)
=> ( cType___24t(Vvar__1__B__29439)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__29438,Vvar__1__B__29439,VX29440)
=> ( ? [Vvar__2___24Anonymous__29443] :
( t(Vvar__2___24Anonymous__29443,Vvar__0__A__29438)
& VX29440 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__29438,Vvar__1__B__29439,Vvar__2___24Anonymous__29443) )
| ? [Vvar__2___24Anonymous__29446] :
( t(Vvar__2___24Anonymous__29446,Vvar__1__B__29439)
& VX29440 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__29438,Vvar__1__B__29439,Vvar__2___24Anonymous__29446) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX6174] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX6174)
=> VX6174 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX29539] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX29539)
=> ( ? [Vvar__0__d__29540] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__29540)
& VX29539 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__29540) )
| ? [Vvar__0__d__29541] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__29541)
& VX29539 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__29541) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX12103] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX12103)
=> ( VX12103 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__12104] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12104)
& VX12103 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__12104) )
| ? [Vvar__0___24Anonymous__12105] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12105)
& VX12103 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__12105) )
| ? [Vvar__0___24Anonymous__12106] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12106)
& VX12103 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__12106) )
| ? [Vvar__0___24Anonymous__12107] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12107)
& VX12103 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__12107) )
| ? [Vvar__0___24Anonymous__12108] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12108)
& VX12103 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__12108) )
| ? [Vvar__0___24Anonymous__12109] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12109)
& VX12103 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__12109) )
| ? [Vvar__0___24Anonymous__12110] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12110)
& VX12103 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__12110) )
| ? [Vvar__0___24Anonymous__12111] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12111)
& VX12103 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__12111) )
| ? [Vvar__0___24Anonymous__12112] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12112)
& VX12103 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__12112) )
| ? [Vvar__0___24Anonymous__12113] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12113)
& VX12103 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__12113) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__32493,Vvar__1___24Anonymous__32494] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__32493)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__32494)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__32493,Vvar__1___24Anonymous__32494)
=> ( Vvar__1___24Anonymous__32494 = Vvar__0__n__32493
| ? [Vvar__1__m__32498] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__32498)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__32493,Vvar__1__m__32498)
& Vvar__1___24Anonymous__32494 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__32498) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__11554,Vvar__1__P__11555,VX11558] :
( cType___24t(Vvar__0__A__11554)
=> ( c_24__type__11568___24t(Vvar__0__A__11554,Vvar__1__P__11555,Vvar__1__P__11555)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__11554,Vvar__1__P__11555,VX11558)
=> ? [Vvar__2__x__11563] :
( t(Vvar__2__x__11563,Vvar__0__A__11554)
& p(happ(Vvar__1__P__11555,Vvar__2__x__11563))
& VX11558 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__11554,Vvar__1__P__11555,Vvar__2__x__11563) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__28065,Vvar__1__B__28066,VX28067] :
( cProp___24t(Vvar__0__A__28065)
=> ( cProp___24t(Vvar__1__B__28066)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__28065,Vvar__1__B__28066,VX28067)
=> ( ( p(Vvar__0__A__28065)
& VX28067 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__28065,Vvar__1__B__28066) )
| ( p(Vvar__1__B__28066)
& VX28067 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__28065,Vvar__1__B__28066) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__11593,Vvar__1__B__11594,VX11595] :
( cType___24t(Vvar__0__A__11593)
=> ( cProp___24t(Vvar__1__B__11594)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__11593,Vvar__1__B__11594,VX11595)
=> ( ? [Vvar__2___24Anonymous__11598] :
( t(Vvar__2___24Anonymous__11598,Vvar__0__A__11593)
& VX11595 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__11593,Vvar__1__B__11594,Vvar__2___24Anonymous__11598) )
| ( p(Vvar__1__B__11594)
& VX11595 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__11593,Vvar__1__B__11594) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__30630,Vvar__1__R__30631,Vvar__2__x__30636] :
( cType___24t(Vvar__0__A__30630)
=> ( c_24__type__30665___24t(Vvar__0__A__30630,Vvar__1__R__30631,Vvar__2__x__30636,Vvar__1__R__30631)
=> ( t(Vvar__2__x__30636,Vvar__0__A__30630)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__30630,Vvar__1__R__30631,Vvar__2__x__30636)
=> ( ! [Vvar__var__var__var__var__3__y__30646__30648__30650__30652__30654] :
( t(Vvar__var__var__var__var__3__y__30646__30648__30650__30652__30654,Vvar__0__A__30630)
=> ( p(happ(happ(Vvar__1__R__30631,Vvar__var__var__var__var__3__y__30646__30648__30650__30652__30654),Vvar__2__x__30636))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__30630,Vvar__1__R__30631,Vvar__var__var__var__var__3__y__30646__30648__30650__30652__30654) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX302] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX302)
=> ( VX302 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__303] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__303)
& VX302 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__303) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX11806] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX11806)
=> ( VX11806 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__11807] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11807)
& VX11806 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11807) )
| ? [Vvar__0___24Anonymous__11808] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11808)
& VX11806 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11808) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX291] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX291)
=> ( ? [Vvar__0___24Anonymous__292] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__292)
& VX291 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__292) )
| ? [Vvar__0___24Anonymous__293] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__293)
& VX291 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__293) )
| VX291 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SqrtSpec',axiom,
! [Vvar__0___24Anonymous__35203,Vvar__1___24Anonymous__35204] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2ePArith_2eBinPosDef_2ePos_2emask,Vvar__0___24Anonymous__35203)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__35204)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSqrtSpec___24a2(Vvar__0___24Anonymous__35203,Vvar__1___24Anonymous__35204)
=> ( ? [Vvar__0__s__35206] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__s__35206)
& ? [Vvar__1__x__35207] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__x__35207)
& Vvar__1__x__35207 = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0__s__35206,Vvar__0__s__35206)
& Vvar__1___24Anonymous__35204 = Vvar__1__x__35207
& Vvar__0___24Anonymous__35203 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2ePArith_2eBinPosDef_2ePos_2emask,Vvar__0__s__35206,cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ) )
| ? [Vvar__0__s__35209] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__s__35209)
& ? [Vvar__1__r__35210] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__r__35210)
& ? [Vvar__2__x__35211] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__x__35211)
& Vvar__2__x__35211 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0__s__35209,Vvar__0__s__35209),Vvar__1__r__35210)
& cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(Vvar__1__r__35210,cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0__s__35209))
& Vvar__1___24Anonymous__35204 = Vvar__2__x__35211
& Vvar__0___24Anonymous__35203 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2ePArith_2eBinPosDef_2ePos_2emask,Vvar__0__s__35209,cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__1__r__35210)) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX29407] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX29407)
=> ( VX29407 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__29408] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29408)
& VX29407 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__29408) )
| VX29407 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX19797] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX19797)
=> ? [Vvar__0__Qnum__19798] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__19798)
& ? [Vvar__1__Qden__19799] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__19799)
& VX19797 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__19798,Vvar__1__Qden__19799) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX29413] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX29413)
=> ? [Vvar__0___24Anonymous__29414] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__29414)
& ? [Vvar__1___24Anonymous__29415] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__29415)
& ? [Vvar__2___24Anonymous__29416] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__29416)
& ? [Vvar__3___24Anonymous__29417] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__29417)
& ? [Vvar__4___24Anonymous__29418] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__29418)
& ? [Vvar__5___24Anonymous__29419] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__29419)
& ? [Vvar__6___24Anonymous__29420] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__29420)
& ? [Vvar__7___24Anonymous__29421] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__29421)
& VX29413 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__29414,Vvar__1___24Anonymous__29415,Vvar__2___24Anonymous__29416,Vvar__3___24Anonymous__29417,Vvar__4___24Anonymous__29418,Vvar__5___24Anonymous__29419,Vvar__6___24Anonymous__29420,Vvar__7___24Anonymous__29421) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__19511,Vvar__1__lt__19512,Vvar__2__eq__19517,Vvar__3__x__19522,Vvar__4__y__19523,VX19524] :
( cType___24t(Vvar__0__X__19511)
=> ( c_24__type__19584___24t(Vvar__0__X__19511,Vvar__1__lt__19512,Vvar__2__eq__19517,Vvar__3__x__19522,Vvar__4__y__19523,Vvar__1__lt__19512)
=> ( c_24__type__19603___24t(Vvar__0__X__19511,Vvar__1__lt__19512,Vvar__2__eq__19517,Vvar__3__x__19522,Vvar__4__y__19523,Vvar__2__eq__19517)
=> ( t(Vvar__3__x__19522,Vvar__0__X__19511)
=> ( t(Vvar__4__y__19523,Vvar__0__X__19511)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__19511,Vvar__1__lt__19512,Vvar__2__eq__19517,Vvar__3__x__19522,Vvar__4__y__19523,VX19524)
=> ( ( p(happ(happ(Vvar__1__lt__19512,Vvar__3__x__19522),Vvar__4__y__19523))
& VX19524 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__19511,Vvar__1__lt__19512,Vvar__2__eq__19517,Vvar__3__x__19522,Vvar__4__y__19523) )
| ( p(happ(happ(Vvar__2__eq__19517,Vvar__3__x__19522),Vvar__4__y__19523))
& VX19524 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__19511,Vvar__1__lt__19512,Vvar__2__eq__19517,Vvar__3__x__19522,Vvar__4__y__19523) )
| ( p(happ(happ(Vvar__1__lt__19512,Vvar__4__y__19523),Vvar__3__x__19522))
& VX19524 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__19511,Vvar__1__lt__19512,Vvar__2__eq__19517,Vvar__3__x__19522,Vvar__4__y__19523) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX19796] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX19796)
=> ( VX19796 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX19796 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX19796 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__32198,VX32199] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32198)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__32198,VX32199)
=> ( ? [Vvar__0__n__32200] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__32200)
& Vvar__0___24Anonymous__32198 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__32200)
& VX32199 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__32200) )
| ? [Vvar__0__n__32201] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__32201)
& ? [Vvar__1___24Anonymous__32202] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__32201,Vvar__1___24Anonymous__32202)
& Vvar__0___24Anonymous__32198 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__32201)
& VX32199 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__32201,Vvar__1___24Anonymous__32202) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__29361,Vvar__1___24Anonymous__29362,VX29363] :
( cType___24t(Vvar__0__A__29361)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__29362)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__29361,Vvar__1___24Anonymous__29362,VX29363)
=> ( ( Vvar__1___24Anonymous__29362 = cCoq_2eInit_2eDatatypes_2eO
& VX29363 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__29361) )
| ? [Vvar__1__h__29366] :
( t(Vvar__1__h__29366,Vvar__0__A__29361)
& ? [Vvar__2__n__29367] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__29367)
& ? [Vvar__3___24Anonymous__29368] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__29361,Vvar__2__n__29367,Vvar__3___24Anonymous__29368)
& Vvar__1___24Anonymous__29362 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__29367)
& VX29363 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__29361,Vvar__1__h__29366,Vvar__2__n__29367,Vvar__3___24Anonymous__29368) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__12258,VX12259] :
( cType___24t(Vvar__0__C__12258)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__12258,VX12259)
=> ( ? [Vvar__1___24Anonymous__12261] :
( t(Vvar__1___24Anonymous__12261,Vvar__0__C__12258)
& VX12259 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__12258,Vvar__1___24Anonymous__12261) )
| ? [Vvar__1___24Anonymous__12263] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12263)
& VX12259 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__12258,Vvar__1___24Anonymous__12263) )
| ? [Vvar__1___24Anonymous__12265] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__12258,Vvar__1___24Anonymous__12265)
& ? [Vvar__2___24Anonymous__12266] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__12258,Vvar__2___24Anonymous__12266)
& VX12259 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__12258,Vvar__1___24Anonymous__12265,Vvar__2___24Anonymous__12266) ) )
| ? [Vvar__1___24Anonymous__12268] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__12258,Vvar__1___24Anonymous__12268)
& ? [Vvar__2___24Anonymous__12269] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__12258,Vvar__2___24Anonymous__12269)
& VX12259 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__12258,Vvar__1___24Anonymous__12268,Vvar__2___24Anonymous__12269) ) )
| ? [Vvar__1___24Anonymous__12271] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__12258,Vvar__1___24Anonymous__12271)
& ? [Vvar__2___24Anonymous__12272] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__12258,Vvar__2___24Anonymous__12272)
& VX12259 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__12258,Vvar__1___24Anonymous__12271,Vvar__2___24Anonymous__12272) ) )
| ? [Vvar__1___24Anonymous__12274] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__12258,Vvar__1___24Anonymous__12274)
& VX12259 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__12258,Vvar__1___24Anonymous__12274) )
| ? [Vvar__1___24Anonymous__12276] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__12258,Vvar__1___24Anonymous__12276)
& ? [Vvar__2___24Anonymous__12277] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__12277)
& VX12259 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__12258,Vvar__1___24Anonymous__12276,Vvar__2___24Anonymous__12277) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__12447,VX12448] :
( cType___24t(Vvar__0__C__12447)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__12447,VX12448)
=> ( ? [Vvar__1___24Anonymous__12450] :
( t(Vvar__1___24Anonymous__12450,Vvar__0__C__12447)
& VX12448 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__12447,Vvar__1___24Anonymous__12450) )
| ? [Vvar__1___24Anonymous__12452] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12452)
& ? [Vvar__2___24Anonymous__12453] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__12447,Vvar__2___24Anonymous__12453)
& VX12448 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__12447,Vvar__1___24Anonymous__12452,Vvar__2___24Anonymous__12453) ) )
| ? [Vvar__1___24Anonymous__12455] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__12447,Vvar__1___24Anonymous__12455)
& ? [Vvar__2___24Anonymous__12456] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12456)
& ? [Vvar__3___24Anonymous__12457] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__12447,Vvar__3___24Anonymous__12457)
& VX12448 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__12447,Vvar__1___24Anonymous__12455,Vvar__2___24Anonymous__12456,Vvar__3___24Anonymous__12457) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__18167,Vvar__1__rO__18168,Vvar__2__rI__18169,Vvar__3__rplus__18170,Vvar__4__rtimes__18175,Vvar__5__rminus__18180,Vvar__6__ropp__18185,Vvar__7__req__18188,Vvar__8__rle__18193,Vvar__9__rlt__18198] :
( cType___24t(Vvar__0__R__18167)
=> ( t(Vvar__1__rO__18168,Vvar__0__R__18167)
=> ( t(Vvar__2__rI__18169,Vvar__0__R__18167)
=> ( c_24__type__18599___24t(Vvar__0__R__18167,Vvar__1__rO__18168,Vvar__2__rI__18169,Vvar__3__rplus__18170,Vvar__4__rtimes__18175,Vvar__5__rminus__18180,Vvar__6__ropp__18185,Vvar__7__req__18188,Vvar__8__rle__18193,Vvar__9__rlt__18198,Vvar__3__rplus__18170)
=> ( c_24__type__18700___24t(Vvar__0__R__18167,Vvar__1__rO__18168,Vvar__2__rI__18169,Vvar__3__rplus__18170,Vvar__4__rtimes__18175,Vvar__5__rminus__18180,Vvar__6__ropp__18185,Vvar__7__req__18188,Vvar__8__rle__18193,Vvar__9__rlt__18198,Vvar__4__rtimes__18175)
=> ( c_24__type__18801___24t(Vvar__0__R__18167,Vvar__1__rO__18168,Vvar__2__rI__18169,Vvar__3__rplus__18170,Vvar__4__rtimes__18175,Vvar__5__rminus__18180,Vvar__6__ropp__18185,Vvar__7__req__18188,Vvar__8__rle__18193,Vvar__9__rlt__18198,Vvar__5__rminus__18180)
=> ( c_24__type__18891___24t(Vvar__0__R__18167,Vvar__1__rO__18168,Vvar__2__rI__18169,Vvar__3__rplus__18170,Vvar__4__rtimes__18175,Vvar__5__rminus__18180,Vvar__6__ropp__18185,Vvar__7__req__18188,Vvar__8__rle__18193,Vvar__9__rlt__18198,Vvar__6__ropp__18185)
=> ( c_24__type__18992___24t(Vvar__0__R__18167,Vvar__1__rO__18168,Vvar__2__rI__18169,Vvar__3__rplus__18170,Vvar__4__rtimes__18175,Vvar__5__rminus__18180,Vvar__6__ropp__18185,Vvar__7__req__18188,Vvar__8__rle__18193,Vvar__9__rlt__18198,Vvar__7__req__18188)
=> ( c_24__type__19093___24t(Vvar__0__R__18167,Vvar__1__rO__18168,Vvar__2__rI__18169,Vvar__3__rplus__18170,Vvar__4__rtimes__18175,Vvar__5__rminus__18180,Vvar__6__ropp__18185,Vvar__7__req__18188,Vvar__8__rle__18193,Vvar__9__rlt__18198,Vvar__8__rle__18193)
=> ( c_24__type__19194___24t(Vvar__0__R__18167,Vvar__1__rO__18168,Vvar__2__rI__18169,Vvar__3__rplus__18170,Vvar__4__rtimes__18175,Vvar__5__rminus__18180,Vvar__6__ropp__18185,Vvar__7__req__18188,Vvar__8__rle__18193,Vvar__9__rlt__18198,Vvar__9__rlt__18198)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__18167,Vvar__1__rO__18168,Vvar__2__rI__18169,Vvar__3__rplus__18170,Vvar__4__rtimes__18175,Vvar__5__rminus__18180,Vvar__6__ropp__18185,Vvar__7__req__18188,Vvar__8__rle__18193,Vvar__9__rlt__18198)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__18167,Vvar__7__req__18188)
& ! [Vvar__var__var__var__var__11__x1__18242__18248__18353__18359__18365] :
( t(Vvar__var__var__var__var__11__x1__18242__18248__18353__18359__18365,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__12__x2__18243__18249__18354__18360__18366] :
( t(Vvar__var__var__var__var__12__x2__18243__18249__18354__18360__18366,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__7__req__18188,Vvar__var__var__var__var__11__x1__18242__18248__18353__18359__18365),Vvar__var__var__var__var__12__x2__18243__18249__18354__18360__18366))
=> ! [Vvar__var__var__var__var__14__y1__18244__18250__18355__18361__18367] :
( t(Vvar__var__var__var__var__14__y1__18244__18250__18355__18361__18367,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__15__y2__18245__18251__18356__18362__18368] :
( t(Vvar__var__var__var__var__15__y2__18245__18251__18356__18362__18368,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__7__req__18188,Vvar__var__var__var__var__14__y1__18244__18250__18355__18361__18367),Vvar__var__var__var__var__15__y2__18245__18251__18356__18362__18368))
=> p(happ(happ(Vvar__7__req__18188,happ(happ(Vvar__3__rplus__18170,Vvar__var__var__var__var__11__x1__18242__18248__18353__18359__18365),Vvar__var__var__var__var__14__y1__18244__18250__18355__18361__18367)),happ(happ(Vvar__3__rplus__18170,Vvar__var__var__var__var__12__x2__18243__18249__18354__18360__18366),Vvar__var__var__var__var__15__y2__18245__18251__18356__18362__18368))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__18255__18261__18371__18377__18383] :
( t(Vvar__var__var__var__var__12__x1__18255__18261__18371__18377__18383,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__13__x2__18256__18262__18372__18378__18384] :
( t(Vvar__var__var__var__var__13__x2__18256__18262__18372__18378__18384,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__7__req__18188,Vvar__var__var__var__var__12__x1__18255__18261__18371__18377__18383),Vvar__var__var__var__var__13__x2__18256__18262__18372__18378__18384))
=> ! [Vvar__var__var__var__var__15__y1__18257__18263__18373__18379__18385] :
( t(Vvar__var__var__var__var__15__y1__18257__18263__18373__18379__18385,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__16__y2__18258__18264__18374__18380__18386] :
( t(Vvar__var__var__var__var__16__y2__18258__18264__18374__18380__18386,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__7__req__18188,Vvar__var__var__var__var__15__y1__18257__18263__18373__18379__18385),Vvar__var__var__var__var__16__y2__18258__18264__18374__18380__18386))
=> p(happ(happ(Vvar__7__req__18188,happ(happ(Vvar__4__rtimes__18175,Vvar__var__var__var__var__12__x1__18255__18261__18371__18377__18383),Vvar__var__var__var__var__15__y1__18257__18263__18373__18379__18385)),happ(happ(Vvar__4__rtimes__18175,Vvar__var__var__var__var__13__x2__18256__18262__18372__18378__18384),Vvar__var__var__var__var__16__y2__18258__18264__18374__18380__18386))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__18268__18271__18389__18392__18395] :
( t(Vvar__var__var__var__var__13__x1__18268__18271__18389__18392__18395,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__14__x2__18269__18272__18390__18393__18396] :
( t(Vvar__var__var__var__var__14__x2__18269__18272__18390__18393__18396,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__7__req__18188,Vvar__var__var__var__var__13__x1__18268__18271__18389__18392__18395),Vvar__var__var__var__var__14__x2__18269__18272__18390__18393__18396))
=> p(happ(happ(Vvar__7__req__18188,happ(Vvar__6__ropp__18185,Vvar__var__var__var__var__13__x1__18268__18271__18389__18392__18395)),happ(Vvar__6__ropp__18185,Vvar__var__var__var__var__14__x2__18269__18272__18390__18393__18396))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__18275__18281__18398__18404__18410] :
( t(Vvar__var__var__var__var__14__x1__18275__18281__18398__18404__18410,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__15__x2__18276__18282__18399__18405__18411] :
( t(Vvar__var__var__var__var__15__x2__18276__18282__18399__18405__18411,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__7__req__18188,Vvar__var__var__var__var__14__x1__18275__18281__18398__18404__18410),Vvar__var__var__var__var__15__x2__18276__18282__18399__18405__18411))
=> ! [Vvar__var__var__var__var__17__y1__18277__18283__18400__18406__18412] :
( t(Vvar__var__var__var__var__17__y1__18277__18283__18400__18406__18412,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__18__y2__18278__18284__18401__18407__18413] :
( t(Vvar__var__var__var__var__18__y2__18278__18284__18401__18407__18413,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__7__req__18188,Vvar__var__var__var__var__17__y1__18277__18283__18400__18406__18412),Vvar__var__var__var__var__18__y2__18278__18284__18401__18407__18413))
=> ( p(happ(happ(Vvar__8__rle__18193,Vvar__var__var__var__var__14__x1__18275__18281__18398__18404__18410),Vvar__var__var__var__var__17__y1__18277__18283__18400__18406__18412))
<=> p(happ(happ(Vvar__8__rle__18193,Vvar__var__var__var__var__15__x2__18276__18282__18399__18405__18411),Vvar__var__var__var__var__18__y2__18278__18284__18401__18407__18413)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__18288__18294__18416__18422__18428] :
( t(Vvar__var__var__var__var__15__x1__18288__18294__18416__18422__18428,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__16__x2__18289__18295__18417__18423__18429] :
( t(Vvar__var__var__var__var__16__x2__18289__18295__18417__18423__18429,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__7__req__18188,Vvar__var__var__var__var__15__x1__18288__18294__18416__18422__18428),Vvar__var__var__var__var__16__x2__18289__18295__18417__18423__18429))
=> ! [Vvar__var__var__var__var__18__y1__18290__18296__18418__18424__18430] :
( t(Vvar__var__var__var__var__18__y1__18290__18296__18418__18424__18430,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__19__y2__18291__18297__18419__18425__18431] :
( t(Vvar__var__var__var__var__19__y2__18291__18297__18419__18425__18431,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__7__req__18188,Vvar__var__var__var__var__18__y1__18290__18296__18418__18424__18430),Vvar__var__var__var__var__19__y2__18291__18297__18419__18425__18431))
=> ( p(happ(happ(Vvar__9__rlt__18198,Vvar__var__var__var__var__15__x1__18288__18294__18416__18422__18428),Vvar__var__var__var__var__18__y1__18290__18296__18418__18424__18430))
<=> p(happ(happ(Vvar__9__rlt__18198,Vvar__var__var__var__var__16__x2__18289__18295__18417__18423__18429),Vvar__var__var__var__var__19__y2__18291__18297__18419__18425__18431)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__18167,Vvar__1__rO__18168,Vvar__2__rI__18169,Vvar__3__rplus__18170,Vvar__4__rtimes__18175,Vvar__5__rminus__18180,Vvar__6__ropp__18185,Vvar__7__req__18188)
& ! [Vvar__var__var__var__17__n__18302__18303__18434__18435] :
( t(Vvar__var__var__var__17__n__18302__18303__18434__18435,Vvar__0__R__18167)
=> p(happ(happ(Vvar__8__rle__18193,Vvar__var__var__var__17__n__18302__18303__18434__18435),Vvar__var__var__var__17__n__18302__18303__18434__18435)) )
& ! [Vvar__var__var__var__var__18__n__18305__18309__18436__18440__18444] :
( t(Vvar__var__var__var__var__18__n__18305__18309__18436__18440__18444,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__19__m__18306__18310__18437__18441__18445] :
( t(Vvar__var__var__var__var__19__m__18306__18310__18437__18441__18445,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__8__rle__18193,Vvar__var__var__var__var__18__n__18305__18309__18436__18440__18444),Vvar__var__var__var__var__19__m__18306__18310__18437__18441__18445))
=> ( p(happ(happ(Vvar__8__rle__18193,Vvar__var__var__var__var__19__m__18306__18310__18437__18441__18445),Vvar__var__var__var__var__18__n__18305__18309__18436__18440__18444))
=> p(happ(happ(Vvar__7__req__18188,Vvar__var__var__var__var__18__n__18305__18309__18436__18440__18444),Vvar__var__var__var__var__19__m__18306__18310__18437__18441__18445)) ) ) ) )
& ! [Vvar__var__var__var__19__n__18314__18319__18448__18453] :
( t(Vvar__var__var__var__19__n__18314__18319__18448__18453,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__20__m__18315__18320__18449__18454] :
( t(Vvar__var__var__var__20__m__18315__18320__18449__18454,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__21__p__18316__18321__18450__18455] :
( t(Vvar__var__var__var__21__p__18316__18321__18450__18455,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__8__rle__18193,Vvar__var__var__var__19__n__18314__18319__18448__18453),Vvar__var__var__var__20__m__18315__18320__18449__18454))
=> ( p(happ(happ(Vvar__8__rle__18193,Vvar__var__var__var__20__m__18315__18320__18449__18454),Vvar__var__var__var__21__p__18316__18321__18450__18455))
=> p(happ(happ(Vvar__8__rle__18193,Vvar__var__var__var__19__n__18314__18319__18448__18453),Vvar__var__var__var__21__p__18316__18321__18450__18455)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__18325__18327__18458__18460__18462__18464] :
( t(Vvar__var__var__var__var__var__20__n__18325__18327__18458__18460__18462__18464,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__var__21__m__18326__18328__18459__18461__18463__18465] :
( t(Vvar__var__var__var__var__var__21__m__18326__18328__18459__18461__18463__18465,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__9__rlt__18198,Vvar__var__var__var__var__var__20__n__18325__18327__18458__18460__18462__18464),Vvar__var__var__var__var__var__21__m__18326__18328__18459__18461__18463__18465))
<=> ( p(happ(happ(Vvar__8__rle__18193,Vvar__var__var__var__var__var__20__n__18325__18327__18458__18460__18462__18464),Vvar__var__var__var__var__var__21__m__18326__18328__18459__18461__18463__18465))
& ~ p(happ(happ(Vvar__7__req__18188,Vvar__var__var__var__var__var__20__n__18325__18327__18458__18460__18462__18464),Vvar__var__var__var__var__var__21__m__18326__18328__18459__18461__18463__18465)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__18330__18332__18466__18468__18470] :
( t(Vvar__var__var__var__var__21__n__18330__18332__18466__18468__18470,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__22__m__18331__18333__18467__18469__18471] :
( t(Vvar__var__var__var__var__22__m__18331__18333__18467__18469__18471,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__9__rlt__18198,Vvar__var__var__var__var__21__n__18330__18332__18466__18468__18470),Vvar__var__var__var__var__22__m__18331__18333__18467__18469__18471))
| p(happ(happ(Vvar__7__req__18188,Vvar__var__var__var__var__21__n__18330__18332__18466__18468__18470),Vvar__var__var__var__var__22__m__18331__18333__18467__18469__18471))
| p(happ(happ(Vvar__9__rlt__18198,Vvar__var__var__var__var__22__m__18331__18333__18467__18469__18471),Vvar__var__var__var__var__21__n__18330__18332__18466__18468__18470)) ) ) )
& ! [Vvar__var__var__var__var__22__n__18335__18339__18472__18476__18480] :
( t(Vvar__var__var__var__var__22__n__18335__18339__18472__18476__18480,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__23__m__18336__18340__18473__18477__18481] :
( t(Vvar__var__var__var__var__23__m__18336__18340__18473__18477__18481,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__24__p__18337__18341__18474__18478__18482] :
( t(Vvar__var__var__var__var__24__p__18337__18341__18474__18478__18482,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__8__rle__18193,Vvar__var__var__var__var__22__n__18335__18339__18472__18476__18480),Vvar__var__var__var__var__23__m__18336__18340__18473__18477__18481))
=> p(happ(happ(Vvar__8__rle__18193,happ(happ(Vvar__3__rplus__18170,Vvar__var__var__var__var__24__p__18337__18341__18474__18478__18482),Vvar__var__var__var__var__22__n__18335__18339__18472__18476__18480)),happ(happ(Vvar__3__rplus__18170,Vvar__var__var__var__var__24__p__18337__18341__18474__18478__18482),Vvar__var__var__var__var__23__m__18336__18340__18473__18477__18481))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__18344__18348__18484__18488__18492__18496] :
( t(Vvar__var__var__var__var__var__23__n__18344__18348__18484__18488__18492__18496,Vvar__0__R__18167)
=> ! [Vvar__var__var__var__var__var__24__m__18345__18349__18485__18489__18493__18497] :
( t(Vvar__var__var__var__var__var__24__m__18345__18349__18485__18489__18493__18497,Vvar__0__R__18167)
=> ( p(happ(happ(Vvar__9__rlt__18198,Vvar__1__rO__18168),Vvar__var__var__var__var__var__23__n__18344__18348__18484__18488__18492__18496))
=> ( p(happ(happ(Vvar__9__rlt__18198,Vvar__1__rO__18168),Vvar__var__var__var__var__var__24__m__18345__18349__18485__18489__18493__18497))
=> p(happ(happ(Vvar__9__rlt__18198,Vvar__1__rO__18168),happ(happ(Vvar__4__rtimes__18175,Vvar__var__var__var__var__var__23__n__18344__18348__18484__18488__18492__18496),Vvar__var__var__var__var__var__24__m__18345__18349__18485__18489__18493__18497))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__18188,Vvar__1__rO__18168),Vvar__2__rI__18169))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__22139,VX22140] :
( cType___24t(Vvar__0__T__22139)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__22139,VX22140)
=> ? [Vvar__1__Flhs__22142] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__22139,Vvar__1__Flhs__22142)
& ? [Vvar__2__Fop__22143] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__22143)
& ? [Vvar__3__Frhs__22144] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__22139,Vvar__3__Frhs__22144)
& VX22140 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__22139,Vvar__1__Flhs__22142,Vvar__2__Fop__22143,Vvar__3__Frhs__22144) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX20442] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX20442)
=> ( VX20442 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX20442 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX20442 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX20442 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX21917] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX21917)
=> ( VX21917 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX21917 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX21917 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX21917 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX21917 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX21917 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__20662,VX20663] :
( cType___24t(Vvar__0__C__20662)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20662,VX20663)
=> ( ? [Vvar__1___24Anonymous__20665] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__20665)
& VX20663 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__20662,Vvar__1___24Anonymous__20665) )
| ? [Vvar__1___24Anonymous__20667] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__20662,Vvar__1___24Anonymous__20667)
& VX20663 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__20662,Vvar__1___24Anonymous__20667) )
| ? [Vvar__1___24Anonymous__20669] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__20662,Vvar__1___24Anonymous__20669)
& ? [Vvar__2___24Anonymous__20670] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20662,Vvar__2___24Anonymous__20670)
& VX20663 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__20662,Vvar__1___24Anonymous__20669,Vvar__2___24Anonymous__20670) ) )
| ? [Vvar__1___24Anonymous__20672] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20662,Vvar__1___24Anonymous__20672)
& ? [Vvar__2___24Anonymous__20673] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20662,Vvar__2___24Anonymous__20673)
& VX20663 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__20662,Vvar__1___24Anonymous__20672,Vvar__2___24Anonymous__20673) ) )
| ? [Vvar__1___24Anonymous__20675] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20662,Vvar__1___24Anonymous__20675)
& ? [Vvar__2___24Anonymous__20676] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20662,Vvar__2___24Anonymous__20676)
& VX20663 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__20662,Vvar__1___24Anonymous__20675,Vvar__2___24Anonymous__20676) ) )
| ? [Vvar__1___24Anonymous__20678] :
( t(Vvar__1___24Anonymous__20678,Vvar__0__C__20662)
& VX20663 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__20662,Vvar__1___24Anonymous__20678) )
| VX20663 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__20662) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275] :
( cType___24t(Vvar__0__R__6206)
=> ( t(Vvar__1__rO__6207,Vvar__0__R__6206)
=> ( t(Vvar__2__rI__6208,Vvar__0__R__6206)
=> ( c_24__type__6739___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__3__rplus__6209)
=> ( c_24__type__7085___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__4__rtimes__6214)
=> ( c_24__type__7431___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__5__rminus__6219)
=> ( c_24__type__7754___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__6__ropp__6224)
=> ( c_24__type__8100___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__7__req__6227)
=> ( c_24__type__8446___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__8__rle__6232)
=> ( cType___24t(Vvar__9__C__6237)
=> ( t(Vvar__10__cO__6238,Vvar__9__C__6237)
=> ( t(Vvar__11__cI__6239,Vvar__9__C__6237)
=> ( c_24__type__8792___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__12__cplus__6240)
=> ( c_24__type__9138___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__13__ctimes__6245)
=> ( c_24__type__9484___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__14__cminus__6250)
=> ( c_24__type__9807___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__15__copp__6255)
=> ( c_24__type__10153___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__16__ceqb__6258)
=> ( c_24__type__10499___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__17__cleb__6263)
=> ( c_24__type__10822___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__18__phi__6268)
=> ( cType___24t(Vvar__19__E__6271)
=> ( c_24__type__11145___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__20__pow__phi__6272)
=> ( c_24__type__11491___24t(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275,Vvar__21__rpow__6275)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__8__rle__6232,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__17__cleb__6263,Vvar__18__phi__6268,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__6206,Vvar__1__rO__6207,Vvar__2__rI__6208,Vvar__3__rplus__6209,Vvar__4__rtimes__6214,Vvar__5__rminus__6219,Vvar__6__ropp__6224,Vvar__7__req__6227,Vvar__9__C__6237,Vvar__10__cO__6238,Vvar__11__cI__6239,Vvar__12__cplus__6240,Vvar__13__ctimes__6245,Vvar__14__cminus__6250,Vvar__15__copp__6255,Vvar__16__ceqb__6258,Vvar__18__phi__6268)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__6206,Vvar__2__rI__6208,Vvar__4__rtimes__6214,Vvar__7__req__6227,Vvar__19__E__6271,Vvar__20__pow__phi__6272,Vvar__21__rpow__6275)
& ! [Vvar__var__var__var__var__var__24__x__6358__6361__6371__6374__6377__6380] :
( t(Vvar__var__var__var__var__var__24__x__6358__6361__6371__6374__6377__6380,Vvar__9__C__6237)
=> ! [Vvar__var__var__var__var__var__25__y__6359__6362__6372__6375__6378__6381] :
( t(Vvar__var__var__var__var__var__25__y__6359__6362__6372__6375__6378__6381,Vvar__9__C__6237)
=> ( happ(happ(Vvar__16__ceqb__6258,Vvar__var__var__var__var__var__24__x__6358__6361__6371__6374__6377__6380),Vvar__var__var__var__var__var__25__y__6359__6362__6372__6375__6378__6381) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__6227,happ(Vvar__18__phi__6268,Vvar__var__var__var__var__var__24__x__6358__6361__6371__6374__6377__6380)),happ(Vvar__18__phi__6268,Vvar__var__var__var__var__var__25__y__6359__6362__6372__6375__6378__6381))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__6365__6368__6383__6386__6389__6392] :
( t(Vvar__var__var__var__var__var__25__x__6365__6368__6383__6386__6389__6392,Vvar__9__C__6237)
=> ! [Vvar__var__var__var__var__var__26__y__6366__6369__6384__6387__6390__6393] :
( t(Vvar__var__var__var__var__var__26__y__6366__6369__6384__6387__6390__6393,Vvar__9__C__6237)
=> ( happ(happ(Vvar__17__cleb__6263,Vvar__var__var__var__var__var__25__x__6365__6368__6383__6386__6389__6392),Vvar__var__var__var__var__var__26__y__6366__6369__6384__6387__6390__6393) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__6232,happ(Vvar__18__phi__6268,Vvar__var__var__var__var__var__25__x__6365__6368__6383__6386__6389__6392)),happ(Vvar__18__phi__6268,Vvar__var__var__var__var__var__26__y__6366__6369__6384__6387__6390__6393))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__15216,VX15217] :
( cType___24t(Vvar__0__C__15216)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15216,VX15217)
=> ( VX15217 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__15216)
| VX15217 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__15216)
| ? [Vvar__1___24Anonymous__15221] :
( t(Vvar__1___24Anonymous__15221,Vvar__0__C__15216)
& VX15217 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__15216,Vvar__1___24Anonymous__15221) )
| ? [Vvar__1___24Anonymous__15223] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15223)
& VX15217 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__15216,Vvar__1___24Anonymous__15223) )
| ? [Vvar__1___24Anonymous__15225] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15216,Vvar__1___24Anonymous__15225)
& ? [Vvar__2___24Anonymous__15226] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15216,Vvar__2___24Anonymous__15226)
& VX15217 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__15216,Vvar__1___24Anonymous__15225,Vvar__2___24Anonymous__15226) ) )
| ? [Vvar__1___24Anonymous__15228] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15216,Vvar__1___24Anonymous__15228)
& ? [Vvar__2___24Anonymous__15229] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15216,Vvar__2___24Anonymous__15229)
& VX15217 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__15216,Vvar__1___24Anonymous__15228,Vvar__2___24Anonymous__15229) ) )
| ? [Vvar__1___24Anonymous__15231] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15216,Vvar__1___24Anonymous__15231)
& ? [Vvar__2___24Anonymous__15232] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15216,Vvar__2___24Anonymous__15232)
& VX15217 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__15216,Vvar__1___24Anonymous__15231,Vvar__2___24Anonymous__15232) ) )
| ? [Vvar__1___24Anonymous__15234] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15216,Vvar__1___24Anonymous__15234)
& VX15217 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__15216,Vvar__1___24Anonymous__15234) )
| ? [Vvar__1___24Anonymous__15236] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15216,Vvar__1___24Anonymous__15236)
& VX15217 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__15216,Vvar__1___24Anonymous__15236) )
| ? [Vvar__1___24Anonymous__15238] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15216,Vvar__1___24Anonymous__15238)
& ? [Vvar__2___24Anonymous__15239] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15216,Vvar__2___24Anonymous__15239)
& VX15217 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__15216,Vvar__1___24Anonymous__15238,Vvar__2___24Anonymous__15239) ) )
| ? [Vvar__1___24Anonymous__15241] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__15216,Vvar__1___24Anonymous__15241)
& ? [Vvar__2___24Anonymous__15242] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__15242)
& VX15217 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__15216,Vvar__1___24Anonymous__15241,Vvar__2___24Anonymous__15242) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__393,Vvar__1__rO__394,Vvar__2__rI__395,Vvar__3__radd__396,Vvar__4__rmul__401,Vvar__5__rsub__406,Vvar__6__ropp__411,Vvar__7__rdiv__414,Vvar__8__rinv__419,Vvar__9__req__422] :
( cType___24t(Vvar__0__R__393)
=> ( t(Vvar__1__rO__394,Vvar__0__R__393)
=> ( t(Vvar__2__rI__395,Vvar__0__R__393)
=> ( c_24__type__587___24t(Vvar__0__R__393,Vvar__1__rO__394,Vvar__2__rI__395,Vvar__3__radd__396,Vvar__4__rmul__401,Vvar__5__rsub__406,Vvar__6__ropp__411,Vvar__7__rdiv__414,Vvar__8__rinv__419,Vvar__9__req__422,Vvar__3__radd__396)
=> ( c_24__type__680___24t(Vvar__0__R__393,Vvar__1__rO__394,Vvar__2__rI__395,Vvar__3__radd__396,Vvar__4__rmul__401,Vvar__5__rsub__406,Vvar__6__ropp__411,Vvar__7__rdiv__414,Vvar__8__rinv__419,Vvar__9__req__422,Vvar__4__rmul__401)
=> ( c_24__type__773___24t(Vvar__0__R__393,Vvar__1__rO__394,Vvar__2__rI__395,Vvar__3__radd__396,Vvar__4__rmul__401,Vvar__5__rsub__406,Vvar__6__ropp__411,Vvar__7__rdiv__414,Vvar__8__rinv__419,Vvar__9__req__422,Vvar__5__rsub__406)
=> ( c_24__type__855___24t(Vvar__0__R__393,Vvar__1__rO__394,Vvar__2__rI__395,Vvar__3__radd__396,Vvar__4__rmul__401,Vvar__5__rsub__406,Vvar__6__ropp__411,Vvar__7__rdiv__414,Vvar__8__rinv__419,Vvar__9__req__422,Vvar__6__ropp__411)
=> ( c_24__type__948___24t(Vvar__0__R__393,Vvar__1__rO__394,Vvar__2__rI__395,Vvar__3__radd__396,Vvar__4__rmul__401,Vvar__5__rsub__406,Vvar__6__ropp__411,Vvar__7__rdiv__414,Vvar__8__rinv__419,Vvar__9__req__422,Vvar__7__rdiv__414)
=> ( c_24__type__1030___24t(Vvar__0__R__393,Vvar__1__rO__394,Vvar__2__rI__395,Vvar__3__radd__396,Vvar__4__rmul__401,Vvar__5__rsub__406,Vvar__6__ropp__411,Vvar__7__rdiv__414,Vvar__8__rinv__419,Vvar__9__req__422,Vvar__8__rinv__419)
=> ( c_24__type__1123___24t(Vvar__0__R__393,Vvar__1__rO__394,Vvar__2__rI__395,Vvar__3__radd__396,Vvar__4__rmul__401,Vvar__5__rsub__406,Vvar__6__ropp__411,Vvar__7__rdiv__414,Vvar__8__rinv__419,Vvar__9__req__422,Vvar__9__req__422)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__393,Vvar__1__rO__394,Vvar__2__rI__395,Vvar__3__radd__396,Vvar__4__rmul__401,Vvar__5__rsub__406,Vvar__6__ropp__411,Vvar__7__rdiv__414,Vvar__8__rinv__419,Vvar__9__req__422)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__393,Vvar__1__rO__394,Vvar__2__rI__395,Vvar__3__radd__396,Vvar__4__rmul__401,Vvar__5__rsub__406,Vvar__6__ropp__411,Vvar__9__req__422)
& ~ p(happ(happ(Vvar__9__req__422,Vvar__2__rI__395),Vvar__1__rO__394))
& ! [Vvar__var__var__var__var__var__var__12__p__465__467__474__476__478__480__482] :
( t(Vvar__var__var__var__var__var__var__12__p__465__467__474__476__478__480__482,Vvar__0__R__393)
=> ! [Vvar__var__var__var__var__var__var__13__q__466__468__475__477__479__481__483] :
( t(Vvar__var__var__var__var__var__var__13__q__466__468__475__477__479__481__483,Vvar__0__R__393)
=> p(happ(happ(Vvar__9__req__422,happ(happ(Vvar__7__rdiv__414,Vvar__var__var__var__var__var__var__12__p__465__467__474__476__478__480__482),Vvar__var__var__var__var__var__var__13__q__466__468__475__477__479__481__483)),happ(happ(Vvar__4__rmul__401,Vvar__var__var__var__var__var__var__12__p__465__467__474__476__478__480__482),happ(Vvar__8__rinv__419,Vvar__var__var__var__var__var__var__13__q__466__468__475__477__479__481__483)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__470__472__484__486__488__490__492__494] :
( t(Vvar__var__var__var__var__var__var__var__13__p__470__472__484__486__488__490__492__494,Vvar__0__R__393)
=> ( ~ p(happ(happ(Vvar__9__req__422,Vvar__var__var__var__var__var__var__var__13__p__470__472__484__486__488__490__492__494),Vvar__1__rO__394))
=> p(happ(happ(Vvar__9__req__422,happ(happ(Vvar__4__rmul__401,happ(Vvar__8__rinv__419,Vvar__var__var__var__var__var__var__var__13__p__470__472__484__486__488__490__492__494)),Vvar__var__var__var__var__var__var__var__13__p__470__472__484__486__488__490__492__494)),Vvar__2__rI__395)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__15887,VX15888] :
( cType___24t(Vvar__0__C__15887)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__15887,VX15888)
=> ? [Vvar__1__num__15890] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15887,Vvar__1__num__15890)
& ? [Vvar__2__denum__15891] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15887,Vvar__2__denum__15891)
& ? [Vvar__3__condition__15892] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__15887),Vvar__3__condition__15892)
& VX15888 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__15887,Vvar__1__num__15890,Vvar__2__denum__15891,Vvar__3__condition__15892) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__16316,VX16317] :
( cType___24t(Vvar__0__C__16316)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__16316,VX16317)
=> ? [Vvar__1__rsplit__left__16319] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__16316,Vvar__1__rsplit__left__16319)
& ? [Vvar__2__rsplit__common__16320] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__16316,Vvar__2__rsplit__common__16320)
& ? [Vvar__3__rsplit__right__16321] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__16316,Vvar__3__rsplit__right__16321)
& VX16317 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__16316,Vvar__1__rsplit__left__16319,Vvar__2__rsplit__common__16320,Vvar__3__rsplit__right__16321) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX24107] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX24107)
=> ( VX24107 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__24108] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24108)
& ? [Vvar__1___24Anonymous__24109] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__24109)
& VX24107 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__24108,Vvar__1___24Anonymous__24109) ) )
| ? [Vvar__0___24Anonymous__24110] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24110)
& ? [Vvar__1___24Anonymous__24111] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__24111)
& VX24107 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__24110,Vvar__1___24Anonymous__24111) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__2021,VX2022] :
( cType___24t(Vvar__0__C__2021)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2021,VX2022)
=> ( VX2022 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2021)
| VX2022 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2021)
| ? [Vvar__1___24Anonymous__2026] :
( t(Vvar__1___24Anonymous__2026,Vvar__0__C__2021)
& VX2022 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2021,Vvar__1___24Anonymous__2026) )
| ? [Vvar__1___24Anonymous__2028] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2028)
& VX2022 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2021,Vvar__1___24Anonymous__2028) )
| ? [Vvar__1___24Anonymous__2030] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2021,Vvar__1___24Anonymous__2030)
& ? [Vvar__2___24Anonymous__2031] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2021,Vvar__2___24Anonymous__2031)
& VX2022 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2021,Vvar__1___24Anonymous__2030,Vvar__2___24Anonymous__2031) ) )
| ? [Vvar__1___24Anonymous__2033] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2021,Vvar__1___24Anonymous__2033)
& ? [Vvar__2___24Anonymous__2034] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2021,Vvar__2___24Anonymous__2034)
& VX2022 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2021,Vvar__1___24Anonymous__2033,Vvar__2___24Anonymous__2034) ) )
| ? [Vvar__1___24Anonymous__2036] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2021,Vvar__1___24Anonymous__2036)
& ? [Vvar__2___24Anonymous__2037] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2021,Vvar__2___24Anonymous__2037)
& VX2022 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2021,Vvar__1___24Anonymous__2036,Vvar__2___24Anonymous__2037) ) )
| ? [Vvar__1___24Anonymous__2039] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2021,Vvar__1___24Anonymous__2039)
& VX2022 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2021,Vvar__1___24Anonymous__2039) )
| ? [Vvar__1___24Anonymous__2041] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2021,Vvar__1___24Anonymous__2041)
& ? [Vvar__2___24Anonymous__2042] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2042)
& VX2022 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2021,Vvar__1___24Anonymous__2041,Vvar__2___24Anonymous__2042) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__23448,VX23449] :
( cType___24t(Vvar__0__C__23448)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__23448,VX23449)
=> ( ? [Vvar__1___24Anonymous__23451] :
( t(Vvar__1___24Anonymous__23451,Vvar__0__C__23448)
& VX23449 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__23448,Vvar__1___24Anonymous__23451) )
| ? [Vvar__1___24Anonymous__23453] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23453)
& ? [Vvar__2___24Anonymous__23454] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__23448,Vvar__2___24Anonymous__23454)
& VX23449 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__23448,Vvar__1___24Anonymous__23453,Vvar__2___24Anonymous__23454) ) )
| ? [Vvar__1___24Anonymous__23456] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__23448,Vvar__1___24Anonymous__23456)
& ? [Vvar__2___24Anonymous__23457] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23457)
& ? [Vvar__3___24Anonymous__23458] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__23448,Vvar__3___24Anonymous__23458)
& VX23449 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__23448,Vvar__1___24Anonymous__23456,Vvar__2___24Anonymous__23457,Vvar__3___24Anonymous__23458) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__2528,Vvar__1__rO__2529,Vvar__2__rI__2530,Vvar__3__radd__2531,Vvar__4__rmul__2536,Vvar__5__rsub__2541,Vvar__6__ropp__2546,Vvar__7__req__2549] :
( cType___24t(Vvar__0__R__2528)
=> ( t(Vvar__1__rO__2529,Vvar__0__R__2528)
=> ( t(Vvar__2__rI__2530,Vvar__0__R__2528)
=> ( c_24__type__2777___24t(Vvar__0__R__2528,Vvar__1__rO__2529,Vvar__2__rI__2530,Vvar__3__radd__2531,Vvar__4__rmul__2536,Vvar__5__rsub__2541,Vvar__6__ropp__2546,Vvar__7__req__2549,Vvar__3__radd__2531)
=> ( c_24__type__2840___24t(Vvar__0__R__2528,Vvar__1__rO__2529,Vvar__2__rI__2530,Vvar__3__radd__2531,Vvar__4__rmul__2536,Vvar__5__rsub__2541,Vvar__6__ropp__2546,Vvar__7__req__2549,Vvar__4__rmul__2536)
=> ( c_24__type__2903___24t(Vvar__0__R__2528,Vvar__1__rO__2529,Vvar__2__rI__2530,Vvar__3__radd__2531,Vvar__4__rmul__2536,Vvar__5__rsub__2541,Vvar__6__ropp__2546,Vvar__7__req__2549,Vvar__5__rsub__2541)
=> ( c_24__type__2957___24t(Vvar__0__R__2528,Vvar__1__rO__2529,Vvar__2__rI__2530,Vvar__3__radd__2531,Vvar__4__rmul__2536,Vvar__5__rsub__2541,Vvar__6__ropp__2546,Vvar__7__req__2549,Vvar__6__ropp__2546)
=> ( c_24__type__3020___24t(Vvar__0__R__2528,Vvar__1__rO__2529,Vvar__2__rI__2530,Vvar__3__radd__2531,Vvar__4__rmul__2536,Vvar__5__rsub__2541,Vvar__6__ropp__2546,Vvar__7__req__2549,Vvar__7__req__2549)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__2528,Vvar__1__rO__2529,Vvar__2__rI__2530,Vvar__3__radd__2531,Vvar__4__rmul__2536,Vvar__5__rsub__2541,Vvar__6__ropp__2546,Vvar__7__req__2549)
=> ( ! [Vvar__var__var__var__var__var__8__x__2582__2583__2636__2637__2638__2639] :
( t(Vvar__var__var__var__var__var__8__x__2582__2583__2636__2637__2638__2639,Vvar__0__R__2528)
=> p(happ(happ(Vvar__7__req__2549,happ(happ(Vvar__3__radd__2531,Vvar__1__rO__2529),Vvar__var__var__var__var__var__8__x__2582__2583__2636__2637__2638__2639)),Vvar__var__var__var__var__var__8__x__2582__2583__2636__2637__2638__2639)) )
& ! [Vvar__var__var__var__var__9__x__2585__2587__2640__2642__2644] :
( t(Vvar__var__var__var__var__9__x__2585__2587__2640__2642__2644,Vvar__0__R__2528)
=> ! [Vvar__var__var__var__var__10__y__2586__2588__2641__2643__2645] :
( t(Vvar__var__var__var__var__10__y__2586__2588__2641__2643__2645,Vvar__0__R__2528)
=> p(happ(happ(Vvar__7__req__2549,happ(happ(Vvar__3__radd__2531,Vvar__var__var__var__var__9__x__2585__2587__2640__2642__2644),Vvar__var__var__var__var__10__y__2586__2588__2641__2643__2645)),happ(happ(Vvar__3__radd__2531,Vvar__var__var__var__var__10__y__2586__2588__2641__2643__2645),Vvar__var__var__var__var__9__x__2585__2587__2640__2642__2644))) ) )
& ! [Vvar__var__var__var__var__10__x__2590__2593__2646__2649__2652] :
( t(Vvar__var__var__var__var__10__x__2590__2593__2646__2649__2652,Vvar__0__R__2528)
=> ! [Vvar__var__var__var__var__11__y__2591__2594__2647__2650__2653] :
( t(Vvar__var__var__var__var__11__y__2591__2594__2647__2650__2653,Vvar__0__R__2528)
=> ! [Vvar__var__var__var__var__12__z__2592__2595__2648__2651__2654] :
( t(Vvar__var__var__var__var__12__z__2592__2595__2648__2651__2654,Vvar__0__R__2528)
=> p(happ(happ(Vvar__7__req__2549,happ(happ(Vvar__3__radd__2531,Vvar__var__var__var__var__10__x__2590__2593__2646__2649__2652),happ(happ(Vvar__3__radd__2531,Vvar__var__var__var__var__11__y__2591__2594__2647__2650__2653),Vvar__var__var__var__var__12__z__2592__2595__2648__2651__2654))),happ(happ(Vvar__3__radd__2531,happ(happ(Vvar__3__radd__2531,Vvar__var__var__var__var__10__x__2590__2593__2646__2649__2652),Vvar__var__var__var__var__11__y__2591__2594__2647__2650__2653)),Vvar__var__var__var__var__12__z__2592__2595__2648__2651__2654))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__2597__2598__2655__2656__2657__2658] :
( t(Vvar__var__var__var__var__var__11__x__2597__2598__2655__2656__2657__2658,Vvar__0__R__2528)
=> p(happ(happ(Vvar__7__req__2549,happ(happ(Vvar__4__rmul__2536,Vvar__2__rI__2530),Vvar__var__var__var__var__var__11__x__2597__2598__2655__2656__2657__2658)),Vvar__var__var__var__var__var__11__x__2597__2598__2655__2656__2657__2658)) )
& ! [Vvar__var__var__var__var__var__12__x__2600__2601__2659__2660__2661__2662] :
( t(Vvar__var__var__var__var__var__12__x__2600__2601__2659__2660__2661__2662,Vvar__0__R__2528)
=> p(happ(happ(Vvar__7__req__2549,happ(happ(Vvar__4__rmul__2536,Vvar__1__rO__2529),Vvar__var__var__var__var__var__12__x__2600__2601__2659__2660__2661__2662)),Vvar__1__rO__2529)) )
& ! [Vvar__var__var__var__var__13__x__2603__2605__2663__2665__2667] :
( t(Vvar__var__var__var__var__13__x__2603__2605__2663__2665__2667,Vvar__0__R__2528)
=> ! [Vvar__var__var__var__var__14__y__2604__2606__2664__2666__2668] :
( t(Vvar__var__var__var__var__14__y__2604__2606__2664__2666__2668,Vvar__0__R__2528)
=> p(happ(happ(Vvar__7__req__2549,happ(happ(Vvar__4__rmul__2536,Vvar__var__var__var__var__13__x__2603__2605__2663__2665__2667),Vvar__var__var__var__var__14__y__2604__2606__2664__2666__2668)),happ(happ(Vvar__4__rmul__2536,Vvar__var__var__var__var__14__y__2604__2606__2664__2666__2668),Vvar__var__var__var__var__13__x__2603__2605__2663__2665__2667))) ) )
& ! [Vvar__var__var__var__var__14__x__2608__2611__2669__2672__2675] :
( t(Vvar__var__var__var__var__14__x__2608__2611__2669__2672__2675,Vvar__0__R__2528)
=> ! [Vvar__var__var__var__var__15__y__2609__2612__2670__2673__2676] :
( t(Vvar__var__var__var__var__15__y__2609__2612__2670__2673__2676,Vvar__0__R__2528)
=> ! [Vvar__var__var__var__var__16__z__2610__2613__2671__2674__2677] :
( t(Vvar__var__var__var__var__16__z__2610__2613__2671__2674__2677,Vvar__0__R__2528)
=> p(happ(happ(Vvar__7__req__2549,happ(happ(Vvar__4__rmul__2536,Vvar__var__var__var__var__14__x__2608__2611__2669__2672__2675),happ(happ(Vvar__4__rmul__2536,Vvar__var__var__var__var__15__y__2609__2612__2670__2673__2676),Vvar__var__var__var__var__16__z__2610__2613__2671__2674__2677))),happ(happ(Vvar__4__rmul__2536,happ(happ(Vvar__4__rmul__2536,Vvar__var__var__var__var__14__x__2608__2611__2669__2672__2675),Vvar__var__var__var__var__15__y__2609__2612__2670__2673__2676)),Vvar__var__var__var__var__16__z__2610__2613__2671__2674__2677))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__2615__2618__2678__2681__2684__2687] :
( t(Vvar__var__var__var__var__var__15__x__2615__2618__2678__2681__2684__2687,Vvar__0__R__2528)
=> ! [Vvar__var__var__var__var__var__16__y__2616__2619__2679__2682__2685__2688] :
( t(Vvar__var__var__var__var__var__16__y__2616__2619__2679__2682__2685__2688,Vvar__0__R__2528)
=> ! [Vvar__var__var__var__var__var__17__z__2617__2620__2680__2683__2686__2689] :
( t(Vvar__var__var__var__var__var__17__z__2617__2620__2680__2683__2686__2689,Vvar__0__R__2528)
=> p(happ(happ(Vvar__7__req__2549,happ(happ(Vvar__4__rmul__2536,happ(happ(Vvar__3__radd__2531,Vvar__var__var__var__var__var__15__x__2615__2618__2678__2681__2684__2687),Vvar__var__var__var__var__var__16__y__2616__2619__2679__2682__2685__2688)),Vvar__var__var__var__var__var__17__z__2617__2620__2680__2683__2686__2689)),happ(happ(Vvar__3__radd__2531,happ(happ(Vvar__4__rmul__2536,Vvar__var__var__var__var__var__15__x__2615__2618__2678__2681__2684__2687),Vvar__var__var__var__var__var__17__z__2617__2620__2680__2683__2686__2689)),happ(happ(Vvar__4__rmul__2536,Vvar__var__var__var__var__var__16__y__2616__2619__2679__2682__2685__2688),Vvar__var__var__var__var__var__17__z__2617__2620__2680__2683__2686__2689)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__2622__2624__2690__2692__2694__2696] :
( t(Vvar__var__var__var__var__var__16__x__2622__2624__2690__2692__2694__2696,Vvar__0__R__2528)
=> ! [Vvar__var__var__var__var__var__17__y__2623__2625__2691__2693__2695__2697] :
( t(Vvar__var__var__var__var__var__17__y__2623__2625__2691__2693__2695__2697,Vvar__0__R__2528)
=> p(happ(happ(Vvar__7__req__2549,happ(Vvar__6__ropp__2546,happ(happ(Vvar__4__rmul__2536,Vvar__var__var__var__var__var__16__x__2622__2624__2690__2692__2694__2696),Vvar__var__var__var__var__var__17__y__2623__2625__2691__2693__2695__2697))),happ(happ(Vvar__4__rmul__2536,happ(Vvar__6__ropp__2546,Vvar__var__var__var__var__var__16__x__2622__2624__2690__2692__2694__2696)),Vvar__var__var__var__var__var__17__y__2623__2625__2691__2693__2695__2697))) ) )
& ! [Vvar__var__var__var__var__var__17__x__2627__2629__2698__2700__2702__2704] :
( t(Vvar__var__var__var__var__var__17__x__2627__2629__2698__2700__2702__2704,Vvar__0__R__2528)
=> ! [Vvar__var__var__var__var__var__18__y__2628__2630__2699__2701__2703__2705] :
( t(Vvar__var__var__var__var__var__18__y__2628__2630__2699__2701__2703__2705,Vvar__0__R__2528)
=> p(happ(happ(Vvar__7__req__2549,happ(Vvar__6__ropp__2546,happ(happ(Vvar__3__radd__2531,Vvar__var__var__var__var__var__17__x__2627__2629__2698__2700__2702__2704),Vvar__var__var__var__var__var__18__y__2628__2630__2699__2701__2703__2705))),happ(happ(Vvar__3__radd__2531,happ(Vvar__6__ropp__2546,Vvar__var__var__var__var__var__17__x__2627__2629__2698__2700__2702__2704)),happ(Vvar__6__ropp__2546,Vvar__var__var__var__var__var__18__y__2628__2630__2699__2701__2703__2705)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__2632__2634__2706__2708__2710__2712__2714] :
( t(Vvar__var__var__var__var__var__var__18__x__2632__2634__2706__2708__2710__2712__2714,Vvar__0__R__2528)
=> ! [Vvar__var__var__var__var__var__var__19__y__2633__2635__2707__2709__2711__2713__2715] :
( t(Vvar__var__var__var__var__var__var__19__y__2633__2635__2707__2709__2711__2713__2715,Vvar__0__R__2528)
=> p(happ(happ(Vvar__7__req__2549,happ(happ(Vvar__5__rsub__2541,Vvar__var__var__var__var__var__var__18__x__2632__2634__2706__2708__2710__2712__2714),Vvar__var__var__var__var__var__var__19__y__2633__2635__2707__2709__2711__2713__2715)),happ(happ(Vvar__3__radd__2531,Vvar__var__var__var__var__var__var__18__x__2632__2634__2706__2708__2710__2712__2714),happ(Vvar__6__ropp__2546,Vvar__var__var__var__var__var__var__19__y__2633__2635__2707__2709__2711__2713__2715)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__27471,Vvar__1__req__27472,Vvar__2__C__27477,Vvar__3__cadd__27478,Vvar__4__cmul__27483,Vvar__5__phi__27488,Vvar__6__cdiv__27491] :
( cType___24t(Vvar__0__R__27471)
=> ( c_24__type__27611___24t(Vvar__0__R__27471,Vvar__1__req__27472,Vvar__2__C__27477,Vvar__3__cadd__27478,Vvar__4__cmul__27483,Vvar__5__phi__27488,Vvar__6__cdiv__27491,Vvar__1__req__27472)
=> ( cType___24t(Vvar__2__C__27477)
=> ( c_24__type__27661___24t(Vvar__0__R__27471,Vvar__1__req__27472,Vvar__2__C__27477,Vvar__3__cadd__27478,Vvar__4__cmul__27483,Vvar__5__phi__27488,Vvar__6__cdiv__27491,Vvar__3__cadd__27478)
=> ( c_24__type__27711___24t(Vvar__0__R__27471,Vvar__1__req__27472,Vvar__2__C__27477,Vvar__3__cadd__27478,Vvar__4__cmul__27483,Vvar__5__phi__27488,Vvar__6__cdiv__27491,Vvar__4__cmul__27483)
=> ( c_24__type__27753___24t(Vvar__0__R__27471,Vvar__1__req__27472,Vvar__2__C__27477,Vvar__3__cadd__27478,Vvar__4__cmul__27483,Vvar__5__phi__27488,Vvar__6__cdiv__27491,Vvar__5__phi__27488)
=> ( c_24__type__27803___24t(Vvar__0__R__27471,Vvar__1__req__27472,Vvar__2__C__27477,Vvar__3__cadd__27478,Vvar__4__cmul__27483,Vvar__5__phi__27488,Vvar__6__cdiv__27491,Vvar__6__cdiv__27491)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__27471,Vvar__1__req__27472,Vvar__2__C__27477,Vvar__3__cadd__27478,Vvar__4__cmul__27483,Vvar__5__phi__27488,Vvar__6__cdiv__27491)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__27523__27528__27533__27538__27543__27548__27553__27558] :
( t(Vvar__var__var__var__var__var__var__var__7__a__27523__27528__27533__27538__27543__27548__27553__27558,Vvar__2__C__27477)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__27524__27529__27534__27539__27544__27549__27554__27559] :
( t(Vvar__var__var__var__var__var__var__var__8__b__27524__27529__27534__27539__27544__27549__27554__27559,Vvar__2__C__27477)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2427866___24a9(Vvar__0__R__27471,Vvar__1__req__27472,Vvar__2__C__27477,Vvar__3__cadd__27478,Vvar__4__cmul__27483,Vvar__5__phi__27488,Vvar__6__cdiv__27491,Vvar__var__var__var__var__var__var__var__7__a__27523__27528__27533__27538__27543__27548__27553__27558,Vvar__var__var__var__var__var__var__var__8__b__27524__27529__27534__27539__27544__27549__27554__27559) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__5895,Vvar__1__rI__5896,Vvar__2__rmul__5897,Vvar__3__req__5902,Vvar__4__Cpow__5907,Vvar__5__Cp__phi__5908,Vvar__6__rpow__5911] :
( cType___24t(Vvar__0__R__5895)
=> ( t(Vvar__1__rI__5896,Vvar__0__R__5895)
=> ( c_24__type__5997___24t(Vvar__0__R__5895,Vvar__1__rI__5896,Vvar__2__rmul__5897,Vvar__3__req__5902,Vvar__4__Cpow__5907,Vvar__5__Cp__phi__5908,Vvar__6__rpow__5911,Vvar__2__rmul__5897)
=> ( c_24__type__6041___24t(Vvar__0__R__5895,Vvar__1__rI__5896,Vvar__2__rmul__5897,Vvar__3__req__5902,Vvar__4__Cpow__5907,Vvar__5__Cp__phi__5908,Vvar__6__rpow__5911,Vvar__3__req__5902)
=> ( cType___24t(Vvar__4__Cpow__5907)
=> ( c_24__type__6077___24t(Vvar__0__R__5895,Vvar__1__rI__5896,Vvar__2__rmul__5897,Vvar__3__req__5902,Vvar__4__Cpow__5907,Vvar__5__Cp__phi__5908,Vvar__6__rpow__5911,Vvar__5__Cp__phi__5908)
=> ( c_24__type__6121___24t(Vvar__0__R__5895,Vvar__1__rI__5896,Vvar__2__rmul__5897,Vvar__3__req__5902,Vvar__4__Cpow__5907,Vvar__5__Cp__phi__5908,Vvar__6__rpow__5911,Vvar__6__rpow__5911)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__5895,Vvar__1__rI__5896,Vvar__2__rmul__5897,Vvar__3__req__5902,Vvar__4__Cpow__5907,Vvar__5__Cp__phi__5908,Vvar__6__rpow__5911)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__5939__5941__5943__5945__5947__5949__5951__5953] :
( t(Vvar__var__var__var__var__var__var__var__7__r__5939__5941__5943__5945__5947__5949__5951__5953,Vvar__0__R__5895)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__5940__5942__5944__5946__5948__5950__5952__5954] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__5940__5942__5944__5946__5948__5950__5952__5954)
=> p(happ(happ(Vvar__3__req__5902,happ(happ(Vvar__6__rpow__5911,Vvar__var__var__var__var__var__var__var__7__r__5939__5941__5943__5945__5947__5949__5951__5953),happ(Vvar__5__Cp__phi__5908,Vvar__var__var__var__var__var__var__var__8__n__5940__5942__5944__5946__5948__5950__5952__5954))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__5895,Vvar__1__rI__5896,Vvar__2__rmul__5897,Vvar__var__var__var__var__var__var__var__7__r__5939__5941__5943__5945__5947__5949__5951__5953,Vvar__var__var__var__var__var__var__var__8__n__5940__5942__5944__5946__5948__5950__5952__5954))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058] :
( cType___24t(Vvar__0__R__3044)
=> ( c_24__type__3149___24t(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058,Vvar__1__radd__3045)
=> ( c_24__type__3179___24t(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058,Vvar__2__rmul__3050)
=> ( c_24__type__3203___24t(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058,Vvar__3__ropp__3055)
=> ( c_24__type__3233___24t(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058,Vvar__4__req__3058)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3263___24a5(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__3044,c_24__type__3287___24a5(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058),Vvar__4__req__3058,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__3044,Vvar__0__R__3044,Vvar__4__req__3058,Vvar__4__req__3058)),Vvar__1__radd__3045)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3320___24a5(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__3044,c_24__type__3344___24a5(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058),Vvar__4__req__3058,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__3044,Vvar__0__R__3044,Vvar__4__req__3058,Vvar__4__req__3058)),Vvar__2__rmul__3050)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3371___24a5(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__3044,Vvar__0__R__3044,Vvar__4__req__3058,Vvar__4__req__3058),Vvar__3__ropp__3055)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426] :
( cType___24t(Vvar__0__R__3374)
=> ( t(Vvar__1__rO__3375,Vvar__0__R__3374)
=> ( t(Vvar__2__rI__3376,Vvar__0__R__3374)
=> ( c_24__type__3770___24t(Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426,Vvar__3__radd__3377)
=> ( c_24__type__3983___24t(Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426,Vvar__4__rmul__3382)
=> ( c_24__type__4196___24t(Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426,Vvar__5__rsub__3387)
=> ( c_24__type__4391___24t(Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426,Vvar__6__ropp__3392)
=> ( c_24__type__4604___24t(Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426,Vvar__7__req__3395)
=> ( cType___24t(Vvar__8__C__3400)
=> ( t(Vvar__9__cO__3401,Vvar__8__C__3400)
=> ( t(Vvar__10__cI__3402,Vvar__8__C__3400)
=> ( c_24__type__4817___24t(Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426,Vvar__11__cadd__3403)
=> ( c_24__type__5030___24t(Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426,Vvar__12__cmul__3408)
=> ( c_24__type__5243___24t(Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426,Vvar__13__csub__3413)
=> ( c_24__type__5438___24t(Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426,Vvar__14__copp__3418)
=> ( c_24__type__5651___24t(Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426,Vvar__15__ceqb__3421)
=> ( c_24__type__5846___24t(Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426,Vvar__16__phi__3426)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__3374,Vvar__1__rO__3375,Vvar__2__rI__3376,Vvar__3__radd__3377,Vvar__4__rmul__3382,Vvar__5__rsub__3387,Vvar__6__ropp__3392,Vvar__7__req__3395,Vvar__8__C__3400,Vvar__9__cO__3401,Vvar__10__cI__3402,Vvar__11__cadd__3403,Vvar__12__cmul__3408,Vvar__13__csub__3413,Vvar__14__copp__3418,Vvar__15__ceqb__3421,Vvar__16__phi__3426)
=> ( p(happ(happ(Vvar__7__req__3395,happ(Vvar__16__phi__3426,Vvar__9__cO__3401)),Vvar__1__rO__3375))
& p(happ(happ(Vvar__7__req__3395,happ(Vvar__16__phi__3426,Vvar__10__cI__3402)),Vvar__2__rI__3376))
& ! [Vvar__var__var__var__var__var__var__19__x__3488__3490__3512__3514__3516__3518__3520] :
( t(Vvar__var__var__var__var__var__var__19__x__3488__3490__3512__3514__3516__3518__3520,Vvar__8__C__3400)
=> ! [Vvar__var__var__var__var__var__var__20__y__3489__3491__3513__3515__3517__3519__3521] :
( t(Vvar__var__var__var__var__var__var__20__y__3489__3491__3513__3515__3517__3519__3521,Vvar__8__C__3400)
=> p(happ(happ(Vvar__7__req__3395,happ(Vvar__16__phi__3426,happ(happ(Vvar__11__cadd__3403,Vvar__var__var__var__var__var__var__19__x__3488__3490__3512__3514__3516__3518__3520),Vvar__var__var__var__var__var__var__20__y__3489__3491__3513__3515__3517__3519__3521))),happ(happ(Vvar__3__radd__3377,happ(Vvar__16__phi__3426,Vvar__var__var__var__var__var__var__19__x__3488__3490__3512__3514__3516__3518__3520)),happ(Vvar__16__phi__3426,Vvar__var__var__var__var__var__var__20__y__3489__3491__3513__3515__3517__3519__3521)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__3493__3495__3522__3524__3526__3528__3530] :
( t(Vvar__var__var__var__var__var__var__20__x__3493__3495__3522__3524__3526__3528__3530,Vvar__8__C__3400)
=> ! [Vvar__var__var__var__var__var__var__21__y__3494__3496__3523__3525__3527__3529__3531] :
( t(Vvar__var__var__var__var__var__var__21__y__3494__3496__3523__3525__3527__3529__3531,Vvar__8__C__3400)
=> p(happ(happ(Vvar__7__req__3395,happ(Vvar__16__phi__3426,happ(happ(Vvar__13__csub__3413,Vvar__var__var__var__var__var__var__20__x__3493__3495__3522__3524__3526__3528__3530),Vvar__var__var__var__var__var__var__21__y__3494__3496__3523__3525__3527__3529__3531))),happ(happ(Vvar__5__rsub__3387,happ(Vvar__16__phi__3426,Vvar__var__var__var__var__var__var__20__x__3493__3495__3522__3524__3526__3528__3530)),happ(Vvar__16__phi__3426,Vvar__var__var__var__var__var__var__21__y__3494__3496__3523__3525__3527__3529__3531)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__3498__3500__3532__3534__3536__3538__3540] :
( t(Vvar__var__var__var__var__var__var__21__x__3498__3500__3532__3534__3536__3538__3540,Vvar__8__C__3400)
=> ! [Vvar__var__var__var__var__var__var__22__y__3499__3501__3533__3535__3537__3539__3541] :
( t(Vvar__var__var__var__var__var__var__22__y__3499__3501__3533__3535__3537__3539__3541,Vvar__8__C__3400)
=> p(happ(happ(Vvar__7__req__3395,happ(Vvar__16__phi__3426,happ(happ(Vvar__12__cmul__3408,Vvar__var__var__var__var__var__var__21__x__3498__3500__3532__3534__3536__3538__3540),Vvar__var__var__var__var__var__var__22__y__3499__3501__3533__3535__3537__3539__3541))),happ(happ(Vvar__4__rmul__3382,happ(Vvar__16__phi__3426,Vvar__var__var__var__var__var__var__21__x__3498__3500__3532__3534__3536__3538__3540)),happ(Vvar__16__phi__3426,Vvar__var__var__var__var__var__var__22__y__3499__3501__3533__3535__3537__3539__3541)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__3503__3504__3542__3543__3544__3545__3546] :
( t(Vvar__var__var__var__var__var__var__22__x__3503__3504__3542__3543__3544__3545__3546,Vvar__8__C__3400)
=> p(happ(happ(Vvar__7__req__3395,happ(Vvar__16__phi__3426,happ(Vvar__14__copp__3418,Vvar__var__var__var__var__var__var__22__x__3503__3504__3542__3543__3544__3545__3546))),happ(Vvar__6__ropp__3392,happ(Vvar__16__phi__3426,Vvar__var__var__var__var__var__var__22__x__3503__3504__3542__3543__3544__3545__3546)))) )
& ! [Vvar__var__var__var__var__var__23__x__3506__3509__3547__3550__3553__3556] :
( t(Vvar__var__var__var__var__var__23__x__3506__3509__3547__3550__3553__3556,Vvar__8__C__3400)
=> ! [Vvar__var__var__var__var__var__24__y__3507__3510__3548__3551__3554__3557] :
( t(Vvar__var__var__var__var__var__24__y__3507__3510__3548__3551__3554__3557,Vvar__8__C__3400)
=> ( happ(happ(Vvar__15__ceqb__3421,Vvar__var__var__var__var__var__23__x__3506__3509__3547__3550__3553__3556),Vvar__var__var__var__var__var__24__y__3507__3510__3548__3551__3554__3557) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__3395,happ(Vvar__16__phi__3426,Vvar__var__var__var__var__var__23__x__3506__3509__3547__3550__3553__3556)),happ(Vvar__16__phi__3426,Vvar__var__var__var__var__var__24__y__3507__3510__3548__3551__3554__3557))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__29632,Vvar__1__rO__29633,Vvar__2__rI__29634,Vvar__3__radd__29635,Vvar__4__rmul__29640,Vvar__5__req__29645,Vvar__6__C__29650,Vvar__7__cO__29651,Vvar__8__cI__29652,Vvar__9__cadd__29653,Vvar__10__cmul__29658,Vvar__11__ceqb__29663,Vvar__12__phi__29668] :
( cType___24t(Vvar__0__R__29632)
=> ( t(Vvar__1__rO__29633,Vvar__0__R__29632)
=> ( t(Vvar__2__rI__29634,Vvar__0__R__29632)
=> ( c_24__type__29885___24t(Vvar__0__R__29632,Vvar__1__rO__29633,Vvar__2__rI__29634,Vvar__3__radd__29635,Vvar__4__rmul__29640,Vvar__5__req__29645,Vvar__6__C__29650,Vvar__7__cO__29651,Vvar__8__cI__29652,Vvar__9__cadd__29653,Vvar__10__cmul__29658,Vvar__11__ceqb__29663,Vvar__12__phi__29668,Vvar__3__radd__29635)
=> ( c_24__type__30010___24t(Vvar__0__R__29632,Vvar__1__rO__29633,Vvar__2__rI__29634,Vvar__3__radd__29635,Vvar__4__rmul__29640,Vvar__5__req__29645,Vvar__6__C__29650,Vvar__7__cO__29651,Vvar__8__cI__29652,Vvar__9__cadd__29653,Vvar__10__cmul__29658,Vvar__11__ceqb__29663,Vvar__12__phi__29668,Vvar__4__rmul__29640)
=> ( c_24__type__30135___24t(Vvar__0__R__29632,Vvar__1__rO__29633,Vvar__2__rI__29634,Vvar__3__radd__29635,Vvar__4__rmul__29640,Vvar__5__req__29645,Vvar__6__C__29650,Vvar__7__cO__29651,Vvar__8__cI__29652,Vvar__9__cadd__29653,Vvar__10__cmul__29658,Vvar__11__ceqb__29663,Vvar__12__phi__29668,Vvar__5__req__29645)
=> ( cType___24t(Vvar__6__C__29650)
=> ( t(Vvar__7__cO__29651,Vvar__6__C__29650)
=> ( t(Vvar__8__cI__29652,Vvar__6__C__29650)
=> ( c_24__type__30260___24t(Vvar__0__R__29632,Vvar__1__rO__29633,Vvar__2__rI__29634,Vvar__3__radd__29635,Vvar__4__rmul__29640,Vvar__5__req__29645,Vvar__6__C__29650,Vvar__7__cO__29651,Vvar__8__cI__29652,Vvar__9__cadd__29653,Vvar__10__cmul__29658,Vvar__11__ceqb__29663,Vvar__12__phi__29668,Vvar__9__cadd__29653)
=> ( c_24__type__30385___24t(Vvar__0__R__29632,Vvar__1__rO__29633,Vvar__2__rI__29634,Vvar__3__radd__29635,Vvar__4__rmul__29640,Vvar__5__req__29645,Vvar__6__C__29650,Vvar__7__cO__29651,Vvar__8__cI__29652,Vvar__9__cadd__29653,Vvar__10__cmul__29658,Vvar__11__ceqb__29663,Vvar__12__phi__29668,Vvar__10__cmul__29658)
=> ( c_24__type__30510___24t(Vvar__0__R__29632,Vvar__1__rO__29633,Vvar__2__rI__29634,Vvar__3__radd__29635,Vvar__4__rmul__29640,Vvar__5__req__29645,Vvar__6__C__29650,Vvar__7__cO__29651,Vvar__8__cI__29652,Vvar__9__cadd__29653,Vvar__10__cmul__29658,Vvar__11__ceqb__29663,Vvar__12__phi__29668,Vvar__11__ceqb__29663)
=> ( c_24__type__30621___24t(Vvar__0__R__29632,Vvar__1__rO__29633,Vvar__2__rI__29634,Vvar__3__radd__29635,Vvar__4__rmul__29640,Vvar__5__req__29645,Vvar__6__C__29650,Vvar__7__cO__29651,Vvar__8__cI__29652,Vvar__9__cadd__29653,Vvar__10__cmul__29658,Vvar__11__ceqb__29663,Vvar__12__phi__29668,Vvar__12__phi__29668)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__29632,Vvar__1__rO__29633,Vvar__2__rI__29634,Vvar__3__radd__29635,Vvar__4__rmul__29640,Vvar__5__req__29645,Vvar__6__C__29650,Vvar__7__cO__29651,Vvar__8__cI__29652,Vvar__9__cadd__29653,Vvar__10__cmul__29658,Vvar__11__ceqb__29663,Vvar__12__phi__29668)
=> ( p(happ(happ(Vvar__5__req__29645,happ(Vvar__12__phi__29668,Vvar__7__cO__29651)),Vvar__1__rO__29633))
& p(happ(happ(Vvar__5__req__29645,happ(Vvar__12__phi__29668,Vvar__8__cI__29652)),Vvar__2__rI__29634))
& ! [Vvar__var__var__var__var__var__var__15__x__29714__29716__29730__29732__29734__29736__29738] :
( t(Vvar__var__var__var__var__var__var__15__x__29714__29716__29730__29732__29734__29736__29738,Vvar__6__C__29650)
=> ! [Vvar__var__var__var__var__var__var__16__y__29715__29717__29731__29733__29735__29737__29739] :
( t(Vvar__var__var__var__var__var__var__16__y__29715__29717__29731__29733__29735__29737__29739,Vvar__6__C__29650)
=> p(happ(happ(Vvar__5__req__29645,happ(Vvar__12__phi__29668,happ(happ(Vvar__9__cadd__29653,Vvar__var__var__var__var__var__var__15__x__29714__29716__29730__29732__29734__29736__29738),Vvar__var__var__var__var__var__var__16__y__29715__29717__29731__29733__29735__29737__29739))),happ(happ(Vvar__3__radd__29635,happ(Vvar__12__phi__29668,Vvar__var__var__var__var__var__var__15__x__29714__29716__29730__29732__29734__29736__29738)),happ(Vvar__12__phi__29668,Vvar__var__var__var__var__var__var__16__y__29715__29717__29731__29733__29735__29737__29739)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__29719__29721__29740__29742__29744__29746__29748] :
( t(Vvar__var__var__var__var__var__var__16__x__29719__29721__29740__29742__29744__29746__29748,Vvar__6__C__29650)
=> ! [Vvar__var__var__var__var__var__var__17__y__29720__29722__29741__29743__29745__29747__29749] :
( t(Vvar__var__var__var__var__var__var__17__y__29720__29722__29741__29743__29745__29747__29749,Vvar__6__C__29650)
=> p(happ(happ(Vvar__5__req__29645,happ(Vvar__12__phi__29668,happ(happ(Vvar__10__cmul__29658,Vvar__var__var__var__var__var__var__16__x__29719__29721__29740__29742__29744__29746__29748),Vvar__var__var__var__var__var__var__17__y__29720__29722__29741__29743__29745__29747__29749))),happ(happ(Vvar__4__rmul__29640,happ(Vvar__12__phi__29668,Vvar__var__var__var__var__var__var__16__x__29719__29721__29740__29742__29744__29746__29748)),happ(Vvar__12__phi__29668,Vvar__var__var__var__var__var__var__17__y__29720__29722__29741__29743__29745__29747__29749)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__29724__29727__29750__29753__29756__29759] :
( t(Vvar__var__var__var__var__var__17__x__29724__29727__29750__29753__29756__29759,Vvar__6__C__29650)
=> ! [Vvar__var__var__var__var__var__18__y__29725__29728__29751__29754__29757__29760] :
( t(Vvar__var__var__var__var__var__18__y__29725__29728__29751__29754__29757__29760,Vvar__6__C__29650)
=> ( happ(happ(Vvar__11__ceqb__29663,Vvar__var__var__var__var__var__17__x__29724__29727__29750__29753__29756__29759),Vvar__var__var__var__var__var__18__y__29725__29728__29751__29754__29757__29760) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__29645,happ(Vvar__12__phi__29668,Vvar__var__var__var__var__var__17__x__29724__29727__29750__29753__29756__29759)),happ(Vvar__12__phi__29668,Vvar__var__var__var__var__var__18__y__29725__29728__29751__29754__29757__29760))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__26905,Vvar__1__rO__26906,Vvar__2__rI__26907,Vvar__3__radd__26908,Vvar__4__rmul__26913,Vvar__5__req__26918] :
( cType___24t(Vvar__0__R__26905)
=> ( t(Vvar__1__rO__26906,Vvar__0__R__26905)
=> ( t(Vvar__2__rI__26907,Vvar__0__R__26905)
=> ( c_24__type__27073___24t(Vvar__0__R__26905,Vvar__1__rO__26906,Vvar__2__rI__26907,Vvar__3__radd__26908,Vvar__4__rmul__26913,Vvar__5__req__26918,Vvar__3__radd__26908)
=> ( c_24__type__27112___24t(Vvar__0__R__26905,Vvar__1__rO__26906,Vvar__2__rI__26907,Vvar__3__radd__26908,Vvar__4__rmul__26913,Vvar__5__req__26918,Vvar__4__rmul__26913)
=> ( c_24__type__27151___24t(Vvar__0__R__26905,Vvar__1__rO__26906,Vvar__2__rI__26907,Vvar__3__radd__26908,Vvar__4__rmul__26913,Vvar__5__req__26918,Vvar__5__req__26918)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__26905,Vvar__1__rO__26906,Vvar__2__rI__26907,Vvar__3__radd__26908,Vvar__4__rmul__26913,Vvar__5__req__26918)
=> ( ! [Vvar__var__var__var__var__var__6__n__26943__26944__26982__26983__26984__26985] :
( t(Vvar__var__var__var__var__var__6__n__26943__26944__26982__26983__26984__26985,Vvar__0__R__26905)
=> p(happ(happ(Vvar__5__req__26918,happ(happ(Vvar__3__radd__26908,Vvar__1__rO__26906),Vvar__var__var__var__var__var__6__n__26943__26944__26982__26983__26984__26985)),Vvar__var__var__var__var__var__6__n__26943__26944__26982__26983__26984__26985)) )
& ! [Vvar__var__var__var__var__7__n__26946__26948__26986__26988__26990] :
( t(Vvar__var__var__var__var__7__n__26946__26948__26986__26988__26990,Vvar__0__R__26905)
=> ! [Vvar__var__var__var__var__8__m__26947__26949__26987__26989__26991] :
( t(Vvar__var__var__var__var__8__m__26947__26949__26987__26989__26991,Vvar__0__R__26905)
=> p(happ(happ(Vvar__5__req__26918,happ(happ(Vvar__3__radd__26908,Vvar__var__var__var__var__7__n__26946__26948__26986__26988__26990),Vvar__var__var__var__var__8__m__26947__26949__26987__26989__26991)),happ(happ(Vvar__3__radd__26908,Vvar__var__var__var__var__8__m__26947__26949__26987__26989__26991),Vvar__var__var__var__var__7__n__26946__26948__26986__26988__26990))) ) )
& ! [Vvar__var__var__var__var__8__n__26951__26954__26992__26995__26998] :
( t(Vvar__var__var__var__var__8__n__26951__26954__26992__26995__26998,Vvar__0__R__26905)
=> ! [Vvar__var__var__var__var__9__m__26952__26955__26993__26996__26999] :
( t(Vvar__var__var__var__var__9__m__26952__26955__26993__26996__26999,Vvar__0__R__26905)
=> ! [Vvar__var__var__var__var__10__p__26953__26956__26994__26997__27000] :
( t(Vvar__var__var__var__var__10__p__26953__26956__26994__26997__27000,Vvar__0__R__26905)
=> p(happ(happ(Vvar__5__req__26918,happ(happ(Vvar__3__radd__26908,Vvar__var__var__var__var__8__n__26951__26954__26992__26995__26998),happ(happ(Vvar__3__radd__26908,Vvar__var__var__var__var__9__m__26952__26955__26993__26996__26999),Vvar__var__var__var__var__10__p__26953__26956__26994__26997__27000))),happ(happ(Vvar__3__radd__26908,happ(happ(Vvar__3__radd__26908,Vvar__var__var__var__var__8__n__26951__26954__26992__26995__26998),Vvar__var__var__var__var__9__m__26952__26955__26993__26996__26999)),Vvar__var__var__var__var__10__p__26953__26956__26994__26997__27000))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__26958__26959__27001__27002__27003__27004] :
( t(Vvar__var__var__var__var__var__9__n__26958__26959__27001__27002__27003__27004,Vvar__0__R__26905)
=> p(happ(happ(Vvar__5__req__26918,happ(happ(Vvar__4__rmul__26913,Vvar__2__rI__26907),Vvar__var__var__var__var__var__9__n__26958__26959__27001__27002__27003__27004)),Vvar__var__var__var__var__var__9__n__26958__26959__27001__27002__27003__27004)) )
& ! [Vvar__var__var__var__var__var__10__n__26961__26962__27005__27006__27007__27008] :
( t(Vvar__var__var__var__var__var__10__n__26961__26962__27005__27006__27007__27008,Vvar__0__R__26905)
=> p(happ(happ(Vvar__5__req__26918,happ(happ(Vvar__4__rmul__26913,Vvar__1__rO__26906),Vvar__var__var__var__var__var__10__n__26961__26962__27005__27006__27007__27008)),Vvar__1__rO__26906)) )
& ! [Vvar__var__var__var__var__11__n__26964__26966__27009__27011__27013] :
( t(Vvar__var__var__var__var__11__n__26964__26966__27009__27011__27013,Vvar__0__R__26905)
=> ! [Vvar__var__var__var__var__12__m__26965__26967__27010__27012__27014] :
( t(Vvar__var__var__var__var__12__m__26965__26967__27010__27012__27014,Vvar__0__R__26905)
=> p(happ(happ(Vvar__5__req__26918,happ(happ(Vvar__4__rmul__26913,Vvar__var__var__var__var__11__n__26964__26966__27009__27011__27013),Vvar__var__var__var__var__12__m__26965__26967__27010__27012__27014)),happ(happ(Vvar__4__rmul__26913,Vvar__var__var__var__var__12__m__26965__26967__27010__27012__27014),Vvar__var__var__var__var__11__n__26964__26966__27009__27011__27013))) ) )
& ! [Vvar__var__var__var__var__12__n__26969__26972__27015__27018__27021] :
( t(Vvar__var__var__var__var__12__n__26969__26972__27015__27018__27021,Vvar__0__R__26905)
=> ! [Vvar__var__var__var__var__13__m__26970__26973__27016__27019__27022] :
( t(Vvar__var__var__var__var__13__m__26970__26973__27016__27019__27022,Vvar__0__R__26905)
=> ! [Vvar__var__var__var__var__14__p__26971__26974__27017__27020__27023] :
( t(Vvar__var__var__var__var__14__p__26971__26974__27017__27020__27023,Vvar__0__R__26905)
=> p(happ(happ(Vvar__5__req__26918,happ(happ(Vvar__4__rmul__26913,Vvar__var__var__var__var__12__n__26969__26972__27015__27018__27021),happ(happ(Vvar__4__rmul__26913,Vvar__var__var__var__var__13__m__26970__26973__27016__27019__27022),Vvar__var__var__var__var__14__p__26971__26974__27017__27020__27023))),happ(happ(Vvar__4__rmul__26913,happ(happ(Vvar__4__rmul__26913,Vvar__var__var__var__var__12__n__26969__26972__27015__27018__27021),Vvar__var__var__var__var__13__m__26970__26973__27016__27019__27022)),Vvar__var__var__var__var__14__p__26971__26974__27017__27020__27023))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__26976__26979__27024__27027__27030__27033] :
( t(Vvar__var__var__var__var__var__13__n__26976__26979__27024__27027__27030__27033,Vvar__0__R__26905)
=> ! [Vvar__var__var__var__var__var__14__m__26977__26980__27025__27028__27031__27034] :
( t(Vvar__var__var__var__var__var__14__m__26977__26980__27025__27028__27031__27034,Vvar__0__R__26905)
=> ! [Vvar__var__var__var__var__var__15__p__26978__26981__27026__27029__27032__27035] :
( t(Vvar__var__var__var__var__var__15__p__26978__26981__27026__27029__27032__27035,Vvar__0__R__26905)
=> p(happ(happ(Vvar__5__req__26918,happ(happ(Vvar__4__rmul__26913,happ(happ(Vvar__3__radd__26908,Vvar__var__var__var__var__var__13__n__26976__26979__27024__27027__27030__27033),Vvar__var__var__var__var__var__14__m__26977__26980__27025__27028__27031__27034)),Vvar__var__var__var__var__var__15__p__26978__26981__27026__27029__27032__27035)),happ(happ(Vvar__3__radd__26908,happ(happ(Vvar__4__rmul__26913,Vvar__var__var__var__var__var__13__n__26976__26979__27024__27027__27030__27033),Vvar__var__var__var__var__var__15__p__26978__26981__27026__27029__27032__27035)),happ(happ(Vvar__4__rmul__26913,Vvar__var__var__var__var__var__14__m__26977__26980__27025__27028__27031__27034),Vvar__var__var__var__var__var__15__p__26978__26981__27026__27029__27032__27035)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__27372,Vvar__1__copp__27373,Vvar__2__ceqb__27376,Vvar__3__get__sign__27381] :
( cType___24t(Vvar__0__C__27372)
=> ( c_24__type__27428___24t(Vvar__0__C__27372,Vvar__1__copp__27373,Vvar__2__ceqb__27376,Vvar__3__get__sign__27381,Vvar__1__copp__27373)
=> ( c_24__type__27447___24t(Vvar__0__C__27372,Vvar__1__copp__27373,Vvar__2__ceqb__27376,Vvar__3__get__sign__27381,Vvar__2__ceqb__27376)
=> ( c_24__type__27461___24t(Vvar__0__C__27372,Vvar__1__copp__27373,Vvar__2__ceqb__27376,Vvar__3__get__sign__27381,Vvar__3__get__sign__27381)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__27372,Vvar__1__copp__27373,Vvar__2__ceqb__27376,Vvar__3__get__sign__27381)
=> ( ! [Vvar__var__var__var__var__var__4__c__27398__27401__27404__27407__27410__27413] :
( t(Vvar__var__var__var__var__var__4__c__27398__27401__27404__27407__27410__27413,Vvar__0__C__27372)
=> ! [Vvar__var__var__var__var__var__5__c_27__27399__27402__27405__27408__27411__27414] :
( t(Vvar__var__var__var__var__var__5__c_27__27399__27402__27405__27408__27411__27414,Vvar__0__C__27372)
=> ( happ(Vvar__3__get__sign__27381,Vvar__var__var__var__var__var__4__c__27398__27401__27404__27407__27410__27413) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__27372,Vvar__var__var__var__var__var__5__c_27__27399__27402__27405__27408__27411__27414)
=> happ(happ(Vvar__2__ceqb__27376,Vvar__var__var__var__var__var__4__c__27398__27401__27404__27407__27410__27413),happ(Vvar__1__copp__27373,Vvar__var__var__var__var__var__5__c_27__27399__27402__27405__27408__27411__27414)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__29139,Vvar__1__radd__29140,Vvar__2__rmul__29145,Vvar__3__req__29150] :
( cType___24t(Vvar__0__R__29139)
=> ( c_24__type__29225___24t(Vvar__0__R__29139,Vvar__1__radd__29140,Vvar__2__rmul__29145,Vvar__3__req__29150,Vvar__1__radd__29140)
=> ( c_24__type__29248___24t(Vvar__0__R__29139,Vvar__1__radd__29140,Vvar__2__rmul__29145,Vvar__3__req__29150,Vvar__2__rmul__29145)
=> ( c_24__type__29271___24t(Vvar__0__R__29139,Vvar__1__radd__29140,Vvar__2__rmul__29145,Vvar__3__req__29150,Vvar__3__req__29150)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__29139,Vvar__1__radd__29140,Vvar__2__rmul__29145,Vvar__3__req__29150)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__29294___24a4(Vvar__0__R__29139,Vvar__1__radd__29140,Vvar__2__rmul__29145,Vvar__3__req__29150),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29139,c_24__type__29312___24a4(Vvar__0__R__29139,Vvar__1__radd__29140,Vvar__2__rmul__29145,Vvar__3__req__29150),Vvar__3__req__29150,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29139,Vvar__0__R__29139,Vvar__3__req__29150,Vvar__3__req__29150)),Vvar__1__radd__29140)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__29338___24a4(Vvar__0__R__29139,Vvar__1__radd__29140,Vvar__2__rmul__29145,Vvar__3__req__29150),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29139,c_24__type__29356___24a4(Vvar__0__R__29139,Vvar__1__radd__29140,Vvar__2__rmul__29145,Vvar__3__req__29150),Vvar__3__req__29150,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__29139,Vvar__0__R__29139,Vvar__3__req__29150,Vvar__3__req__29150)),Vvar__2__rmul__29145)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_ExtLib.Core.Type.type',axiom,
! [Vvar__0__T__18,VX19] :
( cType___24t(Vvar__0__T__18)
=> ( cExtLib_2eCore_2eType_2etype___24t(Vvar__0__T__18,VX19)
=> ? [Vvar__1__equal__21] :
( c_24__type__14___24t(Vvar__0__T__18,Vvar__1__equal__21)
& ? [Vvar__2__proper__26] :
( c_24__type__8___24t(Vvar__0__T__18,Vvar__2__proper__26)
& VX19 = cExtLib_2eCore_2eType_2eBuild__type___24a3(Vvar__0__T__18,Vvar__1__equal__21,Vvar__2__proper__26) ) ) ) ) ).
fof('$_inversion_ExtLib.Core.Type.typeOk',axiom,
! [Vvar__0__T__125,Vvar__1__tT__126] :
( cType___24t(Vvar__0__T__125)
=> ( cExtLib_2eCore_2eType_2etype___24t(Vvar__0__T__125,Vvar__1__tT__126)
=> ( cExtLib_2eCore_2eType_2etypeOk___24a2(Vvar__0__T__125,Vvar__1__tT__126)
=> ( ! [Vvar__var__var__var__2__x__131__134__140__143] :
( t(Vvar__var__var__var__2__x__131__134__140__143,Vvar__0__T__125)
=> ! [Vvar__var__var__var__3__y__132__135__141__144] :
( t(Vvar__var__var__var__3__y__132__135__141__144,Vvar__0__T__125)
=> ( cExtLib_2eCore_2eType_2eequal___24a4(Vvar__0__T__125,Vvar__1__tT__126,Vvar__var__var__var__2__x__131__134__140__143,Vvar__var__var__var__3__y__132__135__141__144)
=> ( cExtLib_2eCore_2eType_2eproper___24a3(Vvar__0__T__125,Vvar__1__tT__126,Vvar__var__var__var__2__x__131__134__140__143)
& cExtLib_2eCore_2eType_2eproper___24a3(Vvar__0__T__125,Vvar__1__tT__126,Vvar__var__var__var__3__y__132__135__141__144) ) ) ) )
& cExtLib_2eStructures_2eProper_2ePReflexive___24a3(Vvar__0__T__125,cExtLib_2eCore_2eType_2eproper___24a2(Vvar__0__T__125,Vvar__1__tT__126),cExtLib_2eCore_2eType_2eequal___24a2(Vvar__0__T__125,Vvar__1__tT__126))
& cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(Vvar__0__T__125,cExtLib_2eCore_2eType_2eequal___24a2(Vvar__0__T__125,Vvar__1__tT__126))
& cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(Vvar__0__T__125,cExtLib_2eCore_2eType_2eequal___24a2(Vvar__0__T__125,Vvar__1__tT__126))
& p(c_24True) ) ) ) ) ).
fof('$_lam_20450',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__20450___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_20458',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__20458___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_20466',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__20466___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_20474',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__20474___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_21925',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__21925___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_21933',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__21933___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('$_lam_21941',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__21941___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_21949',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__21949___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('$_lam_28137',axiom,
! [Vv__CANONICAL__0] : c_24__lam__28137___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eN ).
fof('$_lam_28138',axiom,
! [Vv__CANONICAL__0] : c_24__lam__28138___24a1(Vv__CANONICAL__0) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble ).
fof('$_lam_28142',axiom,
! [Vv__CANONICAL__0] : c_24__lam__28142___24a1(Vv__CANONICAL__0) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2 ).
fof('$_lam_28659',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__28659___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__28660] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28660)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28660)
& c_24__lam__28659___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__28660) ) ) ) ).
fof('$_lam_28666',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__28666___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__28667] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28667)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28667)
& c_24__lam__28666___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__28667) ) ) ) ).
fof('$_lam_28670',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__28670___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__28671] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28671)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28671)
& c_24__lam__28670___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_lam_29388',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__29388___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_321',axiom,
! [Vv__CANONICAL__0] : c_24__lam__321___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_lam_35031',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__35031___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
& p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_lam_35035',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__35035___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1))
& p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0)) ) ) ).
fof('$_lam_35284',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__35284___24a1(Vv__CANONICAL__0)
<=> p(c_24True) ) ).
fof('$_lam_35768',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__35768___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_35775',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__35775___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ).
fof('$_lam_35782',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__35782___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ).
fof('$_lam_45270',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__45270___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_45277',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__45277___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ).
fof('$_lam_45284',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__45284___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ).
fof('$_prop_11684',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__11684___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_28352',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__28352___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_45121',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__45121___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_45122',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__45122___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_type_10153',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__10154] :
( c_24__type__10153___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__10154)
<=> ! [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__10154,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_1030',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1031] :
( c_24__type__1030___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1031)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__1031,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_10499',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__10500] :
( c_24__type__10499___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__10500)
<=> ! [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__10500,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_105',axiom,
! [Vvar__106] :
( c_24__type__105___24t(Vvar__106)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cExtLib_2eCore_2eType_2etype___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__106,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_10822',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__10823] :
( c_24__type__10822___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__10823)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__10823,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_11145',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__11146] :
( c_24__type__11145___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__11146)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__11146,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_1123',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__1124] :
( c_24__type__1123___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__1124)
<=> ! [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__1124,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_1132',axiom,
! [Vv__CANONICAL__0,Vvar__1133] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vvar__1133)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1133,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1141',axiom,
! [Vv__CANONICAL__0,Vvar__1142] :
( c_24__type__1141___24t(Vv__CANONICAL__0,Vvar__1142)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__1142,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_11491',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__11492] :
( c_24__type__11491___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__11492)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__11492,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11568',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11569] :
( c_24__type__11568___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11569)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__11569,Vv__CANONICAL__2)) ) ) ).
fof('$_type_11572',axiom,
! [Vvar__11573] :
( c_24__type__11572___24t(Vvar__11573)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__11573,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11590',axiom,
! [Vvar__11591] :
( c_24__type__11590___24t(Vvar__11591)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8___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__11591,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_11603',axiom,
! [Vvar__11604] :
( c_24__type__11603___24t(Vvar__11604)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__11604,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11626',axiom,
! [Vvar__11627] :
( c_24__type__11626___24t(Vvar__11627)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__11627,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_11631',axiom,
! [Vvar__11632] :
( c_24__type__11631___24t(Vvar__11632)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__11632,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_11644',axiom,
! [Vvar__11645] :
( c_24__type__11644___24t(Vvar__11645)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__11645,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11664',axiom,
! [Vvar__11665] :
( c_24__type__11664___24t(Vvar__11665)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__11665,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11697',axiom,
! [Vvar__11698] :
( c_24__type__11697___24t(Vvar__11698)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__11699___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__11699___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__11698,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11699',axiom,
! [Vvar__11700] :
( c_24__type__11699___24t(Vvar__11700)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__11700,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11710',axiom,
! [Vvar__11711] :
( c_24__type__11710___24t(Vvar__11711)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__11711,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11750',axiom,
! [Vvar__11751] :
( c_24__type__11750___24t(Vvar__11751)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__11751,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11800',axiom,
! [Vvar__11801] :
( c_24__type__11800___24t(Vvar__11801)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__11801,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11817',axiom,
! [Vvar__11818] :
( c_24__type__11817___24t(Vvar__11818)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__11818,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11976',axiom,
! [Vvar__11977] :
( c_24__type__11976___24t(Vvar__11977)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__11977,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11988',axiom,
! [Vvar__11989] :
( c_24__type__11988___24t(Vvar__11989)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__11989,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11993',axiom,
! [Vv__CANONICAL__0,Vvar__11994] :
( c_24__type__11993___24t(Vv__CANONICAL__0,Vvar__11994)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__11994,Vv__CANONICAL__1)) ) ) ).
fof('$_type_12006',axiom,
! [Vvar__12007] :
( c_24__type__12006___24t(Vvar__12007)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12008___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__12013___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__12007,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_12008',axiom,
! [Vvar__12009] :
( c_24__type__12008___24t(Vvar__12009)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__12009,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12013',axiom,
! [Vv__CANONICAL__0,Vvar__12014] :
( c_24__type__12013___24t(Vv__CANONICAL__0,Vvar__12014)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__12014,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_12030',axiom,
! [Vvar__12031] :
( c_24__type__12030___24t(Vvar__12031)
<=> ! [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__12031,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12032',axiom,
! [Vvar__12033] :
( c_24__type__12032___24t(Vvar__12033)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__12033,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12056',axiom,
! [Vvar__12057] :
( c_24__type__12056___24t(Vvar__12057)
<=> ! [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__12057,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_12068',axiom,
! [Vvar__12069] :
( c_24__type__12068___24t(Vvar__12069)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__12069,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_12080',axiom,
! [Vvar__12081] :
( c_24__type__12080___24t(Vvar__12081)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__12081,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_12082',axiom,
! [Vvar__12083] :
( c_24__type__12082___24t(Vvar__12083)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__12083,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12087',axiom,
! [Vvar__12088] :
( c_24__type__12087___24t(Vvar__12088)
<=> ! [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__12088,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12099',axiom,
! [Vvar__12100] :
( c_24__type__12099___24t(Vvar__12100)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__12100,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12101',axiom,
! [Vvar__12102] :
( c_24__type__12101___24t(Vvar__12102)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__12102,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12235',axiom,
! [Vv__CANONICAL__0,Vvar__12236] :
( c_24__type__12235___24t(Vv__CANONICAL__0,Vvar__12236)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__12236,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_12248',axiom,
! [Vvar__12249] :
( c_24__type__12248___24t(Vvar__12249)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__12249,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_12423',axiom,
! [Vvar__12424] :
( c_24__type__12423___24t(Vvar__12424)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__12424,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12426',axiom,
! [Vvar__12427] :
( c_24__type__12426___24t(Vvar__12427)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__12427,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12431',axiom,
! [Vvar__12432] :
( c_24__type__12431___24t(Vvar__12432)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__12432,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12440',axiom,
! [Vvar__12441] :
( c_24__type__12440___24t(Vvar__12441)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__12441,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12445',axiom,
! [Vvar__12446] :
( c_24__type__12445___24t(Vvar__12446)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__12446,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12495',axiom,
! [Vvar__12496] :
( c_24__type__12495___24t(Vvar__12496)
<=> ! [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__12496,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12500',axiom,
! [Vvar__12501] :
( c_24__type__12500___24t(Vvar__12501)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__12501,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12508',axiom,
! [Vvar__12509] :
( c_24__type__12508___24t(Vvar__12509)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__12509,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1348',axiom,
! [Vvar__1349] :
( c_24__type__1348___24t(Vvar__1349)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1141___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__1365___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1370___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1379___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__1349,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1365',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1366] :
( c_24__type__1365___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1366)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__1366,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_1370',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1371] :
( c_24__type__1370___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1371)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__1371,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_1379',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1380] :
( c_24__type__1379___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1380)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__1380,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_14',axiom,
! [Vv__CANONICAL__0,Vvar__15] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vvar__15)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__15,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_15543',axiom,
! [Vvar__15544] :
( c_24__type__15543___24t(Vvar__15544)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(Vvar__15544,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15546',axiom,
! [Vvar__15547] :
( c_24__type__15546___24t(Vvar__15547)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__15547,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15549',axiom,
! [Vvar__15550] :
( c_24__type__15549___24t(Vvar__15550)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__15550,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15554',axiom,
! [Vvar__15555] :
( c_24__type__15554___24t(Vvar__15555)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__15555,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_15563',axiom,
! [Vvar__15564] :
( c_24__type__15563___24t(Vvar__15564)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__15564,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15572',axiom,
! [Vvar__15573] :
( c_24__type__15572___24t(Vvar__15573)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__15573,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_15859',axiom,
! [Vvar__15860] :
( c_24__type__15859___24t(Vvar__15860)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1141___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1141___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__1365___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1370___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__1379___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__9,Vv__CANONICAL__15)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__15860,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_16',axiom,
! [Vvar__17] :
( c_24__type__16___24t(Vvar__17)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__17,Vv__CANONICAL__0)) ) ) ).
fof('$_type_16149',axiom,
! [Vvar__16150] :
( c_24__type__16149___24t(Vvar__16150)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1141___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__1365___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1370___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1379___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__16150,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_175',axiom,
! [Vvar__176] :
( c_24__type__175___24t(Vvar__176)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__176,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17597',axiom,
! [Vvar__17598] :
( c_24__type__17597___24t(Vvar__17598)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__17602___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__17598,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_17602',axiom,
! [Vv__CANONICAL__0,Vvar__17603] :
( c_24__type__17602___24t(Vv__CANONICAL__0,Vvar__17603)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__17603,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_18021',axiom,
! [Vvar__18022] :
( c_24__type__18021___24t(Vvar__18022)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1132___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__18022,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_18062',axiom,
! [Vvar__18063] :
( c_24__type__18062___24t(Vvar__18063)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__18063,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_18113',axiom,
! [Vvar__18114] :
( c_24__type__18113___24t(Vvar__18114)
<=> ! [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__18114,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_18138',axiom,
! [Vvar__18139] :
( c_24__type__18138___24t(Vvar__18139)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__18139,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_18152',axiom,
! [Vvar__18153] :
( c_24__type__18152___24t(Vvar__18153)
<=> ! [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__18153,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18599',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18600] :
( c_24__type__18599___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18600)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18600,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18700',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__18701] :
( c_24__type__18700___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__18701)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18701,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18801',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18802] :
( c_24__type__18801___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18802)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18802,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18891',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__18892] :
( c_24__type__18891___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__18892)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__18892,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_18992',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18993] :
( c_24__type__18992___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18993)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__18993,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_19093',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__19094] :
( c_24__type__19093___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__19094)
<=> ! [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__19094,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_19194',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19195] :
( c_24__type__19194___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19195)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__19195,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_1938',axiom,
! [Vv__CANONICAL__0,Vvar__1939] :
( c_24__type__1938___24t(Vv__CANONICAL__0,Vvar__1939)
<=> ! [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__1939,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_19584',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__19585] :
( c_24__type__19584___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__19585)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__19585,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_19603',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__19604] :
( c_24__type__19603___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__19604)
<=> ! [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__19604,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_19623',axiom,
! [Vvar__19624] :
( c_24__type__19623___24t(Vvar__19624)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__19624,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_19726',axiom,
! [Vvar__19727] :
( c_24__type__19726___24t(Vvar__19727)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14___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)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__19727,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_19757',axiom,
! [Vvar__19758] :
( c_24__type__19757___24t(Vvar__19758)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__19758,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_19788',axiom,
! [Vvar__19789] :
( c_24__type__19788___24t(Vvar__19789)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14___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)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__19789,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_19859',axiom,
! [Vvar__19860] :
( c_24__type__19859___24t(Vvar__19860)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__19860,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1986',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1987] :
( c_24__type__1986___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1987)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__1987,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_19885',axiom,
! [Vvar__19886] :
( c_24__type__19885___24t(Vvar__19886)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__19886,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2000',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2001] :
( c_24__type__2000___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2001)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__2001,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_2007',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2008] :
( c_24__type__2007___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2008)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__2008,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_20200',axiom,
! [Vvar__20201] :
( c_24__type__20200___24t(Vvar__20201)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1938___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)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__20201,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_20432',axiom,
! [Vvar__20433] :
( c_24__type__20432___24t(Vvar__20433)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1365___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__3,Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__20433,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_20517',axiom,
! [Vvar__20518] :
( c_24__type__20517___24t(Vvar__20518)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__20518,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_20809',axiom,
! [Vvar__20810] :
( c_24__type__20809___24t(Vvar__20810)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__20810,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20828',axiom,
! [Vvar__20829] :
( c_24__type__20828___24t(Vvar__20829)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__20829,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20830',axiom,
! [Vvar__20831] :
( c_24__type__20830___24t(Vvar__20831)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(Vvar__20831,Vv__CANONICAL__0)) ) ) ).
fof('$_type_21986',axiom,
! [Vvar__21987] :
( c_24__type__21986___24t(Vvar__21987)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__21987,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_22115',axiom,
! [Vvar__22116] :
( c_24__type__22115___24t(Vvar__22116)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1141___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1365___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1370___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__1379___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__7,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__5,Vv__CANONICAL__11)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__22116,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_2243',axiom,
! [Vvar__2244] :
( c_24__type__2243___24t(Vvar__2244)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__2244,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2246',axiom,
! [Vvar__2247] :
( c_24__type__2246___24t(Vvar__2247)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__2247,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2249',axiom,
! [Vvar__2250] :
( c_24__type__2249___24t(Vvar__2250)
<=> ! [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__2250,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2254',axiom,
! [Vvar__2255] :
( c_24__type__2254___24t(Vvar__2255)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2255,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2263',axiom,
! [Vvar__2264] :
( c_24__type__2263___24t(Vvar__2264)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__2264,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2268',axiom,
! [Vvar__2269] :
( c_24__type__2268___24t(Vvar__2269)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2269,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23180',axiom,
! [Vvar__23181] :
( c_24__type__23180___24t(Vvar__23181)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1141___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__6133___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__6140___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__23202___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__11)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__23181,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_23202',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23203] :
( c_24__type__23202___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23203)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__2)
=> t(happ(Vvar__23203,Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ).
fof('$_type_23496',axiom,
! [Vvar__23497] :
( c_24__type__23496___24t(Vvar__23497)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__23497,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23625',axiom,
! [Vvar__23626] :
( c_24__type__23625___24t(Vvar__23626)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1938___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__23626,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2483',axiom,
! [Vvar__2484] :
( c_24__type__2483___24t(Vvar__2484)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1141___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1365___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__1370___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1379___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__2484,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_2523',axiom,
! [Vvar__2524] :
( c_24__type__2523___24t(Vvar__2524)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__2524,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_26894',axiom,
! [Vvar__26895] :
( c_24__type__26894___24t(Vvar__26895)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1132___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__26895,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_27073',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27074] :
( c_24__type__27073___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27074)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27074,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27112',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27113] :
( c_24__type__27112___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27113)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27113,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27151',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27152] :
( c_24__type__27151___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27152)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__27152,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_27428',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27429] :
( c_24__type__27428___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27429)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__27429,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_27447',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27448] :
( c_24__type__27447___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27448)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__27448,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_27461',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27462] :
( c_24__type__27461___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27462)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__27462,Vv__CANONICAL__4)) ) ) ).
fof('$_type_27611',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27612] :
( c_24__type__27611___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27612)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__27612,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_27661',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27662] :
( c_24__type__27661___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27662)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__27662,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_27711',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27712] :
( c_24__type__27711___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27712)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__27712,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_27753',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27754] :
( c_24__type__27753___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27754)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__27754,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_2777',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__2778] :
( c_24__type__2777___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__2778)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2778,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27803',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27804] :
( c_24__type__27803___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27804)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__27804,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_27879',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27880] :
( c_24__type__27879___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27880)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__27880,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_27887',axiom,
! [Vvar__27888] :
( c_24__type__27887___24t(Vvar__27888)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27888,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27945',axiom,
! [Vvar__27946] :
( c_24__type__27945___24t(Vvar__27946)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__27946,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_28063',axiom,
! [Vvar__28064] :
( c_24__type__28063___24t(Vvar__28064)
<=> ! [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__28064,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28075',axiom,
! [Vvar__28076] :
( c_24__type__28075___24t(Vvar__28076)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__28076,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28096',axiom,
! [Vvar__28097] :
( c_24__type__28096___24t(Vvar__28097)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__28097,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28101',axiom,
! [Vvar__28102] :
( c_24__type__28101___24t(Vvar__28102)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__28102,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28124',axiom,
! [Vvar__28125] :
( c_24__type__28124___24t(Vvar__28125)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,happ(happ(Vvar__28125,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28140',axiom,
! [Vvar__28141] :
( c_24__type__28140___24t(Vvar__28141)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__28141,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28147',axiom,
! [Vvar__28148] :
( c_24__type__28147___24t(Vvar__28148)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__28148,Vv__CANONICAL__0)) ) ) ).
fof('$_type_282',axiom,
! [Vvar__283] :
( c_24__type__282___24t(Vvar__283)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__283,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28336',axiom,
! [Vvar__28337] :
( c_24__type__28336___24t(Vvar__28337)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__11750___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__28341___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__28337,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_28341',axiom,
! [Vv__CANONICAL__0,Vvar__28342] :
( c_24__type__28341___24t(Vv__CANONICAL__0,Vvar__28342)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__28342,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_2840',axiom,
! [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__2841] :
( c_24__type__2840___24t(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__2841)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2841,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28532',axiom,
! [Vvar__28533] :
( c_24__type__28532___24t(Vvar__28533)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__28533,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_28544',axiom,
! [Vvar__28545] :
( c_24__type__28544___24t(Vvar__28545)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__28545,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28608',axiom,
! [Vvar__28609] :
( c_24__type__28608___24t(Vvar__28609)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1141___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__28609,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_28617',axiom,
! [Vvar__28618] :
( c_24__type__28617___24t(Vvar__28618)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__28618,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28641',axiom,
! [Vvar__28642] :
( c_24__type__28641___24t(Vvar__28642)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__28642,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28673',axiom,
! [Vvar__28674] :
( c_24__type__28673___24t(Vvar__28674)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__28674,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28675',axiom,
! [Vvar__28676] :
( c_24__type__28675___24t(Vvar__28676)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__28676,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28679',axiom,
! [Vvar__28680] :
( c_24__type__28679___24t(Vvar__28680)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__28680,Vv__CANONICAL__0)) ) ) ).
fof('$_type_289',axiom,
! [Vvar__290] :
( c_24__type__289___24t(Vvar__290)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__290,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29002',axiom,
! [Vvar__29003] :
( c_24__type__29002___24t(Vvar__29003)
<=> ! [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__29003,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29006',axiom,
! [Vvar__29007] :
( c_24__type__29006___24t(Vvar__29007)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__29007,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2903',axiom,
! [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__2904] :
( c_24__type__2903___24t(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__2904)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2904,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29040',axiom,
! [Vvar__29041] :
( c_24__type__29040___24t(Vvar__29041)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__29041,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29045',axiom,
! [Vvar__29046] :
( c_24__type__29045___24t(Vvar__29046)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__29046,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29049',axiom,
! [Vvar__29050] :
( c_24__type__29049___24t(Vvar__29050)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__29050,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29054',axiom,
! [Vvar__29055] :
( c_24__type__29054___24t(Vvar__29055)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__29055,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29132',axiom,
! [Vvar__29133] :
( c_24__type__29132___24t(Vvar__29133)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__29133,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29225',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29226] :
( c_24__type__29225___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29226)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29226,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29248',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29249] :
( c_24__type__29248___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29249)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29249,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29271',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29272] :
( c_24__type__29271___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29272)
<=> ! [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__29272,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_29294',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29295] :
( c_24__type__29294___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29295)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29295,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29312',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29313] :
( c_24__type__29312___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29313)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__29313,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_29338',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29339] :
( c_24__type__29338___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29339)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29339,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29356',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29357] :
( c_24__type__29356___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29357)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__29357,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_29370',axiom,
! [Vvar__29371] :
( c_24__type__29370___24t(Vvar__29371)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__29371,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29400',axiom,
! [Vvar__29401] :
( c_24__type__29400___24t(Vvar__29401)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__29405___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__29401,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_29405',axiom,
! [Vv__CANONICAL__0,Vvar__29406] :
( c_24__type__29405___24t(Vv__CANONICAL__0,Vvar__29406)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29406,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29489',axiom,
! [Vvar__29490] :
( c_24__type__29489___24t(Vvar__29490)
<=> ! [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__29490,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2957',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__2958] :
( c_24__type__2957___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__2958)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__2958,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_29630',axiom,
! [Vvar__29631] :
( c_24__type__29630___24t(Vvar__29631)
<=> ! [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__29631,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29885',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__29886] :
( c_24__type__29885___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__29886)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29886,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30010',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__30011] :
( c_24__type__30010___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__30011)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30011,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30135',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__30136] :
( c_24__type__30135___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__30136)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30136,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_3020',axiom,
! [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__3021] :
( c_24__type__3020___24t(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__3021)
<=> ! [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__3021,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_30260',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__30261] :
( c_24__type__30260___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__30261)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__30261,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_30385',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__30386] :
( c_24__type__30385___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__30386)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__30386,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_30510',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__30511] :
( c_24__type__30510___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__30511)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__30511,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_30621',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__30622] :
( c_24__type__30621___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__30622)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__30622,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_30665',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30666] :
( c_24__type__30665___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30666)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30666,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_30678',axiom,
! [Vvar__30679] :
( c_24__type__30678___24t(Vvar__30679)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1141___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(happ(happ(Vvar__30679,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ) ) ).
fof('$_type_30688',axiom,
! [Vvar__30689] :
( c_24__type__30688___24t(Vvar__30689)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__30689,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30694',axiom,
! [Vvar__30695] :
( c_24__type__30694___24t(Vvar__30695)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eStrings_2eAscii_2eascii___24t(happ(Vvar__30695,Vv__CANONICAL__0)) ) ) ).
fof('$_type_307',axiom,
! [Vvar__308] :
( c_24__type__307___24t(Vvar__308)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__308,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30785',axiom,
! [Vvar__30786] :
( c_24__type__30785___24t(Vvar__30786)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__30786,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30789',axiom,
! [Vv__CANONICAL__0,Vvar__30790] :
( c_24__type__30789___24t(Vv__CANONICAL__0,Vvar__30790)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__30790,Vv__CANONICAL__1)) ) ) ).
fof('$_type_30799',axiom,
! [Vvar__30800] :
( c_24__type__30799___24t(Vvar__30800)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__11750___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__30802___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__30800,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30802',axiom,
! [Vv__CANONICAL__0,Vvar__30803] :
( c_24__type__30802___24t(Vv__CANONICAL__0,Vvar__30803)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__30803,Vv__CANONICAL__1),happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vv__CANONICAL__1))) ) ) ).
fof('$_type_30811',axiom,
! [Vvar__30812] :
( c_24__type__30811___24t(Vvar__30812)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30812,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30818',axiom,
! [Vvar__30819] :
( c_24__type__30818___24t(Vvar__30819)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__30819,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30823',axiom,
! [Vvar__30824] :
( c_24__type__30823___24t(Vvar__30824)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__30824,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30826',axiom,
! [Vv__CANONICAL__0,Vvar__30827] :
( c_24__type__30826___24t(Vv__CANONICAL__0,Vvar__30827)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__30827,Vv__CANONICAL__1)) ) ) ).
fof('$_type_30854',axiom,
! [Vvar__30855] :
( c_24__type__30854___24t(Vvar__30855)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14___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)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__5)
=> cType___24t(happ(happ(happ(happ(happ(happ(Vvar__30855,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_30869',axiom,
! [Vvar__30870] :
( c_24__type__30869___24t(Vvar__30870)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2euint___24t(happ(Vvar__30870,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30871',axiom,
! [Vvar__30872] :
( c_24__type__30871___24t(Vvar__30872)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__30872,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30960',axiom,
! [Vvar__30961] :
( c_24__type__30960___24t(Vvar__30961)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__30961,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3149',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3150] :
( c_24__type__3149___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3150)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3150,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_317',axiom,
! [Vvar__318] :
( c_24__type__317___24t(Vvar__318)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__319___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__319___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__318,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3179',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3180] :
( c_24__type__3179___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3180)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3180,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_319',axiom,
! [Vvar__320] :
( c_24__type__319___24t(Vvar__320)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__320,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3203',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3204] :
( c_24__type__3203___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3204)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__3204,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_32256',axiom,
! [Vvar__32257] :
( c_24__type__32256___24t(Vvar__32257)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1141___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__32257,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_3233',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3234] :
( c_24__type__3233___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3234)
<=> ! [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__3234,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_32379',axiom,
! [Vvar__32380] :
( c_24__type__32379___24t(Vvar__32380)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1132___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1141___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vv__CANONICAL__7)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__32380,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ).
fof('$_type_32416',axiom,
! [Vvar__32417] :
( c_24__type__32416___24t(Vvar__32417)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1938___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__32417,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_32437',axiom,
! [Vvar__32438] :
( c_24__type__32437___24t(Vvar__32438)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__32438,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_32446',axiom,
! [Vvar__32447] :
( c_24__type__32446___24t(Vvar__32447)
<=> ! [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__32447,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32463',axiom,
! [Vvar__32464] :
( c_24__type__32463___24t(Vvar__32464)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32467___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__32464,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_32467',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32468] :
( c_24__type__32467___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32468)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__32468,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_32479',axiom,
! [Vvar__32480] :
( c_24__type__32479___24t(Vvar__32480)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__32480,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3263',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3264] :
( c_24__type__3263___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3264)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3264,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32682',axiom,
! [Vvar__32683] :
( c_24__type__32682___24t(Vvar__32683)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__32683,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32685',axiom,
! [Vvar__32686] :
( c_24__type__32685___24t(Vvar__32686)
<=> ! [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__32686,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32692',axiom,
! [Vvar__32693] :
( c_24__type__32692___24t(Vvar__32693)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__32693,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32833',axiom,
! [Vvar__32834] :
( c_24__type__32833___24t(Vvar__32834)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__32834,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_32841',axiom,
! [Vvar__32842] :
( c_24__type__32841___24t(Vvar__32842)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__32842,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3287',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3288] :
( c_24__type__3287___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3288)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__3288,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_3320',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3321] :
( c_24__type__3320___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3321)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3321,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_334',axiom,
! [Vvar__335] :
( c_24__type__334___24t(Vvar__335)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__335,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3344',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3345] :
( c_24__type__3344___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3345)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__3345,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_337',axiom,
! [Vvar__338] :
( c_24__type__337___24t(Vvar__338)
<=> ! [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__338,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3371',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3372] :
( c_24__type__3371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3372)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__3372,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_34067',axiom,
! [Vvar__34068] :
( c_24__type__34067___24t(Vvar__34068)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__34068,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_34072',axiom,
! [Vvar__34073] :
( c_24__type__34072___24t(Vvar__34073)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__34073,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_342',axiom,
! [Vvar__343] :
( c_24__type__342___24t(Vvar__343)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__343,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34599',axiom,
! [Vvar__34600] :
( c_24__type__34599___24t(Vvar__34600)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__34600,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34607',axiom,
! [Vvar__34608] :
( c_24__type__34607___24t(Vvar__34608)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),happ(happ(happ(happ(Vvar__34608,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_34618',axiom,
! [Vvar__34619] :
( c_24__type__34618___24t(Vvar__34619)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__34619,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_349',axiom,
! [Vvar__350] :
( c_24__type__349___24t(Vvar__350)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__350,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35068',axiom,
! [Vvar__35069] :
( c_24__type__35068___24t(Vvar__35069)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__35069,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35102',axiom,
! [Vvar__35103] :
( c_24__type__35102___24t(Vvar__35103)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__35103,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35122',axiom,
! [Vvar__35123] :
( c_24__type__35122___24t(Vvar__35123)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__35123,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35192',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35193] :
( c_24__type__35192___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35193)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__35193,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_35198',axiom,
! [Vvar__35199] :
( c_24__type__35198___24t(Vvar__35199)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__35199,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35201',axiom,
! [Vvar__35202] :
( c_24__type__35201___24t(Vvar__35202)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__35202,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35262',axiom,
! [Vvar__35263] :
( c_24__type__35262___24t(Vvar__35263)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__35263,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35795',axiom,
! [Vvar__35796] :
( c_24__type__35795___24t(Vvar__35796)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__11750___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__0))
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__2,Vv__CANONICAL__1))
=> t(happ(happ(happ(happ(happ(Vvar__35796,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ) ) ) ) ).
fof('$_type_360',axiom,
! [Vvar__361] :
( c_24__type__360___24t(Vvar__361)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__361,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3770',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__3771] :
( c_24__type__3770___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__3771)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3771,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3983',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3984] :
( c_24__type__3983___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3984)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3984,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4196',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__4197] :
( c_24__type__4196___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__4197)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4197,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4391',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4392] :
( c_24__type__4391___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4392)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__4392,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_45119',axiom,
! [Vvar__45120] :
( c_24__type__45119___24t(Vvar__45120)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__45121___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__45122___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__45120,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45297',axiom,
! [Vvar__45298] :
( c_24__type__45297___24t(Vvar__45298)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__11750___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__0))
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__2,Vv__CANONICAL__1))
=> t(happ(happ(happ(happ(happ(Vvar__45298,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ) ) ) ) ).
fof('$_type_4604',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__4605] :
( c_24__type__4604___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__4605)
<=> ! [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__4605,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_4817',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4818] :
( c_24__type__4817___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4818)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__4818,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_5',axiom,
! [Vvar__6] :
( c_24__type__5___24t(Vvar__6)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8___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__6,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5030',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__5031] :
( c_24__type__5030___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__5031)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__5031,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_5243',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__5244] :
( c_24__type__5243___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__5244)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__5244,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_5438',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__5439] :
( c_24__type__5438___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__5439)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__5439,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_5651',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__5652] :
( c_24__type__5651___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__5652)
<=> ! [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__5652,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_5846',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__5847] :
( c_24__type__5846___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__5847)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__5847,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_587',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__588] :
( c_24__type__587___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__588)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__588,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5997',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__5998] :
( c_24__type__5997___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__5998)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5998,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6041',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__6042] :
( c_24__type__6041___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__6042)
<=> ! [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__6042,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_6077',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__6078] :
( c_24__type__6077___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__6078)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__6078,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_6121',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__6122] :
( c_24__type__6121___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__6122)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__6122,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6133',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6134] :
( c_24__type__6133___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6134)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__6134,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_6140',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6141] :
( c_24__type__6140___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6141)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__6141,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6161',axiom,
! [Vvar__6162] :
( c_24__type__6161___24t(Vvar__6162)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__6162,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6176',axiom,
! [Vvar__6177] :
( c_24__type__6176___24t(Vvar__6177)
<=> ! [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__6177,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6178',axiom,
! [Vvar__6179] :
( c_24__type__6178___24t(Vvar__6179)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__6179,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6203',axiom,
! [Vvar__6204] :
( c_24__type__6203___24t(Vvar__6204)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__6204,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6739',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__6740] :
( c_24__type__6739___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__6740)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6740,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_680',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__681] :
( c_24__type__680___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__681)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__681,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7085',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__7086] :
( c_24__type__7085___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__7086)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7086,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7431',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__7432] :
( c_24__type__7431___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__7432)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7432,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_773',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__774] :
( c_24__type__773___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__774)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__774,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7754',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__7755] :
( c_24__type__7754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__7755)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__7755,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_8',axiom,
! [Vv__CANONICAL__0,Vvar__9] :
( c_24__type__8___24t(Vv__CANONICAL__0,Vvar__9)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__9,Vv__CANONICAL__1)) ) ) ).
fof('$_type_81',axiom,
! [Vvar__82] :
( c_24__type__81___24t(Vvar__82)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cExtLib_2eCore_2eType_2etype___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__82,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8100',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__8101] :
( c_24__type__8100___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__8101)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__8101,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_8446',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__8447] :
( c_24__type__8446___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__8447)
<=> ! [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__8447,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_855',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__856] :
( c_24__type__855___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__856)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__856,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_8792',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__8793] :
( c_24__type__8792___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__8793)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__8793,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_9138',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__9139] :
( c_24__type__9138___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__9139)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__9139,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_948',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__949] :
( c_24__type__948___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__949)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__949,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9484',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__9485] :
( c_24__type__9484___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__9485)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__9485,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_9807',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__9808] :
( c_24__type__9807___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__9808)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__9808,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__6176___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__360___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
c_24__type__12008___24t(cCoq_2eBool_2eBvector_2eBvector) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Byte.x00',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex00) ).
fof('$_typeof_Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex01) ).
fof('$_typeof_Coq.Init.Byte.x02',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex02) ).
fof('$_typeof_Coq.Init.Byte.x03',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex03) ).
fof('$_typeof_Coq.Init.Byte.x04',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex04) ).
fof('$_typeof_Coq.Init.Byte.x05',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex05) ).
fof('$_typeof_Coq.Init.Byte.x06',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex06) ).
fof('$_typeof_Coq.Init.Byte.x07',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex07) ).
fof('$_typeof_Coq.Init.Byte.x08',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex08) ).
fof('$_typeof_Coq.Init.Byte.x09',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex09) ).
fof('$_typeof_Coq.Init.Byte.x0a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0a) ).
fof('$_typeof_Coq.Init.Byte.x0b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0b) ).
fof('$_typeof_Coq.Init.Byte.x0c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0c) ).
fof('$_typeof_Coq.Init.Byte.x0d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0d) ).
fof('$_typeof_Coq.Init.Byte.x0e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0e) ).
fof('$_typeof_Coq.Init.Byte.x0f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0f) ).
fof('$_typeof_Coq.Init.Byte.x10',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex10) ).
fof('$_typeof_Coq.Init.Byte.x11',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex11) ).
fof('$_typeof_Coq.Init.Byte.x12',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex12) ).
fof('$_typeof_Coq.Init.Byte.x13',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex13) ).
fof('$_typeof_Coq.Init.Byte.x14',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex14) ).
fof('$_typeof_Coq.Init.Byte.x15',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex15) ).
fof('$_typeof_Coq.Init.Byte.x16',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex16) ).
fof('$_typeof_Coq.Init.Byte.x17',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex17) ).
fof('$_typeof_Coq.Init.Byte.x18',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex18) ).
fof('$_typeof_Coq.Init.Byte.x19',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex19) ).
fof('$_typeof_Coq.Init.Byte.x1a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1a) ).
fof('$_typeof_Coq.Init.Byte.x1b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1b) ).
fof('$_typeof_Coq.Init.Byte.x1c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1c) ).
fof('$_typeof_Coq.Init.Byte.x1d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1d) ).
fof('$_typeof_Coq.Init.Byte.x1e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1e) ).
fof('$_typeof_Coq.Init.Byte.x1f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1f) ).
fof('$_typeof_Coq.Init.Byte.x20',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex20) ).
fof('$_typeof_Coq.Init.Byte.x21',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex21) ).
fof('$_typeof_Coq.Init.Byte.x22',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex22) ).
fof('$_typeof_Coq.Init.Byte.x23',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex23) ).
fof('$_typeof_Coq.Init.Byte.x24',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex24) ).
fof('$_typeof_Coq.Init.Byte.x25',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex25) ).
fof('$_typeof_Coq.Init.Byte.x26',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex26) ).
fof('$_typeof_Coq.Init.Byte.x27',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex27) ).
fof('$_typeof_Coq.Init.Byte.x28',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex28) ).
fof('$_typeof_Coq.Init.Byte.x29',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex29) ).
fof('$_typeof_Coq.Init.Byte.x2a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2a) ).
fof('$_typeof_Coq.Init.Byte.x2b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2b) ).
fof('$_typeof_Coq.Init.Byte.x2c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2c) ).
fof('$_typeof_Coq.Init.Byte.x2d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2d) ).
fof('$_typeof_Coq.Init.Byte.x2e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2e) ).
fof('$_typeof_Coq.Init.Byte.x2f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2f) ).
fof('$_typeof_Coq.Init.Byte.x30',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex30) ).
fof('$_typeof_Coq.Init.Byte.x31',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex31) ).
fof('$_typeof_Coq.Init.Byte.x32',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex32) ).
fof('$_typeof_Coq.Init.Byte.x33',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex33) ).
fof('$_typeof_Coq.Init.Byte.x34',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex34) ).
fof('$_typeof_Coq.Init.Byte.x35',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex35) ).
fof('$_typeof_Coq.Init.Byte.x36',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex36) ).
fof('$_typeof_Coq.Init.Byte.x37',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex37) ).
fof('$_typeof_Coq.Init.Byte.x38',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex38) ).
fof('$_typeof_Coq.Init.Byte.x39',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex39) ).
fof('$_typeof_Coq.Init.Byte.x3a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3a) ).
fof('$_typeof_Coq.Init.Byte.x3b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3b) ).
fof('$_typeof_Coq.Init.Byte.x3c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3c) ).
fof('$_typeof_Coq.Init.Byte.x3d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3d) ).
fof('$_typeof_Coq.Init.Byte.x3e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3e) ).
fof('$_typeof_Coq.Init.Byte.x3f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3f) ).
fof('$_typeof_Coq.Init.Byte.x40',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex40) ).
fof('$_typeof_Coq.Init.Byte.x41',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex41) ).
fof('$_typeof_Coq.Init.Byte.x42',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex42) ).
fof('$_typeof_Coq.Init.Byte.x43',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex43) ).
fof('$_typeof_Coq.Init.Byte.x44',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex44) ).
fof('$_typeof_Coq.Init.Byte.x45',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex45) ).
fof('$_typeof_Coq.Init.Byte.x46',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex46) ).
fof('$_typeof_Coq.Init.Byte.x47',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex47) ).
fof('$_typeof_Coq.Init.Byte.x48',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex48) ).
fof('$_typeof_Coq.Init.Byte.x49',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex49) ).
fof('$_typeof_Coq.Init.Byte.x4a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4a) ).
fof('$_typeof_Coq.Init.Byte.x4b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4b) ).
fof('$_typeof_Coq.Init.Byte.x4c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4c) ).
fof('$_typeof_Coq.Init.Byte.x4d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4d) ).
fof('$_typeof_Coq.Init.Byte.x4e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4e) ).
fof('$_typeof_Coq.Init.Byte.x4f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4f) ).
fof('$_typeof_Coq.Init.Byte.x50',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex50) ).
fof('$_typeof_Coq.Init.Byte.x51',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex51) ).
fof('$_typeof_Coq.Init.Byte.x52',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex52) ).
fof('$_typeof_Coq.Init.Byte.x53',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex53) ).
fof('$_typeof_Coq.Init.Byte.x54',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex54) ).
fof('$_typeof_Coq.Init.Byte.x55',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex55) ).
fof('$_typeof_Coq.Init.Byte.x56',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex56) ).
fof('$_typeof_Coq.Init.Byte.x57',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex57) ).
fof('$_typeof_Coq.Init.Byte.x58',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex58) ).
fof('$_typeof_Coq.Init.Byte.x59',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex59) ).
fof('$_typeof_Coq.Init.Byte.x5a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5a) ).
fof('$_typeof_Coq.Init.Byte.x5b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5b) ).
fof('$_typeof_Coq.Init.Byte.x5c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5c) ).
fof('$_typeof_Coq.Init.Byte.x5d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5d) ).
fof('$_typeof_Coq.Init.Byte.x5e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5e) ).
fof('$_typeof_Coq.Init.Byte.x5f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5f) ).
fof('$_typeof_Coq.Init.Byte.x60',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex60) ).
fof('$_typeof_Coq.Init.Byte.x61',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex61) ).
fof('$_typeof_Coq.Init.Byte.x62',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex62) ).
fof('$_typeof_Coq.Init.Byte.x63',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex63) ).
fof('$_typeof_Coq.Init.Byte.x64',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex64) ).
fof('$_typeof_Coq.Init.Byte.x65',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex65) ).
fof('$_typeof_Coq.Init.Byte.x66',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex66) ).
fof('$_typeof_Coq.Init.Byte.x67',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex67) ).
fof('$_typeof_Coq.Init.Byte.x68',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex68) ).
fof('$_typeof_Coq.Init.Byte.x69',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex69) ).
fof('$_typeof_Coq.Init.Byte.x6a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6a) ).
fof('$_typeof_Coq.Init.Byte.x6b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6b) ).
fof('$_typeof_Coq.Init.Byte.x6c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6c) ).
fof('$_typeof_Coq.Init.Byte.x6d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6d) ).
fof('$_typeof_Coq.Init.Byte.x6e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6e) ).
fof('$_typeof_Coq.Init.Byte.x6f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6f) ).
fof('$_typeof_Coq.Init.Byte.x70',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex70) ).
fof('$_typeof_Coq.Init.Byte.x71',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex71) ).
fof('$_typeof_Coq.Init.Byte.x72',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex72) ).
fof('$_typeof_Coq.Init.Byte.x73',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex73) ).
fof('$_typeof_Coq.Init.Byte.x74',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex74) ).
fof('$_typeof_Coq.Init.Byte.x75',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex75) ).
fof('$_typeof_Coq.Init.Byte.x76',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex76) ).
fof('$_typeof_Coq.Init.Byte.x77',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex77) ).
fof('$_typeof_Coq.Init.Byte.x78',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex78) ).
fof('$_typeof_Coq.Init.Byte.x79',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex79) ).
fof('$_typeof_Coq.Init.Byte.x7a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7a) ).
fof('$_typeof_Coq.Init.Byte.x7b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7b) ).
fof('$_typeof_Coq.Init.Byte.x7c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7c) ).
fof('$_typeof_Coq.Init.Byte.x7d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7d) ).
fof('$_typeof_Coq.Init.Byte.x7e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7e) ).
fof('$_typeof_Coq.Init.Byte.x7f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7f) ).
fof('$_typeof_Coq.Init.Byte.x80',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex80) ).
fof('$_typeof_Coq.Init.Byte.x81',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex81) ).
fof('$_typeof_Coq.Init.Byte.x82',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex82) ).
fof('$_typeof_Coq.Init.Byte.x83',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex83) ).
fof('$_typeof_Coq.Init.Byte.x84',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex84) ).
fof('$_typeof_Coq.Init.Byte.x85',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex85) ).
fof('$_typeof_Coq.Init.Byte.x86',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex86) ).
fof('$_typeof_Coq.Init.Byte.x87',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex87) ).
fof('$_typeof_Coq.Init.Byte.x88',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex88) ).
fof('$_typeof_Coq.Init.Byte.x89',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex89) ).
fof('$_typeof_Coq.Init.Byte.x8a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8a) ).
fof('$_typeof_Coq.Init.Byte.x8b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8b) ).
fof('$_typeof_Coq.Init.Byte.x8c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8c) ).
fof('$_typeof_Coq.Init.Byte.x8d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8d) ).
fof('$_typeof_Coq.Init.Byte.x8e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8e) ).
fof('$_typeof_Coq.Init.Byte.x8f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8f) ).
fof('$_typeof_Coq.Init.Byte.x90',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex90) ).
fof('$_typeof_Coq.Init.Byte.x91',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex91) ).
fof('$_typeof_Coq.Init.Byte.x92',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex92) ).
fof('$_typeof_Coq.Init.Byte.x93',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex93) ).
fof('$_typeof_Coq.Init.Byte.x94',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex94) ).
fof('$_typeof_Coq.Init.Byte.x95',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex95) ).
fof('$_typeof_Coq.Init.Byte.x96',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex96) ).
fof('$_typeof_Coq.Init.Byte.x97',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex97) ).
fof('$_typeof_Coq.Init.Byte.x98',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex98) ).
fof('$_typeof_Coq.Init.Byte.x99',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex99) ).
fof('$_typeof_Coq.Init.Byte.x9a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9a) ).
fof('$_typeof_Coq.Init.Byte.x9b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9b) ).
fof('$_typeof_Coq.Init.Byte.x9c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9c) ).
fof('$_typeof_Coq.Init.Byte.x9d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9d) ).
fof('$_typeof_Coq.Init.Byte.x9e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9e) ).
fof('$_typeof_Coq.Init.Byte.x9f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9f) ).
fof('$_typeof_Coq.Init.Byte.xa0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa0) ).
fof('$_typeof_Coq.Init.Byte.xa1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa1) ).
fof('$_typeof_Coq.Init.Byte.xa2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa2) ).
fof('$_typeof_Coq.Init.Byte.xa3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa3) ).
fof('$_typeof_Coq.Init.Byte.xa4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa4) ).
fof('$_typeof_Coq.Init.Byte.xa5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa5) ).
fof('$_typeof_Coq.Init.Byte.xa6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa6) ).
fof('$_typeof_Coq.Init.Byte.xa7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa7) ).
fof('$_typeof_Coq.Init.Byte.xa8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa8) ).
fof('$_typeof_Coq.Init.Byte.xa9',axiom,
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fof('$_typeof_Coq.Init.Byte.xaa',axiom,
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fof('$_typeof_Coq.Init.Byte.xab',axiom,
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fof('$_typeof_Coq.Init.Byte.xac',axiom,
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fof('$_typeof_Coq.Init.Byte.xad',axiom,
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fof('$_typeof_Coq.Init.Byte.xae',axiom,
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fof('$_typeof_Coq.Init.Byte.xaf',axiom,
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fof('$_typeof_Coq.Init.Byte.xb0',axiom,
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fof('$_typeof_Coq.Init.Byte.xb1',axiom,
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fof('$_typeof_Coq.Init.Byte.xb2',axiom,
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fof('$_typeof_Coq.Init.Byte.xb3',axiom,
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fof('$_typeof_Coq.Init.Byte.xb4',axiom,
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fof('$_typeof_Coq.Init.Byte.xb5',axiom,
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fof('$_typeof_Coq.Init.Byte.xb6',axiom,
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fof('$_typeof_Coq.Init.Byte.xb7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb7) ).
fof('$_typeof_Coq.Init.Byte.xb8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb8) ).
fof('$_typeof_Coq.Init.Byte.xb9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb9) ).
fof('$_typeof_Coq.Init.Byte.xba',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exba) ).
fof('$_typeof_Coq.Init.Byte.xbb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbb) ).
fof('$_typeof_Coq.Init.Byte.xbc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbc) ).
fof('$_typeof_Coq.Init.Byte.xbd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbd) ).
fof('$_typeof_Coq.Init.Byte.xbe',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbe) ).
fof('$_typeof_Coq.Init.Byte.xbf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbf) ).
fof('$_typeof_Coq.Init.Byte.xc0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc0) ).
fof('$_typeof_Coq.Init.Byte.xc1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc1) ).
fof('$_typeof_Coq.Init.Byte.xc2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc2) ).
fof('$_typeof_Coq.Init.Byte.xc3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc3) ).
fof('$_typeof_Coq.Init.Byte.xc4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc4) ).
fof('$_typeof_Coq.Init.Byte.xc5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc5) ).
fof('$_typeof_Coq.Init.Byte.xc6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc6) ).
fof('$_typeof_Coq.Init.Byte.xc7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc7) ).
fof('$_typeof_Coq.Init.Byte.xc8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc8) ).
fof('$_typeof_Coq.Init.Byte.xc9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc9) ).
fof('$_typeof_Coq.Init.Byte.xca',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exca) ).
fof('$_typeof_Coq.Init.Byte.xcb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excb) ).
fof('$_typeof_Coq.Init.Byte.xcc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excc) ).
fof('$_typeof_Coq.Init.Byte.xcd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excd) ).
fof('$_typeof_Coq.Init.Byte.xce',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exce) ).
fof('$_typeof_Coq.Init.Byte.xcf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excf) ).
fof('$_typeof_Coq.Init.Byte.xd0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd0) ).
fof('$_typeof_Coq.Init.Byte.xd1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd1) ).
fof('$_typeof_Coq.Init.Byte.xd2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd2) ).
fof('$_typeof_Coq.Init.Byte.xd3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd3) ).
fof('$_typeof_Coq.Init.Byte.xd4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd4) ).
fof('$_typeof_Coq.Init.Byte.xd5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd5) ).
fof('$_typeof_Coq.Init.Byte.xd6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd6) ).
fof('$_typeof_Coq.Init.Byte.xd7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd7) ).
fof('$_typeof_Coq.Init.Byte.xd8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd8) ).
fof('$_typeof_Coq.Init.Byte.xd9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd9) ).
fof('$_typeof_Coq.Init.Byte.xda',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exda) ).
fof('$_typeof_Coq.Init.Byte.xdb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdb) ).
fof('$_typeof_Coq.Init.Byte.xdc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdc) ).
fof('$_typeof_Coq.Init.Byte.xdd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdd) ).
fof('$_typeof_Coq.Init.Byte.xde',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exde) ).
fof('$_typeof_Coq.Init.Byte.xdf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdf) ).
fof('$_typeof_Coq.Init.Byte.xe0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe0) ).
fof('$_typeof_Coq.Init.Byte.xe1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe1) ).
fof('$_typeof_Coq.Init.Byte.xe2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe2) ).
fof('$_typeof_Coq.Init.Byte.xe3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe3) ).
fof('$_typeof_Coq.Init.Byte.xe4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe4) ).
fof('$_typeof_Coq.Init.Byte.xe5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe5) ).
fof('$_typeof_Coq.Init.Byte.xe6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe6) ).
fof('$_typeof_Coq.Init.Byte.xe7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe7) ).
fof('$_typeof_Coq.Init.Byte.xe8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe8) ).
fof('$_typeof_Coq.Init.Byte.xe9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe9) ).
fof('$_typeof_Coq.Init.Byte.xea',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exea) ).
fof('$_typeof_Coq.Init.Byte.xeb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exeb) ).
fof('$_typeof_Coq.Init.Byte.xec',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exec) ).
fof('$_typeof_Coq.Init.Byte.xed',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exed) ).
fof('$_typeof_Coq.Init.Byte.xee',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exee) ).
fof('$_typeof_Coq.Init.Byte.xef',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exef) ).
fof('$_typeof_Coq.Init.Byte.xf0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf0) ).
fof('$_typeof_Coq.Init.Byte.xf1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf1) ).
fof('$_typeof_Coq.Init.Byte.xf2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf2) ).
fof('$_typeof_Coq.Init.Byte.xf3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf3) ).
fof('$_typeof_Coq.Init.Byte.xf4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf4) ).
fof('$_typeof_Coq.Init.Byte.xf5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf5) ).
fof('$_typeof_Coq.Init.Byte.xf6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf6) ).
fof('$_typeof_Coq.Init.Byte.xf7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf7) ).
fof('$_typeof_Coq.Init.Byte.xf8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf8) ).
fof('$_typeof_Coq.Init.Byte.xf9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf9) ).
fof('$_typeof_Coq.Init.Byte.xfa',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfa) ).
fof('$_typeof_Coq.Init.Byte.xfb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfb) ).
fof('$_typeof_Coq.Init.Byte.xfc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfc) ).
fof('$_typeof_Coq.Init.Byte.xfd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfd) ).
fof('$_typeof_Coq.Init.Byte.xfe',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfe) ).
fof('$_typeof_Coq.Init.Byte.xff',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exff) ).
fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__6178___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.CompSpecT',axiom,
c_24__type__30854___24t(cCoq_2eInit_2eDatatypes_2eCompSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__29489___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__12032___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__11988___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__12030___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__6176___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__12099___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_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__12087___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__12068___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__30818___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__30823___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__16___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
c_24__type__12006___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__11976___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__12082___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__16___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__6176___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__12056___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__175___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__12080___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__175___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.xorb',axiom,
c_24__type__6176___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Decimal.D0',axiom,
c_24__type__30869___24t(cCoq_2eInit_2eDecimal_2eD0) ).
fof('$_typeof_Coq.Init.Decimal.Nil',axiom,
cCoq_2eInit_2eDecimal_2euint___24t(cCoq_2eInit_2eDecimal_2eNil) ).
fof('$_typeof_Coq.Init.Decimal.Pos',axiom,
c_24__type__30871___24t(cCoq_2eInit_2eDecimal_2ePos) ).
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('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__18152___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__32479___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__11988___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__6203___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__18152___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__18152___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__18152___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__11988___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__18152___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__30960___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__11590___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__11626___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__11631___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__34067___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__34072___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__11572___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__28075___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__11603___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__34618___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__18113___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__32437___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__32463___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__18138___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.tl',axiom,
c_24__type__32446___24t(cCoq_2eLists_2eList_2etl) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__12101___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.NArith.BinNat.N.Bezout',axiom,
c_24__type__28532___24t(cCoq_2eNArith_2eBinNat_2eN_2eBezout) ).
fof('$_typeof_Coq.NArith.BinNat.N.Even',axiom,
c_24__type__342___24t(cCoq_2eNArith_2eBinNat_2eN_2eEven) ).
fof('$_typeof_Coq.NArith.BinNat.N.Private_OrderTac.Tac.interp_ord',axiom,
c_24__type__35262___24t(cCoq_2eNArith_2eBinNat_2eN_2ePrivate__OrderTac_2eTac_2einterp__ord) ).
fof('$_typeof_Coq.NArith.BinNat.N.Private_Tac.interp_ord',axiom,
c_24__type__35262___24t(cCoq_2eNArith_2eBinNat_2eN_2ePrivate__Tac_2einterp__ord) ).
fof('$_typeof_Coq.NArith.BinNat.N.b2n',axiom,
c_24__type__28544___24t(cCoq_2eNArith_2eBinNat_2eN_2eb2n) ).
fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
c_24__type__337___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
c_24__type__337___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__11697___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.ge',axiom,
c_24__type__337___24t(cCoq_2eNArith_2eBinNat_2eN_2ege) ).
fof('$_typeof_Coq.NArith.BinNat.N.gt',axiom,
c_24__type__337___24t(cCoq_2eNArith_2eBinNat_2eN_2egt) ).
fof('$_typeof_Coq.NArith.BinNat.N.lcm',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNat_2eN_2elcm) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__337___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.le_alt',axiom,
c_24__type__337___24t(cCoq_2eNArith_2eBinNat_2eN_2ele__alt) ).
fof('$_typeof_Coq.NArith.BinNat.N.lnot',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNat_2eN_2elnot) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__337___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt_alt',axiom,
c_24__type__337___24t(cCoq_2eNArith_2eBinNat_2eN_2elt__alt) ).
fof('$_typeof_Coq.NArith.BinNat.N.max_case',axiom,
c_24__type__35795___24t(cCoq_2eNArith_2eBinNat_2eN_2emax__case) ).
fof('$_typeof_Coq.NArith.BinNat.N.min_case',axiom,
c_24__type__45297___24t(cCoq_2eNArith_2eBinNat_2eN_2emin__case) ).
fof('$_typeof_Coq.NArith.BinNat.N.ones',axiom,
c_24__type__282___24t(cCoq_2eNArith_2eBinNat_2eN_2eones) ).
fof('$_typeof_Coq.NArith.BinNat.N.peano_rec',axiom,
c_24__type__28336___24t(cCoq_2eNArith_2eBinNat_2eN_2epeano__rec) ).
fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
c_24__type__29400___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).
fof('$_typeof_Coq.NArith.BinNat.N.sqrt_up',axiom,
c_24__type__282___24t(cCoq_2eNArith_2eBinNat_2eN_2esqrt__up) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.compare',axiom,
c_24__type__11644___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
c_24__type__282___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__28124___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__282___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__6161___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__11699___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.gcd',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2egcd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.iter',axiom,
c_24__type__30678___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eiter) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.land',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eland) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.ldiff',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eldiff) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.leb',axiom,
c_24__type__6161___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eleb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.log2',axiom,
c_24__type__282___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elog2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.lor',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elor) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.ltb',axiom,
c_24__type__6161___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eltb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.modulo',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.odd',axiom,
c_24__type__11699___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eodd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.of_nat',axiom,
c_24__type__28147___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.one',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eone) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pow',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epow) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__282___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.shiftl',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.shiftl_nat',axiom,
c_24__type__28140___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.shiftr',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftr) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.shiftr_nat',axiom,
c_24__type__28140___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftr__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.size',axiom,
c_24__type__282___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esize) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.size_nat',axiom,
c_24__type__11664___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esize__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.sqrt',axiom,
c_24__type__282___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esqrt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.square',axiom,
c_24__type__282___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esquare) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.sub',axiom,
c_24__type__289___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esub) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__282___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ_double',axiom,
c_24__type__282___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ_pos',axiom,
c_24__type__28101___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.t',axiom,
cType___24t(cCoq_2eNArith_2eBinNatDef_2eN_2et) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__6161___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit_nat',axiom,
c_24__type__334___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__11664___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.two',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etwo) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ezero) ).
fof('$_typeof_Coq.NArith.Ndec.Nleb',axiom,
c_24__type__6161___24t(cCoq_2eNArith_2eNdec_2eNleb) ).
fof('$_typeof_Coq.NArith.Ndigits.Neven',axiom,
c_24__type__342___24t(cCoq_2eNArith_2eNdigits_2eNeven) ).
fof('$_typeof_Coq.NArith.Ndigits.Nless',axiom,
c_24__type__6161___24t(cCoq_2eNArith_2eNdigits_2eNless) ).
fof('$_typeof_Coq.NArith.Ndigits.Nodd',axiom,
c_24__type__342___24t(cCoq_2eNArith_2eNdigits_2eNodd) ).
fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
c_24__type__317___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).
fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('$_typeof_Coq.Numbers.BinNums.N_rec',axiom,
c_24__type__30799___24t(cCoq_2eNumbers_2eBinNums_2eN__rec) ).
fof('$_typeof_Coq.Numbers.BinNums.N_rect',axiom,
c_24__type__30799___24t(cCoq_2eNumbers_2eBinNums_2eN__rect) ).
fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__307___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__11817___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__11817___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__349___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__349___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
c_24__type__35122___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__35122___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.mask2cmp',axiom,
c_24__type__35201___24t(cCoq_2ePArith_2eBinPos_2ePos_2emask2cmp) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
c_24__type__35198___24t(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq) ).
fof('$_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__30688___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.Ndouble',axiom,
c_24__type__282___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eNdouble) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.Nsucc_double',axiom,
c_24__type__282___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eNsucc__double) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__11710___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__28617___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
c_24__type__349___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
c_24__type__35068___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__28608___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.lor',axiom,
c_24__type__11710___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2elor) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__11710___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__28679___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_N',axiom,
c_24__type__307___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
c_24__type__349___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.shiftl',axiom,
c_24__type__28641___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eshiftl) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size',axiom,
c_24__type__349___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
c_24__type__28675___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__11710___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__349___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit',axiom,
c_24__type__35102___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
c_24__type__28673___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
c_24__type__28675___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__29630___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__32692___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__32685___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__16___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__28063___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.Ascii.ascii_of_N',axiom,
c_24__type__30694___24t(cCoq_2eStrings_2eAscii_2eascii__of__N) ).
fof('$_typeof_Coq.Strings.ByteVector.ByteVector',axiom,
c_24__type__12008___24t(cCoq_2eStrings_2eByteVector_2eByteVector) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__19623___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedType.EQ',axiom,
c_24__type__19757___24t(cCoq_2eStructures_2eOrderedType_2eEQ) ).
fof('$_typeof_Coq.Structures.OrderedType.GT',axiom,
c_24__type__19788___24t(cCoq_2eStructures_2eOrderedType_2eGT) ).
fof('$_typeof_Coq.Structures.OrderedType.LT',axiom,
c_24__type__19726___24t(cCoq_2eStructures_2eOrderedType_2eLT) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__337___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq_dec',axiom,
c_24__type__45119___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq__dec) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__337___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.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__12008___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__34607___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__34599___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__29370___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__29132___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__29132___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__29132___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__29006___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
c_24__type__29049___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
c_24__type__29045___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__29002___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__29040___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__29002___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__28096___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__29002___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__29002___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__29002___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__29002___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__29054___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__29006___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__29002___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__29006___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quot',axiom,
c_24__type__29002___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equot) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.rem',axiom,
c_24__type__29002___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2erem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__29002___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__29006___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_N',axiom,
c_24__type__29049___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
c_24__type__29045___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__28096___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__16___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.Env.nth',axiom,
c_24__type__12248___24t(cCoq_2emicromega_2eEnv_2enth) ).
fof('$_typeof_Coq.micromega.EnvRing.P1',axiom,
c_24__type__12495___24t(cCoq_2emicromega_2eEnvRing_2eP1) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__12426___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEadd',axiom,
c_24__type__12431___24t(cCoq_2emicromega_2eEnvRing_2ePEadd) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__12423___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PEmul',axiom,
c_24__type__12431___24t(cCoq_2emicromega_2eEnvRing_2ePEmul) ).
fof('$_typeof_Coq.micromega.EnvRing.PEopp',axiom,
c_24__type__12440___24t(cCoq_2emicromega_2eEnvRing_2ePEopp) ).
fof('$_typeof_Coq.micromega.EnvRing.PEpow',axiom,
c_24__type__12445___24t(cCoq_2emicromega_2eEnvRing_2ePEpow) ).
fof('$_typeof_Coq.micromega.EnvRing.PEsub',axiom,
c_24__type__12431___24t(cCoq_2emicromega_2eEnvRing_2ePEsub) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__16___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
c_24__type__12508___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__12495___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
c_24__type__12500___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__16___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.RMicromega.INZ',axiom,
c_24__type__32682___24t(cCoq_2emicromega_2eRMicromega_2eINZ) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__19885___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__19859___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__16___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__16___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.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__16___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__16___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__16___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
c_24__type__20828___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzIn',axiom,
c_24__type__20809___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzIn) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzZ',axiom,
c_24__type__20830___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzZ) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.cneqb',axiom,
c_24__type__20200___24t(cCoq_2emicromega_2eRingMicromega_2ecneqb) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
c_24__type__20517___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op2',axiom,
c_24__type__21986___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op2) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_pexpr',axiom,
c_24__type__22115___24t(cCoq_2emicromega_2eRingMicromega_2eeval__pexpr) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_pol',axiom,
c_24__type__20432___24t(cCoq_2emicromega_2eRingMicromega_2eeval__pol) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_sexpr',axiom,
c_24__type__23180___24t(cCoq_2emicromega_2eRingMicromega_2eeval__sexpr) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__175___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_N\'',axiom,
c_24__type__29054___24t(cCoq_2eomega_2ePreOmega_2eZ__of__N_27) ).
fof('$_typeof_Coq.setoid_ring.ArithRing.protected_to_nat',axiom,
c_24__type__11664___24t(cCoq_2esetoid__ring_2eArithRing_2eprotected__to__nat) ).
fof('$_typeof_Coq.setoid_ring.BinList.jump',axiom,
c_24__type__30785___24t(cCoq_2esetoid__ring_2eBinList_2ejump) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEI',axiom,
c_24__type__15543___24t(cCoq_2esetoid__ring_2eField__theory_2eFEI) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEO',axiom,
c_24__type__15543___24t(cCoq_2esetoid__ring_2eField__theory_2eFEO) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__15549___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__15554___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__15546___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEdiv',axiom,
c_24__type__15554___24t(cCoq_2esetoid__ring_2eField__theory_2eFEdiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__15859___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__15563___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__15554___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEopp',axiom,
c_24__type__15563___24t(cCoq_2esetoid__ring_2eField__theory_2eFEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEpow',axiom,
c_24__type__15572___24t(cCoq_2esetoid__ring_2eField__theory_2eFEpow) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEsub',axiom,
c_24__type__15554___24t(cCoq_2esetoid__ring_2eField__theory_2eFEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__16___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__17597___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
c_24__type__1348___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NtoZ',axiom,
c_24__type__29054___24t(cCoq_2esetoid__ring_2eField__theory_2eNtoZ) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__16149___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.ZtoN',axiom,
c_24__type__29049___24t(cCoq_2esetoid__ring_2eField__theory_2eZtoN) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__16___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__16___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__282___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nsub',axiom,
c_24__type__289___24t(cCoq_2esetoid__ring_2eInitialRing_2eNsub) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.NwO',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(cCoq_2esetoid__ring_2eInitialRing_2eNwO) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__18062___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN1',axiom,
c_24__type__18062___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiNword',axiom,
c_24__type__32379___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__18021___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__18021___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__32256___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.triv_div',axiom,
c_24__type__32416___24t(cCoq_2esetoid__ring_2eInitialRing_2etriv__div) ).
fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
c_24__type__6176___24t(cCoq_2esetoid__ring_2eRing_2ebool__eq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.P0',axiom,
c_24__type__23496___24t(cCoq_2esetoid__ring_2eRing__polynom_2eP0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.P1',axiom,
c_24__type__23496___24t(cCoq_2esetoid__ring_2eRing__polynom_2eP1) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__2243___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__2243___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__2249___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__2254___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__2246___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__2483___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__2254___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__2263___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__2268___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__2254___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__16___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__32841___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__23496___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__23625___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__32833___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__16___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__27887___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__27887___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__27945___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
c_24__type__12030___24t(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__282___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__2523___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__26894___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_ExtLib.Core.Type.equal',axiom,
c_24__type__81___24t(cExtLib_2eCore_2eType_2eequal) ).
fof('$_typeof_ExtLib.Core.Type.proper',axiom,
c_24__type__105___24t(cExtLib_2eCore_2eType_2eproper) ).
fof('$_typeof_ExtLib.Core.Type.type',axiom,
c_24__type__16___24t(cExtLib_2eCore_2eType_2etype) ).
fof('$_typeof_ExtLib.Structures.Proper.PReflexive',axiom,
c_24__type__5___24t(cExtLib_2eStructures_2eProper_2ePReflexive) ).
fof('$_typeof_N.type_N',axiom,
cExtLib_2eCore_2eType_2etype___24t(cCoq_2eNumbers_2eBinNums_2eN,cN_2etype__N) ).
fof('$_typeof_n',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cn) ).
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.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_le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Bool.Bool.andb_assoc',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ! [V2__b3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__b3)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,cCoq_2eInit_2eDatatypes_2eandb___24a2(V1__b2,V2__b3)) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2),V2__b3) ) ) ) ).
fof('Coq.Bool.Bool.andb_comm',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V1__b2,V0__b1) ) ) ).
fof('Coq.Bool.Bool.andb_diag',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,V0__b) = V0__b ) ).
fof('Coq.Bool.Bool.andb_false_r',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.Bool.Bool.andb_true_r',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2etrue) = V0__b ) ).
fof('Coq.Bool.Bool.eq_iff_eq_true',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = V1__b2
<=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.Bool.Bool.eq_true_iff_eq',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue )
=> V0__b1 = V1__b2 ) ) ) ).
fof('Coq.Bool.Bool.negb_involutive',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b)) = V0__b ) ).
fof('Coq.Bool.Bool.orb_comm',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V1__b2,V0__b1) ) ) ).
fof('Coq.Bool.Bool.orb_diag',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b,V0__b) = V0__b ) ).
fof('Coq.Bool.Bool.xorb_comm',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ! [V1__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
=> cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b,V1__b_27) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V1__b_27,V0__b) ) ) ).
fof('Coq.Init.Datatypes.BoolSpecF',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( p(V1__Q)
=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V0__P,V1__Q,cCoq_2eInit_2eDatatypes_2efalse) ) ) ) ).
fof('Coq.Init.Datatypes.BoolSpecT',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( p(V0__P)
=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V0__P,V1__Q,cCoq_2eInit_2eDatatypes_2etrue) ) ) ) ).
fof('Coq.Init.Datatypes.CompOpp_iff',axiom,
! [V0__c] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__c)
=> ! [V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__c) = V1__c_27
<=> V0__c = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V1__c_27) ) ) ) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__30826___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__l))) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__30811___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.Wf.Acc_intro',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__14___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.NArith.BinNat.N.A\'A_left',axiom,
! [V0__A] :
( c_24__type__342___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__z)
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ! [Vvar__4__m__30681] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__4__m__30681)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(Vvar__4__m__30681,V1__z))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__n,Vvar__4__m__30681))
=> p(happ(V0__A,Vvar__4__m__30681)) ) ) ) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V3__n,V1__z))
=> p(happ(V0__A,V3__n)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.A\'A_right',axiom,
! [V0__A] :
( c_24__type__342___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__z)
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ! [Vvar__4__m__35018] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__4__m__35018)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__z,Vvar__4__m__35018))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(Vvar__4__m__35018,V2__n))
=> p(happ(V0__A,Vvar__4__m__35018)) ) ) ) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__z,V3__n))
=> p(happ(V0__A,V3__n)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Even_or_Odd',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ( cCoq_2eNArith_2eBinNat_2eN_2eEven___24a1(V0__x)
| cCoq_2eNArith_2eBinNat_2eN_2eOdd___24a1(V0__x) ) ) ).
fof('Coq.NArith.BinNat.N.Private_NZPow.pow_1_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__a ) ).
fof('Coq.NArith.BinNat.N.Private_NZPow.pow_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__a))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,V1__b))) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_NZSqrt.sqrt_0',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(cCoq_2eNumbers_2eBinNums_2eN0) = cCoq_2eNumbers_2eBinNums_2eN0 ).
fof('Coq.NArith.BinNat.N.Private_NZSqrt.sqrt_le_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__a,V1__b))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V1__b))) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_NZSqrt.sqrt_lt_cancel',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V1__b)))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_NZSqrt.sqrt_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V0__a))) ) ).
fof('Coq.NArith.BinNat.N.Private_NZSqrt.sqrt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__282,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)),cCoq_2eNArith_2eBinNatDef_2eN_2esqrt) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.IsTotal.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.IsTotal.le_lteq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
<=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.IsTotal.lt_strorder',axiom,
cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.IsTotal.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.add_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = V0__n ) ).
fof('Coq.NArith.BinNat.N.add_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) ) ).
fof('Coq.NArith.BinNat.N.add_1_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) ) ).
fof('Coq.NArith.BinNat.N.add_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V0__n) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V2__p) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V2__p)
<=> V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.add_dichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( ? [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V0__n) = V1__m )
| ? [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V1__m) = V0__n ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_le_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__q)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V3__q)))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V2__p))
| p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V3__q)) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_le_lt_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__q)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V2__p,V3__q))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_le_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__q)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__p,V3__q))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_le_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_le_mono_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V2__p))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_lt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__q)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V3__q)))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p))
| p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V3__q)) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_lt_le_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__q)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__p,V3__q))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_lt_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__q)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V2__p,V3__q))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_lt_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_lt_mono_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V2__p))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_nonneg_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_pos_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m))) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_pos_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_pos_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m))) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_shuffle0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_shuffle1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__q)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V3__q)) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V3__q)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_shuffle2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__q)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V3__q)) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V3__q),cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V2__p)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_shuffle3',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V2__p)) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_sub',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m),V1__m) = V0__n ) ) ).
fof('Coq.NArith.BinNat.N.add_succ_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m)) ) ) ).
fof('Coq.NArith.BinNat.N.add_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.NArith.BinNat.N.add_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.NArith.BinNat.N.bi_induction',axiom,
! [V0__A] :
( c_24__type__342___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__342,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.bits_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.NArith.BinNat.N.bits_inj',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a1(V1__b))
=> V0__a = V1__b ) ) ) ).
fof('Coq.NArith.BinNat.N.case_analysis',axiom,
! [V0__A] :
( c_24__type__342___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__342,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,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.compare_spec',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(c_24__prop__11684___24a2(V0__x,V1__y),cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y),cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x),cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.NArith.BinNat.N.div2_double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n)) = V0__n ) ).
fof('Coq.NArith.BinNat.N.div2_succ_double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__n)) = V0__n ) ).
fof('Coq.NArith.BinNat.N.div_1_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__a ) ).
fof('Coq.NArith.BinNat.N.div_small',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__a,V1__b))
=> cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.NArith.BinNat.N.divide_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n)
=> V0__n = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ).
fof('Coq.NArith.BinNat.N.divide_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) ) ).
fof('Coq.NArith.BinNat.N.divide_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) ) ).
fof('Coq.NArith.BinNat.N.divide_add_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V2__p))
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.divide_antisym_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V1__m))
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.divide_factor_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.NArith.BinNat.N.divide_factor_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V0__n)) ) ) ).
fof('Coq.NArith.BinNat.N.divide_lcm_eq_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2elcm___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.divide_lcm_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__a,cCoq_2eNArith_2eBinNat_2eN_2elcm___24a2(V0__a,V1__b)) ) ) ).
fof('Coq.NArith.BinNat.N.divide_mul_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V2__p)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.divide_mul_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V2__p)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V2__p)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.divide_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V0__n) ) ).
fof('Coq.NArith.BinNat.N.divide_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V1__m,V2__p)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.divide_transitive',axiom,
cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('Coq.NArith.BinNat.N.divide_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__337,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__342,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_2edivide) ).
fof('Coq.NArith.BinNat.N.double_inj',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_0_gt_0_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
| p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n)) ) ) ).
fof('Coq.NArith.BinNat.N.eq_add_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0
<=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& V1__m = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__28352___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.NArith.BinNat.N.eq_dne',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( ~ ( V0__n != V1__m )
<=> V0__n = V1__m ) ) ) ).
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
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_mul_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0
<=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
| V1__m = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_square_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V0__n) = cCoq_2eNumbers_2eBinNums_2eN0
<=> V0__n = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ).
fof('Coq.NArith.BinNat.N.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_sym_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
<=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.eqb_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> V0__n = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.eqf_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(c_24__type__11699,cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('Coq.NArith.BinNat.N.gcd_add_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V0__n)) = cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__n,V1__m) ) ) ).
fof('Coq.NArith.BinNat.N.gcd_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.NArith.BinNat.N.gcd_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.gcd_diag_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n))
=> cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__n,V0__n) = V0__n ) ) ).
fof('Coq.NArith.BinNat.N.gcd_divide_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b),V0__a) ) ) ).
fof('Coq.NArith.BinNat.N.gcd_divide_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b),V1__b) ) ) ).
fof('Coq.NArith.BinNat.N.gcd_eq_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0
<=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& V1__m = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ).
fof('Coq.NArith.BinNat.N.gcd_greatest',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__c)
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V2__c,V0__a)
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V2__c,V1__b)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V2__c,cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.gcd_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b))) ) ) ).
fof('Coq.NArith.BinNat.N.gcd_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__289,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__282,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN))),cCoq_2eNArith_2eBinNatDef_2eN_2egcd) ).
fof('Coq.NArith.BinNat.N.gt_lt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2egt___24a2(V0__n,V1__m)
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.NArith.BinNat.N.gt_wf',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__z)
=> cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_24__lam__35035___24a1(V0__z)) ) ).
fof('Coq.NArith.BinNat.N.induction',axiom,
! [V0__A] :
( c_24__type__342___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__342,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.land_0_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eN0) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.land_assoc',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__c)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__a,cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V1__b,V2__c)) = cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__a,V1__b),V2__c) ) ) ) ).
fof('Coq.NArith.BinNat.N.land_comm',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V1__b,V0__a) ) ) ).
fof('Coq.NArith.BinNat.N.land_diag',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__a,V0__a) = V0__a ) ).
fof('Coq.NArith.BinNat.N.land_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__289,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__282,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN))),cCoq_2eNArith_2eBinNatDef_2eN_2eland) ).
fof('Coq.NArith.BinNat.N.lbase',axiom,
! [V0__A] :
( c_24__type__342___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__z)
=> ! [Vvar__3__m__35025] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3__m__35025)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(Vvar__3__m__35025,V1__z))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__z),Vvar__3__m__35025))
=> p(happ(V0__A,Vvar__3__m__35025)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lcm_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNat_2eN_2elcm___24a2(V0__n,cCoq_2eNArith_2eBinNat_2eN_2elcm___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNat_2eN_2elcm___24a2(cCoq_2eNArith_2eBinNat_2eN_2elcm___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.NArith.BinNat.N.lcm_comm',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> cCoq_2eNArith_2eBinNat_2eN_2elcm___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNat_2eN_2elcm___24a2(V1__b,V0__a) ) ) ).
fof('Coq.NArith.BinNat.N.lcm_diag',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2elcm___24a2(V0__n,V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.lcm_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__289,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__282,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN))),cCoq_2eNArith_2eBinNat_2eN_2elcm) ).
fof('Coq.NArith.BinNat.N.ldiff_0_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eN0) = V0__a ) ).
fof('Coq.NArith.BinNat.N.ldiff_diag',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V0__a,V0__a) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.ldiff_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__289,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__282,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN))),cCoq_2eNArith_2eBinNatDef_2eN_2eldiff) ).
fof('Coq.NArith.BinNat.N.le_0_1',axiom,
p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.NArith.BinNat.N.le_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n)) ) ).
fof('Coq.NArith.BinNat.N.le_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0))
<=> V0__n = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ).
fof('Coq.NArith.BinNat.N.le_add_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m))) ) ) ).
fof('Coq.NArith.BinNat.N.le_alt_dichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele__alt___24a2(V0__n,V1__m)
| cCoq_2eNArith_2eBinNat_2eN_2ele__alt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n))
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.NArith.BinNat.N.le_exists_sub',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> ? [V3__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__p)
& V1__m = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V3__p,V0__n)
& p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V3__p)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_le_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m))) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_lteq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
<=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_ngt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
<=> ~ p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_pred_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n),V0__n)) ) ).
fof('Coq.NArith.BinNat.N.le_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('Coq.NArith.BinNat.N.le_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.NArith.BinNat.N.le_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y))
=> ( V0__x = V2__z
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__z,V1__y)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_stepr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(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)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m))
<=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__337,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__342,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.lnot_involutive',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> cCoq_2eNArith_2eBinNat_2eN_2elnot___24a2(cCoq_2eNArith_2eBinNat_2eN_2elnot___24a2(V0__a,V1__n),V1__n) = V0__a ) ) ).
fof('Coq.NArith.BinNat.N.log2_le_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__a,V1__b))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V1__b))) ) ) ) ).
fof('Coq.NArith.BinNat.N.log2_lt_cancel',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V1__b)))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.NArith.BinNat.N.log2_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__a))) ) ).
fof('Coq.NArith.BinNat.N.log2_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0))
=> cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ).
fof('Coq.NArith.BinNat.N.log2_up_le_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__a,V1__b))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNat_2eN_2elog2__up___24a1(V0__a),cCoq_2eNArith_2eBinNat_2eN_2elog2__up___24a1(V1__b))) ) ) ) ).
fof('Coq.NArith.BinNat.N.log2_up_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNat_2eN_2elog2__up___24a1(V0__a))) ) ).
fof('Coq.NArith.BinNat.N.log2_up_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__282,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)),cCoq_2eNArith_2eBinNat_2eN_2elog2__up) ).
fof('Coq.NArith.BinNat.N.log2_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__282,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)),cCoq_2eNArith_2eBinNatDef_2eN_2elog2) ).
fof('Coq.NArith.BinNat.N.lor_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__a) = V0__a ) ).
fof('Coq.NArith.BinNat.N.lor_0_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eN0) = V0__a ) ).
fof('Coq.NArith.BinNat.N.lor_assoc',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__c)
=> cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V0__a,cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V1__b,V2__c)) = cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V0__a,V1__b),V2__c) ) ) ) ).
fof('Coq.NArith.BinNat.N.lor_comm',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V1__b,V0__a) ) ) ).
fof('Coq.NArith.BinNat.N.lor_diag',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V0__a,V0__a) = V0__a ) ).
fof('Coq.NArith.BinNat.N.lor_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__289,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__282,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN))),cCoq_2eNArith_2eBinNatDef_2eN_2elor) ).
fof('Coq.NArith.BinNat.N.lt_0_1',axiom,
p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.NArith.BinNat.N.lt_0_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n))) ) ).
fof('Coq.NArith.BinNat.N.lt_1_2',axiom,
p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('Coq.NArith.BinNat.N.lt_asymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
<=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m ) ) ) ) ).
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)
=> ( p(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)
& p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__z,V3__k)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n != V1__m
<=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x)) ) ).
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)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_lt_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V1__m)) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m))) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_neq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
=> V0__n != V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y))
=> ( V0__x = V2__z
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V2__z,V1__y)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_stepr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_strorder',axiom,
cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('Coq.NArith.BinNat.N.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> p(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)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_succ_pred',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__z,V1__n))
=> cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V1__n)) = V1__n ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m)))
<=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_wf',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__z)
=> cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_24__lam__35031___24a1(V0__z)) ) ).
fof('Coq.NArith.BinNat.N.lxor_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__a) = V0__a ) ).
fof('Coq.NArith.BinNat.N.lxor_0_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eN0) = V0__a ) ).
fof('Coq.NArith.BinNat.N.lxor_assoc',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__c)
=> cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__b),V2__c) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V1__b,V2__c)) ) ) ) ).
fof('Coq.NArith.BinNat.N.lxor_comm',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V1__b,V0__a) ) ) ).
fof('Coq.NArith.BinNat.N.lxor_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eN0
=> V0__a = V1__a_27 ) ) ) ).
fof('Coq.NArith.BinNat.N.lxor_nilpotent',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V0__a) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.lxor_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__289,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__282,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN))),cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).
fof('Coq.NArith.BinNat.N.max_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.max_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = V0__n ) ).
fof('Coq.NArith.BinNat.N.max_assoc',axiom,
! [V0__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__m)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__m,cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V1__n,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__m,V1__n),V2__p) ) ) ) ).
fof('Coq.NArith.BinNat.N.max_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.max_compat',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__289,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__282,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN))),cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('Coq.NArith.BinNat.N.max_id',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.max_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n))
=> cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.NArith.BinNat.N.max_le_compat_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V2__p,V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.max_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.max_spec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__m) = V1__m )
| ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n))
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('Coq.NArith.BinNat.N.max_spec_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__m) = V1__m )
| ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n))
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('Coq.NArith.BinNat.N.min_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.min_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.min_assoc',axiom,
! [V0__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__m)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__m,cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V1__n,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__m,V1__n),V2__p) ) ) ) ).
fof('Coq.NArith.BinNat.N.min_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.min_compat',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__289,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__282,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN))),cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('Coq.NArith.BinNat.N.min_id',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.min_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.NArith.BinNat.N.min_le_compat_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V2__p,V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.min_le_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m),V2__p))
<=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V2__p))
| p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.min_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n))
=> cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.min_spec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m) = V0__n )
| ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n))
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.min_spec_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m) = V0__n )
| ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n))
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mod_small',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__a,V1__b))
=> cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V0__a,V1__b) = V0__a ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.mul_1_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n ) ).
fof('Coq.NArith.BinNat.N.mul_add_distr_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V2__p)) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_add_distr_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V2__p)) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eN0
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V0__n) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.mul_divide_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V1__m)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_le_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_le_mono_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__q)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V2__p))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__p,V3__q))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V3__q))) ) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_le_mono_nonneg_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V2__p))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V1__m))) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_le_mono_nonneg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V2__p))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V2__p))) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_le_mono_nonpos_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V1__m),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V0__n))) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_le_mono_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V2__p))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_lt_mono_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__q)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V2__p))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V2__p,V3__q))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V3__q))) ) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_lt_mono_pos_l',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__p)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__p))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__n,V2__m))
<=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__p,V1__n),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__p,V2__m))) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_lt_mono_pos_r',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__p)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__p))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__n,V2__m))
<=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__n,V0__p),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__m,V0__p))) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_neg_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eN0))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_neg_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eN0)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_nonneg_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_pos_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eN0))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eN0)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_pos_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_shuffle0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m),V2__p) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_shuffle1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__q)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V3__q)) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V3__q)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_shuffle2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__q)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V3__q)) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V3__q),cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V2__p)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_shuffle3',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V2__p)) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m),V1__m) ) ) ).
fof('Coq.NArith.BinNat.N.mul_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m),V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.neq_0',axiom,
~ ! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> V0__n = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.neq_0_lt_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eN0
<=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n)) ) ) ).
fof('Coq.NArith.BinNat.N.neq_0_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) ) ).
fof('Coq.NArith.BinNat.N.neq_succ_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) != cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.neq_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) != V0__n ) ).
fof('Coq.NArith.BinNat.N.neq_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> V0__n != cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) ) ).
fof('Coq.NArith.BinNat.N.neq_sym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.NArith.BinNat.N.nle_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( ~ p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.NArith.BinNat.N.nle_succ_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ~ p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),cCoq_2eNumbers_2eBinNums_2eN0)) ) ).
fof('Coq.NArith.BinNat.N.nlt_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ~ p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0)) ) ).
fof('Coq.NArith.BinNat.N.one_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('Coq.NArith.BinNat.N.ones_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__282,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)),cCoq_2eNArith_2eBinNat_2eN_2eones) ).
fof('Coq.NArith.BinNat.N.peano_ind',axiom,
! [V0__P] :
( c_24__type__342___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.pos_pred_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V0__n)) = V0__n ) ).
fof('Coq.NArith.BinNat.N.pow_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ).
fof('Coq.NArith.BinNat.N.pow_add_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__c)
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__b,V2__c)) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,V1__b),cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,V2__c)) ) ) ) ).
fof('Coq.NArith.BinNat.N.pow_neg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__p,cCoq_2eNumbers_2eBinNums_2eN0))
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.NArith.BinNat.N.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eN0
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.NArith.BinNat.N.pred_0',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(cCoq_2eNumbers_2eBinNums_2eN0) = cCoq_2eNumbers_2eBinNums_2eN0 ).
fof('Coq.NArith.BinNat.N.pred_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) = V0__n ) ).
fof('Coq.NArith.BinNat.N.rbase',axiom,
! [V0__A] :
( c_24__type__342___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__z)
=> ! [Vvar__3__m__35015] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3__m__35015)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__z,Vvar__3__m__35015))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(Vvar__3__m__35015,V1__z))
=> p(happ(V0__A,Vvar__3__m__35015)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.shiftl_0_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eN0) = V0__a ) ).
fof('Coq.NArith.BinNat.N.shiftr_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eshiftr___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.shiftr_0_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eshiftr___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eN0) = V0__a ) ).
fof('Coq.NArith.BinNat.N.shiftr_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__289,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__282,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN))),cCoq_2eNArith_2eBinNatDef_2eN_2eshiftr) ).
fof('Coq.NArith.BinNat.N.sqrt_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0))
=> cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ).
fof('Coq.NArith.BinNat.N.sqrt_square',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__a,V0__a)) = V0__a ) ).
fof('Coq.NArith.BinNat.N.sqrt_up_0',axiom,
cCoq_2eNArith_2eBinNat_2eN_2esqrt__up___24a1(cCoq_2eNumbers_2eBinNums_2eN0) = cCoq_2eNumbers_2eBinNums_2eN0 ).
fof('Coq.NArith.BinNat.N.sqrt_up_eqn0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eN0))
=> cCoq_2eNArith_2eBinNat_2eN_2esqrt__up___24a1(V0__a) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ).
fof('Coq.NArith.BinNat.N.sqrt_up_le_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__a,V1__b))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNat_2eN_2esqrt__up___24a1(V0__a),cCoq_2eNArith_2eBinNat_2eN_2esqrt__up___24a1(V1__b))) ) ) ) ).
fof('Coq.NArith.BinNat.N.sqrt_up_lt_cancel',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNat_2eN_2esqrt__up___24a1(V0__a),cCoq_2eNArith_2eBinNat_2eN_2esqrt__up___24a1(V1__b)))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.NArith.BinNat.N.sqrt_up_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNat_2eN_2esqrt__up___24a1(V0__a))) ) ).
fof('Coq.NArith.BinNat.N.sqrt_up_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__282,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)),cCoq_2eNArith_2eBinNat_2eN_2esqrt__up) ).
fof('Coq.NArith.BinNat.N.square_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__a,V0__a))) ) ).
fof('Coq.NArith.BinNat.N.sub_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = V0__n ) ).
fof('Coq.NArith.BinNat.N.sub_add',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V1__m,V0__n),V0__n) = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.sub_diag',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.sub_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n))
=> cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) != cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.NArith.BinNat.N.sub_le_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V2__p,V1__m),cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V2__p,V0__n))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.sub_le_mono_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V2__p),cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V1__m,V2__p))) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.sub_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) ) ) ).
fof('Coq.NArith.BinNat.N.succ_0_discr',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) != cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.succ_double_inj',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__n) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.succ_inj',axiom,
! [V0__n1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n2)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__n2)
=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.NArith.BinNat.N.succ_inj_wd',axiom,
! [V0__n1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n2)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__n2)
<=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.NArith.BinNat.N.succ_inj_wd_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) != cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m)
<=> V0__n != V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.succ_le_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m))) ) ) ) ).
fof('Coq.NArith.BinNat.N.succ_lt_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m))) ) ) ) ).
fof('Coq.NArith.BinNat.N.succ_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eN0
=> cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n)) = V0__n ) ) ).
fof('Coq.NArith.BinNat.N.two_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.NArith.BinNat.N.zero_or_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
| ? [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
& V0__n = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.Nplus_reg_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V2__p)
=> V1__m = V2__p ) ) ) ) ).
fof('Coq.NArith.Ndigits.Nbit_faithful',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( cCoq_2eNArith_2eNdigits_2eeqf___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat___24a1(V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat___24a1(V1__n_27))
=> V0__n = V1__n_27 ) ) ) ).
fof('Coq.NArith.Nnat.N2Nat.id',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a)) = V0__a ) ).
fof('Coq.NArith.Nnat.N2Nat.inj',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V1__a_27)
=> V0__a = V1__a_27 ) ) ) ).
fof('Coq.NArith.Nnat.N2Nat.inj_iff',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V1__a_27)
<=> V0__a = V1__a_27 ) ) ) ).
fof('Coq.Numbers.BinNums.N_ind',axiom,
! [V0__P] :
( c_24__type__342___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V2__p))) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Numbers.BinNums.N_sind',axiom,
! [V0__P] :
( c_24__type__342___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V2__p))) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__11800___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.add_comm',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V1__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V0__p) ) ) ).
fof('Coq.PArith.BinPos.Pos.iter_swap_gen',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__32467___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__35192___24t(V0__A,V1__B,V3__g)
=> ! [V4__h] :
( c_24__type__2000___24t(V0__A,V1__B,V4__h)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> happ(V2__f,happ(V3__g,V5__a)) = happ(V4__h,happ(V2__f,V5__a)) )
=> ! [V6__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> happ(V2__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V3__g,V7__a,V6__p)) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__B,V4__h,happ(V2__f,V7__a),V6__p) ) ) ) ) ) ) ) ) ).
fof('Coq.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.Structures.OrderedTypeEx.N_as_OT.lt_not_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
=> V0__n != V1__m ) ) ) ).
fof('Coq.Structures.OrderedTypeEx.N_as_OT.lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('Coq.ZArith.Znat.N2Z.id',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.Znat.N2Z.inj',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.Znat.N2Z.inj_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V1__m)
<=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2N.id',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n)) = V0__n ) ).
fof('Coq.micromega.EnvRing.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1132___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1132___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1141___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__14___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1132___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1141___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_0_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__1132___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1132___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1132___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__14___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__14___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_square_nonneg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__1132___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1132___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1132___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__14___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__14___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.rtimes_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__1132___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1132___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1132___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__14___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__14___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1132___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1141___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V4__rtimes) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AF_AR',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1132___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1141___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__14___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AFinv_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1132___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1141___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__14___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V11__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V11__p)),V11__p)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.radd_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1132___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1132___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1141___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__14___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1132___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1141___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1132___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1132___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1141___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__14___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1132___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1141___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.Neqb_ok',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
=> V0__x = V1__y ) ) ) ).
fof('Coq.setoid_ring.InitialRing.radd_ext5_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1132___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1132___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1141___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__14___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1132___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1141___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.radd_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1132___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1132___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1141___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__14___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1132___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1141___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1132___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1132___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1141___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__14___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1132___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1141___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_0_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),V1__rO)),V10__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_assoc',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),happ(happ(V3__radd,V10__y),V11__z))),happ(happ(V3__radd,happ(happ(V3__radd,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARdistr_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V9__x),V10__y)),V11__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V9__x),V11__z)),happ(happ(V4__rmul,V10__y),V11__z)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARdistr_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> ! [V12__y] :
( t(V12__y,V0__R)
=> ! [V13__z] :
( t(V13__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V13__z),happ(happ(V3__radd,V11__x),V12__y))),happ(happ(V3__radd,happ(happ(V4__rmul,V13__z),V11__x)),happ(happ(V4__rmul,V13__z),V12__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V1__rO),V9__x)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_1_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_1_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V2__rI)),V10__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_assoc',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),happ(happ(V4__rmul,V10__y),V11__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V9__x),V10__y))),happ(happ(V4__rmul,happ(V6__ropp,V9__x)),V10__y))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_zero',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> p(happ(happ(V7__req,happ(V6__ropp,V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARsub_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARth_SRth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V7__req) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1132___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1132___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1141___24t(V0__R,V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,c_3d___24a1(V0__R)) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_s_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1132___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1132___24t(V0__R,V2__rmul)
=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V0__R,V1__radd,V2__rmul,c_3d___24a1(V0__R)) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eqsth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).
fof('Coq.setoid_ring.Ring_theory.Radd_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1132___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1132___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1141___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__14___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1132___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1141___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Rth_ARth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_reqe',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1132___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1132___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1141___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__14___24t(V0__R,V4__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1132___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1141___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1132___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1141___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1141___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_srt',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__req] :
( c_24__type__14___24t(V0__R,V5__req)
=> ( ! [V6__n] :
( t(V6__n,V0__R)
=> p(happ(happ(V5__req,happ(happ(V3__radd,V1__rO),V6__n)),V6__n)) )
=> ( ! [V7__n] :
( t(V7__n,V0__R)
=> ! [V8__m] :
( t(V8__m,V0__R)
=> p(happ(happ(V5__req,happ(happ(V3__radd,V7__n),V8__m)),happ(happ(V3__radd,V8__m),V7__n))) ) )
=> ( ! [V8__n] :
( t(V8__n,V0__R)
=> ! [V9__m] :
( t(V9__m,V0__R)
=> ! [V10__p] :
( t(V10__p,V0__R)
=> p(happ(happ(V5__req,happ(happ(V3__radd,V8__n),happ(happ(V3__radd,V9__m),V10__p))),happ(happ(V3__radd,happ(happ(V3__radd,V8__n),V9__m)),V10__p))) ) ) )
=> ( ! [V9__n] :
( t(V9__n,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,V2__rI),V9__n)),V9__n)) )
=> ( ! [V10__n] :
( t(V10__n,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,V1__rO),V10__n)),V1__rO)) )
=> ( ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,V11__n),V12__m)),happ(happ(V4__rmul,V12__m),V11__n))) ) )
=> ( ! [V12__n] :
( t(V12__n,V0__R)
=> ! [V13__m] :
( t(V13__m,V0__R)
=> ! [V14__p] :
( t(V14__p,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,V12__n),happ(happ(V4__rmul,V13__m),V14__p))),happ(happ(V4__rmul,happ(happ(V4__rmul,V12__n),V13__m)),V14__p))) ) ) )
=> ( ! [V13__n] :
( t(V13__n,V0__R)
=> ! [V14__m] :
( t(V14__m,V0__R)
=> ! [V15__p] :
( t(V15__p,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,happ(happ(V3__radd,V13__n),V14__m)),V15__p)),happ(happ(V3__radd,happ(happ(V4__rmul,V13__n),V15__p)),happ(happ(V4__rmul,V14__m),V15__p)))) ) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mkpow_th',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__1132___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__14___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__6133___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__6140___24t(V0__R,V4__Cpow,V6__rpow)
=> ( ! [V7__r] :
( t(V7__r,V0__R)
=> ! [V8__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V8__n)
=> p(happ(happ(V3__req,happ(happ(V6__rpow,V7__r),happ(V5__Cp__phi,V8__n))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V7__r,V8__n))) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V1__rI,V2__rmul,V3__req,V4__Cpow,V5__Cp__phi,V6__rpow) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__1986___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__1986___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__1986___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__2000___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__2007___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1365___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V9__cO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1132___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1132___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1132___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1141___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__14___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__1986___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__1986___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__1986___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__2000___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__2007___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1365___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.rpow_pow_N',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__1132___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__14___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__6133___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__6140___24t(V0__R,V4__Cpow,V6__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V1__rI,V2__rmul,V3__req,V4__Cpow,V5__Cp__phi,V6__rpow)
=> ! [V8__r] :
( t(V8__r,V0__R)
=> ! [V9__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V9__n)
=> p(happ(happ(V3__req,happ(happ(V6__rpow,V8__r),happ(V5__Cp__phi,V9__n))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V8__r,V9__n))) ) ) ) ) ) ) ) ) ) ) ).
fof('ExtLib.Core.Type.Build_typeOk',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__tT] :
( cExtLib_2eCore_2eType_2etype___24t(V0__T,V1__tT)
=> ( ! [V2__x] :
( t(V2__x,V0__T)
=> ! [V3__y] :
( t(V3__y,V0__T)
=> ( cExtLib_2eCore_2eType_2eequal___24a4(V0__T,V1__tT,V2__x,V3__y)
=> ( cExtLib_2eCore_2eType_2eproper___24a3(V0__T,V1__tT,V2__x)
& cExtLib_2eCore_2eType_2eproper___24a3(V0__T,V1__tT,V3__y) ) ) ) )
=> ( cExtLib_2eStructures_2eProper_2ePReflexive___24a3(V0__T,cExtLib_2eCore_2eType_2eproper___24a2(V0__T,V1__tT),cExtLib_2eCore_2eType_2eequal___24a2(V0__T,V1__tT))
=> ( cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__T,cExtLib_2eCore_2eType_2eequal___24a2(V0__T,V1__tT))
=> ( cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__T,cExtLib_2eCore_2eType_2eequal___24a2(V0__T,V1__tT))
=> cExtLib_2eCore_2eType_2etypeOk___24a2(V0__T,V1__tT) ) ) ) ) ) ) ).
fof('ExtLib.Core.Type.equiv_prefl',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__tT] :
( cExtLib_2eCore_2eType_2etype___24t(V0__T,V1__tT)
=> ( cExtLib_2eCore_2eType_2etypeOk___24a2(V0__T,V1__tT)
=> cExtLib_2eStructures_2eProper_2ePReflexive___24a3(V0__T,cExtLib_2eCore_2eType_2eproper___24a2(V0__T,V1__tT),cExtLib_2eCore_2eType_2eequal___24a2(V0__T,V1__tT)) ) ) ) ).
fof('ExtLib.Core.Type.equiv_sym',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__tT] :
( cExtLib_2eCore_2eType_2etype___24t(V0__T,V1__tT)
=> ( cExtLib_2eCore_2eType_2etypeOk___24a2(V0__T,V1__tT)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__T,cExtLib_2eCore_2eType_2eequal___24a2(V0__T,V1__tT)) ) ) ) ).
fof('ExtLib.Core.Type.equiv_trans',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__tT] :
( cExtLib_2eCore_2eType_2etype___24t(V0__T,V1__tT)
=> ( cExtLib_2eCore_2eType_2etypeOk___24a2(V0__T,V1__tT)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__T,cExtLib_2eCore_2eType_2eequal___24a2(V0__T,V1__tT)) ) ) ) ).
fof('ExtLib.Core.Type.only_proper',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__tT] :
( cExtLib_2eCore_2eType_2etype___24t(V0__T,V1__tT)
=> ( cExtLib_2eCore_2eType_2etypeOk___24a2(V0__T,V1__tT)
=> ! [V3__x] :
( t(V3__x,V0__T)
=> ! [V4__y] :
( t(V4__y,V0__T)
=> ( cExtLib_2eCore_2eType_2eequal___24a4(V0__T,V1__tT,V3__x,V4__y)
=> ( cExtLib_2eCore_2eType_2eproper___24a3(V0__T,V1__tT,V3__x)
& cExtLib_2eCore_2eType_2eproper___24a3(V0__T,V1__tT,V4__y) ) ) ) ) ) ) ) ).
fof('ExtLib.Core.Type.proper_left',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__tT] :
( cExtLib_2eCore_2eType_2etype___24t(V0__T,V1__tT)
=> ( cExtLib_2eCore_2eType_2etypeOk___24a2(V0__T,V1__tT)
=> ! [V3__x] :
( t(V3__x,V0__T)
=> ! [V4__y] :
( t(V4__y,V0__T)
=> ( cExtLib_2eCore_2eType_2eequal___24a4(V0__T,V1__tT,V3__x,V4__y)
=> cExtLib_2eCore_2eType_2eproper___24a3(V0__T,V1__tT,V3__x) ) ) ) ) ) ) ).
fof('ExtLib.Core.Type.proper_right',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__tT] :
( cExtLib_2eCore_2eType_2etype___24t(V0__T,V1__tT)
=> ( cExtLib_2eCore_2eType_2etypeOk___24a2(V0__T,V1__tT)
=> ! [V3__x] :
( t(V3__x,V0__T)
=> ! [V4__y] :
( t(V4__y,V0__T)
=> ( cExtLib_2eCore_2eType_2eequal___24a4(V0__T,V1__tT,V3__x,V4__y)
=> cExtLib_2eCore_2eType_2eproper___24a3(V0__T,V1__tT,V4__y) ) ) ) ) ) ) ).
fof('N.typeOk_N',axiom,
cExtLib_2eCore_2eType_2etypeOk___24a2(cCoq_2eNumbers_2eBinNums_2eN,cN_2etype__N) ).
fof('$adef_Coq.NArith.BinNatDef.N.land_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eland,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.SqrtSpec_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eSqrtSpec,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2eSqrtSpec___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNat.N.lt_alt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt__alt,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2elt__alt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D7_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).
fof('$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.setoid_ring.Field_theory.NtoZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eNtoZ,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eNtoZ___24a1(V_24X1) ).
fof('$adef_Coq.NArith.Ndigits.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eNdigits_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eNdigits_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_$_lam_20450_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__20450,V_24X1),V_24X2),V_24X3) = c_24__lam__20450___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_28670_$a1',axiom,
! [V_24X1] : happ(c_24__lam__28670,V_24X1) = c_24__lam__28670___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Strings.Ascii.ascii_of_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2eascii__of__N,V_24X1) = cCoq_2eStrings_2eAscii_2eascii__of__N___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.INZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eINZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eINZ___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V_24X1) ).
fof('$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.PArith.BinPosDef.Pos.size_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.CompLtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompLtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEequiv_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.mask2cmp_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPos_2ePos_2emask2cmp,V_24X1) = cCoq_2ePArith_2eBinPos_2ePos_2emask2cmp___24a1(V_24X1) ).
fof('$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.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiN1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RingMicromega.eval_op2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.NArith.BinNat.N.lnot_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elnot,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNat_2eN_2elnot___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.eval_pol_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__pol,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.get_sign_None_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.ZtoN_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eZtoN,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eZtoN___24a1(V_24X1) ).
fof('$adef_$_lam_35035_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__35035,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__35035___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_$_fix_28566_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__28566__1__add__carry,V_24X1),V_24X2) = c_24__fix__28566__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$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.NArith.BinNatDef.N.succ_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V_24X1) ).
fof('$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.NArith.BinNat.N.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2egt,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_21941_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__21941,V_24X1),V_24X2) = c_24__lam__21941___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.NArith.BinNatDef.N.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.square_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esquare,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esquare___24a1(V_24X1) ).
fof('$adef_$_lam_29388_$a1',axiom,
! [V_24X1] : happ(c_24__lam__29388,V_24X1) = c_24__lam__29388___24a1(V_24X1) ).
fof('$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.setoid_ring.BinList.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_21925_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__21925,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__21925___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.NArith.BinNat.N.max_case_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2emax__case,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eNArith_2eBinNat_2eN_2emax__case___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_20458_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__20458,V_24X1),V_24X2),V_24X3) = c_24__lam__20458___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_$_lam_28142_$a1',axiom,
! [V_24X1] : happ(c_24__lam__28142,V_24X1) = c_24__lam__28142___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.lor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.N_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eNumbers_2eBinNums_2eN__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eNumbers_2eBinNums_2eN__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.shiftl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl___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('$adef_Coq.Init.Nat.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$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('$adef_Coq.PArith.BinPosDef.Pos.square_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esquare,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esquare___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D6_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_lam_35035_$a1',axiom,
! [V_24X1] : happ(c_24__lam__35035,V_24X1) = c_24__lam__35035___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_20450_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__20450,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__20450___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esqrt,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2egcd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eNArith_2eBinNat_2eN_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.NArith.BinNat.N.peano_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rec,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rec___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNat.N.peano_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1) = cCoq_2eVectors_2eVectorDef_2et___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Env.nth_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnv_2enth,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnv_2enth___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.eval_sexpr_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__sexpr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = cCoq_2emicromega_2eRingMicromega_2eeval__sexpr___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D4_$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_45270_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__45270,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__45270___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_11684_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__11684,V_24X1),V_24X2) = c_24__prop__11684___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.StrictOrder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eStrictOrder,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_45284_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__45284,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__45284___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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.NArith.BinNat.N.log2_up_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2elog2__up,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2elog2__up___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNat.N.sqrt_up_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2esqrt__up,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2esqrt__up___24a1(V_24X1) ).
fof('$adef_$_prop_45121_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__45121,V_24X1),V_24X2) = c_24__prop__45121___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.eval_pexpr_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__pexpr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = cCoq_2emicromega_2eRingMicromega_2eeval__pexpr___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$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('$adef_Coq.NArith.Ndigits.Nless_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eNdigits_2eNless,V_24X1),V_24X2) = cCoq_2eNArith_2eNdigits_2eNless___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epow,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_35782_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__35782,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__35782___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_Coq.NArith.BinNatDef.N.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eleb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.hd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2ehd,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2ehd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat___24a1(V_24X1) ).
fof('$adef_Coq.NArith.Ndigits.Neven_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eNArith_2eNdigits_2eNeven,V_24X1))
<=> cCoq_2eNArith_2eNdigits_2eNeven___24a1(V_24X1) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.lor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2esub,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.LT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.NArith.BinNat.N.min_case_strong_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2emin__case__strong,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eNArith_2eBinNat_2eN_2emin__case__strong___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.NArith.Ndigits.Nless_aux_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eNArith_2eNdigits_2eNless__aux,V_24X1),V_24X2),V_24X3) = cCoq_2eNArith_2eNdigits_2eNless__aux___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNat.N.max_case_strong_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2emax__case__strong,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eNArith_2eBinNat_2eN_2emax__case__strong___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.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.micromega.RingMicromega.cneqb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecneqb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.Ascii.ascii_of_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2eascii__of__pos,V_24X1) = cCoq_2eStrings_2eAscii_2eascii__of__pos___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.NArith.BinNat.N.Private_OrderTac.Tac.interp_ord_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2ePrivate__OrderTac_2eTac_2einterp__ord,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2ePrivate__OrderTac_2eTac_2einterp__ord___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$27866_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2427866,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2427866___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_28138_$a1',axiom,
! [V_24X1] : happ(c_24__lam__28138,V_24X1) = c_24__lam__28138___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.P1_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2eP1,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2eP1___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PEeval_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = cCoq_2emicromega_2eEnvRing_2ePEeval___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.micromega.RingMicromega.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.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_$_let_var_6_p_26880_26883_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__26880__26883,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__26880__26883___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2eb2n,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.N_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eN__rec,V_24X1) = cCoq_2eNumbers_2eBinNums_2eN__rec___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eodd,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eleb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_20474_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__20474,V_24X1),V_24X2),V_24X3) = c_24__lam__20474___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.size_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esize,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esize___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.NArith.BinNat.N.min_case_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2emin__case,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eNArith_2eBinNat_2eN_2emin__case___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.ones_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2eones,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2eones___24a1(V_24X1) ).
fof('$adef_$_lam_20474_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__20474,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__20474___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_prop_28352_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__28352,V_24X1),V_24X2) = c_24__prop__28352___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_28666_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__28666,V_24X1),V_24X2) = c_24__lam__28666___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_21933_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__21933,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__21933___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_20458_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__20458,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__20458___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_ExtLib.Core.Type.equal_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cExtLib_2eCore_2eType_2eequal,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cExtLib_2eCore_2eType_2eequal___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_20466_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__20466,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__20466___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.BinList.jump_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2ejump,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.Neg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eNeg,V_24X1) = cCoq_2eInit_2eDecimal_2eNeg___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2edivide,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNat.N.Even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eNArith_2eBinNat_2eN_2eEven,V_24X1))
<=> cCoq_2eNArith_2eBinNat_2eN_2eEven___24a1(V_24X1) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V_24X1) ).
fof('$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.micromega.RingMicromega.eval_op1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Decimal.D9_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).
fof('$adef_$_lam_35284_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__35284,V_24X1))
<=> c_24__lam__35284___24a1(V_24X1) ) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiNword_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.setoid_ring.Ring.bool_eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing_2ebool__eq,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.ldiff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eldiff,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eldiff___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('$adef_$_let_var_6_p_26882_26884_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__26882__26884,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__26882__26884___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_29388_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__29388,V_24X1),V_24X2) = c_24__lam__29388___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.Odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eNArith_2eBinNat_2eN_2eOdd,V_24X1))
<=> cCoq_2eNArith_2eBinNat_2eN_2eOdd___24a1(V_24X1) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.shiftr_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftr__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eshiftr__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emax,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.rem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2erem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_ExtLib.Core.Type.type_$a1',axiom,
! [V_24X1] : happ(cExtLib_2eCore_2eType_2etype,V_24X1) = cExtLib_2eCore_2eType_2etype___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_21941_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__21941,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__21941___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.P0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eP0,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_Coq.setoid_ring.Ring_theory.SRsub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.ldiff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eldiff,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V_24X1,V_24X2) ).
fof('$adef_ExtLib.Core.Type.proper_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cExtLib_2eCore_2eType_2eproper,V_24X1),V_24X2),V_24X3))
<=> cExtLib_2eCore_2eType_2eproper___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_21925_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__21925,V_24X1),V_24X2) = c_24__lam__21925___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quot_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equot,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2elog2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
<=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V_24X1) ).
fof('$adef_$_lam_28137_$a1',axiom,
! [V_24X1] : happ(c_24__lam__28137,V_24X1) = c_24__lam__28137___24a1(V_24X1) ).
fof('$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.NArith.Ndigits.Nodd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eNArith_2eNdigits_2eNodd,V_24X1))
<=> cCoq_2eNArith_2eNdigits_2eNodd___24a1(V_24X1) ) ).
fof('$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.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.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).
fof('$adef_$_lam_45270_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__45270,V_24X1),V_24X2),V_24X3) = c_24__lam__45270___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.Ndec.Nleb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eNdec_2eNleb,V_24X1),V_24X2) = cCoq_2eNArith_2eNdec_2eNleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V_24X1) ).
fof('$adef_ExtLib.Core.Type.typeOk_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cExtLib_2eCore_2eType_2etypeOk,V_24X1),V_24X2))
<=> cExtLib_2eCore_2eType_2etypeOk___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.P1_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eP1,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2eP1___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_$_lam_35775_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__35775,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__35775___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ege,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.shiftr_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftr,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eshiftr___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).
fof('$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_ExtLib.Structures.Proper.PReflexive_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cExtLib_2eStructures_2eProper_2ePReflexive,V_24X1),V_24X2),V_24X3))
<=> cExtLib_2eStructures_2eProper_2ePReflexive___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.Tauto.clause_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2eclause,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_20466_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__20466,V_24X1),V_24X2),V_24X3) = c_24__lam__20466___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___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('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$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('$adef_ExtLib.Core.Type.equal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cExtLib_2eCore_2eType_2eequal,V_24X1),V_24X2) = cExtLib_2eCore_2eType_2eequal___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('$adef_Coq.NArith.BinNatDef.N.size_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esize__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esize__nat___24a1(V_24X1) ).
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('$adef_Coq.Numbers.BinNums.N_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eN__rect,V_24X1) = cCoq_2eNumbers_2eBinNums_2eN__rect___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elxor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_28659_$a1',axiom,
! [V_24X1] : happ(c_24__lam__28659,V_24X1) = c_24__lam__28659___24a1(V_24X1) ).
fof('$adef_$_lam_321_$a1',axiom,
! [V_24X1] : happ(c_24__lam__321,V_24X1) = c_24__lam__321___24a1(V_24X1) ).
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('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$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('$adef_Coq.PArith.BinPosDef.Pos.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$a13',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.add_$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('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.Private_Tac.interp_ord_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2ePrivate__Tac_2einterp__ord,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2ePrivate__Tac_2einterp__ord___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$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('$adef_Coq.setoid_ring.InitialRing.gen_phiN_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$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('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_45122_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__45122,V_24X1),V_24X2) = c_24__prop__45122___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_35768_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__35768,V_24X1),V_24X2),V_24X3) = c_24__lam__35768___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.lcm_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elcm,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNat_2eN_2elcm___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_21949_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__21949,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__21949___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eNArith_2eBinNatDef_2eN_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.PArith.BinPosDef.Pos.Nsucc_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eNsucc__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eNsucc__double___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epow,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_28666_$a1',axiom,
! [V_24X1] : happ(c_24__lam__28666,V_24X1) = c_24__lam__28666___24a1(V_24X1) ).
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('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.switch_Eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.tl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2etl,V_24X1),V_24X2) = cCoq_2eLists_2eList_2etl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.Symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eSymmetric,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_35031_$a1',axiom,
! [V_24X1] : happ(c_24__lam__35031,V_24X1) = c_24__lam__35031___24a1(V_24X1) ).
fof('$adef_$_lam_35768_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__35768,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__35768___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_21933_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__21933,V_24X1),V_24X2) = c_24__lam__21933___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.land_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eland,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(V_24X1,V_24X2) ).
fof('$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_Coq.NArith.BinNatDef.N.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).
fof('$adef_$_lam_28659_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__28659,V_24X1),V_24X2) = c_24__lam__28659___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.Pphi_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eEnvRing_2ePphi___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_35031_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__35031,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__35031___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.NArith.BinNat.N.le_alt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele__alt,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele__alt___24a2(V_24X1,V_24X2) ) ).
fof('$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.PArith.BinPosDef.Pos.Ndouble_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eNdouble,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eNdouble___24a1(V_24X1) ).
fof('$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.NArith.BinNatDef.N.ltb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eltb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eltb___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_21949_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__21949,V_24X1),V_24X2) = c_24__lam__21949___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D3_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D8_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.NFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eNFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$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('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEeval_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.shiftl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eshiftl,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eshiftl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$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('$adef_Coq.PArith.BinPosDef.Pos.size_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V_24X1) ).
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('$adef_Coq.Init.Datatypes.CompSpecT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompSpecT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2eCompSpecT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.InitialRing.triv_div_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2etriv__div,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Vectors.Fin.t_$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] : happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.PreOrder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2ePreOrder,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2ePreOrder___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('$adef_ExtLib.Core.Type.proper_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cExtLib_2eCore_2eType_2eproper,V_24X1),V_24X2) = cExtLib_2eCore_2eType_2eproper___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.shiftl_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl__nat___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$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('$adef_$_lam_45277_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__45277,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__45277___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_ExtLib.Core.Type.Build_type_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cExtLib_2eCore_2eType_2eBuild__type,V_24X1),V_24X2),V_24X3) = cExtLib_2eCore_2eType_2eBuild__type___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$tdef_$_type_27428',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__27428___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__27428___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_2254',axiom,
! [V_24Y] :
( c_24__type__2254___24t(V_24Y)
<=> t(V_24Y,c_24__type__2254) ) ).
fof('$tdef_$_type_12440',axiom,
! [V_24Y] :
( c_24__type__12440___24t(V_24Y)
<=> t(V_24Y,c_24__type__12440) ) ).
fof('$tdef_$_type_29370',axiom,
! [V_24Y] :
( c_24__type__29370___24t(V_24Y)
<=> t(V_24Y,c_24__type__29370) ) ).
fof('$tdef_$_type_1370',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1370___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1370___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.micromega.Env.Env',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6077',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__6077___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__6077___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32682',axiom,
! [V_24Y] :
( c_24__type__32682___24t(V_24Y)
<=> t(V_24Y,c_24__type__32682) ) ).
fof('$tdef_$_type_3770',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__3770___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__3770___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_35201',axiom,
! [V_24Y] :
( c_24__type__35201___24t(V_24Y)
<=> t(V_24Y,c_24__type__35201) ) ).
fof('$tdef_$_type_32833',axiom,
! [V_24Y] :
( c_24__type__32833___24t(V_24Y)
<=> t(V_24Y,c_24__type__32833) ) ).
fof('$tdef_$_type_12080',axiom,
! [V_24Y] :
( c_24__type__12080___24t(V_24Y)
<=> t(V_24Y,c_24__type__12080) ) ).
fof('$tdef_$_type_3344',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3344___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3344___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_317',axiom,
! [V_24Y] :
( c_24__type__317___24t(V_24Y)
<=> t(V_24Y,c_24__type__317) ) ).
fof('$tdef_$_type_27611',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27611___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27611___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_18992',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__18992___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__18992___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_11631',axiom,
! [V_24Y] :
( c_24__type__11631___24t(V_24Y)
<=> t(V_24Y,c_24__type__11631) ) ).
fof('$tdef_$_type_30811',axiom,
! [V_24Y] :
( c_24__type__30811___24t(V_24Y)
<=> t(V_24Y,c_24__type__30811) ) ).
fof('$tdef_$_type_81',axiom,
! [V_24Y] :
( c_24__type__81___24t(V_24Y)
<=> t(V_24Y,c_24__type__81) ) ).
fof('$tdef_$_type_30799',axiom,
! [V_24Y] :
( c_24__type__30799___24t(V_24Y)
<=> t(V_24Y,c_24__type__30799) ) ).
fof('$tdef_$_type_12099',axiom,
! [V_24Y] :
( c_24__type__12099___24t(V_24Y)
<=> t(V_24Y,c_24__type__12099) ) ).
fof('$tdef_$_type_34067',axiom,
! [V_24Y] :
( c_24__type__34067___24t(V_24Y)
<=> t(V_24Y,c_24__type__34067) ) ).
fof('$tdef_$_type_6176',axiom,
! [V_24Y] :
( c_24__type__6176___24t(V_24Y)
<=> t(V_24Y,c_24__type__6176) ) ).
fof('$tdef_$_type_29049',axiom,
! [V_24Y] :
( c_24__type__29049___24t(V_24Y)
<=> t(V_24Y,c_24__type__29049) ) ).
fof('$tdef_$_type_15572',axiom,
! [V_24Y] :
( c_24__type__15572___24t(V_24Y)
<=> t(V_24Y,c_24__type__15572) ) ).
fof('$tdef_$_type_28544',axiom,
! [V_24Y] :
( c_24__type__28544___24t(V_24Y)
<=> t(V_24Y,c_24__type__28544) ) ).
fof('$tdef_$_type_29040',axiom,
! [V_24Y] :
( c_24__type__29040___24t(V_24Y)
<=> t(V_24Y,c_24__type__29040) ) ).
fof('$tdef_$_type_11993',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11993___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11993___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15563',axiom,
! [V_24Y] :
( c_24__type__15563___24t(V_24Y)
<=> t(V_24Y,c_24__type__15563) ) ).
fof('$tdef_$_type_35102',axiom,
! [V_24Y] :
( c_24__type__35102___24t(V_24Y)
<=> t(V_24Y,c_24__type__35102) ) ).
fof('$tdef_$_type_30802',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30802___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30802___24a1(V_24X1)) ) ).
fof('$tdef_$_type_11603',axiom,
! [V_24Y] :
( c_24__type__11603___24t(V_24Y)
<=> t(V_24Y,c_24__type__11603) ) ).
fof('$tdef_$_type_11626',axiom,
! [V_24Y] :
( c_24__type__11626___24t(V_24Y)
<=> t(V_24Y,c_24__type__11626) ) ).
fof('$tdef_$_type_2840',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__2840___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__2840___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_8792',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__8792___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__8792___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_32685',axiom,
! [V_24Y] :
( c_24__type__32685___24t(V_24Y)
<=> t(V_24Y,c_24__type__32685) ) ).
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_$_type_11710',axiom,
! [V_24Y] :
( c_24__type__11710___24t(V_24Y)
<=> t(V_24Y,c_24__type__11710) ) ).
fof('$tdef_ExtLib.Core.Type.type',axiom,
! [V_24X1,V_24Y] :
( cExtLib_2eCore_2eType_2etype___24t(V_24X1,V_24Y)
<=> t(V_24Y,cExtLib_2eCore_2eType_2etype___24a1(V_24X1)) ) ).
fof('$tdef_$_type_29045',axiom,
! [V_24Y] :
( c_24__type__29045___24t(V_24Y)
<=> t(V_24Y,c_24__type__29045) ) ).
fof('$tdef_$_type_2000',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2000___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2000___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5846',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__5846___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__5846___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_28341',axiom,
! [V_24X1,V_24Y] :
( c_24__type__28341___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__28341___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12500',axiom,
! [V_24Y] :
( c_24__type__12500___24t(V_24Y)
<=> t(V_24Y,c_24__type__12500) ) ).
fof('$tdef_$_type_30960',axiom,
! [V_24Y] :
( c_24__type__30960___24t(V_24Y)
<=> t(V_24Y,c_24__type__30960) ) ).
fof('$tdef_$_type_28675',axiom,
! [V_24Y] :
( c_24__type__28675___24t(V_24Y)
<=> t(V_24Y,c_24__type__28675) ) ).
fof('$tdef_$_type_28075',axiom,
! [V_24Y] :
( c_24__type__28075___24t(V_24Y)
<=> t(V_24Y,c_24__type__28075) ) ).
fof('$tdef_$_type_6140',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__6140___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__6140___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15546',axiom,
! [V_24Y] :
( c_24__type__15546___24t(V_24Y)
<=> t(V_24Y,c_24__type__15546) ) ).
fof('$tdef_$_type_3020',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__3020___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__3020___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_12235',axiom,
! [V_24X1,V_24Y] :
( c_24__type__12235___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__12235___24a1(V_24X1)) ) ).
fof('$tdef_$_type_29885',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__29885___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__29885___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_18021',axiom,
! [V_24Y] :
( c_24__type__18021___24t(V_24Y)
<=> t(V_24Y,c_24__type__18021) ) ).
fof('$tdef_$_type_1132',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1132___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1132___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12087',axiom,
! [V_24Y] :
( c_24__type__12087___24t(V_24Y)
<=> t(V_24Y,c_24__type__12087) ) ).
fof('$tdef_$_type_11817',axiom,
! [V_24Y] :
( c_24__type__11817___24t(V_24Y)
<=> t(V_24Y,c_24__type__11817) ) ).
fof('$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_1938',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1938___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1938___24a1(V_24X1)) ) ).
fof('$tdef_$_type_27461',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__27461___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__27461___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_20200',axiom,
! [V_24Y] :
( c_24__type__20200___24t(V_24Y)
<=> t(V_24Y,c_24__type__20200) ) ).
fof('$tdef_$_type_6041',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__6041___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__6041___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_2903',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__2903___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__2903___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_349',axiom,
! [V_24Y] :
( c_24__type__349___24t(V_24Y)
<=> t(V_24Y,c_24__type__349) ) ).
fof('$tdef_$_type_18062',axiom,
! [V_24Y] :
( c_24__type__18062___24t(V_24Y)
<=> t(V_24Y,c_24__type__18062) ) ).
fof('$tdef_$_type_5243',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__5243___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__5243___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_4604',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__4604___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__4604___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_19788',axiom,
! [V_24Y] :
( c_24__type__19788___24t(V_24Y)
<=> t(V_24Y,c_24__type__19788) ) ).
fof('$tdef_$_type_12445',axiom,
! [V_24Y] :
( c_24__type__12445___24t(V_24Y)
<=> t(V_24Y,c_24__type__12445) ) ).
fof('$tdef_$_type_12030',axiom,
! [V_24Y] :
( c_24__type__12030___24t(V_24Y)
<=> t(V_24Y,c_24__type__12030) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_$_type_8446',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__8446___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__8446___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_$_type_5997',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__5997___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__5997___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_19726',axiom,
! [V_24Y] :
( c_24__type__19726___24t(V_24Y)
<=> t(V_24Y,c_24__type__19726) ) ).
fof('$tdef_$_type_9807',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__9807___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__9807___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_20830',axiom,
! [V_24Y] :
( c_24__type__20830___24t(V_24Y)
<=> t(V_24Y,c_24__type__20830) ) ).
fof('$tdef_$_type_29248',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29248___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29248___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_28673',axiom,
! [V_24Y] :
( c_24__type__28673___24t(V_24Y)
<=> t(V_24Y,c_24__type__28673) ) ).
fof('$tdef_Coq.Numbers.BinNums.N',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).
fof('$tdef_$_type_23625',axiom,
! [V_24Y] :
( c_24__type__23625___24t(V_24Y)
<=> t(V_24Y,c_24__type__23625) ) ).
fof('$tdef_$_type_28147',axiom,
! [V_24Y] :
( c_24__type__28147___24t(V_24Y)
<=> t(V_24Y,c_24__type__28147) ) ).
fof('$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_11988',axiom,
! [V_24Y] :
( c_24__type__11988___24t(V_24Y)
<=> t(V_24Y,c_24__type__11988) ) ).
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_$_type_29312',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29312___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29312___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_30688',axiom,
! [V_24Y] :
( c_24__type__30688___24t(V_24Y)
<=> t(V_24Y,c_24__type__30688) ) ).
fof('$tdef_$_type_20517',axiom,
! [V_24Y] :
( c_24__type__20517___24t(V_24Y)
<=> t(V_24Y,c_24__type__20517) ) ).
fof('$tdef_$_type_27151',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__27151___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__27151___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_12248',axiom,
! [V_24Y] :
( c_24__type__12248___24t(V_24Y)
<=> t(V_24Y,c_24__type__12248) ) ).
fof('$tdef_$_type_14',axiom,
! [V_24X1,V_24Y] :
( c_24__type__14___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__14___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32446',axiom,
! [V_24Y] :
( c_24__type__32446___24t(V_24Y)
<=> t(V_24Y,c_24__type__32446) ) ).
fof('$tdef_$_type_15543',axiom,
! [V_24Y] :
( c_24__type__15543___24t(V_24Y)
<=> t(V_24Y,c_24__type__15543) ) ).
fof('$tdef_$_type_26894',axiom,
! [V_24Y] :
( c_24__type__26894___24t(V_24Y)
<=> t(V_24Y,c_24__type__26894) ) ).
fof('$tdef_$_type_12426',axiom,
! [V_24Y] :
( c_24__type__12426___24t(V_24Y)
<=> t(V_24Y,c_24__type__12426) ) ).
fof('$tdef_$_type_7085',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__7085___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__7085___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_12032',axiom,
! [V_24Y] :
( c_24__type__12032___24t(V_24Y)
<=> t(V_24Y,c_24__type__12032) ) ).
fof('$tdef_$_type_11800',axiom,
! [V_24Y] :
( c_24__type__11800___24t(V_24Y)
<=> t(V_24Y,c_24__type__11800) ) ).
fof('$tdef_$_type_29225',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29225___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29225___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_20432',axiom,
! [V_24Y] :
( c_24__type__20432___24t(V_24Y)
<=> t(V_24Y,c_24__type__20432) ) ).
fof('$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('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_$_type_34599',axiom,
! [V_24Y] :
( c_24__type__34599___24t(V_24Y)
<=> t(V_24Y,c_24__type__34599) ) ).
fof('$tdef_$_type_30826',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30826___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30826___24a1(V_24X1)) ) ).
fof('$tdef_$_type_30665',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30665___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30665___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_175',axiom,
! [V_24Y] :
( c_24__type__175___24t(V_24Y)
<=> t(V_24Y,c_24__type__175) ) ).
fof('$tdef_$_type_11491',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__11491___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__11491___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_22115',axiom,
! [V_24Y] :
( c_24__type__22115___24t(V_24Y)
<=> t(V_24Y,c_24__type__22115) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1)) ) ).
fof('$tdef_$_type_11750',axiom,
! [V_24Y] :
( c_24__type__11750___24t(V_24Y)
<=> t(V_24Y,c_24__type__11750) ) ).
fof('$tdef_$_type_3149',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3149___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3149___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_$_type_11664',axiom,
! [V_24Y] :
( c_24__type__11664___24t(V_24Y)
<=> t(V_24Y,c_24__type__11664) ) ).
fof('$tdef_$_type_30385',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__30385___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__30385___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_35192',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35192___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35192___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12495',axiom,
! [V_24Y] :
( c_24__type__12495___24t(V_24Y)
<=> t(V_24Y,c_24__type__12495) ) ).
fof('$tdef_Coq.Strings.Ascii.ascii',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).
fof('$tdef_$_type_5',axiom,
! [V_24Y] :
( c_24__type__5___24t(V_24Y)
<=> t(V_24Y,c_24__type__5) ) ).
fof('$tdef_$_type_282',axiom,
! [V_24Y] :
( c_24__type__282___24t(V_24Y)
<=> t(V_24Y,c_24__type__282) ) ).
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_$_type_32416',axiom,
! [V_24Y] :
( c_24__type__32416___24t(V_24Y)
<=> t(V_24Y,c_24__type__32416) ) ).
fof('$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_17597',axiom,
! [V_24Y] :
( c_24__type__17597___24t(V_24Y)
<=> t(V_24Y,c_24__type__17597) ) ).
fof('$tdef_$_type_28124',axiom,
! [V_24Y] :
( c_24__type__28124___24t(V_24Y)
<=> t(V_24Y,c_24__type__28124) ) ).
fof('$tdef_$_type_105',axiom,
! [V_24Y] :
( c_24__type__105___24t(V_24Y)
<=> t(V_24Y,c_24__type__105) ) ).
fof('$tdef_$_type_30785',axiom,
! [V_24Y] :
( c_24__type__30785___24t(V_24Y)
<=> t(V_24Y,c_24__type__30785) ) ).
fof('$tdef_$_type_27803',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27803___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27803___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_10153',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__10153___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__10153___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_1365',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1365___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1365___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3983',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__3983___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__3983___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_35198',axiom,
! [V_24Y] :
( c_24__type__35198___24t(V_24Y)
<=> t(V_24Y,c_24__type__35198) ) ).
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_$_type_4817',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__4817___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__4817___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Init.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_$_type_18138',axiom,
! [V_24Y] :
( c_24__type__18138___24t(V_24Y)
<=> t(V_24Y,c_24__type__18138) ) ).
fof('$tdef_$_type_7431',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__7431___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__7431___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_32467',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32467___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32467___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1379',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1379___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1379___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1348',axiom,
! [V_24Y] :
( c_24__type__1348___24t(V_24Y)
<=> t(V_24Y,c_24__type__1348) ) ).
fof('$tdef_$_type_9484',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__9484___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__9484___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op2',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp2) ) ).
fof('$tdef_$_type_27879',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__27879___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__27879___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32692',axiom,
! [V_24Y] :
( c_24__type__32692___24t(V_24Y)
<=> t(V_24Y,c_24__type__32692) ) ).
fof('$tdef_$_type_2777',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__2777___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__2777___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_29132',axiom,
! [V_24Y] :
( c_24__type__29132___24t(V_24Y)
<=> t(V_24Y,c_24__type__29132) ) ).
fof('$tdef_$_type_12068',axiom,
! [V_24Y] :
( c_24__type__12068___24t(V_24Y)
<=> t(V_24Y,c_24__type__12068) ) ).
fof('$tdef_$_type_1030',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__1030___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__1030___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_7754',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__7754___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__7754___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Byte.byte',axiom,
! [V_24Y] :
( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).
fof('$tdef_$_type_29294',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29294___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29294___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_15859',axiom,
! [V_24Y] :
( c_24__type__15859___24t(V_24Y)
<=> t(V_24Y,c_24__type__15859) ) ).
fof('$tdef_$_type_12101',axiom,
! [V_24Y] :
( c_24__type__12101___24t(V_24Y)
<=> t(V_24Y,c_24__type__12101) ) ).
fof('$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_342',axiom,
! [V_24Y] :
( c_24__type__342___24t(V_24Y)
<=> t(V_24Y,c_24__type__342) ) ).
fof('$tdef_$_type_18113',axiom,
! [V_24Y] :
( c_24__type__18113___24t(V_24Y)
<=> t(V_24Y,c_24__type__18113) ) ).
fof('$tdef_$_type_19194',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__19194___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__19194___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_307',axiom,
! [V_24Y] :
( c_24__type__307___24t(V_24Y)
<=> t(V_24Y,c_24__type__307) ) ).
fof('$tdef_$_type_948',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__948___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__948___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_773',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__773___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__773___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_32437',axiom,
! [V_24Y] :
( c_24__type__32437___24t(V_24Y)
<=> t(V_24Y,c_24__type__32437) ) ).
fof('$tdef_$_type_337',axiom,
! [V_24Y] :
( c_24__type__337___24t(V_24Y)
<=> t(V_24Y,c_24__type__337) ) ).
fof('$tdef_$_type_4391',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__4391___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__4391___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_19623',axiom,
! [V_24Y] :
( c_24__type__19623___24t(V_24Y)
<=> t(V_24Y,c_24__type__19623) ) ).
fof('$tdef_$_type_12423',axiom,
! [V_24Y] :
( c_24__type__12423___24t(V_24Y)
<=> t(V_24Y,c_24__type__12423) ) ).
fof('$tdef_$_type_6203',axiom,
! [V_24Y] :
( c_24__type__6203___24t(V_24Y)
<=> t(V_24Y,c_24__type__6203) ) ).
fof('$tdef_$_type_35795',axiom,
! [V_24Y] :
( c_24__type__35795___24t(V_24Y)
<=> t(V_24Y,c_24__type__35795) ) ).
fof('$tdef_Coq.Init.Datatypes.CompareSpecT',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_$_type_5651',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__5651___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__5651___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_30010',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__30010___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__30010___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_28336',axiom,
! [V_24Y] :
( c_24__type__28336___24t(V_24Y)
<=> t(V_24Y,c_24__type__28336) ) ).
fof('$tdef_$_type_1123',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__1123___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__1123___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3263',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3263___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3263___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_19584',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__19584___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__19584___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_29630',axiom,
! [V_24Y] :
( c_24__type__29630___24t(V_24Y)
<=> t(V_24Y,c_24__type__29630) ) ).
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_$_type_12082',axiom,
! [V_24Y] :
( c_24__type__12082___24t(V_24Y)
<=> t(V_24Y,c_24__type__12082) ) ).
fof('$tdef_$_type_11590',axiom,
! [V_24Y] :
( c_24__type__11590___24t(V_24Y)
<=> t(V_24Y,c_24__type__11590) ) ).
fof('$tdef_$_type_30869',axiom,
! [V_24Y] :
( c_24__type__30869___24t(V_24Y)
<=> t(V_24Y,c_24__type__30869) ) ).
fof('$tdef_$_type_19859',axiom,
! [V_24Y] :
( c_24__type__19859___24t(V_24Y)
<=> t(V_24Y,c_24__type__19859) ) ).
fof('$tdef_$_type_30854',axiom,
! [V_24Y] :
( c_24__type__30854___24t(V_24Y)
<=> t(V_24Y,c_24__type__30854) ) ).
fof('$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_29405',axiom,
! [V_24X1,V_24Y] :
( c_24__type__29405___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__29405___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28063',axiom,
! [V_24Y] :
( c_24__type__28063___24t(V_24Y)
<=> t(V_24Y,c_24__type__28063) ) ).
fof('$tdef_$_type_11568',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__11568___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__11568___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_16',axiom,
! [V_24Y] :
( c_24__type__16___24t(V_24Y)
<=> t(V_24Y,c_24__type__16) ) ).
fof('$tdef_$_type_3203',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3203___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3203___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_18891',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__18891___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__18891___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_30510',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__30510___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__30510___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_2007',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2007___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2007___24a2(V_24X1,V_24X2)) ) ).
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_$_type_19603',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__19603___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__19603___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_29002',axiom,
! [V_24Y] :
( c_24__type__29002___24t(V_24Y)
<=> t(V_24Y,c_24__type__29002) ) ).
fof('$tdef_$_type_2246',axiom,
! [V_24Y] :
( c_24__type__2246___24t(V_24Y)
<=> t(V_24Y,c_24__type__2246) ) ).
fof('$tdef_$_type_28096',axiom,
! [V_24Y] :
( c_24__type__28096___24t(V_24Y)
<=> t(V_24Y,c_24__type__28096) ) ).
fof('$tdef_$_type_2523',axiom,
! [V_24Y] :
( c_24__type__2523___24t(V_24Y)
<=> t(V_24Y,c_24__type__2523) ) ).
fof('$tdef_$_type_34072',axiom,
! [V_24Y] :
( c_24__type__34072___24t(V_24Y)
<=> t(V_24Y,c_24__type__34072) ) ).
fof('$tdef_$_type_27073',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__27073___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__27073___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_27945',axiom,
! [V_24Y] :
( c_24__type__27945___24t(V_24Y)
<=> t(V_24Y,c_24__type__27945) ) ).
fof('$tdef_$_type_11572',axiom,
! [V_24Y] :
( c_24__type__11572___24t(V_24Y)
<=> t(V_24Y,c_24__type__11572) ) ).
fof('$tdef_$_type_3320',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3320___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3320___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_29489',axiom,
! [V_24Y] :
( c_24__type__29489___24t(V_24Y)
<=> t(V_24Y,c_24__type__29489) ) ).
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_$_type_28101',axiom,
! [V_24Y] :
( c_24__type__28101___24t(V_24Y)
<=> t(V_24Y,c_24__type__28101) ) ).
fof('$tdef_$_type_3179',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3179___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3179___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_23180',axiom,
! [V_24Y] :
( c_24__type__23180___24t(V_24Y)
<=> t(V_24Y,c_24__type__23180) ) ).
fof('$tdef_$_type_18599',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__18599___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__18599___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$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_10822',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__10822___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__10822___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_18801',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__18801___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__18801___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_23496',axiom,
! [V_24Y] :
( c_24__type__23496___24t(V_24Y)
<=> t(V_24Y,c_24__type__23496) ) ).
fof('$tdef_$_type_32256',axiom,
! [V_24Y] :
( c_24__type__32256___24t(V_24Y)
<=> t(V_24Y,c_24__type__32256) ) ).
fof('$tdef_$_type_28608',axiom,
! [V_24Y] :
( c_24__type__28608___24t(V_24Y)
<=> t(V_24Y,c_24__type__28608) ) ).
fof('$tdef_$_type_29271',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29271___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29271___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_30260',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__30260___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__30260___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_360',axiom,
! [V_24Y] :
( c_24__type__360___24t(V_24Y)
<=> t(V_24Y,c_24__type__360) ) ).
fof('$tdef_$_type_34618',axiom,
! [V_24Y] :
( c_24__type__34618___24t(V_24Y)
<=> t(V_24Y,c_24__type__34618) ) ).
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_$_type_32463',axiom,
! [V_24Y] :
( c_24__type__32463___24t(V_24Y)
<=> t(V_24Y,c_24__type__32463) ) ).
fof('$tdef_$_type_27753',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27753___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27753___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_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_2249',axiom,
! [V_24Y] :
( c_24__type__2249___24t(V_24Y)
<=> t(V_24Y,c_24__type__2249) ) ).
fof('$tdef_$_type_11699',axiom,
! [V_24Y] :
( c_24__type__11699___24t(V_24Y)
<=> t(V_24Y,c_24__type__11699) ) ).
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_$_type_11976',axiom,
! [V_24Y] :
( c_24__type__11976___24t(V_24Y)
<=> t(V_24Y,c_24__type__11976) ) ).
fof('$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_587',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__587___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__587___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_10499',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__10499___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__10499___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_28617',axiom,
! [V_24Y] :
( c_24__type__28617___24t(V_24Y)
<=> t(V_24Y,c_24__type__28617) ) ).
fof('$tdef_$_type_35068',axiom,
! [V_24Y] :
( c_24__type__35068___24t(V_24Y)
<=> t(V_24Y,c_24__type__35068) ) ).
fof('$tdef_$_type_16149',axiom,
! [V_24Y] :
( c_24__type__16149___24t(V_24Y)
<=> t(V_24Y,c_24__type__16149) ) ).
fof('$tdef_$_type_27112',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__27112___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__27112___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_5438',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__5438___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__5438___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_30818',axiom,
! [V_24Y] :
( c_24__type__30818___24t(V_24Y)
<=> t(V_24Y,c_24__type__30818) ) ).
fof('$tdef_$_type_28532',axiom,
! [V_24Y] :
( c_24__type__28532___24t(V_24Y)
<=> t(V_24Y,c_24__type__28532) ) ).
fof('$tdef_$_type_30621',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__30621___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__30621___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_27661',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27661___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27661___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_2263',axiom,
! [V_24Y] :
( c_24__type__2263___24t(V_24Y)
<=> t(V_24Y,c_24__type__2263) ) ).
fof('$tdef_$_type_1986',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1986___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1986___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12056',axiom,
! [V_24Y] :
( c_24__type__12056___24t(V_24Y)
<=> t(V_24Y,c_24__type__12056) ) ).
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_$_type_3287',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3287___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3287___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_15554',axiom,
! [V_24Y] :
( c_24__type__15554___24t(V_24Y)
<=> t(V_24Y,c_24__type__15554) ) ).
fof('$tdef_$_type_15549',axiom,
! [V_24Y] :
( c_24__type__15549___24t(V_24Y)
<=> t(V_24Y,c_24__type__15549) ) ).
fof('$tdef_$_type_18700',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__18700___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__18700___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_30694',axiom,
! [V_24Y] :
( c_24__type__30694___24t(V_24Y)
<=> t(V_24Y,c_24__type__30694) ) ).
fof('$tdef_$_type_6133',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__6133___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__6133___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12508',axiom,
! [V_24Y] :
( c_24__type__12508___24t(V_24Y)
<=> t(V_24Y,c_24__type__12508) ) ).
fof('$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_17602',axiom,
! [V_24X1,V_24Y] :
( c_24__type__17602___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__17602___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2268',axiom,
! [V_24Y] :
( c_24__type__2268___24t(V_24Y)
<=> t(V_24Y,c_24__type__2268) ) ).
fof('$tdef_$_type_20809',axiom,
! [V_24Y] :
( c_24__type__20809___24t(V_24Y)
<=> t(V_24Y,c_24__type__20809) ) ).
fof('$tdef_$_type_18152',axiom,
! [V_24Y] :
( c_24__type__18152___24t(V_24Y)
<=> t(V_24Y,c_24__type__18152) ) ).
fof('$tdef_$_type_30135',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__30135___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__30135___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_11145',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__11145___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__11145___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_12013',axiom,
! [V_24X1,V_24Y] :
( c_24__type__12013___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__12013___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_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('$tdef_$_type_29400',axiom,
! [V_24Y] :
( c_24__type__29400___24t(V_24Y)
<=> t(V_24Y,c_24__type__29400) ) ).
fof('$tdef_$_type_6121',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__6121___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__6121___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_28641',axiom,
! [V_24Y] :
( c_24__type__28641___24t(V_24Y)
<=> t(V_24Y,c_24__type__28641) ) ).
fof('$tdef_$_type_12431',axiom,
! [V_24Y] :
( c_24__type__12431___24t(V_24Y)
<=> t(V_24Y,c_24__type__12431) ) ).
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_$_type_19757',axiom,
! [V_24Y] :
( c_24__type__19757___24t(V_24Y)
<=> t(V_24Y,c_24__type__19757) ) ).
fof('$tdef_$_type_34607',axiom,
! [V_24Y] :
( c_24__type__34607___24t(V_24Y)
<=> t(V_24Y,c_24__type__34607) ) ).
fof('$tdef_$_type_11697',axiom,
! [V_24Y] :
( c_24__type__11697___24t(V_24Y)
<=> t(V_24Y,c_24__type__11697) ) ).
fof('$tdef_$_type_29338',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29338___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29338___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_8100',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__8100___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__8100___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_2243',axiom,
! [V_24Y] :
( c_24__type__2243___24t(V_24Y)
<=> t(V_24Y,c_24__type__2243) ) ).
fof('$tdef_$_type_680',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__680___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__680___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_6739',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__6739___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__6739___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_4196',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__4196___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__4196___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Vectors.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_35122',axiom,
! [V_24Y] :
( c_24__type__35122___24t(V_24Y)
<=> t(V_24Y,c_24__type__35122) ) ).
fof('$tdef_$_type_5030',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__5030___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__5030___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_9138',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__9138___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__9138___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_45297',axiom,
! [V_24Y] :
( c_24__type__45297___24t(V_24Y)
<=> t(V_24Y,c_24__type__45297) ) ).
fof('$tdef_$_type_12006',axiom,
! [V_24Y] :
( c_24__type__12006___24t(V_24Y)
<=> t(V_24Y,c_24__type__12006) ) ).
fof('$tdef_$_type_2483',axiom,
! [V_24Y] :
( c_24__type__2483___24t(V_24Y)
<=> t(V_24Y,c_24__type__2483) ) ).
fof('$tdef_$_type_855',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__855___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__855___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_30871',axiom,
! [V_24Y] :
( c_24__type__30871___24t(V_24Y)
<=> t(V_24Y,c_24__type__30871) ) ).
fof('$tdef_$_type_2957',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__2957___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__2957___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_45119',axiom,
! [V_24Y] :
( c_24__type__45119___24t(V_24Y)
<=> t(V_24Y,c_24__type__45119) ) ).
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_21986',axiom,
! [V_24Y] :
( c_24__type__21986___24t(V_24Y)
<=> t(V_24Y,c_24__type__21986) ) ).
fof('$tdef_$_type_35262',axiom,
! [V_24Y] :
( c_24__type__35262___24t(V_24Y)
<=> t(V_24Y,c_24__type__35262) ) ).
fof('$tdef_$_type_19885',axiom,
! [V_24Y] :
( c_24__type__19885___24t(V_24Y)
<=> t(V_24Y,c_24__type__19885) ) ).
fof('$tdef_$_type_11644',axiom,
! [V_24Y] :
( c_24__type__11644___24t(V_24Y)
<=> t(V_24Y,c_24__type__11644) ) ).
fof('$tdef_$_type_3371',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3371___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3371___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_29356',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29356___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29356___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_6161',axiom,
! [V_24Y] :
( c_24__type__6161___24t(V_24Y)
<=> t(V_24Y,c_24__type__6161) ) ).
fof('$tdef_$_type_27711',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27711___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27711___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_8',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32841',axiom,
! [V_24Y] :
( c_24__type__32841___24t(V_24Y)
<=> t(V_24Y,c_24__type__32841) ) ).
fof('$tdef_$_type_27447',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__27447___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__27447___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_29054',axiom,
! [V_24Y] :
( c_24__type__29054___24t(V_24Y)
<=> t(V_24Y,c_24__type__29054) ) ).
fof('$tdef_$_type_29006',axiom,
! [V_24Y] :
( c_24__type__29006___24t(V_24Y)
<=> t(V_24Y,c_24__type__29006) ) ).
fof('$tdef_$_type_28140',axiom,
! [V_24Y] :
( c_24__type__28140___24t(V_24Y)
<=> t(V_24Y,c_24__type__28140) ) ).
fof('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$tdef_$_type_289',axiom,
! [V_24Y] :
( c_24__type__289___24t(V_24Y)
<=> t(V_24Y,c_24__type__289) ) ).
fof('$tdef_$_type_27887',axiom,
! [V_24Y] :
( c_24__type__27887___24t(V_24Y)
<=> t(V_24Y,c_24__type__27887) ) ).
fof('$tdef_$_type_3233',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3233___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3233___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_12008',axiom,
! [V_24Y] :
( c_24__type__12008___24t(V_24Y)
<=> t(V_24Y,c_24__type__12008) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.Nword',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2eNword) ) ).
fof('$tdef_$_type_30823',axiom,
! [V_24Y] :
( c_24__type__30823___24t(V_24Y)
<=> t(V_24Y,c_24__type__30823) ) ).
fof('$tdef_$_type_19093',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__19093___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__19093___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_32379',axiom,
! [V_24Y] :
( c_24__type__32379___24t(V_24Y)
<=> t(V_24Y,c_24__type__32379) ) ).
fof('$tdef_$_type_1141',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1141___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1141___24a1(V_24X1)) ) ).
fof('$tdef_$_type_334',axiom,
! [V_24Y] :
( c_24__type__334___24t(V_24Y)
<=> t(V_24Y,c_24__type__334) ) ).
fof('$tdef_$_type_319',axiom,
! [V_24Y] :
( c_24__type__319___24t(V_24Y)
<=> t(V_24Y,c_24__type__319) ) ).
fof('$tdef_$_type_6178',axiom,
! [V_24Y] :
( c_24__type__6178___24t(V_24Y)
<=> t(V_24Y,c_24__type__6178) ) ).
fof('$tdef_$_type_32479',axiom,
! [V_24Y] :
( c_24__type__32479___24t(V_24Y)
<=> t(V_24Y,c_24__type__32479) ) ).
fof('$tdef_$_type_20828',axiom,
! [V_24Y] :
( c_24__type__20828___24t(V_24Y)
<=> t(V_24Y,c_24__type__20828) ) ).
fof('$tdef_$_type_30678',axiom,
! [V_24Y] :
( c_24__type__30678___24t(V_24Y)
<=> t(V_24Y,c_24__type__30678) ) ).
fof('$tdef_$_type_30789',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30789___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30789___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28679',axiom,
! [V_24Y] :
( c_24__type__28679___24t(V_24Y)
<=> t(V_24Y,c_24__type__28679) ) ).
fof('$tdef_$_type_23202',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23202___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23202___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('_HAMMER_GOAL',conjecture,
cExtLib_2eCore_2eType_2eproper___24a3(cCoq_2eNumbers_2eBinNums_2eN,cN_2etype__N,cn) ).
%------------------------------------------------------------------------------